Utilizing ionanofluid is one of the best ways to improve the thermal performance of working fluids for storage, energy conversion, and transportation in contemporary thermal systems. It is a group of nano dispersions where ionic liquids create the continuous phase. This article's goal is to examine how various nanofluids perform when the natural convection of long single-walled carbon nanotubes (SWCNTs) nanoparticle occurring in a cavity which is made up of two connected oblique triangles. The cavity has a thin cold wall (Tc) with angular diameter √2m. Both halves of the left and bottom walls are heated and kept at constant temperature (Th). The remaining walls are insulated. The Navier-Stokes equations and energy conservation equation with appropriate boundary conditions are applied for modeling the considered physics and FEM is used to solve it. The heat-transferring mediums are assumed as the ionanofluid of SWCNT and 1-butyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}imide ([C4mim][NTf2]) ionic liquid (IL), nanofluid of water-SWCNT and pure water. The effective parameters in a range of Rayleigh number (103 ≤ 𝑅𝑎 ≤ 106 ) and solid concentration (0.1% ≤ 𝜙 ≤ 5%) are considered. The findings show that due to higher thermal conductivity and appealing rheological features of ionanofluid, the heat transfer rate is found significantly higher than nanofluid and pure water. A higher solid concentration of SWCNTs represents greater values of mean Nusselt number. Additionally, fluid velocity and heat transfer rate increase at larger values of Ra

With recent technological advances, thermal transport from different electronic and electrical devices is the most vital concern. The microchannel heat sink (MCHS) of liquid cooling is a useful device to remove over thermal load. Ionanofluid is a brand new and super potential cooling fluid for its ionic conductivity, non-flammability, negligible volatility, and high-level heat stability. In this research, the ionanofluid's velocity and thermal field characteristics through a triangular grooved MCHS are investigated using numerical tools. The combination of ionic liquid (IL) 1-Butyl-3-methylimidazolium Bis(trifluoromethanesulfonyl)imide [C4mim]NTf2 and propylene glycol (PG) is used as base fluid whereas graphene (G) and single-walled carbon nanotube (SWCNT) are chosen as hybrid nanoparticles to make the working ionanofluid. The governing equations of nonlinear partial differential equations describing the physical phenomena along with proper border settings are resolved by applying the finite element method (FEM). Different ratios of hybrid nanoparticles (G: SWCNT) like (1: 0, 1/3: 2/3, 1/2: 1/2, 2/3: 1/3, 0: 1) are suspended in the base fluid mixture. In addition, the base fluid mixture is assumed in different combinations of (IL: PG) as (100: 0, 50: 50, 0: 100). The numerical results are displayed in the forms of streamlines, isothermal lines, and rate of thermal transfer for the pertinent parameters namely forced convection (Re = 100–900) and solid concentration (φ = 0.001–0.05). Also, pressure drop, field synergy number, relative fanning friction feature, relative Nusselt number, and temperature enhancement efficiency are calculated. The results indicate that a higher heat transport rate is found using the IL-based ionanofluid with the highest solid concentration. Moreover, the higher forced convection enhances the thermal efficiency of MCHS. Two linear regression equations along with very good correlation coefficients have been derived from the numerical results.

The effects of Lorentz force and inclined angle on time-dependent free-convective thermal-material transport by micropolar binary mixture of fluid passing a continuous permeable surface have been analyzed in this article. Using the local similarity transformation, the governing partial differential equations have been converted into ordinary differential equations. The shooting technique was then employed to solve non-dimensional ordinary differential equations with boundary conditions using the "MATLAB ODE45" software. The effects of emerging Lorentz force (M) and inclined angle (γ) on the fluid velocity, concentration, temperature, and microrotation have been investigated within the boundary layer. Other non-dimensional parameters in this study, such as Schmidt number, suction parameter, and Prandtl number are kept fixed at Sc = 0.22, c = 0.5, and Pr = 0.71, respectively. The numerically simulated result shows that the velocity falls for uplifting values of the inclined angle and Lorentz force. The skin friction coefficient decreases by 49%, and 20% due to increasing the values of inclined angle (00-600), and Lorentz force (1.0 - 4.0), respectively. The surface couple stress is found to be increased about 24%, and 44% with the upturning values of M (1.0 - 4.0), and γ (00-600), respectively. Through this research, the behavior of the fluid flow has been explored.

The purposes of the current research are to study the consequences of radiation and heat generation on the time-dependent BL stream over a vertical permeable plate. The considered fluid is unsteady, viscous, and incompressible as well as electrically conducting. The heat transfer mechanism happens due to free convection. The non-dimensional PDEs of continuity, momentum, energy, and concentration are discussed using appropriate modifications. A set of nonlinear dimensionless PDEs can be solved by applying explicit finite difference method for numerical modeling. The stability and convergence analysis are additionally established to complete the formulation of the model. The thermo-physical effects of entering physical parameters (thermal radiation and heat generation) on the flow, thermal, and material fields are analyzed. For the physical interest, the variations in local and average skin friction, material, and heat transmission rates are also discussed. Studio Developer FORTRAN 6.2 and Tecplot 10.0 are used to simulate numerically the schematic model equations and graphical presentation. The present study is significances for petroleum engineering, agriculture engineering, nuclear power plants, gas turbines etc. The temperature is decreasing within the boundary layer for the increasing radiation. To see the rationality of the present research, we make a comparison of these outcomes and the consequences attainable in the literature with outstanding compatibility.

Climate change and the exhaustion of conventional energy sources with the growing demand for energy have caused concern among researchers all over the world. Renewable energy sources are a long-term alternative to our reliance on fossil fuels and reduce carbon emissions. Solar energy is radiant light and heat from the Sun that is harnessed using a range of technologies such as solar power to generate electricity, solar thermal energy, and solar architecture. Photovoltaic thermal (PVT) is a hybrid system, which includes both thermal and electrical energy generations. A 3D solar photovoltaic and thermal hybrid system is considered in this study where the encloser of the heat exchanger is fabricated from corrosion resistive stainless-steel sheet, and uncovered surfaces to the air of the heat exchanger are insulated using the glass wool. The fins manual air circulation and the channels are made of aluminium. The top side of the fins is bended and tightly attached to the lower back floor of the solar PV panel, wherein heat switch from the PV panel to the fins happens via the conduction technique. The equations of the heat transfer for PV layers such as for glass, cell, fins, heat exchangers, and laminar flow equation for the fluid domain are solved numerically applying the finite element method (FEM). Temperatures of air at the inlet-outlet and solar cell of the PVT system, are obtained for the variation of solar irradiance from 200 to 400 W/m2 using the weather situation of Bangladesh. Finally, the overall efficiency is calculated under different weather conditions in Bangladesh. The numerical results depict that the new layout of the heat exchanger efficiently transfers heat to the circulating air and the overall efficiency of the PVT is greater at the lowest solar irradiance of 200 W/m2.

Time-dependent magneto-convective thermal-material transport by micropolar binary mixture passing a vertical permeable surface with chemical reaction, radiative heat transfer and thermophoresis has been studied numerically. The findings of this study have significant industrial applications in the production of molten polymers, pulps, fossil fuels, and fluids containing certain additives, etc. Applying the similarity analysis together with Boussinesq estimate, the governing PDEs have been modified into ODEs. These equations have been solved by applying shooting techniques with the help of “ODE45 MATLAB" software. The results of the numerical solutions of the problem involving velocity, temperature, concentration and micro-rotation are presented graphically for different dimensionless parameters and numbers, namely magnetic intensity, Damköhler number, thermophoresis, temperature dependent dynamicviscosity, thermal radiation, thermal Grashof number, solutal Grashof number, Prandtl number and Schmidt number. The magnetic intensity affects the velocity field only in the increase-decrease mode.An increase in Damköhler number and thermal radiation significantly enhances the velocity fieldswhile interrupting the rate of heat transfer within the boundary layer. The temperature dependent dynamic viscosity greatly enhances the velocity of the fluid but reduces the micro-rotation of the particles very near to the wall. Also, the increase of Prandtl number lessens conduction of heat while increasing the micro-rotation of the particles noticeably very adjacent to the surface.

The slip flow and thermal transfer inside the boundary layer are extremely significant for various problems in aerodynamics, wing stall, skin friction drag on an entity, high-level velocity aircraft, etc. The current research investigated the effect of the slip factor and shape factor on the axisymmetric bullet-shaped object by taking the viscous dissipation parameter and location parameter. The analysis is conducted for both fixed and moving bullet-shaped objects due to thinner and thicker surfaces. The governing equations are transformed into a system of ordinary differential equations using suitable local axisymmetric similarity transformations and solved by applying the spectral quasi-linearization method. A new correlation analysis is made for velocity and temperature gradients. It is observed that the boundary layer structure has no defined shape due to a thicker bullet-shaped object instead it forms a steep angle with the axis which is contradictory to the formation of the boundary layer. A negative correlation is observed for the parameters M, Ec, Q*, and s but a positive correlation is observed for the parameters such as Pr, P, λ, and ε. The surface thickness and stretching ratio significantly affect the fluid flow and heat transfer processes. It is also noticed that the thinner bullet-shaped object performs as a better cooling conductor compared to a thicker one. The skin friction is reduced in the case of a thinner bullet-shaped object compared to a thicker one. The present analysis reveals that the heat transfer rate and the friction factor may be helpful in industrial sectors for controlling the cooling rate and quality of the final product. This research brings forward to increase in the rate of heat transfer inside the boundary layer region. The result may help to design the various types of moving objects in the automobile engineering sector when the objects pass through the fluid.

The objective of this work is to investigate the influences of thermal radiation, heat generation, and buoyancy force on the time-dependent boundary layer (BL) flow across a vertical permeable plate. The fluid is unsteady, incompressible, viscous, and electrically insulating. The heat transfer mechanism happens due to free convection. The nondimensional partial differential equations of continuity, momentum, energy, and concentration are discussed using appropriate transformations. The impressions of thermal radiation and buoyancy forces are exposed in the energy and momentum equation, respectively. For numerical model, a set of nonlinear dimensionless partial differential equations can be solved using an explicit finite difference approach. The stability and convergence analyses are also established to complete the formulation of the model. The thermophysical effects of entering physical parameters on the flow, thermal, and material fields are analyzed. The variations in local and average skin friction, material, and heat transfer rates are also discussed for the physical interest. The analysis of the obtained findings is shown graphically, and relevant parameters pointedly prejudice the flow field. Studio Developer FORTRAN 6.2 and Tecplot 10.0 are applied to simulate the schematic model equations and graphical presentation numerically. The intensifying values of the magnetic field are affected decreasingly in the flow field. The temperature profiles decrease within the BL to increase the value of radiation parameters. The present study is on the consequences for petroleum engineering, agriculture engineering, extraction, purification processes, nuclear power plants, gas turbines, etc. To see the rationality of the present research, we compare these results and the results available in the literature with outstanding compatibility.

We investigate the unsteady laminar convective magnetohydrodynamic nanofluids flow in a square cavity driven by an exothermic chemical reaction. Because exothermic chemical reactions are intrinsic in nanofluidic flow applications, we consider this exothermic chemical reaction in the analysis, which is governed by Arrhenius kinetics energy. A water-based nanofluid containing iron oxide (Fe3O4) nanoparticles is employed in the simulation. The square cavity is accurately propounded by a combination of suitable heating and flow conditions. The left vertical wall of the enclosure is considered a higher unevenly heated wall, the right vertical wall of the domain is considered a relatively cool constant temperature, and the upper and lower walls are considered insulating walls. Each wall assumes a no-slip condition. The nanofluid governing equations are transformed into the non-dimensional set of equations using similarity analysis and then modified into finite element equations. Galerkin's method in finite element analysis is used to obtain the results of the problem. The results show that the Rayleigh number, the Frank-Kamenetsky number, and the nanosolid volume ratio all have significant effects on the convective flow regime, and the average Nusselt number increases with these parameters. Due to the greater value of the Rayleigh number (Ra = 106), the average Nusselt number increased to 75.92%, and heat generation due to a strongly exothermic reaction (higher Frank-Kamenetskii number) can blow up the bounded solution. The water-Fe3O4 nanofluid achieves a greater rate of heat transfer (maximum 22.65%) than that of the base fluid.

Radiation is an important branch of thermal engineering which includes geophysical thermal insulation, ground water pollution, food processing, cooling of electronic components, oil recovery processes etc. An analysis of unsteady magneto-convective heat-mass transport by micropolar binary mixture of fluid passing a continuous permeable surface with thermal radiation effect has been introduced in this paper. The governing equations are transformed into coupled ordinary differential equations along with Boussinesq approximation by imposing the similarity analysis. Applying the shooting technique, the obtained non-linear coupled similarity equations are solved numerically with the help of “ODE45 MATLAB” software. The results of the numerical solutions to the problem involving velocity, temperature, concentration and micro-rotation are presented graphically for different dimensionless parameters and numbers encountered. With an increase of suction parameter, the velocity distributions very closed to the inclined permeable wall decrease slightly where . But for the uplifting values of sunction, both micro-rotation profile and species concentration enhance through the boundary layer. The skin-friction coefficient increases about 61%, 13%, 27% for rising values of Prandtl number (0.71-7), radiation effect (0 - 1) and thermal Grashof number (5-10), respectively, but an adverse effect is observed for magnetic field (1 - 4), inclined angle and Schmidt number (0.22 - 0.75). Heat transfer and mass transfer reduce about 82%, 53%, respectively, in increasing of Pr (0.71-1) and 36%, 11%, respectively, in increasing of thermal radiation (0 - 1). The surface couple stress increases about 26%, 49%, 64% and 30% with the increasing values of magnetic field (1-4), inclination angle , suction (0-1) and Schmidt number (0.22-0.75), respectively. Finally, the present study has been compared with the earlier published results. It is observed that the comparison bears a good agreement.

Interruption of continuous process and decreasing flow rate over time are very common challenges in peristaltic flow. This research takes an initiative to restrain the thermal and fluid flow rate over time by unsteady finite element analysis of Casson fluid flow through a two-dimensional peristaltic duct. The time-dependent flow equation exists in conjugate forced convection and the energy equation consists of radiative heat flux and entropy reduction. The top and bottom walls of the peristaltic duct are considered as contact with air. A circular bolus is set up in the middle of the duct. Four types of Casson fluids like slurry, silicone oil, apple juice, and blood are used as working fluids. The finite element method of Galerkin's residual technique is applied to solve the leading second ordered non-linear partial differential equations with proper border conditions. The effects of pertinent parameters on entropy reduction and thermal transport are analyzed. Results are displayed qualitatively in terms of streamlines, vortex field, and heatline contours as well as quantitatively in the form of average temperature, mean thermal, viscous, and total entropy. The obtained numerical results show that thermal performance and entropy reduction are significantly influenced by forced convection, atmospheric characteristics, internal thermal radiation, and Casson fluids. Approximately 6.99% and 72.13% increment of temperature and flow irreversibility are found for shear stress variation of Casson fluid from thickening to thinning. Decreasing thermal performance of 18.71% and increasing energy loss of 38.07% are noticed within the variation of Casson fluids (slurry, silicone oil, apple juice, and blood). About 14.05% enhancement of thermal transport and 64.91% reduction of total entropy are observed due to increasing internal thermal radiation from 0.5 to 2. The numerical results from this research represent a better thermal and fluid flow rate over time compared to the experimental/existing methodology/numerical research. The obtained flow and thermal transport phenomena expose many attention-grabbing performances which deserve additional investigation on Casson fluid characteristics particularly the continuation of flow rate. A fine approach to the biological peristaltic system is offered by the results.

This research is a good understanding of unsteady convective transport of nanofluids inside a skewed cavity considering MHD, different combinations of base fluids and nanoparticles, shapes, sizes (1–50 nm), volume fractions, and with/without Brownian effects. The right and left sidewalls of the enclosure are heated at low and high temperature, respectively, whereas the bottom and top walls are insulated. The finite element technique with Galerkin’s residual has been implemented for solving non-linear PDEs that govern the flow for the current problem. The numerical simulations have been presented using streamlines, isotherms, and temperature transport rates for different parameters, non-dimensional time, skewed angles, base fluids, nanoparticles, shapes, sizes, and volume fractions. The outcomes show that heat transport rate augments about 12.55% with an additional 2.5% nanoparticles into the base fluid for Cu-H2O nanofluid. An optimal thermal transport rate is observed for kerosene-based nanofluid, blade shape, and 1 nm size of nanoparticles. Magnetite nanoparticles show a greater thermal performance of 4.72% than higher thermal conductivity nanoparticles (copper and cobalt). Thermal transport enhances about 110.78% with Brownian motion for 5% concentrated blade-shaped kerosene-Fe3O4 nanofluid than without Brownian effects. In addition, a new linear regression equation with multiple variables has been derived from the obtained results.

A computational analysis is conducted based on ternary-nanoparticles performance for base fluid mixture through a convergent-divergent (CD) nozzle. Since the thermal phenomena through a CD nozzle exposes many attention-grabbing performances, it deserves additional investigation for laminar flow characteristics. Using ternary-nanoparticles at different base fluid mixture makes the study more robust and interesting to analyze the real situation better. In this study, the properties of cobalt (Co), silver (Ag), and zinc (Zn) nanoparticles along with base fluid mixtures of distilled-water (DW) and ethylene glycol (EG) as (100:0), (60:40), (50:50), and (0:100), are employed. A wide range of inlet velocity, solid concentrations, nanoparticle size and magnitude of nanoparticle shape factor is considered in this research. The mixtures of nanoparticles are considered as a ratio of (0:1/2:1/2), (1/2:0:1/2), (1/2:1/2:0), (1/6:1/6:2/3), (1/6:2/3:1/6), (2/3:1/6:1/6) and (1/3:1/3:1/3). The mathematical model is formulated using Navier-Stokes equations, energy conservation with proper boundary conditions, and solved using finite element method. Among the considered base fluid mixtures, the highest heat transfer rate is obtained for EG-Co-Ag-Zn nanofluid. A relatively higher heat transfer rate is found for all base fluid mixtures with nanoparticles ratio (1/6:2/3:1/6) compared to other combinations. Furthermore, advanced rate of thermal transport is found using laminar shape nanoparticles.

Mathematical modeling of a three-dimensional PVT system is considered and solved using the FEM. Numerical simulation is applied to explore the influence of solar irradiance on the thermal energy, electrical power, and total efficiency of this system. Water is considered HTF. The solar irradiance, inlet fluid mass flow rate, ambient temperature, and partial shading are all chosen in the range of 200-500 W/m2, 30-180 L/h, 10-37 °C, and 0-30%, accordingly based on the weather condition of Bangladesh. The effects of irradiance, fluid flow rate, ambient temperature, and partial shading on temperatures of cell and output fluid, electrical power and thermal energy, electrical efficiency-thermal efficiency, and total efficiency of this system are examined. Numerical results show that increasing each 100 W/m2 solar irradiance enhances the cell and outlet temperatures and electrical and thermal energy by 2.17 and 0.54 °C and 20.7 and 113.3 W, respectively, and devalues the electrical, thermal, and overall efficiencies approximately 0.17, 0.67, and 0.83%, respectively. The cell and output water temperature reduce almost 0.6 and 0.83 °C, respectively; electrical and thermal energy rise by 0.30 and 3.07 W, respectively, and the electrical, thermal, and overall efficiencies escalate about 0.04, 0.4, and 0.44% for every 10 L/h mass flow rate increment. Due to each 10 °C increment of ambient temperature, cell and output water temperature increase 1.7 °C and 0.05 °C, electrical energy decreases to 0.9 W, thermal energy increases to 9.89 W, and electrical efficiency reduces about 0.1%.

A numerical study of microwave cancer therapy for cylindrical-shaped liver tissue with an elliptical-shaped liver tumor has been carried out by this study. The time-dependent electromagnetic wave and the bio-heat transfer equations have been used as the governing equations and solved with appropriate boundary conditions using Galerkin's weighted residual scheme built-in finite element method-based COMSOL Multiphysics software. The coaxial applicator as well as the effects of different microwave input power levels (from 5 to 25 W), frequencies (from 0.7 to 5 GHz), and treatment time (from 0 to 1000 s) on hepatocellular carcinoma have been examined by this simulation and displayed graphically in terms of the microwave power dissipation, isothermal lines inside liver tissue, time-dependent profiles of temperature at different locations inside the tumor, specific absorption rate (SAR), and surface average transient temperature distribution of tumor tissue. The results demonstrate that microwave input antenna power and frequency have significant impacts on the temperature distribution and SAR values of liver tissue. When the microwave input power, as well as frequency, is increased, SAR and tissue temperature values also increase but the high temperature is harmful to healthy tissue. It is observed from the performed analysis that the mean temperature of the tumor cell is about 56.86°C at a time of 180 s using 10 W microwave input power and 2.45 GHz frequency.

The mathematical modeling of two-dimensional unsteady free convective flow and thermal transport inside a half-moon shaped domain charged in the presence of uniform/non-uniform temperature and magnetic effects with Brownian motion of the nanoparticles has been conducted. Thirty-two types of nanofluids in a combination of various nanoparticles and base fluids having different sizes, shapes, and solid concentrations of nanoparticles are chosen to examine the better performance of heat transfer. The circular boundary is cooled while the diameter boundary is heated with uniform/non-uniform temperature. An external uniform/non-uniform/periodic magnetic field is imposed along diameter. The powerful partial differential equations solver, finite element method of Galerkin type, has been engaged in numerical simulation. The numerical solution's heat transfer mechanism reaches a steady state from the unsteady situation within a very short dimensionless time of about 0.65. The thermal transport rate enhances for increasing buoyancy force whereas decreases with higher magnetic intensity. The uniform thermal condition along the diameter of half-moon gives a higher thermal transport rate compared to non-uniform heating conditions. The non-uniform magnetic field provides greater values of the mean Nusselt number than the uniform field. In addition, the outcomes also predict that a better rate of temperature transport for kerosene-based nanofluid than water-based, ethylene glycol-based, and engine oil-based nanofluid. The heat transfer rate is observed at about 67.86 and 23.78% using Co-Kerosene and Co-water nanofluids, respectively, with an additional 1% nanoparticles volume fraction. The blade shape nanoparticles provide a better heat transfer rate than spherical, cylindrical, brick, and platelet shapes. Small size nanoparticles confirm a higher value of average Nusselt number than big size. Mean Nusselt number increases 22.1 and 5.4% using 1% concentrated Cu-water and Cu-engine oil nanofluid, respectively than base fluid.

The ever-increasing water stress and availability of fresh drinking water are becoming a major challenge in rural and urban communities. The current high-end and large-scale technologies are becoming way more expensive and not friendly to the environment. In this regard, solar still is becoming a prominent and promising future technology due to its environment-friendly nature, less maintenance and operational costs, and simple design. The technological challenge regarding solar still is its low distillate yield. In this study, an attempt has been made to investigate the effect of tin oxide (SnO2) on the absorption surface of solar still towards improvement in sunlight absorption, which would lead to high distillate production rates. Various concentrations of SnO2, i.e., 0.5wt%, 1 wt%, 3 wt%, 5 wt%, 7 wt%, 10 wt%, 15 wt%, and 20 wt%, have been mixed in black and applied on the absorber plate to further optimize the suitable concentration. The experiments have been performed in both indoor (simulated) and outdoor conditions. An increase in surface temperature of absorber plate has been observed with increasing concentration of SnO2 under both the indoor and outdoor conditions, which is due to high solar spectrum absorption properties of SnO2 in the ultraviolet (UV) and near to far-infrared (IR) regions. The highest surface temperature of 101.61°C has been observed for specimens containing 15 wt% SnO2 in black paint under indoor conditions at 1000W/m2 irradiation levels, which is 53.67% higher compared to bare aluminum plate and 16.91% higher compared to only black paint coated aluminum plate. On the other hand, the maximum temperature of 74.96°C has been recorded for the identical specimens containing 15 wt% SnO2 under uncontrolled outdoor conditions. The recorded temperature is 47.96% higher than the bare aluminum plate and 14.88% higher than the black paint-coated aluminum plate. The difference of maximum temperatures under indoor and outdoor conditions is due to uncontrolled outdoor conditions and convective losses.

In this research, numerical modeling is conducted on free convective flow inside a trapezoidal domain with sinusoidal material and temperature allocations at both inclined boundaries using Buongiorno’s nanofluid. The model considers thermophoresis with Brownian activity effects taking place in the flow, temperature as well as concentration contours. Non-uniform nanoparticle solid concentration and temperature allocations have been imposed at both inclined surfaces. Top and bottom parallel surfaces have been kept as adiabatic. All the walls have been considered as no-slip and impermeable. The leading equations in addition border conditions are initially converted into a dimensionless pattern by a suitable similarity transformation and then resolved arithmetically employing the finite element technique with Galerkin’s residual. Buongiorno’s model of nanofluid on thermal and material transports, and flow structure has been investigated in detail. Outcomes have been displayed in the form of velocity, temperature, and concentration contours with various governing factors like Brownian action, Lewis number, Buoyancy relation, thermophoresis, Rayleigh number, Prandtl number, etc. Also, the rate of thermal transport has been calculated. The thermophoresis and Brownian effects on velocity, heat, and material fields are identified and finally, the flow, heat, and concentration controlling parameters for a specific material and thermal transport applications inside a trapezium-shaped cavity are obtained. Result demonstrates that the increase of Brownian action guides to enhance thermal transport by 34.75 and 34.27% for the right and left walls, respectively.

Energy transmission in an efficient mode has become a crucial challenge in both industrial and biomedical systems because of the worldwide energy crisis. An initiative has been taken by the present research for designing energy-efficient industrial and biomedical systems using different fluids. This numerical study focuses on investigating magneto-hydrodynamic conjugate natural convection and entropy generation of a hybrid nanofluid (Ag-MgO-water) in a differentially heated square domain including heat-generating sinusoidal solid partition. The partition is mid-positioned with a finite thickness and divides the computational regime into two flow domains. The FEM has been applied for solving the governing PDEs. The effects of magnetic field intensity and orientation, cavity inclination, heat generation from the partition and volume fraction of hybrid nanoparticles on temperature distribution, flow field and local entropy generation have been investigated and displayed by isotherms, streamlines and isentropic lines, respectively. The contours have been plotted at the highest Rayleigh number for better visualization of thermo-fluid interaction. Considering a wide variation of free convection, thermal performance is determined through the computation of the average Nusselt number along the hot wall and system energy loss has been evaluated through the calculation of average total entropy generation as well as average Bejan number in both fluid zones. The obtained numerical results show that thermal performance and entropy generation are significantly influenced by the magnetic field intensity and cavity inclination. Thermo-fluid energy transfer is reduced by 11.62% for the highest magnetic field strength whereas the increase of cavity tilting is responsible for a 56.72% decrease in thermal performance. A new regression equation has been derived from the obtained results. The numerical study carried out in this research has superior results compared to the existing methodology and/or experimental/ numerical research.

The problem of steady two-dimensional boundary layer flow of momentum, heat and mass transfer over a stretching permeable wedge-shaped surface in a nanofluid in presence of magnetic field has been studied. In this respect, the governing partial differential equations have been converted into ordinary differential equations by using the local similarity transformation. The transformed governing equations have been then solved numerically using the bvp4c in MATLAB software. The effects of the pertinent parameters, namely wedge angle parameter (β), Brownian motion (Nb), thermophoresis (Nt), magnetic parameter (M), moving wedge parameter (λ), permeability parameter (K*), Prandtl number (Pr), and Lewis number (Le) on fluid velocity, thermal and concentration within the boundary layer have been analyzed. The numerical results obtained of the skin friction coefficients, local Nusselt number and local Sherwood number, as well as the velocity, temperature and concentration profiles have been presented graphically and also in tabular form. The results indicate that the momentum boundary layer thickness increases with increasing values of wedge angle and moving wedge but reduces for magnetic and permeability effects. The heat transfer rate increases for wedge angle, moving wedge, Brownian motion but decreases for thermoporesis and magnetic effects. The mass transfer rate decreases for Brownian motion and thermoporesis effects but increases for wedge angle and moving wedge parameters. Finally, the numerical results have been compared with previously published research and found to be in good agreement.

Photovoltaic (PV) module is one of the most useful, sustainable and non-harmful products in the field of renewable energy. It offers longer service period for least maintenance cost. The elements of PV are abrasive, easy for designing, and their structure like the stand-alone technique gives production from micro to mega-power level. A 3D numerical system of PV module has been built up and solved applying FEM technique-based software COMSOL Multiphysics in this article. The average solar irradiation and optimum tilt angle for six divisions (Dhaka, Chittagong, Rajshahi, Khulna, Barishal and Sylhet) in Bangladesh have been calculated. The effects of solar radiation, angle of inclination, ambient temperature, and partial shading on temperature of solar cell, electrical power and PV module's electrical efficiency have been investigated. It has been observed from the results that the greatest value of electrical power 15.14 W is found in Rajshahi for solar radiation 209 W/m2. The highest electrical efficiency is found as 12.85% in Sylhet at irradiation level of 189 W/m2. For every 1° increase of inclination angle, electrical power and electrical efficiency level devalue by 0.06 W and 0.05%, respectively. Results also show that the efficiency level decreases from 14.66 to 11.32% due to partial shading area from 0 to 40%. PV module's electrical power; and electrical efficiency reduces approximately 0.01 W and 0.01%, respectively due to every 1°C addition of solar cell temperature.

Temperature dissipation in a proficient mode has turned into a crucial challenge in industrial sectors because of worldwide energy crisis. In heat transfer analysis, shell and tube thermal exchangers is one of the mostly used strategies to control competent heat transfer in industrial progression applications. In this research, a numerical analysis of turbulent flow has been conceded in a shell and tube thermal exchanger using Kays-Crawford model to investigate the thermal performance of pure water and different concentrated water-MWCNT nanofluid. By means of finite element method the Reynold-Averaged Navier-Stokes (RANS) and heat transport equations along with suitable edge conditions have been worked out numerically. The implications of velocity, solid concentration, and temperature of water-MWCNT nanofluid on the fluid flow formation and heat transfer scheme have been inspected thoroughly. The numerical results indicate that the variation of nanoparticles solid volume fraction, inflow fluid velocity and inlet temperature mannerism considerably revolutionize in the flow and thermal completions. It is perceived that using 3% concentrated water-MWCNT nanofluid, higher rate of heat transfer 12.24% is achieved compared that of water and therefore to enhance the efficiency of this heat exchanger. Furthermore, a new correlation has been developed among obtained values of thermal diffusion rate, Reynolds number and volume concentration of nanoparticle and found very good correlation coefficient among the values.

Topology has enormous applications on fuzzy set. An attention can be brought to the mathematicians about these topological applications on fuzzy set by this article. In this research, first we have classified the fuzzy sets and topological spaces, and then we have made relation between elements of them. For expediency, with mathematical view few basic definitions about crisp set and fuzzy set have been recalled. Then we have discussed about topological spaces. Finally, in the last section, the fuzzy topological spaces which is our main object we have developed the relation between fuzzy sets and topological spaces. Moreover, this article has been concluded with the examination of some of its properties and certain relationships among the closure of these spaces.

This numerical study reveals the heat transfer performance of hybrid/single nanofluids inside a lid-driven sinusoidal trapezoidal-shaped enclosure. The right and left inclined surfaces of the trapezium have been considered as insulated, whereas the bottom sinusoidal wavy and the flat top surfaces of the enclosure as hot and cold, respectively. The governing partial differential equations of fluid's velocity and temperature have been resolved by applying the finite element method. The implications of Prandtl number (4.2-6.2), Richardson number (0.1-10.0), undulation number (0-3), nanoparticles volume fraction (0%-3%), and nanofluid/base fluid (water, water–copper (Cu), water–Cu–carbon nanotube, water–Cu–copper oxide (CuO), water–Cu–TiO2, and water–Cu–Al2O3) on the velocity and temperature profiles have been studied. Simulated findings have been represented by means of streamlines, isothermal lines, and average Nusselt number of above-mentioned hybrid nanofluids for varying the governing parameters. The comparison of heat transfer rates using hybrid nanofluids and pure water has been also shown. The heat transfer rate is increased about 15% for varying Richardson number from 0.1 to 10.0. Blending of two nanoparticles suspension in base fluid has a higher heat transfer rate—approximately 5% than a mononanoparticle. Moreover, a higher average Nusselt number is obtained by 14.7% using the wavy surface than the flat surface of the enclosure. Thus, this study showed that applying hybrid nanofluid may be beneficial to obtain expected thermal performance.

This paper is devoted to study numerically a recent development of a non-Newtonian blood flow model for a stenosed artery in human blood vessel. For numerical investigation the blood flow modeling method of this research begins with non-Newtonian power-law model. The governing system of equation based on incompressible Navier-Stokes equations with externally imposed magnetic resonance has been generalized to take into account the mechanical properties of blood. The intent of this research is to examine the effects of inlet velocity and imposed magnetic field on the blood flow throughout the artery. The Galerkin’s weighted residual method of finite element system has been employed to resolve the governing system of equation with proper boundary conditions. The numerical simulation has been conducted for various inlet velocities from 0.005 to 0.1m/s and magnetic field strength from 0 to 6 tesla with superior convergence of the iterative structure. Results have been shown in terms of velocity, surface plot of velocity, pressure and viscosity contours. Cross-sectional plots of velocity and viscosity magnitudes across the stenotic contraction have also been displayed graphically. Obtained results of the blood flow simulations indicate that viscosity increases due to increasing values of inlet velocity of blood and magnetic strength.

A numerical analysis has been conducted to show the effects of magnetohydrodynamic (MHD) and Joule heating on heat transfer phenomenon in a lid driven triangular cavity. The heat transfer fluid (HTF) has been considered as water based hybrid nanofluid composed of equal quantities of Cu and TiO2 nanoparticles. The bottom wall of the cavity is undulated in sinusoidal pattern and cooled isothermally. The left vertical wall of the cavity is heated while the inclined side is insulated. The two dimensional governing partial differential equations of heat transfer and fluid flow with appropriate boundary conditions have been solved by using Galerkin's finite element method built in COMSOL Multyphysics. The effects of Hartmann number, Joule heating, number of undulation and Richardson number on the flow structure and heat transfer characteristics have been studied in details. The values of Prandtl number and solid volume fraction of hybrid nanoparticles have been considered as fixed. Also, the code validation has been shown. The numerical results have been presented in terms of streamlines, isotherms and average Nusselt number of the hybrid nanofluid for different values of governing parameters. The comparison of heat transfer rate by using hybrid nanofluid, Cu-water nanofluid, TiO2 -water nanofluid and clear water has been also shown. Increasing wave number from 0 to 3 enhances the heat transfer rate by 16.89%. The enhanced rate of mean Nusselt number for hybrid nanofluid is found as 4.11% compared to base fluid.

A numerical analysis has been carried out on combined magnetoconvection in a lid driven triangular enclosure with sinusoidal wavy bottom surface filled with hybrid nanofluid composed of equal quantities of Cu and Al2O3 nanoparticles dispersed in water-based fluid. The enclosure left vertical wall is heated while the inclined side of the cavity is cooled isothermally and the bottom wavy wall is insulated. A heat conducting horizontal circular cylinder has been placed at the middle of the enclosure. In this research, the relevant governing equations have been solved by using finite element method of Galerkin weighted residual approach. The implication of Richardson number and solid volume fraction of nanoparticles on the flow structure and heat transfer characteristics has been performed in details while the Reynolds number, Hartmann number and Prandtl number considered as fixed. Results have been presented in terms of streamlines, isotherms and average Nusselt number of the hybrid nanofluid for different values of governing parameters. The numerical results indicate that the Richardson number have significance effect on the flow and heat transfer performance. Moreover, it is noticed that combination of two different nanoparticles suspension has a better performance of heat transfer.

Irradiations incident on the photovoltaic module are converted only 15–20% into electrical energy and remaining are transformed into heat and drop electrical efficiency. Therefore, to harness both the thermal and electrical energy, hybrid photovoltaic thermal system is an optimum option. Moreover, phase change materials add more advantages of PV cell cooling and heat storage. A novel thermal collector has been designed as PVT and PVT-PCM systems to improve the heat transfer and performance. The 3D numerical analysis is done with COMSOL Multiphysics® software, and is validated at different volume flow rates of 0.5LPM to 3LPM, by experimental investigation at conditions of keeping the inlet water and ambient temperature at 27 °C and solar irradiation at 1000 W/m2. The experiment is carried out in indoor weather under controlled operating parameters and conditions with passive cooling of the module. Maximum 12.4% and 12.28% electrical efficiency of PVT is achieved numerically and experimentally respectively. Similarly, 12.75 and 12.59% electrical efficiency for PVT-PCM is obtained for experimental and numerical cases respectively. For PVT system, 10.13 and 9.2% electrical performance is improved. For PVT-PCM the electrical performance improvement is obtained as 12.91 & 12.75% numerically and experimentally respectively.

In this research, a 3D mathematical model of PVT/PCM system has been solved numerically using finite element method. Results have been shown in terms of surface temperature and streamline patterns of PVT/PCM system with time variation. The values of average temperature of solar cell, electrical power, heat energy, electrical-thermal efficiency and overall efficiency have been found. It is observed that using PCM in the PVT module the temperature of solar cell reduces and consequently the output power and efficiency are enhanced.

In this research, a 3D numerical model of PVT with a new baffle-based thermal collector system has been developed and solved using FEM. Water-based different nanofluids (Ag, Cu, Al), various solid volume fractions up to 3%, and variations of inlet temperature (20-40°C) have been applied. The numerical results show that increasing solid volume fraction increases the thermal performance of PVT systems operated by nanofluids, and optimum solid concentration is 2%. The thermal efficiency is enhanced approximately by 7.49, 7.08, and 4.97% for PVT systems operated by water-Ag, water-Cu, and water-Al nanofluids, respectively, compared to water. The extracted thermal energy from the PVT system decreases by 53.13, 52.69, 42.37, and 38.99 W for water, water-Al, water-Cu, and water-Ag nanofluids, respectively, due to each 1°C increase in inlet temperature. The heat transfer rate from the heat exchanger to cooling fluid enhances by about 18.43, 27.45, and 31.37% for the PVT system operated by water-Al, water-Cu, water-Ag, respectively, compared to water.

In this paper, the aluminium material of the thermal collector is used by introducing a novel design to enhance heat transfer performance, which is assembled in PVT and PVT-PCM systems. Experimental validation is carried out for the 3D FEM at 200 to 1000 W/m2 varying irradiation levels while keeping mass flow rate fixed at 0.5 LPM and inlet water temperature at 32 °C. Cell temperature reduction of 12.6 and 10.3 °C is achieved from the PV module in the case of the PVT-PCM system numerically and experimentally, respectively. The highest value of the electrical efficiency achieved is 13.72 and 13.56% for PV and 13.85 and 13.74% for PVT numerically and experimentally respectively. Similarly, for PVT-PCM, electrical efficiency is achieved as 13.98 and 13.87% numerically and experimentally, respectively. In the case of the PVT system, electrical performance is improved by 6.2 and 4.8% and for PVT-PCM, it is improved as 7.2 and 7.6% for numerically and experimentally, respectively.

Solar energy is one of the promising resources to fulfil the energy demands to some level in place of fossil fuels to avoid environmental pollution. The efficiency of solar technology, e.g. photovoltaic panels, thermal systems or a combination of both technologies as photovoltaic thermal is a concern to increase at an optimum level. A three-dimensional numerical analysis of PVT systems using water and MWCNT-water nanofluid has been completed with FEM based software COMSOL Multiphysics®. A numerical investigation has been validated by the indoor experimental research at different mass flow rates of 30 to 120 L/h while keeping solar irradiation fixed at 1000 W/m2, inlet fluid and ambient temperature at 32 and 25 °C, respectively. Percent improvement of electrical efficiency of PV with nanofluid cooling at flow rate 120 L/h is obtained about 10.72 and 12.25% of numerical and experimental cases respectively. Optimization of the nanofluid for weight concentration is achieved at 0.75% MWCNT-water. Solar cell temperature reduces about 0.72 °C experimentally and 0.77 °C numerically per 10 L/h flow rate increment. Approximately 7.74 and 6.89 W thermal energy is enhanced per 10 L/h flow rate increment in numerical and experimental studies respectively. Percentage increment of thermal efficiency is found as 5.62% numerically and 5.13% experimentally for PVT system operated by water/MWCNT nanofluid with compared to water.

In this research, an indoor experiment has been carried out of a PV module under controlled operating conditions and parameters. A novel design of thermal collector has been introduced, a complete PVT system assembled and water/MWCNT nanofluid used to enhance the thermal performance of PVT. An active cooling for PVT system has been maintained by using a centrifugal pump and a radiator have been used in the cycle to dissipate the heat of nanofluid in the environment to maintain proposed inlet temperature. 3D numerical simulation has been conducted with FEM based software COMSOL Multiphysics and validated by an indoor experimental research at different irradiation level from 200 to 1000 W/m2, weight fraction from 0 to 1% while keeping mass flow rate 0.5 L/min and inlet temperature 32 °C. The numerical results show a positive response to the experimental measurements. In experimental case, percentage of enhanced PV performance is found as 9.2% by using water cooling system. Higher thermal performance is obtained as approximately 4 and 3.67% in numerical and experimental studies, respectively by using nanofluid than water. In the PVT system operated by nanofluid at 1000 W/m2 irradiation, the numerical and experimental overall efficiency are found to be 89.2 and 87.65% respectively.

Irradiation level is the key factor of photovoltaic power generation. Photovoltaic/thermal systems are more effective at concentrating power in areas of high irradiation as compared to traditional PV systems. High irradiation maintains the cell temperature and maximizes electrical-thermal energy. An optimum cooling system is required to remove the extra heat from a PVT system, leading to enhancement of overall performance. In this research, the effect of different high irradiation levels and cooling fluid flow rate are investigated in terms of cell temperature, outlet temperature, electrical-thermal energy and overall performance of PVT system. Finite element based software COMSOL Multiphysics has been used to solve the problem numerically in three-dimensional model. The numerical model has been validated with available experimental and numerical results. It is found that overall efficiency increases with increasing fluid flow rate and with an optimum cooling fluid flow rate of about 180 L/h. Electrical and thermal energy increase from 197 to 983 W and 1165–5387 W respectively, for increasing irradiation from 1000 to 5000 W/m2 with an optimized flow rate of 180 L/h. Electrical, thermal and overall efficiency are found to be about 10.6, 71 and 81.6% respectively, at the highest irradiation level of 5000 W/m2.

Solar photovoltaics (PV) is a promising solution to combat against energy crisis and environmental pollution. However, the high manufacturing cost of solar cells along with the huge area required for well-sized PV power plants are the two major issues for the sustainable expansion of this technology. Concentrator technology is one of the solutions of the abovementioned problem. As concentrating the solar radiation over a single cell is now a proven technology, so attempt has been made in this article to extend this concept over PV module. High irradiation intensity from 1000 to 3000 W/m2 has been investigated to measure the power and energy of PV cell. The numerical simulation has been conducted using finite element technique. At 3000 W/m2 irradiation, the electrical power increases by about 190 W compared with 63 W at irradiation level of 1000 W/m2. At the same time, at 3000 W/m2 irradiation, the thermal energy increases by about 996 W compared with 362 W at 1000 W/m2 irradiation. Electrical power and thermal energy are enhanced by about 6.4 and 31.3 W, respectively, for each 100-W/m2 increase of solar radiation. The overall energy is increased by about 179.06% with increasing irradiation level from 1000 to 3000 W/m2. It is concluded that the effect of high solar radiation using concentrator can significantly improve the overall output of the PV module.

In the present study, a numerical investigation has been conducted for the effect of magnetic field on double diffusive natural convection flow inside a square enclosure filled with Cu-H2O nanofluid. The governing equations of the present problem have been converted into non-dimensional form using a set of suitable transformation variables and then solved numerically employing Galerkin weighted residual finite element technique. The numerical solution has been carried out for different magnetic field strength, Rayleigh number and volume fraction of nanoparticles with fixed values of controlling parameters. The obtained results are presented in terms of streamlines, isotherms, iso-concentrations and rate of heat transfer. The results indicate that the influence of magnetic field inside the flow region leads to reduce the fluid movement. It is also observed that the heat transfer rate can be enhanced more for the effect of solid concentration of water/Cu nanofluid than water.

The fluid flow and heat transfer mechanism on steady state solutions obtained in circular and arc-square enclosures filled with water/Cu nanofluid as well as base fluid has been investigated numerically by Galerkin's weighted residual finite element procedure. The left and right boundaries of the cavities are, respectively, heated and cooled at constant temperatures, while their horizontal walls are adiabatic. Effects of buoyancy force (Rayleigh number) and viscous force (Prandtl number) with a wide range of Ra (103 - 106) and Pr (4.2 - 6.2) on heat transfer phenomenon inside cavities are observed. The fluid flow and temperature gradient are shown by streamlines and isotherms patterns. From the investigation, it is reported that the Rayleigh and Prandtl numbers are playing significant role in heat transfer rate. The variation in heat transfer is calculated in terms of average Nusselt number. Heat transfer rate is found to be higher for water/Cu nanofluid with 2% solid volume fraction than pure water. About 2.7% higher heat transfer rate is obtained for circular cavity than that of arc cavity using water/Cu nanofluid at Ra = 104 and Pr = 5.8.

The Lid Driven Cavity Flow is most probably one of the most studied fluid problem in computational fluid dynamics field. Due to the simplicity of the cavity geometry, applying a numerical method on this flow problem in terms of coding is quite easy and straight forward. Despite its simple geometry, the driven cavity flow retains a rich fluid flow physics manifested by multiple counter rotating recirculating regions on the corners of the cavity depending on the Reynolds number.In this articlemixed convective heat-mass transfer phenomena is investigated numerically in a two-sided lid driven square closure. The working fluids are water and water/Cu nanofluid. It is assumed that the temperature difference driving the mixed convection comes from the side moving walls, when both horizontal walls are kept insulated. In order to solve the general coupled equations, a code based on the Galerkin’s finite element method is used and it has been validated after comparison between the present results and those of the literature. To make clear the effect of using nanofluid on heat and mass transfers inside the porous enclosure, a wide range of the nanoparticles solid volume fraction(0% to 3%) is studied. The phenomenon is analyzed through streamlines, isothermal lines, iso-concentration lines plots, with special attention to the Nusselt number and Sherwood number. It is found that heat- mass transfer becomes higher by using water/Cu nanofluid than clear water.

Heat is a form of energy which transfers between bodies which are kept under thermal interactions. When a temperature difference occurs between two bodies or a body with its surroundings, heat transfer occurs. Heat transfer occurs in three modes. Three modes of heat transfer are conduction, convection and radiation. Convection is a very important phenomenon in heat transfer applications and it occurs due to two different gradients, such as, temperature and concentration. This paper reports a numerical study on forced-mixed-natural convections within a lid-driven square enclosure, filled with a mixture of water and 2% concentrated Cu nanoparticles. It is assumed that the temperature difference driving the convection comes from the side moving walls, when both horizontal walls are kept insulated. In order to solve general coupled equations, a code based on the Galerkin's finite element method is used. To make clear the effect of using nanofluid on heat and mass transfers inside the enclosure, a wide range of the Richardson number, taken from 0.1 to 10 is studied. A fair degree of precision can be found between the present and previously published works. The phenomenon is analyzed through streamlines, isotherm and iso-concentration plots, with special attention to the Nusselt number and Sherwood number. The larger heat and mass transfer rates can be achieved with nanofluid than the base fluid for all conditions at Richardson number, Ri = 0.1 to 10. It has been found that the heat and mass transfer rate increase approximately 6% for water with the increase of Ri = 0.1 to 10, whereas these increase about 34% for nanofluid.

The problem of lid-driven flows in cavities has been major topic for research studies due to its fundamental nature and owing to the wide spectrum of engineering applications such as electronic device cooling, crystal growth, highperformance building insulations, multi shield structures used for nuclear reactors, food processing, float glass production, solar power collectors, furnace, drying technologies, etc. In this article Numerical study of the effect of Prandtl number on nanofluid flow inside a porous cavity in a two-sided lid driven square closure is studied. The working fluid is Cu/water nanofluid. By Finite Element Method the governing partial differential equations are solved. The highest Pr causes the greatest heat and mass transfer. The enhancing performance of heat and mass transfer rate is more effective for the waterCu nanofluid than the base fluid. It is assumed that the temperature difference driving the mixed convection comes from the side moving walls, when both horizontal walls are kept insulated. In this research, the effect of Prandtl number from 0.71 to 10 on nanofluid flow is investigated. The values of Richardson number, solid volume fraction of water/Cu nanofluid, Darcy number are kept fixed as 10, 2% and 0.01 respectively. The phenomenon is analysed through streamlines, isothermal lines, iso-concentration lines plots, with special attention to the Nusselt number and Sherwood number. It is found that heat- mass transfer becomes higher by using water/Cu nanofluid than clear water.

In the present research a numerical solution has been carried out to investigate the problem of magnetohydrodynamics (MHD) conjugate natural convection flow in a rectangular enclosure filled with copper water nanofluid. The relevant governing equations have been solved numerically by using finite element method of Galerkin weighted residual approach. The investigation uses a two dimensional rectangular enclosure with heat conducting vertical wall and uniform heat flux. The effect of Hartmann number on the parameter Rayleigh number, divider position and solid volume fraction of nano particles on the flow and temperature fields are examined for the range of Hartmann number (Ha) of 0 to 60. Parametric studies of the fluid flow and heat transfer performance of the enclosure for the pertinent parameters have also been performed. The numerical results have been provided in graphical form of streamlines and isotherms for various dimensionless parameters. It is found that the heat transfer rate increases with an increase of Rayleigh number and divider position but it decreases with an increase of the Hartmann number. It is also obtained that an increase of the solid volume fraction enhances the heat transfer performance. Finally, the implications of the above parameters have been depicted on the average Nusselt number of the fluid.