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.

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.

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.

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.

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.