Population diffusion in river-ocean ecologies and for wild animals, including birds, mainly depends on the availability of resources and habitats. This study explores the dynamics of the resource-based competition model for two interacting species in order to investigate the spatiotemporal effects in a spatially distributed heterogeneous environment with no-flux boundary conditions. The main focus of this study is on the diffusion strategy, under conditions where the carrying capacity for two competing species is considered to be unequal. The same growth function is associated with both species, but they have different migration coefficients. The stability of global coexistence and quasi-trivial equilibria are also studied under different conditions with respect to resource function and carrying capacity. Furthermore, we investigate the case of competitive exclusion for various linear combinations of resource function and carrying capacity. Additionally, we extend the study to the instance where a higher migration rate negatively impacts population growth in competition. The efficacy of the model in the cases of one- and two-dimensional space is also demonstrated through a numerical study.

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.

Population movements are necessary to survive the individuals in many cases and depend on available resources, good habitat, global warming, climate change, supporting the environment, and many other issues. This study explores the spatiotemporal effect on the dynamics of the reaction-diffusion model for two interacting populations in a heterogeneous habitat. Both species are assumed to compete for different fundamental resources, and the diffusion strategies of both organisms follow the resource-based diffusion toward a positive distribution function for a large variety of growth functions. Depending on the values of spatially distributed interspecific competition coefficients, the study is conducted for two cases: weak competition and strong competition, which do not perform earlier in the existing literature. The stability of global attractors is studied for different conditions of resource function and carrying capacity. We investigated that in the case of weak competition, coexistence is attainable, while strong competition leads to competitive exclusion. This is an emphasis on how resource-based diffusion in the niche impacts selection. When natural resources are in sharing, either competition or predator-prey interaction leads to competitive exclusion or coexistence of competing species. However, we concentrate on the situation in which the ideal free pair is achieved without imposing any other additional conditions on the model’s parameters. The effectiveness of the model is accomplished by numerical computation for both one and two space dimension cases, which is very important for biological consideration

In a confined heterogeneous habitat with two species interacting for common resources, the research analyzes a reaction-advection-diffusion type dispersal model with homogeneous Neumann boundary conditions for generalized growth functions. Both species follow the same symmetric growths law, but their dispersal strategies and advection rates are different. The following pattern is used to consider the competition strategy: in a bounded heterogeneous habitat, the first population disperses according to its resource functions, whereas the second population disperses according to its carrying capacity. We investigate the model in two scenarios: when carrying capacity and resource functions are non-proportional, competitive exclusion occurs, and one species drives the other to extinction in the long run for various similar and unequal carrying capacities of competing species. However, coexistence is achievable for different resource distribution consumption if the resource distribution and the carrying capacity phase of the second species are non-constant and similar. A series of numerical computations are used to demonstrate the model’s efficacy in oneand two-dimensional instances, which is particularly significant for environmental considera

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.

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.

An elaborate numerical study of developing a model regarding conjugate effect of fluid flow and heat transfer in a heat conducting vertical walled cavity filled with copper-water nanofluid has been presented in this paper. This model is mainly adopted for a cooling of electronic device and to control the fluid flow and heat transfer mechanism in an enclosure. The numerical results have been provided in graphical form showing effect of various relevant non-dimensional parameters. The relevant governing equations have been solved by using finite element method of Galerkin weighted residual approach. The analysis uses a two dimensional rectangular enclosure under conjugate convective conductive heat transfer conditions. The enclosure exposed to a constant and uniform heat flux at the left vertical thick wall generating a natural convection flow. The thicknesses of the remaining parts of the walls are assumed to be zero. The right wall is kept at a low constant temperature, while the horizontal walls are assumed to be adiabatic. A moveable divider is attached at the bottom wall of the cavity. The governing equations are derived for the conceptual model in the Cartesian coordinate system. The study has been carried out for the Rayleigh number Ra =106 and for the solid volume fraction. The investigation is to be arrived out at different non-dimensional governing parameters. The effect of convective heat transfer coefficient, divider position and thickness of solid wall on the hydrodynamic and thermal characteristic of flow has been analyzed. Results are to be presented in terms of streamlines, isotherms and average Nusselt number of the nanofluid for different values of governing parameters.

The objective of this study is to numerically simulate the effect of conjugate heat transfer in a heat conducting vertical walled cavity filled with Copper-Water nanofluid. The analysis uses a two-dimensional rectangular enclosure under conjugate convective-conductive heat transfer conditions. The enclosure was subject to a constant conduction-convection uniform heat flux at the left wall generating a natural convection flow. The thicknesses of the other boundaries of the wall are assumed to be zero. The right wall is kept at a low constant temperature while the horizontal walls are assumed to be adiabatic. A heat conducting moveable divider is attached on the bottom horizontal wall. The study has been carried out for the Rayleigh number in the range of 104 ≤ Ra ≤ 106 and for the solid volume fraction 0 ≤ ɸ ≤ 0.05. The investigation is to be arrived out at different non-dimensional governing parameters. The effect of Rayleigh number and solid fluid thermal conductivity ratio on the hydrodynamic and thermal characteristic of flow has been analyzed. Results are to be presented in terms of streamlines, isotherms and average Nusselt number of the nanofluid for different values of governing parameters.