This problem deals with the effects of double diffusive, mixed convective flow of an incompressible viscous fluid through a vertical heated plate embedded in a non-Darcy porous medium under the influence of variable fluid properties numerically. The governing equations are modeled for the double diffusive boundary layer flow to understand the behaviour of velocity, temperature and concentration for variable fluid properties namely permeability, porosity, thermal conductivity and solutal diffusivity of the physical modal. Using a suitable similarity transformation, the highly nonlinear coupled PDE's are reduced into a set of coupled ordinary differential equations. By applying the Shooting technique with the help of RungeKutta-Fehlberg integral scheme and Newton-Raphson method, numerical computations have been carried out and are illustrated through the graphs to analyze the behaviour of velocity, temperature, concentration, Skin friction, Nusselt number and Sherwood numbers for the non-dimensional parameters of the physical system for both uniform permeability and variable permeability. To validate our numerical scheme, present results are compared with previously published work in the absence of few non-dimensional parameters and found to be in good agreement up to six decimal places of accuracy.

This article investigates the magnetohydrodynamic mixed convective heat, and mass transfer flow of an incompressible, viscous, Boussinesq, electrically conducting fluid from a vertical plate in a sparsely packed porous medium in the presence of thermal radiation and an nth order homogeneous chemical reaction between the fluid and the diffusing species numerically. In this investigation, the fluid and porous properties like thermal and solutal diffusivity, permeability and porosity are all considered to be vary. The governing non-linear PDE's for the fluid flow are derived and transformed into a system of ODE's using an appropriate similarity transformation. The resultant equations are solved numerically using shooting technique and Runge-Kutta integral scheme with the help of Newton-Raphson algorithm in order to know the characteristics of the fluid for various non-dimensional parameters which are controlling the physical system graphically. The results of the numerical scheme are validated and a numerical comparison has been made with the available literature in the absence of some parameters and found that in good agreement. Nomenclature

Renewable energy is the most prominent energy source due to its industrial and technological needs. A computational examination is performed to explore the result of the nanospray on the film flow of Casson and Sutterby nanofluids over a cylindrical surface. Due to the effective thermal conductivity of graphene oxide, the water–graphene oxide nanofluid is considered in the existence of radiative heat, Catteneo–Christove heat flux, and hydrodynamic effects. A mathematical model is established and resolved numerically by applying appropriate similarities. Simultaneous results are obtained for Sutterby and Casson nano models. The impact of considered physical features on the flow and heat transmission of both liquids is studied with the help of pictorial and mathematical outcomes. The heat transmission rate of the Casson nanoliquid is higher than the Sutterby nanoliquid. Hence, the fluids with Casson rheological nature are helpful in heat transfer applications. Both liquids’ flow and heat transport rate can be regulated by adjusting the film thickness.

A numerical computation has been carriedout for the steady, mixed convective, incompressible, viscous, electrically conducting couple stress fluid through a vertical plate with variable fluid properties in a porous medium. A uniform magnetic field is applied in the transverse direction and parallel to the vertical plate of the physical model and governing equations are derived for it."Using a suitable similarity transformation, governed PDE's are transformed into a set of ODE's which are highly non-linear coupled equations. An advanced Shooting technique is adopted to compute the variations of velocity, temperature, concentration in terms of non-dimensional parameters. Also physical interpretation of non-dimensional parameters like couple stress parameter magnetic field Prandtl number Schmidt number thermal conductivity and solutal diffusivity parameters are examined through plots for both variable permeability and uniform permeability."From the numerical results, an excellent agreement has been observed for the present results, as well as comparison is made between the present and the earlier works for a particular case of the problem.

This paper examines the thermal transfer attributes of ZnO-H2O Walter’s-B nanoliquid flow alongside an upright cone in the bearing of slip mechanism, radiative heat flux, and non-uniform heat source. We adopted suitable similarities to convert the nonlinear PDEs into ODEs and solved the transformed governing system by employing the bvp5c solver package in Matlab software. The prime novelty of this research is to compute the effective thermal diffusivity of the nanoliquid via the Maxwell and Xue nanomodels. Further, simultaneous results are deliberated for Maxwell and Xue cases via pictorial outcomes under various controlling limitations, such as velocity slip, radiative heat flux, buoyancy, viscoelastic, and volume fraction of nanomaterial. The thermal transmission rate of nanoliquid reported by the Xue nanomodel is higher than the Maxwell nanomodel. Therefore, the Xue nanomodel effectively works to enhance the thermal conductivity of the liquids with viscoelastic nature. Further, this study is helpful in industrial processing, where control over heat transport is required.