In the present problem a magnetohydrodynamic (MHD) three dimensional Casson fluid flow past a porous linearly stretching sheet is investigated, introducing convective boundary condition at the surface where the thermal conductivity of the fluid varies linearly with respect to the temperature. Computations are performed for the velocity and temperature fields for different parameters. Spectral Relaxation Method (SRM) is used to solve the governing equations. The present results are compared with existing limited solutions, showing good agreement with each other and with different parameters. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. The influence of the skin friction and local Nusselt number for different parameters is discussed and presented in tabular form

Irreversibility analysis gives an idea of the energy loss of the system which appears in most industrial applications. In the present problem, the irreversibility of a 3-D Darcy–Forchheimer Casson hybrid nanofluid flow caused by a rotating disk is analyzed. Cattaneo–Christov heat flux, Joule’s heating, and nonlinear thermal radiation with heat generation are introduced in the system. The governing important PDEs are transformed into a collection of ODEs with suitable boundary conditions, and then, solved numerically by Runge–Kutta–Fehlberg-based shooting approach. The velocities and temperature are explored with different governing parameters. Further, we analyzed the irreversibility of the system including the Bejan number with the rate of local heat transfer. We have compared our results with the existing literature. The Brinkman number and Reynolds number are observed to increase the entropy generation of the system. Temperature ratio, Cattaneo–Christov heat flux, Prandtl number, and Biot number boost up the rate of heat transfer at the surface. The outcome of the problem leads to an application to industries and solar panels with advanced Darcy–Forchheimer feature and the presence of nanoparticles.

Casson fluid flow has many practical applications such as food processing, metallurgy, drilling operations and bio-engineering operations. In this paper, we study Casson fluid flow through a plate with a convective boundary condition at the surface and quantify the effects of suction/injection, velocity ratio, and Soret and Dufour effects. Firstly we used a similarity transformation to change the governing equations to ordinary differential equations which were then solved numerically. The effect of the rheological parameters on the velocity, temperature, and concentration with skin friction, and heat and mass transfer are shown graphically and discussed briefly. It is observed that the velocity of the fluid at the surface decreases with increase of the velocity ratio while the nature of the flow is in opposite characteristics. The local Nusselt number decreases with increase in the velocity ratio. Skin friction at the surface is enhanced by buoyancy ratio and Casson number. Due to injection of the fluid in the system, the mass transfer rate at the surface increases while it decreases with the velocity ratio parameter

The effects of a homogeneous-heterogeneous reaction on steady micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium are numerically investigated in this paper. The model developed by Chaudhary and Merkin (Fluid Dyn. Res. 16:311-333, 1995) for a homogeneous-heterogeneous reaction in boundary layer flow with equal diffusivities for reactant and autocatalysis is used and extended in this study. The uniqueness of this problem lies in the fact that the solutions are possible for all values of the stretching parameter λ > 0 , while for λ < 0 (shrinking surface), solutions are possible only for a limited range of values. The effects of physical and fluid parameters such as the stretching parameter, micropolar parameter, permeability parameter, Schmidt number, strength of homogeneous and heterogeneous reaction parameter on the skin friction, velocity and concentration are analyzed, and these results are presented through graphs. The solute concentration at the surface is found to decrease with the strength of the homogeneous reaction, and to increase with heterogeneous reactions, the permeability parameter and stretching or shrinking parameters. The velocity at the surface was found to increase with the micropolar parameter.