Effects of viscous dissipation, temperature dependent thermal conductivity, and local thermal non-equilibrium on the heat transfer in a porous channel to Casson fluid

The current paper deals with viscous dissipation effects in a permeable (or porous) channel filled with non-Newtonian Casson fluid by considering the local thermal non-equilibrium (LTNE) model. The dependency of the effective thermal conductivities of the solid and fluid phases on the respective temperatures has been studied along with the spatially varying Biot number. The Brinkman number $\left(\mathrm{Br}\right),$ Casson fluid parameter $\left(\gamma \right)$, thermal conductivity variation parameter $\left(\delta \right)$, porosity $\left(ϵ\right),$ Darcy number $\left(\mathrm{Da}\right)$, and the ratio of fluid and solid phase thermal conductivities $\left(k_r=\frac{k_f}{k_s}\right)$ are the main governing parameters. The Darcy–Brinkman model is employed to govern the fluid flow in permeable media and the velocity profile has been obtained analytically. Moreover, the energy equations for both phases along with suitable boundary conditions are derived and solved with the fourth order boundary value solver. The findings of the current study depict that the Nusselt number increases with the increment in Casson fluid parameter and decreases with the increment in Brinkman number and thermal conductivity variation parameter. Overall, the heat transmission between the solid and fluid phases increases with the decrement in Brinkman number and thermal conductivity variation parameter. On the other hand, the heat transmission between both the phases magnifies by increasing the value of Casson fluid parameter.