Numerical study of dissipative SW/MWCNT-nanofluid coating flow from a stretching wall to a porous medium with shape factor effects

A mathematical model is developed for incompressible steady-state dissipative CNT-aqueous nanofluid boundary layer flow from a stretching sheet to a saturated isotropic porous medium. Three different CNT shapes (spheres, blades and platelets) are considered. Both single-walled (SWCNT) and multi-walled (MWCNT) carbon nanotubes are examined. A Darcy-Brinkman model is adopted for the porous medium and a modified viscous dissipation formulation is considered which features porous media influence in the energy conservation equation. Appropriate expressions are deployed for the CNT-modified nanofluid viscosity, density, specific heat capacity, thermal conductivity and CNT shape factor. Via similarity transformations, the governing conservation equations for mass, momentum and energy with associated boundary conditions are normalized to generate a coupled nonlinear ordinary differential boundary value problem. A numerical solution is presented with the robust MATLAB-based bvp4c method and 4th order Runge-Kutta shooting scheme. Validation with previous studies is included. Velocity, temperature, skin friction and Nusselt number are computed for a range of selected parameters. The computations show that elevation in CNT volume fraction parameter accelerates the boundary layer flow whereas increment in the Darcian (inverse permeability) parameter induces strong deceleration. MWCNTs produce higher velocities than SWCNTs. Temperature and thermal boundary layer thickness are found to be enhanced with increasing Eckert number, Darcian (inverse permeability) parameter, CNT volume fraction and CNT shape factor. Significantly greater temperatures are computed for MWCNTs.