Computational unsteady flow analysis for third‐grade fluid from an isothermal vertical cylinder through a Darcian porous medium

The present study describes a mathematical model for free‐convective laminar incompressible boundary layer flow of a third‐grade fluid of the Reiner‐Rivlin differential type, external to an evenly heated semi‐infinite vertical cylinder through a two‐dimensional porous medium. Assuming a homogenous‐isotropic porous medium, simulation of bulk drag effects at low Reynolds number is conducted with the Darcy model. The resulting partial differential equation boundary value problem is normalized using suitable transformation variables. The highly nonlinear time‐dependent coupled conservation equations along with boundary conditions are resolved computationally with an optimized Crank‐Nicolson finite difference code. Validation with previous studies is included. The heat transport and skin‐friction coefficients are computed for different values of emerging nondimensional parameters. Furthermore, steady‐state and transient fluid flow variables are shown graphically. An enhanced fluid velocity is observed for increased Darcy number and the reverse trend is computed for higher values of third‐grade viscoelastic parameter. Also, the rate of heat transfer is observed to increase with greater Darcy number and a reduction in third‐grade viscoelastic parameter. A key observation which is drawn from the present study is that for third‐grade fluid the flow variables deviate significantly from a hot cylindrical wall as compared with a Newtonian fluid. The study is relevant to thermal polymer coating applications in aerospace materials processing.