The effect of the conjugate-conduction parameter and Prandtl number on the free convective couple stress fluid flow over a vertical cylinder

Abstract

Numerical analysis is performed to study the conjugate heat transfer effects on the transient free convective couple stress fluid flow over a vertical slender hollow circular cylinder with the inner surface at a constant temperature. A set of non-dimensional governing equations namely, the continuity, momentum and energy equations is derived and these equations are unsteady non-linear and coupled. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretised forms of governing equations. These equations are solved using the Thomas and pentadiagonal algorithms. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. Transient velocity and temperature profiles, average skin-friction coefficient and average Nusselt number are shown graphically. In all these profiles it is observed that the time required for the variables to reach the steady-state increases with the increasing values of conjugate-conduction parameter (P) and Prandtl number. In the vicinity of the hot wall, the velocity and temperature of the fluid decrease as P increases. It is noticed that the steady-state values of and decreases as P increases