Conjugate Transient Free Convective Heat Transfer from a Vertical Slender Hollow Cylinder with Heat Generation Effect

Numerical analysis is performed to study the conjugate heat transfer and heat generation effects on the tran- sient free convective boundary layer flow over a vertical slender hollow circular cylinder with the inner surface at a con- stant 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. As there is no analytical or direct numerical method available to solve these equations, they are solved using the CFD techniques. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretized forms of the governing equations. The dis- cretized equations are solved using the tridiagonal algorithm. Numerical results for the transient velocity and temperature profiles, average skin-friction coefficient and average Nusselt number are shown graphically. In all these profiles it is ob- served that the time required to reach the steady-state increases as the conjugate-conduction parameter or heat generation parameter increases.