Unsteady free convection flow and heat transfer from an isothermal truncated cone with variable viscosity

This paper deals with unsteady free convection flow of an incompressible fluid about an isothermal truncated cone with variable viscosity and Prandtl number. The non-linear coupled partial differential equations governing the flow and heat transfer have been solved numerically, by using an efficient implicit finite-difference scheme along with quasilinearization technique. The nonsimilar solutions have been obtained for the problem, overcoming numerical difficulties near the leading edge and in the downstream regime for the whole transient from the initial unsteady-state flow to the final steady state flow, for different Prandtl number fluids. Also, an analytical solution is obtained for transient heat transfer at the leading edge of the truncated cone, valid for small times and found to be in good agreement with numerical solution. Numerical results indicate that skin friction as well as heat transfer are strongly affected by the viscosity-variation parameter and temperature dependent Prandtl number. Further, skin friction is found to decrease along the surface of the cone whereas heat transfer rate increases due to unsteadiness in the flow. It is observed that there is a smooth transition from the small time solution (initial unsteady flow) to the large time solution (final steady-state flow). The time taken to reach steady state is found to increase with increasing of Prandtl number.