Transient convection on a vertical cylinder with variable viscosity and thermal conductivity

A numerical analysis is performed to study the influence of temperature-dependent viscosity and thermal conductivity on the unsteady laminar free-convection flow over a vertical cylinder. It was assumed that the viscosity of the fluid is an exponential function and that the thermal conductivity is a linear function of the temperature. The governing boundary-layer equations are converted into a nondimensional form and a Crank-Nicolson type of implicit finite difference method is used to solve the governing nonlinear set of equations. Numerical results are obtained and presented for air and water, with different parameters for viscosity and thermal conductivity variation. The transient effects of velocity and temperature are analyzed. The effects of varying physical parameters on the average skin-friction coefficient and the average rate of heat transfer are also depicted. For each Prandtl number, the flow characteristics such as the temperature and the average heat transfer rate for the fluid with variable viscosity first coincide with and then deviate from that of the fluid with constant properties and finally reach the steady state asymptotically. When the viscosity-variation parameter is larger, the higher velocity is observed in a region near the wall and it gives a higher average Nusselt number and lower average skin friction. But an increase in the thermal conductivity variation parameter leads to an increase in the average skin-friction coefficient and average Nusselt number.