Numerical study of combined convection heat transfer for thermally developing upward flow in a vertical cylinder

The problem of the laminar upward mixed convection heat transfer for thermally developing air flow in the entrance region of a vertical circular cylinder under buoyancy effect and wall heat flux boundary condition has been numerically investigated. An implicit finite difference method and the Gauss elimination technique have been used to solve the governing partial differential equations of motion (Navier Stocks equations) for two-dimensional model. This investigation covers Reynolds number range from 400 to 1600, heat flux is varied from 70 W/m2 to 400 W/m2. The results present the dimensionless temperature profile, dimensionless velocity profile, dimensionless surface temperature along the cylinder, and the local Nusselt number variation with the dimensionless axial distance Z+. The dimensionless velocity and temperature profile results have revealed that the secondary flow created by natural convection have a significant effect on the heat transfer process. The results have also shown an increase in the Nusselt number values as the heat flux increases. The results have been compared with the available experimental study and with the available analytical solution for pure forced convection in terms of the local Nusselt number. The comparison has shown satisfactory agreement.