Mixed Convective and Radiative Heat Transfer in a Horizontal Concentric and Eccentric Cylindrical Annuli


A numerical investigation has been performed to study the effect of eccentricity on unsteady state, laminar aiding mixed convection in a horizontal concentric and eccentric cylindrical annulus.The outer cylinder was kept at a constant temperature while the inner cylinder was heated with constant heat flux. The study involved numerical solution of transient momentum (Navier-Stokes) and energy equation using finite difference method (FDM), where the body fitted coordinate system (BFC) was used to generate the grid mesh for computational plane.The governing equations were transformed to the vorticity-stream function formula as for momentum equations and to the temperature and stream function for energy equation.A computer program(Fortran 90) was built to calculate the bulk Nusselt number (Nub) after reaching steady state condition for fluid Prandtl number fixed at 0.7 (air) with radius ratio ( =2.6), Rayleigh number (Ra=200), Reynolds number (Re=50) for both concentric and eccentric cylindrical annulus with different eccentricity ratios (ε=0, 0.25, 0.50, 0.75) and angular positions (φo=0o, 45o, 90o, 135o, 180o).The results show a reasonable representation to the relation between Nusselt number and (ε, φo). Generally, Nub decreased with the increase in (ε and φo). Also, results show that the best thermal performance for the inner cylinder was at the angular position(φo=0o) for eccentricity ratio (ε=0.25), while the maximum reduction in the rate of heat transfer for the inner cylinder was at the angular position (φo=180o) for eccentricity ratio (ε=0.75). Comparison of the result with the previous work shows a good agreement.