Numerical Solution to the Natural Convection on Vertical Isoflux Plates by Full Elliptic Equations

A numerical solution to the Navier-Stokes and energy equations in streamfunction and vorticity formulation for steady state air natural convection on a vertical isoflux surface is presented. The velocity and temperature profiles are compared for the three different computational domains employed and different sets of imposed boundary conditions to evaluate the steady entrainment flow from permeable boundary surfaces. The comparison is carried out also with tire similarity and asymptotic expansion solutions obtained by tire boundary layer approximation for two Rayleigh numbers equal to 10(3) and 10(6). The most significant discrepancies are observed when the Ra = 10(3), since the diffusion is more important. The imposition of the second derivative of the streamfunction equal to zero on tire open boundaries seems to give a good physical description of the thermal and fluid dynamic fields. This kind of boundary condition together with a computational domain with reservoirs both upstream and downstream of the heated plate gives good knowledge of the flow near the leading and trailing edges of the plate. This configuration allows the determination of tire location at which the maximum wall temperature is attained together with its value. A good description of the physical phenomenon for the lowest investigated Rayleigh value, 10(3), requires tire employment of the elliptic equations together with adequate computational domain and imposed boundary conditions. Two correlations for the average Nusselt number and the maximum it-all temperature as function of the Rayleigh number are proposed in the range 5.0 x 10(2) less than or equal to Ra less than or equal to 1.0 x 10(6).