Natural convection on horizontal, inclined, and vertical plates with variable surface temperature or heat flux

Abstract

An analysis is performed to study the flow and heat transfer characteristics of laminar free convection in boundary layer flows from horizontal, inclined, and vertical flat plates in which the wall temperature T w ( x) or the surface heat flux q w ( x) varies as the power of the axial coordinate in the form T w ( x) = T ∞ + ax n or q w = bx m . The governing equations are first cast into a dimensionless form by a nonsimilar transformation and the resulting equations are then solved by a finite-difference scheme. Numerical results for fluids with Prandtl numbers of 0.7 and 7 are presented for three representative exponent values under each of the nonuniform surface heating conditions. It has been found that both the local wall shear stress and the local surface heat transfer rate increase as the angle of inclination from the horizontal γ increases or as the local Grashof number increases. An increase in the value of the exponent n or m enhances the surface heat transfer rate, but it causes a decrease in the wall shear stress. Correlation equations for the local and average Nusselt numbers are obtained for the special cases of uniform wall temperature (UWT) and uniform surface heat flux (UHF). Comparisons are also made of the local Nusselt numbers between the present results and available experimental data for the UHF case, and a good agreement is found to exist between the two.