The effect of wall conduction for the extended Graetz problem for laminar and turbulent channel flows

Axial heat conduction effects within the fluid can be important for duct flows if either the Prandtl number is relatively low (liquid metals) or if the dimensions of the duct are small (micro heat exchanger). In addition, axial heat conduction effects in the wall of the duct might be of importance. The present paper shows an entirely analytical solution to the extended Graetz problem including wall conduction (conjugate extended Graetz problem). The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. The obtained analytical solution is relatively simple to compute and valid for all Péclet numbers. The analytical results are compared to own numerical calculations with FLUENT and good agreement is found.