Experimental verification of a heat/mass transfer analogy in two dimensional laminar and turbulent boundary layers.

Abstract

Heat and mass transfer from a solid surface into a fluid stream both are diffusion driven processes. Their mathematical model equations are identical for identical flow and boundary conditions. Problems with engineering applications are transformed from one domain to another for practical and economical advantages. A mass transfer technique using naphthalene sublimation is faster, of higher resolution, economical and more accurate than a direct heat transfer measurement. The diffusion rates of heat transfer in air and naphthalene in air are quantitatively different. Hence, the advantages of naphthalene sublimation technique are justified when the heat/mass transfer analogy is experimentally verified and an analogy factor (F = Nu/Sh ) is determined.

Heat/mass transfer analogy is experimentally verified for two dimensional laminar and turbulent boundary layer flows. Thermal boundary layer technique is used to measure local heat transfer coefficient ( Nu ) and naphthalene sublimation technique is used to measure local mass transfer coefficient ( Sh ) for two identical plates subjected to identical boundary layer flows. The accuracy of the thermal boundary layer technique is determined using a constant heat flux plate made of steel shim subjected to constant electrical power. The convective heat flux is determined using this electrical power after correcting for conduction and radiation effects. These results are compared to the heat flux values determined using the thermal boundary layer technique and are found to agree within 2%.

The effect of conduction within the thermocouple wires is studied with a numerical model using fin analysis and a variable convective heat transfer load. The equilibrium thermocouple temperature is solved for various locations of the thermocouple probe within the boundary layer to simulate an equivalent experiment for an analytically calculated laminar boundary layer flow. The predictions of the model agree within 1% of the experimental measurements and are used to correct them for laminar case.

The heat/mass transfer analogy factor is calculated using the corrected Nu and Sh. It is found to agree with the analytical prediction of 0.677 within 2% for the laminar case and is found to be a constant of 0.667 for the turbulent case.