The heat/mass transfer analogy for a backward facing step

Abstract Heat and mass transfer from a surface to a stream of fluid are governed by Fourier’s law and Fick’s law respectively,which are mathematical manifestations of the process of diffusion. In the realm of transport processes, the mathematical equations describing the two phenomena can become analogous under certain assumptions and boundary conditions. From an engineering perspective, it is difficult to measure heat transfer coefficients in separated flows because of high spatial thermal gradients and the intrusive nature of the various techniques. The analogous mass transfer measurement using the naphthalene sublimation, on the other hand, overcomes these challenges and presents significant advantages of speed, economy, better resolution and accuracy over its heat transfer counter-part. However, quantitatively, the diffusion rates of heat in air and naphthalene in air are different. So, the physical and mathematical similarity between the two processes can be utilized effectively only when the analogy factor ( F  =  Nu / Sh ) is determined. This study investigates the heat/mass transfer analogy in a turbulent separated flow behind a backward facing step. The heat ( Nu ) and mass ( Sh ) transfer measurements were made using the thermal boundary layer measurement technique and the naphthalene sublimation measurement respectively under near identical flow conditions. Analogous boundary conditions of uniform temperature and constant concentration were imposed on the active surfaces, which is the recirculation-reattachment region behind the backward facing step. The Nu and Sh values thus obtained were used to calculate the analogy factor, F , which was found to be 0.692.