Carrier-mediated heat transport

Abstract-It is shown how an asymptotic, boundary-layer method, developed specifically for application to facilitated mass transport, can also be applied to the corresponding problem of facilitated enthalpy transport. The method, which merely entails an implicit algebraic computation, is applied to the (hydrodynamic) film-theory model for heat transfer between a hot or cold wall and a reversibly dissociating gas mixture, 2N0 &2NO + 02, which has previously been treated by Brian and Bodman[l]. Good agreement is found with their approximate analytical formula over the parameter range of their computations. However, for more extreme states of dissociation and larger overall temperature differences, the present results differ from those given by their approximate formula, especially for the cooling (cold wall) problem. INTRODUCTION The conduction of heat in chemically reactive sys- tems is by no means a novel topic in the general area of diffusional transport phenomena. It has been the subject of several previous works, which are exemplified most notably by those of Hirshfelder[2], Brian and Reid[3], Brian and Bodman[l], Bodman et al. [4], Fan and Mason[5], and co-workers. One of the principal objectives of such studies has been to predict theoretically the reactive enhancement of steady-state heat trans- fer through a chemical mixture due to reversible thermal dissociation and recombination accom- panied by molecular diffusion of various chemical species. If, in such systems, say reacting gas mix- tures, the intrinsic rates of the chemical reactions are, in some appropriate sense, small compared to diffusional transport rates then one obtains the so-called ‘frozen’ (conductivity) regime, where reaction exerts a negligible influence on energy transport. At the opposite extreme, where reaction rates are in effect infinitely rapid, one obtains the (reaction) ‘equilibrium’ regime and, usually, max- imum enhancement of heat flux. In either of these asymptotic regimes one is generally able to perform fairly direct computations of the heat flux through a mixture from given trans- port and equilibrium properties; whereas, other- wise, one has to solve a set of non-linear differential equations, involving diffusion and reaction rates and governing spatial temperature and composition fields. While such boundary-value problems are in principle straightforward, albeit not analytically tractable, and actual numerical computation can be difficult and time-consuming, even with advanced computer-executed numerical schemes. These practical difficulties are traceable directly to a boundary layer structure that develops whenever reaction rates are moderately to highly rapid. This boundary-layer nature of the near- equilibrium regime was anticipated in the early works of Hirshfelder[2], but, up to the present, no general mathematical techniques have apparently been proposed to cope with the problem in this particular physical context. However, in very re- cent times there has been a good deal of effort devoted to the treatment of problems closely akin to the above in the related area of facilitated mass transport. Although there had been a previous long- standing interest in the reactive enhancement of mass transport, such problems have received re- newed attention because of their possible relevance to carrier-mediated biological transport in mem- branes and liquid films. Thus, Goddard