Hungarian journal of industrial chemistry, 1990
1. szám - Boyadjiev, Chr.: Asymptotic Theory of Non-Linear Transport Phenomena, II.: Heat Transfer
HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPRÉM Vol. IS. I 5 (1990) ASYMPTOTIC THEORY OF NON-LINEAR TRANSPORT PHENOMENA. II. HEAT TRANSFER Chr. Boyadjiev (Institute of Chemical Engineering, Bulgarian Academy of Sciences, Sofia 1040, Bulgaria) Received : March 29, 1989 An asymptotic theory of heat transfer in the boundary layer, where heat transfer is accompanied with non-linear mass transfer, resulting from intensive mass exchange, is presented. It is demonstrated that the direction of the mass exchange influences the heat transfer rate. Introduction Theoretical study of non-linear mass transfer [1,2] has shown that the changes in mass transfer rate result from the intensive mass exchange influencing the hydrodynamics. This could lead to analogous changes in the heat transfer rate when thermal diffusivity and diffusive heat transfer are neglected [3,4]. The results from the numerical theory [3] show that the rate of heat transfer considerably depends on Schmidt and Lewis numbers. Taking this into consideration, an asymptotic theory, which avoids the need to solve a system of nonlinear equations in each particular case is presented here. The Mathematical Model The mathematical description of the heat transfer, resulting from a simultaneous heat and mass exchange among a semi-infinite plate and a fluid flux flowing along it, is characterized by the nonlinearity of the convective mass transfer equation and linearity of the convective heat transfer equation. From the above, the conclussion follows that the equation describing the convective heat transfer in the boundary layer approximation has to be added to the mathematical description in [1]: