Theoretical Explanation of Heat Transfer in Laminar Region of Bingham Fluid

Abstract

The author has reported before the theoretical explanation of heat transfer in laminar flow of a pseudoplastic fluid, having either cooling or heating effect, without change in phase. By this method the author has tried to explain the heat transfer in laminar flow of Bingham fluid. The velocity distribution in Bingham fluid flowing through a tube are separable into two parts: one is a plug flow and the other is a non-plug flow.Consequently the author proposes two differential equations for heat transfer, which can be proved to hold on the grounds that the bondary condition of temperature r=rp, is variable and that the function is in y-axis direction.The author has obtained the average bulk temperature of outlet by the application of Equation 1.44, and has found that the logarithmic mean of difference between the average bulk temperature of a fluid and the temperature of a wall is theoretically correct.Hence from the theoretical relation, whenThe average bulk temperature when a=0.5 has been obtained by means of Equation 4·5, and Figure 5 shows Nusselt number plotted against Graetz number, revealing their theoretical relation.The author has given, for example, a theoretical solution to the case in which the velocity distribution is a rodlike flow and the wall temperature changes linearly in y-axis direction. The results are shown in Equations 3·5, 3·7, and 3·8.