Generalized Reynolds Analogy: An Engineering Prospective of Thermo-Fluid Physics for Heat Exchanger Design

Abstract

In practical interest of Reynolds analogy for power and process industries, in a unified system approach an engineering prospective of thermo-fluid physics has been proposed by developing a theory of basic heat exchanger design and analysis. Needless to mention of excellent books on heat exchangers, this paper focuses on the novelty of heat exchanger, which in author’s view depends upon the possibility of energy exchange between two fluid streams at different temperatures. Since operation cannot be random, the principal act of design is to engineer a product such that it operates in specified manner to perform its desired function of de-energizing one stream by virtue of energizing the other. With law of the integral as the guiding principle of physics, it shall be made clear that energy exchange in the form of heat must be accompanied by energy transfer such that heat exchanger must operate due to simultaneous process of cooling and heating of the fluid streams with an intervening medium. To unlock the secret of steady operation a fundamental postulate concerning thermodynamic behavior of the system has been made by invoking zeroth law of thermodynamics. Remarkably, it lends itself a necessary and sufficient condition concerning proportionality between heat-flux and required temperature difference to yield fluids unique thermal response in relation to the heat transfer surface temperature. Consequently, far-reaching physical implications of the constant of proportionality on system design can be clearly exposed of with due consideration to Eulerian descriptions of conservation principles according to Newton’s mechanical theory. Consistently enough, because of thermal non-equilibrium, effectiveness of system design and off design performance warrants a fundamental theorem like one suggested by Reynolds concerning augmentation of thermal diffusion due to fluid motion. Accordingly, flow rates become critical operating parameters for thermal performance and pressure drop requirements. Furthermore, and most importantly, in support of the theorem an order magnitude analysis appears to be in order, to show the dependence of flow resistance and hence, system thermal response on fluid flow behavior in terms of non-dimensional parameters. As a result, it is made clear that development of design correlations for friction factor and non-dimensional heat transfer coefficient in terms of both Reynolds number and Prandtl number is an integral part of heat exchanger design process by gathering experimental data. Finally, generalized mathematical statement of Reynolds analogy has been obtained relating Stanton number with friction factor, which reduces to our familiar expression for Prandtl number of unity.