Critical Choice of Variables in the Modeling and Correlation of Mechanisms for Transport and Reaction

Abstract

Although the choice of variables is known to be a major factor in the modeling of mechanisms of transport and reaction, as well as in the derivation of analytical solutions, the efficient execution of numerical solutions, and the development of correlating equations thereof, the analysis presented here may be the broadest and most detailed one yet attempted in this context. Although some general principles and methodologies are identified and described herein, the most effective techniques and choices are found to be somewhat specific to the particular technical topic. The illustrative examples of both effective and ineffective choices of variables are taken from fluid flow, chemical conversions, thermal conduction, thermal radiation, and thermal convection because of their general familiarity, but the results are presumed to be applicable to all aspects of chemical engineering and allied topics, both new and old. The techniques identified as most effective are dimensional analysis, the elimination of unimportant variables, the derivation of asymptotes, the introduction of virtual variables, the recognition of analogies, and the critical testing of results with experimental data or computed values. The most underutilized technique is that of speculation: asking the question "What if?". This particular technique is applicable and often effective in conjunction with each of the others.

Finite Element Simulation with Heatlines and Entropy Generation Minimization during Natural Convection within Porous Tilted Square Cavities

“…Natural convection is a phenomenon of heat transfer via fluid motion due to density difference, which is induced by the temperature gradient in a system. Analysis of natural convection flow has gained considerable attention among the researchers and engineers due to its wide practical applications such as food processing, solar collectors, chemical processes, nuclear reactors, phase change applications, and thermal energy storage. − …”