On Problems of Heat Conduction in a Compressible Fluid

Citation

Wu, Theodore Yao-tsu (1952) On Problems of Heat Conduction in a Compressible Fluid. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/G8DW-K988. https://resolver.caltech.edu/CaltechETD:etd-06032004-135328

Abstract

The present work starts with a study of heat conduction in a non-viscous compressible fluid based on a linearized theory which is similar to that used in the theory of sound. Important features of exact equations of motion and their corresponding linearized equations are studied briefly. For this linear system, which preserves many of the features of the original non-linear system, the fundamental solutions are found and discussed. The additional role played by viscosity in the heat conduction problem is then investigated. The fundamental solutions for this compressible, viscous, heat-conducting flow problem are found and compared with the non-viscous case. The problem of heat conduction in a two-dimensional stationary flow of a viscous compressible fluid is further studied by finding the fundamental solutions and discussing the result in some detail. As an example proposed to show how a superposition of these fundamental solutions can be used to solve a boundary value problem, the problem of the anemometry of a heated flat plate is solved for both large and small values of the Reynolds number. The result obtained herein is discussed and compared with some existing theories and experiments. The causes of the discrepancy resulting from this linearized theory are briefly explained.

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