Analysis of the heat transfer characteristics of an emergent jet



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In this investigation a mathematical model is developed to describe the heat-transfer characteristics of a hot jet emerging into a surrounding coolant. A stable, one-dimensional jet of constant efflux velocity is analyzed, with a constant (average) heat-transfer coefficient on the sides and leading surface of the jet. The analysis begins with the development of a suitable governing differential equation which adequately describes the physical system. The governing equation is then solved using Laplace transform methods for the temperature within the jet as a function of axial distance and time. Computational aspects of the solution are discussed, and mathematical proofs are presented to eliminate machine computational problems for large times. Finally, a computer program is presented which is used to vary the parameters governing the heat-transfer process and to determine the degree of influence of each. Important parameters include heat-transfer coefficient on the jet sides and leading edge, jet radius, and thermal diffusivity. The results illustrate how cooling rates increase with higher heat-transfer coefficients, and how jets of small radius cool more rapidly than large jets. Increases in thermal diffusivity cause more rapid cooling. The effect of variations in jet velocity was not known prior to this investigation, and was found to be insignificant at velocities from 1 to 1000 fps for any given average heat-transfer coefficient, although it is known that the value of the heat-transfer coefficient itself depends largely on efflux velocity. Another result which could not be judged accurately before this work was done is the strong influence of the heat-transfer coefficient at the leading surface. The results show that a significant temperature drop occurs very near the leading edge for reasonable values of the end-heat-transfer coefficient.