Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid

Abstract A method has been developed for determining the streamwise variation of the temperature of a moving sheet in the presence of a co-flowing fluid. The solution does not depend on any material property of the sheet, its velocity, or its thickness. The solution is also independent of the properties of the fluid aside from the Prandtl number. Furthermore, the actual velocities of the sheet and the fluid need not be specified, but only their ratio is required. In the development of the method, a large knowledge base was first created by solving the differential equations for mass, momentum, and energy. The tabulated knowledge base served as input to a purely algebraic procedure whose end result is the streamwise variation of the sheet temperature. The procedure is iterative but requires no more than a least-squares curve-fitting capability. The iterative procedure is robust in that the converged result is independent of the initial iterant. It is also self correcting in the presence of an inadvertent error. Another method for determining the streamwise temperature variation, the relative-velocity model, was also investigated, and its accuracy assessed.

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