TWO DIMENSIONAL ANALYSIS OF TRANSIENT HEAT CONDUCTION IN A SECTOR OF A HOLLOW CIRCULAR CYLINDER.
Final rept., Jan-Aug 63,
MARTIN CO ORLANDO FLA
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An exact mathematical formulation was sought of transient heat conduction to reduce the amount of idealization required by currently employed finite difference techniques. A two-dimensional analysis is developed beginning with the differential equations for conduction of heat in a segment of a hollow cylinder in polar coordinates. An exact solution with constant thermal diffusivity and conditions of prescribed surface temperature, convection, and direct heat input is written in an infinite series of Bessel and trigonometric functions. Provisions are made for incorporating a coordinate varying, arbitrary, initial temperature distribution as well as coordinate and time varying arbitrary surface conditions. A solution that incorporates the effect of temperature dependent thermophysical properties is developed by combining the exact solution with a finite difference approach. The solution has been programmed for an IBM 7090 or 7094 digital computer. Author