Abstract
This paper presents a series solution for the local surface temperature history for a semi-infinite body heated only over a circular region. Inside this region the heat flux is constant with time and position while outside the circular area the surface is insulated. A number of approximate solutions are available in the literature. One exact solution is available but it is in the form of an integral with an infinite domain. The solution developed herein is much more convenient to use for all dimensionless times except the smallest. Extensive curves and tables are provided also. In addition to the surface solution there is a solution for certain interior locations also for ‘large’ times. The solution is important because it is a basic geometry in heat conduction and is frequently needed in connection with cylindrical bodies. The solution can be utilized as a building block for related finite geometries for time-variable heating and for symmetric spatially-varying heat flux cases. It can also be used in a promising new calculation method that is called the surface element method.
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