A NEW COMPUTATIONAL METHOD FOR TRANSIENT HEAT CONDUCTION IN ARBITRARILY SHAPED REGIONS
A new computational method is presented for the solution to transient heat conduction problems in two dimensional regions of arbitrary shape. The procedure is based on an integral representation for the temperature in the
form of surface potential distributions. This reduces the usual partial differential equation problem to one described by a Volterra integral equation of the second kind for the surface potential "strength." As a result,
computations are performed only over the boundary of the region and the usual interior finite difference grid is unnecessary. Once the potential strength is determined, the temperature at any interior point may be obtained.
Alternate numerical schemes are developed which give the user a choice between computational speed or improved accuracy and results are shown for square and circular regions with prescribed boundary temperature. The integral
equation approach is in general applicable to three dimensional, multiply connected regions with convective boundary conditions.