Approved for public release; distribution is unlimited / A FORTRAN 77 computer code employing an adaptation of the finite differencing algorithm proposed by Brian was developed for the solution of transient heat conduction problems in cylindrical geometries. Validation of code was accomplished by comparison with an ana­lytic solution derived for a model with symmetric, linear boundary conditions. Accuracy of results for asymmetric and non-linear boundary conditions was determined by comparison with a similarly vali­dated code employing the explicit method. Code effectiveness was then demonstrated by conducting a transient temperature analysis for a simulated earth-orbiting satellite. Brian's method demonstrated unconditional stability with associated significant reductions in execu­tion time compared to the explicit method. The effects of discretization error on the accuracy of results require further investigation. / http://archive.org/details/applicationofbri00hein / Lieutenant Commander, United States Navy