Journal of Heat Transfer · 1959 · 15 citations · 0 references
EngineeringMechanical EngineeringPhysicsComputational Heat TransferHeat TransferThermodynamicsHeat ConductionHeat Transfer AnalysisHeat Transfer FundamentalsHeat Transfer In FluidsHeat Transfer ModelingTransient Heat TransferElliptical StructureGeneral Heat Conduction EquationHeat Conduction EquationHeat EquationSystem ZerosTransient Heat ConductionTransient Heat Transfer AnalysisZeros
In 1945, N. W. McLachlan published the equations governing the problem of heat conduction in a long elliptical cylinder, including the solution for the case of a cylinder with a uniform initial temperature, subject to a sudden temperature change at the outer surface of the cylinder. This paper describes the numerical evaluation of McLachlan’s solution by the use of a digital computer and includes a table of the necessary zeros of the modified Mathieu functions. Tables of the temperatures in cylinders with eccentricities of 0.6, 0.7, 0.8, and 0.9 are given.