Journal of Applied Physics · 1959 · 53 citations · 2 references
EngineeringChemical EngineeringPhysicsHeat TransferThermodynamicsTransport PhenomenaBoltzmann Transport EquationHeat ConductionHeat Transfer AnalysisHeat Transfer In FluidsHeat Transfer ModelingTransient Heat TransferChemisorptionHeat Conduction EquationHeat Transfer Boundary ConditionsNonlinear Heat ConductionPhysical AdsorptionStefan-boltzmann LawSurface TemperatureVolterra Integral Equations
A study has been made of the time-dependent heat conduction in a semi-infinite medium subject to a boundary condition which can involve the temperature in a nonlinear manner. A formulation for the determination of the surface temperature, which is often of greatest physical interest, leads to a nonlinear Volterra integral equation. A simple iterative solution method, with an accuracy suitable for many practical purposes is presented. As an example, the problem of the time-dependent surface temperature of a body receiving heat according to the Stefan-Boltzmann law is treated. The analysis is also applicable to physical adsorption or chemisorption processes which occur at the boundary.
2