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Together with the
numerical methods this part serves as a fundament for making the mathematical
model of operation for electroresistance furnaces. The basic laws of thermal transfer are discussed as well
as the deduction and transformation of the equations into a kind suitable for application in the software products.
On this basis the transition processes are described which take place in the furnaces and the mechanisms of making
the systems of differential equation are determined:
2D NonIsothermal
constant temperature: constant heat flux: RADIATION
reflector: CONVECTION
NonIsothermal Heat: CONDUCTION + RADIATION + CONVECTION
constant temperature: constant heat flux: CONVECTION + RADIATION
Heat Transfer Physical Process Modeling LOGO
LINKS:
Created by Physical Process Modeling 
Heat Transfer Demo Process
The Heat EquationThe mathematical model for heat transfer by conduction is the heat equation: Heat flux with surfacetoambient radiation: Heat flux with surfacetosurface radiation: The radiation heat flux term is:  surface emissivity;  StefanBoltzmann constant; T_{amb}  ambient radiation temperature; G  surface irradiation; Example: conductive and radiation Equation – Conduction and Convection Example: Convective and Conductive
Surfacetosurface radiation includes radiation from both the ambient and other surfaces.
A generalized equation for the irradiative flux is:
NonIsothermal Heat Equation  Dynamic viscosity; k  Dilatational viscosity;  Density; u  Velocity field; p  Pressure; F  Volume force field such as gravity; 
