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   Together with the numerical methods this part serves as a fundament for making the mathematical model of operation for electro-resistance 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:

heat transfer theory - conductivity

heat transfer theory - convection

heat transfer theory - radiation

heat transfer theory - mixed<

heat transfer theory - indirect heating

heat transfer theory - transient process




heat transfer modeling - demo movie

subdomain
isosurface

heat transfer modeling - demo movie

slice
isosurface

heat transfer modeling - demo movie

heat transfer modeling - demo movie

heat transfer modeling - demo movie

heat transfer modeling - demo movie

2D Non-Isothermal
2D Non-Isothermal
2D Non-Isothermal
2D Non-Isothermal





Heat Transfer
Demo Movies


CONDUCTION

constant temperature:


constant heat flux:



RADIATION

reflector:



CONVECTION

Non-Isothermal 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
demo 1 demo 2 demo 3 demo 4 demo 5 demo 6
demo 7 demo 8 demo 9 demo 10 demo 11 demo 12
demo 13 demo 14 demo 15 demo 16 demo 17 demo 18
demo 19 demo 20 demo 21 demo 22 demo 23 demo 24


The Heat Equation



    The mathematical model for heat transfer by conduction is the heat equation:

heat transfer - theory

heat transfer - theory

    Heat flux with surface-to-ambient radiation:

heat transfer - theory

    The radiation heat flux term is:

heat transfer - theory


    Heat flux with surface-to-surface radiation:

heat transfer - theory


    The radiation heat flux term is:

heat transfer - theory


surface emissivity - surface emissivity;
Stefan-Boltzmann constant - Stefan-Boltzmann constant;
Tamb - ambient radiation temperature;
G - surface irradiation;


   
Example: conductive and radiation



radiation modeling - example

radiation modeling - example


    Equation Conduction and Convection

heat transfer theory


heat transfer theory

Example: Convective and Conductive



heat transfer Navier-Stokes


heat transfer Navier-Stokes


heat transfer Navier-Stokes


    Surface-to-surface radiation includes radiation from both the ambient and other surfaces. A generalized equation for the irradiative flux is:

surface-to-surface radiation theory



surface-to-surface radiation example


surface-to-surface radiation example


Non-Isothermal Heat Equation



Non-Isothermal theory


Non-Isothermal theory - Dynamic viscosity;
k - Dilatational viscosity;
Non-Isothermal theory - Density;
u - Velocity field;
p - Pressure;
F - Volume force field such as gravity;


Navier-Stokes model example

Navier-Stokes model example

Navier-Stokes model example

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