Noncartesian coordinates. Temperature dependent material properties

4 Noncartesian coordinates. Temperature dependent material properties 

In the following we will discuss the difference method with consideration for temperature dependent material properties as well as for cylindrical and spherical coordinates, whereby geometric one-dimensional heat flow is assumed in the radial direction. The decisive differential equation for the temperature field is then 

The establishment of difference equations is based on the discretisation of the self-adjoint differential operator 

We will now discuss this and derive the difference equations for different coordinates systems with and without consideration of the temperature dependence of the properties of the material. 

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