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Steady-State Thermal Analysis

1,011 bytes added, 00:43, 17 June 2018
where &Omega; is the boundary surface and f(<b>r</b>) is a function.
 
== The Analogy between Thermal and Electrostatic Equations ==
 
Let us now compare the steady-state thermal Poisson equation to the electrostatic Poisson equation:
 
<math> \nabla^2 T(\mathbf{r}) = - \frac{w(\mathbf{r})}{k} \quad \Rightarrow \quad \nabla^2 \Phi(\mathbf{r}) = -\frac{\rho(\mathbf{r})}{\epsilon} </math>
 
 
 
It is important to note that there is a one-to-one correspondence between electrostatic and thermal simulation entities:
 
{| class="wikitable"
|-
! scope="col"| Electrostatic Item
! scope="col"| Corresponding Thermal Item
|-
| style="width:200px;" | Electric Scalar Potential
| style="width:200px;" | Temperature
|-
| style="width:200px;" | Electric Field
| style="width:200px;" | Heat Flux Density
|-
| style="width:200px;" | Perfect Electric Conductor
| style="width:200px;" | Perfect Thermal Conductor
|-
| style="width:200px;" | Dielectric Material
| style="width:200px;" | Insulator Material
|-
| style="width:200px;" | Volume Charge
| style="width:200px;" | Volume Heat Source
|}
 
 
 
== The Finite Difference Technique ==
Kazem Sabet
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