Like Stress analysis, SOLIDWORKS thermal analysis is validated by independent bodies against theoretical math.
In this blog I will explain one of these studies.
A square plat of dimensions (4m x 4m x 0.1m) has one edge maintained at 100°C. The temperature at the other 3 edges are 0°C. Find the temperature in the centre of the plate.
Model half of the plate as there is symmetry running through the model. Add a split line to make the centre of the plate easily identifiable.
Apply a 100°C to the left-hand edge and 0°C to the bottom and right-hand edges and run the study. Use the results tools to probe the vertex at the centre of the model.
This gives a value of 25°C
Using Hand Calculations
This can be estimated mathematically by splitting the face into nodes.
We can then estimate the temperature at each node by the sum of the surrounding nodes divided by the number of nodes.
These can then be simplified and put into matrix form Ax=b
We then inverse Matrix A giving A-1
A-1b gives the values for the x points
This gives the Central node x5 a value of 25°C
As you can see SOLIDWORKS is much faster for working out temperature at a given point. This is because SOLIDWORKS is capable of meshing to a high density and processors are excellent at doing matrices work. This example uses just a 2D surface, when working on complex 3D dimensional models hand calculations can be massively complex and time consuming. Having SOLIDWORKS complete studies in a margin of the time with higher accuracy becomes a no brainer.