This simple heat transfer model shows the temperature gradient through a block of material that is (perfectly) insulated on four sides and is exposed to 450 Kelvin on the top and 200 Kelvin on the bottom.  As one might expect, they temperature varies linearly through the material in the z direction only.

In this variation on the previous example, the insulation around the block is altered such that a band of material is exposed to 500 Kelvin.  Unlike the linear variation that was seen in the first example, this block has a varying gradient in all three dimensions, making it very difficult to solve analytically.  By testing the model on the solvable problem above, we can say with confidence that this FEA solution is correct here.

This simulation moves beyond a rectilinear geometry.  This hollow sphere has an inner temperature of 500 Kelvin and along the outer surface, a heat flux is applied.  The steady state solution to the problem is is visualized here.

This problem here was to build a time-dependent, thermal model of an egg to determine the perfect cooking time for a soft boil.  Using empirical data from peer-reviewed sources on the density, heat capacity, heat conductivity, geometry, and volume of the shell, albumen (whites), and yolk, the model to the left was constructed.  It begins with the egg at room temperature throughout, 295.15 Kelvin, and boiling water on the outside at 373.15 Kelvin.  This model suggests that the whites will reach the temperature of cooking, about 338 Kelvin, after about 6 minutes.  Empirical experimentation, with small sample size and low resolution, showed that the correct time for soft-boiling was closer to 5 minutes.  There is also a high degree of variability between eggs, especially with regard to the proportions of each component.  To further refine the model would require more testing and better measurement.