Square Plate subject to isothermal boundary conditions

A square plate of unit thickness, size 1m, as shown in next figure is subject to isothermal boundary conditions of 373 ºK on all sides exept the top side, which is subject to 773 ºK. The thermal conductivity of the material is constant and equal to 10 W/mºK. The project used for this simulation can be found here.

The square domain is divided into (2x100)x(2x100) tria elements, as shown in next figure.

The following figure shows a zoomed picture of the mesh, where the tria elements can be clearly observed.

The analytical solution to this prblem is given by Holman, JP 1989 Heat Transfer, McGraw-Hill, Singapore:

Being w the width and H the height of the plate, Ttop the temperature at the top side and Tside the temperature at the other sides of the plate.

Therefore, the expected temperature at the center of the plate would be T(0.5, 0.5) = 473.11K (200.11ºC).

The following figure shows the contour of the temperature obtained after the steady state has been reached. The temperature varies between 273K (100ºC) and 773K (500ºC) at intervals of 13.677 ºK.

The temperature obtained at the center of the plate (x=0.5, y=0.5) has been 472.723K (199.723ªC).