Verification of ANSYS and Matlab Heat Conduction Results Using an Intrinsically-Verified Exact Analytical Solution

A two-dimensional transient thermal conduction problem is examined and numerical solutions to the problem generated by ANSYS and Matlab, employing the finite element (FE) method, are compared against an 'intrinsically' verified analytical solution. Various grid densities and time-step combinations are used in the numerical solutions, including some as recommended by default in the ANSYS software, including coarse, medium and fine spatial grids. The transient temperature solutions from the analytical and numerical schemes are compared at four specific locations on the body and time-dependent error curves are generated for each point. Additionally, tabular values of each solution are presented for a more detailed comparison. Two different test cases are examined for the various numerical solutions using selected grid densities. The first case involves uniform constant heating on a portion of one surface for a long duration, up to a dimensionless time of 30. The second test case still involves uniform constant heating but for a dimensionless time of one, immediately followed by an insulated condition on that same surface for another duration of one dimensionless time unit. Although the errors at large times for both ANSYS and Matlab are extremely small, the errors found within the short-duration test are more significant, in particular when the heating is suddenly set 'on'. Surprisingly, very small errors occur when the heating is suddenly set 'off'.