1. The problem statement, all variables and given/known data Hi, I've got a civ engineering problem relating to conductive heat flow using finite element analysis. I'm investigating the dissipation of heat from square and circular pile foundations. I'm applying a thermal load to the centre of the concrete pile which induces heat flow through the surrounding soil [homogeneous material]. At the end of the test cycle I am able to plot a temperature gradient in the horizontal direction through the soil. I was wondering, is there a way by which I can approximate the heat flow into the soil over the test period from the temperature gradient in terms of heat flux density? It should be noted that the finite element model is dependent on thermal conductivity, heat capacity and density. The key problem I have is that I'm applying cyclic loading by which the magnitude of the applied thermal load is constantly varied over the course of the test period. It should be noted that due to the nature of the problem, I am seeking only approximate solutions as a means of conducting a simple comparison with different model specifications. Any help would be most appreciated. . . 2. Relevant equations ? 3. The attempt at a solution I've attempted obtaining solutions using the basic heat equation. However, this assumed steady-state conditions.