Transient conductive heat flow using finite element method

[rgh107]

I'm looking at project investigating thermal dissiplation around circular and square concrete piles, resting in a homogeneous material (soil) using two-dimensional finite element analysis.

I'm applying a transient thermal loading cycle to the centre of the concrete pile over a 7-day test period. At the end of the test cycle, I am able to plot a horizontal temperature gradient in the soil surrounding the pile. However, I was wondering if there is a means by which I can approximate the heat flux/heat flux density from the temperature graident, given the thermal conductivity, heat capacity and material density?

The main problem that I have is that magnitude of the applied load is varied between 12-25^{o}C over the course of the test cycle.

Any advice would be greatly appreciated. . .

[Redbelly98]

I'm surprised your finite element software doesn't do this, but isn't the heat flux just equal to
(thermal conductivity) x (temperature gradient)
?

Or is there convection involved? That would complicate the equation.

[rgh107]

My initial thought was that I could simply use the basic heat equation by taking the average gradient. The problem is that the temperature gradient is nonlinear.

Furthermore, does the equation not only relate to steady state conditions?

Anyway, I am dealing purely with conduction if that helps.

I've attached a typical temperature gradient from my FE program.

[Redbelly98]

Furthermore, does the equation not only relate to steady state conditions?

No, it applies for transient conditions too.