Is heat transfer, for a fixed time step, constant in transient problems?

Question

So to further explain question in the title, this is my thinking process behind it. I recently been doing some steady state heat transfer problems, most of them I solved with the same algorithm. I was just calculating thermalr resistance of a system and then based on temp difference, eventually calculated heat transfer rate.Then assuming that heat transfer rate is constant, I was able to calculate temperature distribution in the system.

Now I'm onto dealing with transient problems. I was thinking if I can apply the same assumption, so that at fixed time step, heat transfer is constant.I want to understand if it's applicable, because I thought of different algorithm for solving the problem.

Namely I wanted to treat each of the time steps of a problem as steady state one. Knowing temperatures at a boundary and thermal resistances, I would calculate temperature distribution at the next timestep, which will be an input for the same calculations for new timestep. Is it a valid assumption or did I miss something?

Answer 1

In steady state the temperature at each position i a system does not change so if you consider an element the heat flowing into the element is equal to the heat flowing out of the element and you can model this by introducing the idea of thermal resistance.

However in the transient state the temperature/state of an element might change and to effect the change there must be an import or export of heat and in that case one must introduce the idea of a thermal capacity for the element which then means one must include the specific heat capacity / specific latent heat.

The complex system which has a temperature gradient within it can sometimes be simplified to assuming that the temperature of the system is uniform and then one can model the system in a similar way to charging and discharging a capacitor in electrical circuits.

Have a look at Transient Heat Conduction for a description of doing this.
The more comprehensive Transient Heat Conduction might be consulted and One-Dimensional Transient Conduction illustrations as to how one might analyze systems numerically.