Quasi steady state heat flow

[corus]

In dynamic situations where an object is moving, quasi steady state heat transfer can occur. An example of this is an object moving past a stationary heat source. Normally a couple temperature-displacement transient analysis has to be used to obtain a solution.
Can an equation be used to desribe this quasi steady state temperature distribution, similar to the normal steady state heat flow equation div(k.div(T))=0 but which doesn't involve a large scale transient analysis?

corus

 

[IRstuff]

I wouldn't think so, unless you're dealing with some sort of semi-infinite object. In the example you give, the quasi-steady state is actually akin to the convolution of the impulse response with some shape. So unless that shape is sufficiently long and uniform enough, you'd still have transient problem.

Even in the extreme case, you'd still need to find the transient solution and convolve it to get the quasi-steady state

TTFN

 

[corus]

Thanks IRSTuff but I've since found that if dT/dt in the transient heat flow equation is replaced by (dx/dt).(dT/dx) or equivalently v.dT/dx where v is the speed of the object moving in the x direction then a steady state equation for heat flow is made that no longer involves time and can presumably be solved in a single step. The transient heat flow equation is now div^2(T))=v/a.(dT/dx) where a is k/pc and v is the speed. How can this be solved using the finite element method?

corus