# HELP! Heat Transfer Problem

1. Dec 8, 2009

### Seraph042

I'm trying to determine the time required to heat up one side of an insulated wall of length L if there's a known constant heat flux at the non-insulated end of the wall. The wall is at uniform temperature before the heat flux is applied.

I have been working this problem for a few days and I am under pressure to figure this out by tomorrow, so I reallly need some help.

All of the wall material properties are known (conductivity, specific heat, thermal diffusivity, etc)

My Heat Transfer book (and my internet searches, for that matter) have turned up inconclusive for 1-d transient heat conduction with a constant heat flux; the equation I have uses temperatures.

$$\Theta$$(x,t)=$$\frac{T(x,t)-T_{\infty}}{T_{i}-T_{\infty}}$$=A$$_{1}$$*exp(-$$\lambda^{2}_{1}*\tau$$)*cos(x*$$\lambda_{1}/L$$)

Where A1 and lambda_1 are constants based no the Biot number, and tau is the time constant