As we saw before, if we look at transient heat transfer problems in dimensionless form, we get a dimensionless temperature, a dimensionless time, and the Biot number out. Not surprisingly, if we have a problem whereby the Bi is not small, we also get a dimensionless position (since spatial gradients do not disappear).
One of the most practical reasons for making our equation (and therefore our answers!) dimensionless is that our results are then general. That is, since the same dimensionless equation arises for many differing dimensional systems, we can use the SAME dimensionless answer for all of them!
One particularly useful side-effect of this is that people have tabulated results of dimensionless solutions for transient problems.....we can use these for many problems as long as we know three of the four dimensionless parameters defining our system!
This approach works equally well for heat or mass transfer problems!
Use Gurney-Lurie charts to solve heat and mass transfer problems
Let's look at an example...
A flat wall of brick which is 0.5 m thick and originally at 200K
has one side suddenly exposed to hot gas at 1200K. If the heat
transfer coefficient on the hot side is 7.38W/m2K and
the other face is perfectly insulated determine
A. The time it takes to raise the center to 600K
B. The temperature of the insulated side of the wall at this time.
The properties of the brick are as follows....k=1.125 W/mK; c=919 J/kgK; $\rho$=2310 kg/m3