Conduction "what if" questions.... What is the Biot number (hL/k) is greater than 0.1 and I use the lumped capacitance method for analysis (i.e. there are temperature gradients in the "lump" and I have assumed they are absent). What effect does it have on the result? What is the largest number of non-homogeneities that can exist in a conduction solution?
Re: Conduction "what if" questions.... The Biot number is used to determine if the lumped capacitance method is a valid approximation of a transient problem that involves convection about a solid. When the Biot number is much less than 1, the resistance to conductive heat transfer within the solid is much less than the resistance to convective heat transfer accross the fluid boundary layer. Put another way, if the Biot number is much less than 1 then the temperature gradient across the solid is much less than the temperature gradient accross the fluid boundary layer. Given two temperature gradients, if one is much larger than the other then the smaller one can be assumed to have a negligeble effect on the system, and so it may be disregarded. To answer your question, if you use the lumped capacitance method for a system where the biot number is close to or higher than one, the solid your are analyzing will have a non-uniform temperature distribution in it. So if this is the case, the system will take longer to reach steady state than your calculation implies.