- #1

MexChemE

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- 55

First question: Incropera's book introduces energy balances on a surface. The authors mention accumulation and generation terms are not accounted for in a surface balance, because they are volumetric effects; fair enough. But then they say surface balances apply for both steady and transient state, but transient state implies accumulation, negating the last statement. I know the temperature of a surface may change in time if we have a transient state process, so I don't get why they say accumulation terms won't be taken into account.

Next: When using the heat equation to model heat conduction in a solid rod with volumetric heat generation, BSL used the following boundary condition for heat flux at the center of the rod:

[tex]q_r |_{r=0} = q_0[/tex]

"The radial heat flux at the center of the rod is equal to some finite quantity." This was done in order to avoid getting an infinite heat flux at the center, because of the mathematics of radial heat conduction in cylindrical coordinates:

[tex]q_r = \frac{S_e r}{2} + \frac{C_1}{r}[/tex]

Now, in a problem from Incropera's, I had to define boundary conditions for the exact same physical situation (including electric heat generation). Naturally, taking the methods from BSL as dogmas, I set my boundary condition for r = 0 as the heat flux being finite at that point, however, the solutions manual states the heat flux at that point is zero. My thoughts on this are: BSL just stablished the condition it used in order to avoid a mathematical error (division by zero), after all, a heat flux equal to zero is also a finite heat flux, is it not? The way I'm interpretting the physics is that for both cases, the heat flux is zero at the center of the rod. It should be, anyway, as the temperature is at a maximum at the center of the rod.

Last: In that same problem, the conducting rod is covered by a non-conducting cladding. Again, I had to define a boundary condition for the point where both materials meet. I was going for the boundary condition where the heat flux at the point where both materials meet is equal for both regions. However, the solutions manual used a boundary condition where the temperature of the rod and the temperature of the cladding are equal where they meet, argumenting thermal equilibrium. It is a logical answer, but I know temperature may not always be continuous among two different contacting materials. So, apart from the case when there are no air spaces at the interface, in which situations can we say temperature is continous?

That would be all for now. Thanks in advance for any input!