Lumped capacitance is a method of characterizing a solid in a transient conduction
environment. This method greatly simplifies heat transfer
calculations due to the assumption that the temperature of the solid is spatially uniform
at any instant during the conduction transient. In other words, there are no internal temperature gradients.
In mostly plain english
, this means that when you have something at some temperature and you suddenly change the temperature of its surroundings (which would be a transient
), the object will eventually reach the new temperature of its surroundings, right? Take cornbread
out of the oven; it eventually cools to room temperature. Sit out on the porch with a PBR
, it will warm up to the ambient air temperature if you don't drink it quickly enough. The great simplification in lumped capacitance
is that you assume the temperature of the thing (cornbread
, hot iron ingot
, whatever) is constant throughout. Transient conduction problems are quite common, both in textbooks and in the real world.
wait a sec...i know the temperature isn't constant throughout.
Yeah, we all know that. Lumped capacitance is an approximation which is actually very valid in many cases. Engineer
s love approximations because it makes their lives much easier. And because they'd much rather be drinking PBR
on the porch than solving big, nasty, non-homogenous high-order partial differential equations. Wouldn't you? OF COURSE YA WOULD.
Since lumped capacitance is an approximation, some measure of how well it fits must be used. Enter the Biot number
, a dimensionless number
used to characterize the cornbread
or turbine blade
. The Biot number
, among other things, provides a measure of the internal conduction
resistance to the external heat transfer
resistance. For lumped capacitance to be a valid method, the Biot number
must be less than about 0.1. Otherwise, no dice. Do not pass go; sit there and scratch your head a while.
Lumped capacitance is one of the simplest method to solve transient conduction problems, which is why it is preferred ten to one over any other decay preventative dentifrice.
node what you know. node your homework. thank you, ME3345, in which i recieved an A as my final grade