Transient Finite Difference Boundary Conditions
Transient Finite Difference Boundary Conditions
(OP)
Hi everyone,
I am trying to find the temperature through an object of length L surrounded by air at one end and enclosed air at a different temperature on the other end. I am only considering one dimensional heat transfer through the object in the x direction. At x(0) I have the temperature increasing linearly to illustrate changing temperature throughout the year. At x(L) however I have a different case. I want to have T(L) initially at 273k (0 degrees Celsius), and calculate temperatures at each timestep based on convection into the surrounding enclosed air.
My one problem is that I don't know how to calculate the change in temperature of the enclosed air.
So far I have thought about somehow calculating a heat transfer rate "q" based on q=rho*V*A*dT/dt and q=hA(Tin-T(L)). However in order to use those equations I would need to know the change in temperature of the air for each timestep.
Does anyone have any advice on how to solve for that inside air temperature?
Also if anyone needs anything clarified I can probably draw up a diagram to show you.
I am trying to find the temperature through an object of length L surrounded by air at one end and enclosed air at a different temperature on the other end. I am only considering one dimensional heat transfer through the object in the x direction. At x(0) I have the temperature increasing linearly to illustrate changing temperature throughout the year. At x(L) however I have a different case. I want to have T(L) initially at 273k (0 degrees Celsius), and calculate temperatures at each timestep based on convection into the surrounding enclosed air.
My one problem is that I don't know how to calculate the change in temperature of the enclosed air.
So far I have thought about somehow calculating a heat transfer rate "q" based on q=rho*V*A*dT/dt and q=hA(Tin-T(L)). However in order to use those equations I would need to know the change in temperature of the air for each timestep.
Does anyone have any advice on how to solve for that inside air temperature?
Also if anyone needs anything clarified I can probably draw up a diagram to show you.





RE: Transient Finite Difference Boundary Conditions
That comes from the removal(addition) of heat during the previous time step
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RE: Transient Finite Difference Boundary Conditions
One point is unclear to me in your description: I understand that the sides of the object (a bar I assume) are adiabatic and that the only heat loss is from the front area at x=L, correct? If so, it is a very simple problem and finite differences are not necessary to solve.
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RE: Transient Finite Difference Boundary Conditions
My question is how can I calculate the temperature of that enclosed air based on the volume, surface area etc.
RE: Transient Finite Difference Boundary Conditions
And, sorry, I was wrong in saying you don't need finite differences for this problem: only the final steady state solution can be calculated by formula.
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RE: Transient Finite Difference Boundary Conditions
RE: Transient Finite Difference Boundary Conditions
Not an easy problem: a realistic solution requires an assumption on the convective behavior of air in the enclosed space (may vary a lot depending on shape and dimensions).
IMHO only an important research programme would justify a detailed analysis as compared to a test: I recall of such calculations done to estimate the heat loss through the penetrations of the cover of a nuclear reactor.
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads