temperature distribution in metal rod when temp is fixed at both ends 1

[1964693]

Folks,

Where can I find a plot of temp distribution in a metal rod when temperature is fixed at T1 at one end and T2 at the other.

 

[StoneCold]

1964693
Based on the information you have given us you can just plot in excel T1,x1 and T2,x2 where x is the distance from one point to the other. You should get a line.
I am sure what you are asking is more complicated than that so you have to give us more information. How are the temperatures held on the ends? What is the rod made of?
Is it a transient situation or steady state? What is the purpose of the rod? Anything else pertinant?

StoneCold

 

[ko99]

Temp distribution will be a straight line IF convection and radiation are negligible.

I suggest you plug your data (dimensions, materials, and environment) into the basic textbook formulas to estimate the relative contributions of conduction, convection, and radiation. This won't give you a temperature distribution, but it will give you a very good idea of what will be required to solve your problem.

ko (

http://www.ecooling.biz)

 

[prex]

Assuming this is a classical problem of a fin with constant section, the solution is derived from the general solution:
T=C₁e^nx+C₂e^-nx
as (hope to no mistake):
C₁=(T₂-T₁e^-nL)/2sinh(nL)
C₂=(T₁e^nL-T₂)/2sinh(nL)
where the symbols have the known meanings, and:
T(0)=T₁
T(L)=T₂
T_amb=0
c=[√](hP/kA)

prex

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