What is the temperature profile in 1D heat transfer(steady, no heat generation) and why is it linear? Prove.
Ans: The following figure shows a heat transfer through a plane wall,
The temperature profile in 1D heat transfer is linear. It is nothing but just a slope dT/dX.
For one-dimensional heat transfer, dT/dx can be replaced by,
Also, we know the heat diffusion conduction equation for steady, 1D equation without heat generation is given by
If this equation is integrated 2 times we get a temperature distribution through the wall.
The above equation is of the form
which is nothing but an equation of a straight line with slope m.
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