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Edited: Jun 26, 2022

# What is the temperature profile in 1D heat transfer(steady, no heat generation) and why is it linear? Prove.

What is the temperature profile in 1D heat transfer(steady, no heat generation) and why is it linear? Prove.

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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.