An insulated rod of length has its ends A and B maintained at O^ C and 100 degrees * C respectively until steady state conditions prevailFind the steady -state temperature of the rod
Let us remind the heat transfer equation :
as the problem has only one spatial dimension.
The steady state corresponds to the condition . Using this gives us
And the general solution of such equation is given by
Let us place the origin at the point and let us denote the rod's length by . Then we have :
Therefore, the temperature is given by
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