Q. 335.0( 1 Vote )

Find the rate of heat flow through a cross-section of the rod shown in figure (θ2> θ1). Thermal conductivity of the material of the rod is K.



Answer :

Let’s redraw the diagram



From the above diagram we can say that ΔABE is similar to ΔACD.


By the property of similar triangles-


=


x = r1 + (r2 – r1 )


Lets assume-


a =


r = ax + r1 (1)


Thermal resistance is given by –


dR =


Now area


dR =


dR =


=


Solving above integral


R =


R =



Rate of heat flow =


q = Kπr1r2


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