Question

Find the value of the thermal resistance of the non-uniform cylindrical rod of thermal conductivity `K` and length I as shown in
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Answer 1

Consider a small element of width dx at a distance x from one end as shown in From similar triangles
`(r-a)/(x) =(b-a)/(r) rArrr =a+((b-a)/(l))x`
Thermal resistance of the cylinder is
`R =underset(0)overset(l)int(dx)/(Kpir^(2)) = (1)/(Kpi)underset(0)overset(l)int[a+((b-a)/(l))x]^(2-)dx`
`=(1)/(Kpi)[(a+((b-a)/(l))x)^(-1)/(-((b-a)/(l))]]_(0)^(l)`
`=(l)/(Kpi(a-b))[(1)/(b)-(1)/(a)]=(l)/(Kpiab)`
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