A metallic rod of radius R and thermal conductivity K is tightly filled into another hollow cylinder of inner radius R and outer radius $$2R$$ as shown in the figure. Material of the hollow cylinder has a thermal conductivity $$2K$$. Then equivalent thermal conductivity of the composite rod is

Question

Infinity Learn · Accepted Answer

$$R1$$ $$=$$ Thermal resistance of solid rod $$=$$ lK.π$$R2R2$$ $$=$$ thermal resistance of hollow cylinder $$=$$ $$=l2K$$.π$$2R2-R2=l6K$$$$π$$$$R2For$$ the composite rod, $$Re=lKe$$.π$$2R2=l4Ke$$$$π$$$$R2In$$ the composite rod, the solid rod and the cylinder are joined in parallel combination.∴$$1Re=1R1+1R2$$⇒$$4Ke$$$$π$$$$R2l=6K$$.π$$R2l+K$$$$π$$$$R2l$$⇒$$Ke=7K4$$

A metallic rod of radius R and thermal conductivity K is tightly filled into another hollow cylinder of inner radius R and outer radius 2R as shown in the figure. Material of the hollow cylinder has a thermal conductivity 2K. Then equivalent thermal conductivity of the composite rod is

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