A cylinder of radius R made of material of conductivity $$K1$$ is surrounded by a cylindrical shell of internal radius R and outer radius $$2R$$ made of material of conductivity $$K2$$, the two ends of the system are kept at two different temperatures. If there is no loss of heat from the surface, the effective conductivity of the system is

Question

A cylinder of radius R made of material of conductivity $$K1$$  is surrounded by a cylindrical shell of internal radius R and outer radius $$2R$$ made of material of conductivity  $$K2$$, the two ends of the system are kept at two different temperatures. If there is no loss of heat from the surface, the effective conductivity of the system is

Infinity Learn · Accepted Answer

Both are parallelthe effective coefficient of thermal conductivity for a parallel combination of conductors is $$KParallel=K1A1+K2A2A1+A2$$ base area of inner cylinder $$isA1=$$π$$R2area$$ of outer cylinder is $$A2=$$π$$(2R)2-$$π$$R2A2=3$$$$π$$$$R2$$ $$KP=K1$$.π$$R2+K2.3$$$$π$$$$R2$$$$π$$$$R2+3$$$$π$$$$R2$$ $$Keffective=KParallel=K1+3K24$$

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