A cylinder of radius r and thermal conductivity $$K1$$ is surrounded by a cylinder shell of internal radius r and outer radius $$3r$$ whose thermal conductivity is $$K2$$. There is no loss of heat from the surface of the cylinder when the ends of the combined system are maintained at temperatures $$T1$$ and $$T2$$. The effective thermal conductivity of the system under steady state is

Question

A cylinder of radius r and thermal conductivity $$K1$$  is surrounded by a cylinder shell of internal radius r and outer radius $$3r$$ whose thermal conductivity is  $$K2$$. There is no loss of heat from the surface of the cylinder when the ends of the combined system are maintained at temperatures  $$T1$$ and  $$T2$$. The effective thermal conductivity of the system under steady state is

Infinity Learn · Accepted Answer

the cylinders are In parallel $$KParallel=K1A1+K2A2A1+A2---(1)$$, here K is coefficient of thermal conductivity,                                                                A is area of cross section area of cross section inner cylinder is $$A1=$$π$$r2$$, here r $$=$$ radius  area of cross section outer cylinder is $$A2=9$$$$π$$$$r2-$$π$$r2$$  $$A2=8$$$$π$$$$r2$$ substitute given values in $$eqn(1)$$ $$KP=K1$$$$π$$$$r2+K2.8$$$$π$$$$r2$$$$π$$$$r2+8$$$$π$$$$r2$$ $$KParallel=K1+8K29$$

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