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A cylinder of radius R, made up of a mat...

A cylinder of radius R, made up of a material (thermal conductivity `k_1`) is surrounded by a cylindrical sheet of inner radius R and outer radius 2R (thermal conductivity `k_2`). The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. Calculate the effective thermal conductivity of the system.

Text Solution

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The correct Answer is:
`K_1+3K_2`
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A cylinder of radius R made of a material of thermal conductivity K_(1) is surrounded by cylindrical shell of inner radius R and outer radius 2R made of a material of thermal con-ductivity K_(2) The two ends of the combined system are maintained at two differnet tem-peratures There is no loss of heat across the cylindrical surface and system is in steady state What is the effective thermal conductivity of the system .

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and oputer radius 2R. The thermal conductivity of the material of the inner cylinder si k_(1) and that of the outer cylinder is K_(2) ,Assumming no loss of heat , the effective thermal conductivity of the system for heat flowing along the length of the cylionder is :

Knowledge Check

  • A cylinder of radius R made of a material of thermal conductivity K_1 is surrounded by a cylinderical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K_2 . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effictive thermal conductivity of the system is

    A
    `K_1+K_2`
    B
    `K_1K_2//(K_1+K_2)`
    C
    `(K_1+3K_2)//4`
    D
    `(3K_1+3K_2)//4`

  • A cylinder of radius R made of a material of thermal conductivity K_1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K_2 . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is (a) K_1 + K_2 (b) K_1K_2//(K_1+K_2) (c ) (K_1 + 3K_2)//4 (d) (3K_1 + K_2)//4 .

    A
    `K_1 + K_2`
    B
    `(K_1K_2)/(K_1+K_2)`
    C
    `(K_1 + 3K_2)/4`
    D
    `(3K_1 + K_2)/4`

  • A cylinder of radius R made of material of thermal conductivity K_(1) is surrounded by a cylindrical shell of inner radius R and outer radius 3R made of a material of thermal conductivity K_(2) . The two ends of the combined system are maintained at two different temperatures. What is the effective thermal conductivity of the system ?

    A
    `K_(1)+K_(2)`
    B
    `(K_(1)+8K_(2))/(9)`
    C
    `(K_(1)K_(2))/(K_(1)+K_(2))`
    D
    `(8K_(1)+K_(2))/(9)`

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