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The temperature of the two outer surface...

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x respectively. Temperatures on the opposite faces of composite slab are `T_(1) and T_(2)` where `T_(2)gtT_(1)`, as shown in fig. what is the rate of flow of heat through the slab in a steady state?

Text Solution

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Let T be the temperature of the common face of the composite slab of two materails. In the steady state, the rates of flow of heat through the two slabs will be same i.e.,
`(Delta Q)/(Delta t) =(KA(T_(2)-T))/(x) =( 2KA(T-T_(1)))/(4x0`
or `T_(2) -T =(T-T_(1))/(2) or T = (2T_(2)+T_(1))/(3)`
`:. (Delta Q)/(Delta t) = (KA)/(x) [T_(2)-(2T_(2)+T_(1))/(3)] = (KA)/(3x) [T_(2)-T_(1)]`.
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Knowledge Check

  • The temperature of the two outer surfaces of a composite slab consisting of two materials having coefficient of thermal conductivity K and 2K and thickness x and 4x respectively are T_2 and T_1(T_2gtT_1) . The rate of heat transfer through the slab in steady state is ((AK(T_2 -T_1))/x)f . where, f is equal to .

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  • The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficient of thermal conductivity K and 2K and thickness x and 4x, respectively are T_2 and T_1(T_2 gt T_1) . The rate of heat transfer through the slab, in a steady state is ((A(T_2-T_1)K)/x)f , with f equals to

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