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A composite slab consists of two rectang...

A composite slab consists of two rectangular slabs of different materials, having coefficients of conductivity 2K and K. The two ends of the slabs are at temperatures `T_1` and `T_2` (where ` T_1 gt T_2` ). How will the rate of heat flow depend on a where 3a and a are the lengths of two slabs? Consider that the two slabs have equal thickness.

Text Solution

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Let the temperature of interface of two slabs be T. At steady state, rate of heat flow through the two slabs will be equal
` therefore (2KA (T_1 - T) )/(3a) = (KA(T- T_2) )/(a)`
` rArr 3/2 (T_1 - T) = T - T_2`
`2/3 T_1+T_2 = 2/3 T + T = (5T)/(3)`
` rArr (5T)/(3) = (2T_1 3T_2)/(3) `
` rArr T = (2T_1 + 3t_2)/(5)`
` therefore ` Rate of heat flow through slab of thickness 3a and coefficient of thermal conductivity 2K is
`Q_1 = (2KA)/(3a) [ T_2 - ((2T_1 - 3T_2))/(5) ]`
` = (4KA)/(3a) (T_2 - T_1)`
` therefore Q_1 prop 1/a `
The rate of heat flow varies inversely as a.
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Knowledge Check

  • A slab consists of two layers of different materials of the same thickness and having thermal conductivities K_(1) and K_(2) . The equivalent thermal conductivity of the slab is

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