Two walls of thickness in the ratio 1:3 and thermal conductivities in the ratio3:2 from a composite wall of a builiding . If thefree surfaceof the wall be at temperatureof 30^(@)C and 20^(@)Crespectively , whatis thetemperature of theineterface ?

Two walls of thickness in the ratio 1:3 and thermal conductivities in

1.	Two walls of thickness in the ratio 1:3 and thermal conductivities in the ratio3:2 from a composite wall of a builiding . If thefree surfaceof the wall be at temperatureof 30^(@)C and 20^(@)Crespectively , whatis thetemperature of theineterface ?
Answer» Solution :`R_(1)=(l_(1))/(K_(1)A)= (3l)/(KA) and R_(2) = (l_(2))/(K_(2)A) = (2L)/(3KA)` Effective thermal resistance`R = R_(1) +R_(2) = (11)/(3) (l)/(KA)` Now , thermalcurrent `i=(Delta T)/(R) = (30-20)/((11l)/(3KA)) = (30KA)/(11l)` ALSO , themal currentthrough the first slal will be ` i = ((30 -T))/(R_(1))` (where T = temperature of theinterface) i.e., `(30KA)/(11l) = ((30-T)KA)/(3l) rArr 90-330T rArr T = 21.82^(@)C`