For identicalrods AB, CD , CFand DF are connected as shown in figure . Thelength, cross - sectional areaand thermalconductivityof eachrod areL,A,K respectively. The ends A, E,Fare maintainedat temperaturesT_(1),T_(2) andT_(3)respectively. Assuming no loss of heatto theatmosphere, calculate the temperature at B . Let T_(B)be thetemperature at B .

For identicalrods AB, CD , CFand DF are connected as shown in figure .

1.	For identicalrods AB, CD , CFand DF are connected as shown in figure . Thelength, cross - sectional areaand thermalconductivityof eachrod areL,A,K respectively. The ends A, E,Fare maintainedat temperaturesT_(1),T_(2) andT_(3)respectively. Assuming no loss of heatto theatmosphere, calculate the temperature at B . Let T_(B)be thetemperature at B .
Answer» Solution :AB = CD = EF = L , CB = BD`= (L)/(2)""therefore FCB = EDB = (3L)/(2)` Heat flowingper second towardsB from E via A is `H_(1) = (KA(T_(2) - T_(a)))/((3L)/(2))` Heat flowingper second towards B from F via C is `H_(2) =(KA(T_(3) - T_(a)))/((3L)/(2))` Heat flowing per secondtowards A from Bis `H_(3) = (KA(T_(B) - T_(1))^(2))/(L)` In STEADYSTATE`H_(1) + H_(2) = H_(3)` `(KA(T_(2) - T_(B)))/((3L//2)) + (Ka(T_(3) - T_(B)))/((3L//2)) = (KA(T_(B) - T_(1)))/(L) = rArr (2)/(3) (T_(2) - T_(B)) + (2)/(3) (T_(3)- T_(B))- T_(B) - T_(1)` (or) `rArr (2)/(3)T_(2) - (2)/(3) T_(B) + (2)/(3) T_(B)= T_(B) - T_(1)` `therefore T_(B) + (4)/(3) T_(B) = (2)/(3) T_(2) + (2)/(3)T_(1)` `rArr "" T_(B) = (2T_(2) + 2T_(3) + 3T_(1))/(7)`