Question

Consider two walls, each kept at constant temperature T. and joining them is an aluminum fin of length L. There is internal heat generation q in this fin. Air flows over the fin having convective heat transfer coefficient h and temperature T.. Prove that the efficiency of the fin can be given by tanh (mL/2) mL/2 where m2 P= perimeter of the fin, A = area of the fin cross-section, and k = thermal conductivity of the fin. n = hp = kAc'

Answer 1

solution Griven h To 2 hp m= AK wall T woll 2e at x=L ) O O Sakadi Tu so T 늘 dT means 2 वर sput the fin in in two ports Too Toz tempertise p=0 T * SHUundry 16 h K insulated tip So, this case become fin with insulated tip. so heat transfer in insulated tip is given by 9= Shpkaus tauhme) .do [0o=T-To] mapinum heat transfer through fin when the fin at base temperature = hPL.O. efficieney of fin= Actual heat transfer (8) maximum heat transfer (92) n = Shpką do tantum HP Les [2= efficiency tanhme Now h = tanh (my) of fin me mith) KA n= tauh (my) proved, Bus (ml)