A material A of width 10cm is generating heat at a rate of 5

A material (A) of width 10cm is generating heat at a rate of 5kw/m3 when current is passed through it. An unknown material (B) and another material (C) are attached serially to it. You have set up an experiment to determine the thermal conductivity of material B. Material B is 15 cm thick. Material C is also 15 cm thick and has a thermal conductivity of 10 W/mK. The thermal conductivity of material A is 5 W/\'mK. The outer surface of Material C has been measured to be 30 degree C. The outer surfaces are cooled with a fluid at 25 degree C and a heat transfer coefficient of 25W/m^2K. A. Determine surface temperature of Material A that is exposed to the fluid. B. Determine the other surface temperature of Material A C. Determine the thermal conductivity of Material B. D. Determine the maximum temperature in the setup

Solution

let us consider a flat wall constucted of series of 3 layers as showmn.

let the thickness of the layer be L1, l2. l3 and the average thermal conductivities of the materials of which the layers are made be k1, k2, k3 resp. let us consider a hot fluid at a temperature ta and heat transfer coefficeient ha inside tjhe wall and cold fluid at a temperature ta and heat transfer coefficient hb outside the wall . let ta , t2 , t3 and t4 be the interface temperatures. it is desired to derive an equation for calculating the rate of heat flow through the series of resistances.