Please Help! A cylindrical heating element of length L1 and diameter D, shown sh
ID: 1862203 • Letter: P
Question
Please Help!
A cylindrical heating element of length L1 and diameter D, shown shaded in the diagram, is in contact with a circular rod of length L and diameter D. Heat is generated within the element at a rate q per unit volume. The rod is made of chrome steel (5% Cr). All exposed surfaces of the heating element and the rod are perfectly insulated, except for the right-hand end of the rod. That end is in contact with a fluid having a heat transfer coefficient h and a temperature T infinity. Operating data: L1 = 4 cm, D = 2 cm, L = 40 cm q = 0.15 W/cm3, T1 = 140 Degree C, T infinity = 20 Degree C Use the information given in the problem statement to determine the heat transfer coefficient h. Assume one-dimensional heat conduction in the rod. The thermal conductivity of chrome steel is 46.5 W/m-C.Explanation / Answer
Heat generated in the element = q*Volume = q*Area*L1
Since the rod does not have any losses, heat entering the rod = heat leaving
Heat entering = 0.15*4*pi*2^2/4 = 1.885 W
Let T2 be temperature at free end of rod
Heat leaving = h*A*(T2 - Tatm)
Taking a small element of the rod near heat producing element
Rate of Heat entering in that element = 1.885
Rate of Heat leaving = -k*A*dT/dx = -46.5*(T2 - T1)/L*pi*0.02^2/4
Therefore both these must be equal
T2 - 140 = -51.6
T2 = 88.386 C
h = 1.885/A(T2 - Tatm) = 1.885/(3.14*10^(-4)*(88.386-20)) = 87.74