22 1. Consider a solid cylindrical rod of radius R and length L placed between two walls as shown in the figure below. At the connection between the first wall and the rod (z = 0), a constant heat flux, qo, is applied while at the other end of the rod (z = L) the temperature is kept at TL. Air at Too is passed over the rod. The heat transfer coefficient between the rod and air is h for the given conditions. Assume that the thermal conductivity of the rod material, k, can be considered constant. You can also assume that for a given z-position temperature of the rod is uniform, i.e., temperature is not function of radial position. C. a. Obtain a relation for the steady state temperature distribution in the rod. Show all the details of the derivation and specify clearly all the assumptions you make. b. Using the relation obtained in part (a), derive an expression for the steady state heat transfer rate between the rod and air. Calculate the heat transfer rate if qo = 50 103 W/m, TL= 50C, T=27C, R = 2 cm, L = 50 cm, h = 54.5 W/m.K and k = 150 W/m.K. d. Note that we assumed temperature is a function of z-position only and can be considered uniform for a given cross-section of the rod, which implies that the thermal resistance within the rod is negligible compared to the thermal resistance between the rod surface and air. Check if this assumption is valid in this case. 8 P = 0.0145 small TL Wall Wall Cylindrical rod of radius R Go h z=0 Air at TOD z=L Solve problem 18B.6 in the text.