MEE 403 Midterm, Spring 2014

Lebanese American University School of Engineering IME Department MEE 403 HEAT TRANSFER First Midterm, Duration 90 min Name: April 16, 2013 ID: 1 (25 pts) A plane wall of thickness 2L=40 mm and thermal conductivity k=5 W/m.K experiences uniform volumetric heat generation at a rate 𝑞̇, while convection heat transfer occurs at both of its surface (x=-L, +L), each of which is exposed to a fluid of temperature T∞=20oC. Under steady-state conditions, the temperature distribution in the wall is of the form T(x)=a+bx+cx2, where a= 82oC, b=-210oC/m, c=-2x104oC/m2, and x is in meters. The origin of the x-coordinate is at the midplane of the wall. a) Sketch the temperature distribution and identify significant physical features b) What is the volumetric rate of heat generation 𝑞̇ in the wall? c) Determine the surface heat fluxes, ( ) xq  L and ( ) xq  L . How are these fluxes related to the heat generation rate? d) What are the convection coefficients for the surfaces at x=-L and x=+L? e) If the source of the heat generation is suddenly deactivated( q  0 ), what is the rate of change of energy stored in the wall at this instant? 2 (25 pts) Two air flows are separated by a 2 mm-thick plastic wall. A 20.2 cm-long, 1 cm-diameter aluminum rod transfers heat from one flow to the other as shown. The hot air flow is at 70oC, and the convective heat transfer coefficient to the rod is 48 W/m2 K; the cold air flow is at 20oC and is at a lower velocity, giving a heat transfer coefficient of only 24 W/m2 K. Determine the rate of heat transfer and the temperature of the midsection of the rod. Take k=190 W/m K for the aluminum. 3 (25 pts) Radioactive wastes are packed in a long, thin-walled cylindrical container, the wastes generate thermal energy nonuniformly according to the relation   2 ( ) 1 / o o q r q r r       , where q is the local rate of energy generation per unit volume, oq is a constant, and or is the radius of the container. Steady-state conditions are maintained by submerging the container in a liquid that is at T and provides a uniform convection coefficient h. Obtain an expression for the total rate at which energy is generated in a unit length of the container. Use this result to obtain an expression for the temperature sT of the container wall. 4 (25 pts) A 60 cm long, 3 cm- diameter AISI 1010 steel rod k=64 W/m K is welded to a furnace wall and passes thru 20 cm if insulation before emerging into the surrounding air. The furnace wall is at 300oC, and the air temperature is 20oC. Estimate the temperature of the bar tip if the heat transfer coefficient between the rod and the air is taken to be 13 w/m2K