Mech. Eng. Ph.D. Preliminary Qualifying Examination

Mech. Eng. Ph.D. Preliminary Qualifying Examination January 22, 2010 Heat and Mass Transfer This is one of five problems. You are required to do four out of five problems. Clearly indicate which four problems you are selecting. Show all work on the exam sheets provided and write your student number and or social security number on each sheet. Do not write your name on any sheet.

Student Number ______

1. A 45 cm diameter pizza lies on an insulated table and is kept warm at 350K by a circular 15cm diameter infrared heat disc located 45 cm directly above and oriented coaxially and parallel to the pizza. The ambient room temperature is 300K.

a) Calculate the shape factor describing the fraction of radiation leaving the heat lamp that is intercepted by the pizza. Use the relation for Coaxial Parallel Disks as shown in the Table below. b) Applying the reciprocity theorem, calculate the fraction of radiation leaving the pizza that is intercepted by the room. c) Assuming both the pizza and surroundings act as blackbodies, calculate the net radiation heat flux from the pizza to the room. d) If the natural convection coefficient is 5 W/m2-K, calculate the convection heat flux from the pizza. e) Apply an energy balance to the pizza and calculate the temperature of the heat disc required to maintain the temperature of the pizza at 350K. Heating disk

T =300K ambient

45 cm q , h=5 W/m2-K conv Insulated Pizza, table T =350K pizza 45 cm

of 6 1. (contd.)

of 6 Mech. Eng. Ph.D. Preliminary Qualifying Examination January 22, 2010 Heat and Mass Transfer This is one of five problems. You are required to do four out of five problems. Clearly indicate which four problems you are selecting. Show all work on the exam sheets provided and write your student number and or social security number on each sheet. Do not write your name on any sheet.

2. The filament of a 100 Watt incandescent light bulb may be assumed to have the properties of a blackbody and has been determined to be at a temperature of 2750K. The thin-walled glass bulb has transmissivity characteristics according to the figure shown below. The surface temperature of the bulb is 525K.

a) How much power is radiated by the filament within the spectral range of human vision, 400-700nm? b) Neglecting reflectivity, estimate the total absorptivity of the glass bulb wall. c) Calculate the total emissivity of the glass shell of the bulb that is at a temperature of 525K.

3. One of the side walls of an oven has dimensions 1mx1mx7.5 cm. The rest of the oven walls are completely insulated. The wall is primarily made of an insulating material with a thermal conductivity of 0.04W/m °C. If the inside surface temperature of the wall is 150°C and its outside surface temperature is 37°C:

a. Calculate the rate, in watts, at which the electric coils within the oven must dissipate energy to make up for the loss through the wall. b. Calculate the convective coefficient of heat transfer between the outside surface of the wall and the surrounding air. The air temperature is 25°C. c. Calculate the thickness of the wall if we want to reduce the electric energy consumption by 30%, while keeping the same inside wall surface temperature.

4. A thermocouple bead 0.15 cm in diameter is used to measure the temperature in an air stream at atmospheric pressure and 150 °C. To calculate the error in the measured temperature due to radiation, the heat losses by convection from the bead to the air is needed. The air speed is 3 m/s.

a) Compute the average coefficient of heat transfer by convection between the bead and the air. b) Propose a method to reduce the heat loss by radiation from the bead to the surroundings.

The following are the air properties at atmospheric pressure and 150°C: Density = 0.83 kg/m3, viscosity = 2.38 x10-5 kg/ms, thermal conductivity = 0.035 W/m°C and specific heat at constant pressure = 1.017 kJ/kg°C.

1 4 1 2    2 3 0.4   Nu D  2  0.4Re D   0.06Re D  Pr     S 

5. Steam at 120°C flows in a pipe which has an inside radius of 5 cm, outside radius of 5.25 cm and thermal conductivity of 43 W/m°C. The surface coefficient of heat transfer between the steam and the inside pipe wall is 2800 W/m2 °C. Its outside surface is exposed to atmospheric air at 26°C, with a surface coefficient of heat transfer of 9 W/m2 °C.

a. Draw the electrical analogue of the heat transfer process from the steam to the air. b. Calculate the heat transfer rate per meter of the pipe.