Heat Transfer phenomena plays an important role in many industrial and environmental problems. We will devote much time to acquire an understanding of heat transfer effects and to develop skills needed to predict heat transfer rates. In order to get familiar with the subject, please follow the following procedure: 

One of the  "Real World Application" of Heat Transfer is in refrigeration systems. Take a careful look at the refrigerator that you have access to in your house, apartment or dormitory. Look underneath and behind your refrigerator (you may need to pull out the refrigerator carefully and remove a cover). You are likely to see a set of condenser coils which carries the warm refrigerant. Heat transfer occurs from the refrigerant to the room air. 

Sketch the specific design of the condenser coil of your refrigerator. Do you see anything attached to the coil to enhance heat transfer? Explain intuitively how the design increases the heat transfer rate. 

Does your refrigerator have a cooling fan around the coil? If there is one, describe the relative location of the fan and air flow direction generated by the fan (relative to the refrigerator). 

State the manufacture and model of your refrigerator. 

 Check out the Webpage http://www.howstuffworks.com/refrig.htm to see the simple explanation of how a refrigerator works. 

Due Date Feb. 23rd, 2005.
(Problem nos (using 4th Edition)

1.11, 1.15,1.19,1.31 and 1.33 (50%)

Open Ended Problem: (50%)

All modes of heat transfer can affect how one feels about his or her local environment. On average an adult must lose heat at a rate of about 90 watts as a result of his basal metabolism by conduction or convection, and radiation. Heat of vaporization associated with perspiration may also contribute to the balance of thermal energy between a human body and the environment. 

Visit here for explanations of different modes of heat transfer over a human body and methods to estimate the magnitude of heat transfer rates. Then answer the following:

(a) Consider an unclothed person standing in a large room at 20 C. Devise a method that you can use to estimate the skin temperature of the person. State all assumptions and parameters you will use to obtain a quantitative estimate of his skin temperature. Compare the relative magnitudes of different heat transfer mechanisms.

(b) If the person puts on his clothes, how would you now estimate his skin temperature?  Again make proper assumptions and specify necessary thermal properties of clothing in order to give a quantitative estimation of his skin temperature.

To simplify your analysis, you may assume that the perspiration cooling mechanism is not active if the skin temperature is below 37 oC, and that the rate of the perspiration cooling will be regulated by the body to maintain the skin temperature at 37 oC should the net rate of heat loss by other mechanisms is less than 90 watts.

Answers:
1.11: Temperature difference is 1.1C
1.15 For water, h= 4570 W/m2K for air h= 65W/m2K
1.19 Pelec =2.94 W
1.31 (a) Pelec =0.223 W (b) Pelec =3.44W
1.33 T=100C
 

 2.9, 2.17,2.51,3.6(a) and (b),3.8(a),3.11 (60%)

Design Problem: (40%)

A homeowner reported a problem that the water inside the pipe to his kitchen faucet could occasionally freeze during cold winter months. You are hired to look into this problem and to suggest ways to fix it. 

Preliminary examinations show that the pipe runs through the center of an 85-mm fiberglass insulation that is sandwiched between a 20-mm plasterboard inside and a 25-mm brick layer outside. The inside temperature of the house is maintained at 20 oC and the convection heat transfer coefficient inside the house is estimated to be 6 W/m2 oC.  The outdoor temperature in the area can be as low as –20 oC, and in gusty conditions the outdoor convection heat transfer coefficient may be as large as 50 W/m2 oC. 

Can you come up with at least two solutions that would keep the temperature in the water pipe above 5 oC under the worst outdoor conditions? The constraints are that the exterior appearance and the overall thickness of the wall must be maintained. 

The thermal conductivities for the plasterboard, fiberglass, and brick in the existing wall configuration are 0.17 W/m.K, 0.043 W/m.K, and 0.72 W/m.K, respectively. 

Answers:
2.9    2000 K/m, -2000 K/m, 2000 K/m, q"=-200Kw/m2, +200 KW/m2 and -200KW/m2
2.17a        k=15.0 W /m K. at 400K b) k=70 W/mK at 380K
2.51       q= 1.8 10^6 W/m3, (c) q conv= 1.8 x 10^5 W/m2K (d) Eout=7.77x 10^7 J/m2
3.6a         h=996 W/m2K  (b) 14.5 W/m2 K
3.8a        29.4 W
3.11 a 

3.11b L=86 mm 

Design Problem (40%)

In a power plant a 100mm-diameter pipe is used to transport steam at 300 oC. In order to ensure safety of working personnel and to reduce the heat transfer rate to the surroundings, the surface of the pipe must be insulated so that the outer surface of the insulation does not exceed 50 oC when exposed to air at 30 oC. The convective heat transfer coefficient with the outside air is 10 W/m2 oC. Assume that the temperature of the outer surface of the tube to be 300 oC.

Suggest a suitable insulation and keep in mind that since space is at a premium, it is desirable to keep the radial thickness of the insulation as small as possible.
 

Answers

Due Date March 16th, 2005

     5.4(a),(b),(c),5.11, 5.15,  5.41(a) and 5.72

Design of fins 

      An electric heater is made by sandwiching a heating element between two thin plates 40-cm long and 40-cm high. When operating with air at 20C the heater is to transfer 3000 W with a maximum plate temperature of 120C. Propose a suitable system of cylindrical fins. Minimum diameter of the fins should be 3mm with a minimum pitch of 4d. Weight and volume are to be kept low. A fan forces air through the heater with a velocity of 5 m/s so that the convective heat transfer coefficient to the air is 80 W/m2C. 

Problem no: 6.29 and 6.35 , 7.14, 7.18,7.33a 

Design Problem

     Answers 
     6.29(a) 34.3 W/m2C, (b) 59 W/m2K 
     6.35 42.5C 
     7.14 (a) 55KW, (b) 31.1KW,  (c) 90.7 KW 
     7.18 31.7C 

    7.33 (a )64C

Due Date April 18th, 2005 (due by 10:10 am)
Problem nos: 8.16a, 8.26, 8.30a, 8.51,8.64,8.82 and 9.18

Design Problem
 

Design Problem: Internal Convection

Constraints: The tube is to be purchased from a local supply store which carries thin-walled tubes of I.D.  and . The length of the tube section is not to exceed 5 m. For simplicity, you may assume the following constant physical properties

8.64 Tm,o =15.7C and q=438W

8.82 L=1.8 m

9.18  43 cents a day

Problem nos: 11.14,11.18,11.25,11.36a,11.47

Design problem
Design of a Shell and Tube Heat Exchanger

A. You want to cool ethanol at the rate of 10 kg/s from 65C to 35C. Water is available at 10C and at a mass flow rate of 5 kg/s. Design your heat exchanger such that it is less than 1 meter long. In your design address the following:
(1) Properties of the fluids.
(2) Selection of the material for the tubes and their diameter.
(3) Selection of how many passes of the tube and the shell.
(4) Selection of the fluid (water or ethanol) that flows through the tubes
(5) Selection of the correlation for cross flow of the fluid across a bank of tubes to determine ho
(6) Selection of the correlation to determine hi for the flow of water

B. After three months, fouling on the inside of the tubes reduces the overall heat transfer coefficient. This increases the outlet ethanol temperature for your heat exchanger to 40C instead of 35C. You are asked to change the rate at which the ethanol flows such that its outlet temperature will be close to 35C.  Describe and calculate the change in service conditions. 

Solutions

11.14 143.3C,  A=4.75 m2
11.18 Th,o =48C  U= 132 W/m2 K, e=0.8
11.25 UA= 785 W/K and L =5 m
11.36a: T =344.4K
11.47: A=11,100 m2 and m=1994 kg/s
 
 

Assignment #9

May 4, 2005 (by 10:10 am)

Problem nos:  12.10a, 12.16, 12.18, 12.29, 12.65

Design problem: Radiation balance

The top surface of ceramic plates freshly sprayed with an epoxy paint must be cured at 140 oC for an extended period of time. The plates are placed on the floor of a large enclosure and heated from above by a bank of infrared lamps. The top surface of the plate has an emissivity of 0.8. The irradiation from the enclosure walls is estimated to be 450  W/m2, and 70% of which is absorbed by the plate.  A ventilation airstream at  27 oC  provides a convection heat-transfer coefficient of 20 W/m2.K.

Specify the minimum level of irradiation that must be provided by the lamps if the absorptivity of the painted plate surface to the infrared light does not exceed 0.6.

Answers: 12.10a, 2000 W/m2.

                12.16 498K.

12.18    (a) 6.302E7 W/m2, (b) 5774 K, (c) 0.50 mm, (d) 278 K.

12.29 (a) 0.352; (b) dTs/dt = - 1977 K/s assuming the density of the tungsten is 

                19300 kg/m3 and the specific heat is 185 J/kg.K.

12.65    emissivity = 0.34, absorptivity = 0.80,

           Radiosity = 1700 W/ m2, net flux =  - 700 W/m2.
 

Assignment #10

May 11, 2005 (by 10:10 am) 
Problem nos:  12.5(a),(b),(c); 12.8, 13.1(a)(b)(c)(d), 13.11(a), 13.18
Design problem: Radiation Interception and View Factor

A radiation heat flux gauge of 4-mm diameter is positioned normal to and 1 m from the aperture of a blackbody furnace at 3000 K. The aperture is located in the center of a diffuse, gray, opaque circular cover shield (emissivity = 0.2). The cover has an outer diameter of D=100 mm and its temperature is 350 K. The furnace and gauge are located in a large room whose walls are at 300 K.

Design the diameter of the aperture such that
(1) The irradiation on the gage due to emission from the aperture of the furnace is no more than 40 W/m2.
(2) The irradiation on the gage due to radiation from the cover is not to exceed 0.1% of the irradiation due to the aperture.

You may neglect the irradiation due to the small gauge surface onto the cover. Also when computing the view factors, take a note of the fact that  and  .
 

Answers: 12.5(a) 60 mW, (b) 95.5 W/m2.sr, (c) 0.0478 mW.
12.8, 167.6 W/m2.
13.1 (a), F12=1, F21=0.424; (b) F12=0.50, F21=0.25, (c) F12=1, F21=0.637, 
   (d) F12=0.5, F21=0.707.
13.11(a), F12=0.038
13.18, 0.0492 kg/s.m.
 

May 18, 2005 (by 5:00 pm) 
Problem nos:  13.36(a), 13.42, 13.57, 13.67, 13.95

Design problem: Radiation Exchanges and Multimode Heat Transfer
 

Most architects know that the ceiling of an ice-skating rink must have a high reflectivity. Otherwise, condensation may occur on the ceiling, and water may drip onto the ice, causing bumps on the skating surface. Condensation will occur on the ceiling when its surface temperature drops below the dew point of the rink air. 

The following specifications are given: the rink has a diameter of D = 50 m and a height of L = 10 m; the temperatures of the ice and walls are assumed to be -5 C and 15 C, respectively; the rink air temperature is 15 C; and a convection heat transfer coefficient of 5 W/m2.K characterizes conditions on the ceiling surface. The thickness and thermal conductivity of the ceiling insulation are 0.3 m and 0.035 W/m.K, respectively. The temperature of the outdoor air is -5 C. The walls and ice may be approximated as blackbodies. The maximum relative humidity of the rink air may reach 80%, giving a dew point of 11.5 C. You may neglect the convection effect outdoors.

You are to perform an analysis to specify the maximum emissivity that the ceiling surface is allowed to have, so that no condensation will occur on the ceiling. Note that a lower emissivity corresponds to a higher reflectivity of the ceiling surface (which is assumed to be a diffuse-gray surface).

Answers:   13.36(a) 308K
  13.42, (a) 1.580W; (b) 0.986.
  13.57, Qualitative understanding, no answers.
  13.67, 10,100 W/m
  13.95, (a) 306K; (b) 816 w/m2.