Heat transfer sheets PDF

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Cairo University Faculty of Engineering Communication and Computer Science Dept.

2nd Semester 2017/2018 Mechanical Engineering INTN125

St Stead ead eady y-S -Stat tat tate e Co Cond nd ndu ucti ctio on 1- A hollow sphere is constructed of aluminum (k= 205 W/m.°C) with an inner diameter of 4 cm and an outer diameter of 8 cm. The inside temperature is 100°C and the outer temperature is 50°C. Calculate the heat transfer. 2- A wall 2 cm thick is to be constructed from material that has an average thermal conductivity of 1.3 W/m.°C. The wall is to be insulated with material having an average thermal conductivity of 0.35 W/m.°C, so that the heat loss per square meter will not exceed 1830 W. Assuming that the inner and outer surface temperatures of the insulated wall are 1300 and 30°C, calculate the thickness of insulation required. 3- Consider a 1.2-m-high and 2-m-wide double-pane window consisting of two 3-mm-thick layers of glass (k = 0.78 W/m·°C) separated by a 12-mm-wide stagnant air space (k = 0.026 W/m.°C). Determine the steady rate of heat transfer through this double-pane window and the temperature of its inner surface for a day during which the room is maintained at 24°C while the temperature of the outdoors is -5°C. Take the convection heat transfer coefficients on the inner and outer surfaces of the window to be h1 = 10 W/m2·°C and h = 25 W/m2·°C, and disregard any heat transfer by radiation. 4- A pipe whose surface temperature is maintained at 200°C has an outside diameter of 1 cm. Now, it is required to insulate the pipe with a material that has a thermal conductivity of 0.8 W/m.K to obtain an outside temperature (of the insulation) that equals 50°C. Determine the required insulation thickness for steady state conditions if the radiation effect is neglected. Take the ambient temperature and the accompanying heat transfer coefficient as 25°C and 22 W/m2.K, accordingly. 5- Consider a 0.8-m-high and 1.5-m-wide double-pane window consisting of two 4-mm-thick layers of glass (k = 0.78 W/m.°C) separated by a 10-mm-wide stagnant air space (k = 0.026 W/m m.°C). Draw the thermal resistance network and determine the steady rate of heat transfer through this double-pane window and the temperature of its inner surfaces (T2 and T3) for a day during which the room is maintained at 20°C while the temperature of the outdoors is -10°C. Take the convection heat transfer coefficients on the outer surfaces of the window to be h= 40 W/m2°C, and assume that heat transfer occurs by conduction in the stagnant air space. 6- The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA = 20 W/m.K and kC=50 W/m.K, and known thickness, LA = 0.30 m and LC = 0.15 m. The third material, B, which is sandwiched between materials

Cairo University Faculty of Engineering Communication and Computer Science Dept.

2nd Semester 2017/2018 Mechanical Engineering INTN125

A and C, is of known thickness, L B = 0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o = 20°C, an inner surface temperature of Ts,i = 600°C, and an oven air temperature of T∞ = 800°C. The inside convection coefficient h is known to be 25 W/m2.K. What is the value of kB? 7- Steam at T∞1= 320°C flows in a cast iron pipe (k= 80 W/m°C) whose inner and outer diameters are D1= 5 cm and D2=5.5 cm, respectively. The pipe is covered with 17 cm-thick glass wool insulation with k=0.05 W/m°C. Heat is lost to the surroundings at T∞2 =5°C by convection and radiation, with a heat transfer coefficient of h2 = 18 W/m2.°C. Taking the heat transfer coefficient inside the pipe to be h1= 60 W/m2.°C, determine the rate of heat loss from the steam per unit length of the pipe. Also determine the temperature drops across the pipe shell and the insulation. 8- Find the heat transfer per unit area through the shown composite wall. Assume onedimensional heat flow.

9- A spherical tank, 1 m in diameter, is maintained at a temperature of 120°C and exposed to a convection environment. With h = 25 W/m2.°C and T∞ = 15°C, what thickness of urethane foam (k= 0.026 W/m.°C) should be added to ensure that the outer temperature of the insulation does not exceed 40°C? What percentage reduction in heat loss results from installing this insulation? 10- The rear window of an automobile is defogged by passing warm air over its inner surface. If the warm air is at T∞i= 40°C and the corresponding convection coefficient is hi = 30 W/m2.K, what are the inner and outer surface temperatures of 4-mm-thick window glass, if the outside ambient air temperature is T∞o=-10°C and the associated convection coefficient is ho = 65 W/m2.K?

Cairo University Faculty of Engineering Communication and Computer Science Dept.

2nd Semester 2017/2018 Mechanical Engineering INTN125

Int Inter er ernal nal He Hea at G Gener ener enerati ati ation on 1- Heat is generated uniformly in a stainless-steel plate having k = 20 W/m.°C. The thickness of the plate is 1.0 cm and the heat-generation rate is 500 MW/m3. If the two sides of the plate are maintained at 100 and 200°C, respectively, calculate the temperature at the center of the plate. 2- A 3.2-mm-diameter stainless-steel wire 30 cm long has a voltage of 10 V impressed on it. The outer surface temperature of the wire is maintained at 93°C. Calculate the center temperature of the wire. Take the resistivity of the wire as 70 μῼ.cm and the thermal conductivity as 22.5 W/m.°C. 3- A plane wall is a composite of two materials, A and B. The wall of material A has uniform heat generation q’’’=1.5*106 W/m3, kA = 75 W/m.K, and thickness L A = 50 mm. The wall material B has no generation with kB = 150 W/m.K and thickness L B = 20 mm. The inner surface of material A is well insulated, while the outer surface of material B is cooled by a water stream with T∞ = 30°C and h = 1000 W/m2.K. Sketch the temperature distribution that exists in the composite under steady-state conditions and determine the temperature T0 of the insulated surface as well as the temperature T2 of the cooled surface.

Cairo University Faculty of Engineering Communication and Computer Science Dept.

2nd Semester 2017/2018 Mechanical Engineering INTN125

Fr Free ee aand nd For Force ce ced dC Convec onvec onvectio tio tion n 1. Engine oil at 60℃ flows over the upper surface of a 5-mlong flat plate whose temperature is 20℃ with a velocity of 2 m/s. Determine the rate of heat transfer per unit width of the entire plate. 2. The local atmospheric pressure in Denver, Colorado (elevation 1610 m), is 83.4 kPa. Air at this pressure and 20 ℃ flows with a velocity of 8 m/s over a 1.5-m 6-m flat plate whose temperature is 140℃. Determine the rate of heat transfer from the plate if the air flows parallel to the (a) 19m-long side and (b) the 1.5-m side. 3. A circular pipe of 25-mm outside diameter is placed in an airstream at 25℃ and 1-atm pressure. The air moves in cross flow over the pipe at 15 m/s, while the outer surface of the pipe is maintained at 100℃. What is the rate of heat transfer from the pipe per unit length? 4. Consider a sphere with a diameter of 20 mm and a surface temperature of 60℃ that is immersed in a fluid at a temperature of 30℃ and a velocity of 2.5 m/s. Calculate the heat rate when the fluid is air at atmospheric pressure. 5. A 6-m-long section of an 8-cm-diameter horizontal hot-water pipe passes through a large room whose temperature is 20℃. If the outer surface temperature of the pipe is 70℃, determine the rate of heat loss from the pipe by natural convection. 6. A glass-door firescreen, used to reduce exfiltration of room air through a chimney, has a height of 0.71 m and a width of 1.02 m and reaches a temperature of 232℃. If the room temperature is 23℃, estimate the convection heat rate from the fireplace to the room. 7. An electrical heater in the form of a horizontal disk of 400-mm diameter is used to heat the bottom of a tank filled with engine oil at a temperature of ℃. Calculate the power required to maintain the heater surface temperature at 70℃.

Cairo University Faculty of Engineering Communication and Computer Science Dept.

2nd Semester 2017/2018 Mechanical Engineering INTN125

He Heat at T Tra ra ransfer nsfer Da Data ta tashe she sheet et Ge Gene ne neral ral Eq Equat uat uation ion o off C Con on ond duct uction ion Cartesian:

Cylindrical:

Spherical:

Cairo University Faculty of Engineering Communication and Computer Science Dept.

Fre Free e Co Conv nv nvectio ectio ection n Parallel flow over a flat plate:

Cross flow over a cylinder:

Cross flow over a sphere:

2nd Semester 2017/2018 Mechanical Engineering INTN125

Cairo University Faculty of Engineering Communication and Computer Science Dept.

2nd Semester 2017/2018 Mechanical Engineering INTN125

Fre Free e Co Conv nv nvectio ectio ection n Long Horizontal Cylinder:

Horizontal Flat Plate:

Where the characteristic length (L) equals the area divided by the perimeter of the plate. Vertical Flat Plate:

Sphere:

Cairo University Faculty of Engineering Communication and Computer Science Dept.

2nd Semester 2017/2018 Mechanical Engineering INTN125

Thermodynamic properties of air at atmospheric pressure:

Cairo University Faculty of Engineering Communication and Computer Science Dept.

Thermodynamic properties of engine oil:

2nd Semester 2017/2018 Mechanical Engineering INTN125...