7. A composite wall consists of three materials, as shown in Figure 2. The inside wall temperature is 200°C and the outside air temperature is 50°C with a convection coefficient of 10 W/m²-K. Determine the temperature along the composite wall. Where A is the area of cross- section (can be taken to be equal to 1) and k is the conductivity. Problem is governed by the equation d?T 0, -kA ax? 7>x>0 Boundary conditions d?T T(0) = To, kA- +BA(T- = 0 dx2 Where A is the area of cross-section (cab be taken to be equal 1) and k is the conductivity. Material 2. k k = 70 WAm-K) Material 1, k „Material 3, kz Ag - 40 WAm K) ky = 20 WAm K) T50°C Surface arca 4 =2 cm 7,- 200°C A(1) L a2.5 em L 4 cm B= 10 WAm?- K) i 2 3 4

7. A composite wall consists of three materials, as shown in Figure 2. The inside wall temperature is 200°C and the outside air temperature is 50°C with a convection coefficient of 10 W/m²-K. Determine the temperature along the composite wall. Where A is the area of cross- section (can be taken to be equal to 1) and k is the conductivity. Problem is governed by the equation d?T 0, -kA ax? 7>x>0 Boundary conditions d?T T(0) = To, kA- +BA(T- = 0 dx2 Where A is the area of cross-section (cab be taken to be equal 1) and k is the conductivity. Material 2. k k = 70 WAm-K) Material 1, k „Material 3, kz Ag - 40 WAm K) ky = 20 WAm K) T50°C Surface arca 4 =2 cm 7,- 200°C A(1) L a2.5 em L 4 cm B= 10 WAm?- K) i 2 3 4

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.3P: 1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of...

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1.1 On a cold winter day, the outer surface of a 0.2-m-thick concrete wall of a warehouse is exposed to temperature of –5°C, while the inner surface is kept at 20°C. The thermal conductivity of the concrete is 1.2 W/m K. Determine the heat loss through the wall, which is 10-m long and 3-m high. Problem 1.1
A section of a composite wall with the dimensions shown below has uniform temperatures of 200C and 50C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA=70W/mK,kB=60W/mK, kC=40W/mK, and kD=20W/mK, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces.
A section of a composite wall with the dimensions shown below has uniform temperatures of 200C and 50C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA=70W/mK,kB=60W/mK, kC=40W/mK, and kP=20W/mK, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces. Repeat Problem 1.34, including a contact resistance of 0.1 K/W at each of the interfaces.
1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.
2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.
A hollow sphere with inner and outer radii of R1 and R2, respectively, is covered with a layer of insulation having an outer radius of R3. Derive an expression for the rate of heat transfer through the insulated sphere in terms of the radii, the thermal conductivities, the heat transfer coefficients, and the temperatures of the interior and the surrounding medium of the sphere.
One end of a 0.3-m-long steel rod is connected to a wall at 204C. The other end is connected to a wall that is maintained at 93C. Air is blown across the rod so that a heat transfer coefficient of 17W/m2 K is maintained over the entire surface. If the diameter of the rod is 5 cm and the temperature of the air is 38C, what is the net rate of heat loss to the air?
2.3 The shield of a nuclear reactor is idealized by a large 25-cm-thick flat plate having a thermal conductivity of . Radiation from the interior of the reactor penetrates the shield and there produces heat generation that decreases exponentially from a value of at the inner surface to a value of at a distance of 12.5 cm from the interior surface. If the exterior surface is kept at 38°C by forced convection, determine the temperature at the inner surface of the field. Hint: First set up the differential equation for a system in which the heat generation rate varies according to .
Repeat Problem 1.35 but assume that instead of surface temperatures, the given temperatures are those of the air on the left and right sides of the wall and that the convection heat transfer coefficients on the left and right surfaces are 6 and 10W/m2K, respectively.
Both ends of a 0.6-cm copper U-shaped rod are rigidly affixed to a vertical wall as shown in the accompanying sketch. The temperature of the wall is maintained at 93C. The developed length of the rod is 0.6 m, and it is exposed to air at 38C. The combined radiation and convection heat transfer coefficient for this system is 34W/m2K. (a) Calculate the temperature of the midpoint of the rod. (b) What will the rate of heat transfer from the rod be?
1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.
Heat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of TiandTo, respectively. Derive an expression for the temperature distribution.