Sheets os aluminum and steel, each 10 mm thick, are placed in contact. What is the temperature of hte common interface if the outer surface of the aluminum is kept at 212°C while the outer surface of the steel is kept at 56°C? The thermal conductivites of aluminum and steel are in the ratio 5:1.
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- 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?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?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
- 1.4 To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in W/m K. Problem 1.4A 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.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 .
- 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.a hollow styrofoam cubical box, which is perfectly insulated at the bottom, has a length of 2-m on each side and an inside surface temperature of -10 C. What should be the conduction thermal resistance at the top surface of the box in K/w if the heat load inside the box must be kept less than or equal to 500 W when the outside surface temperature of the box is 35 C? the thermal Conductivity of styrofoam is 0.030 W/m kA heat-conducting rod, that is wrapped in insulation, is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have a cross-sectional area of 0.0020 m2. The thermal conductivity of alloy B is known to be 1.8 times as great as that of alloy A. The end of the rod in alloy A is maintained at a temperature of 10 degrees Celcius, and the other end of the rod is maintained at an unknown temperature. When the steady-state flow has been established, the temperature at the junction of the alloys is measured to be 40 degrees Celcius, and the rate of heat flow in the rod is measured at 56 W. What is the temperature of the end of the rod in alloy B.
- 2. In determining the thermal conductivity of a plateflat insulator, the temperature was measured on both sides of the 25 mm thick plate and gave the results of 318.4 K and 303.2 K. FluxThe measured heat is 35.1 W.m-2. Illustrate the problem in a simple schematic/drawing, then calculate the thermal conductivity inbtu/h.ft.oF and in W/m.K! (0.033 ; 0.058) 3. A coil-shaped cooling pipe is made of SS-304 material. This pipe is 1 ft long, 0.4 inch outside diameter, and inch inside diameter. This coil cooling pipe is used to cool the water in the bath. The temperature of the inner coil pipe is 40oF while the outer coil in contact with water is 80oF. The thermal conductivity of SS-304 is a function of temperature where k(T) = 7.75 + (7.78 x 10-3).T where k is in Btu/h.ft.oF and T is in oF. Calculate the rate of heat dissipation in watts! (1287.7)A composite wall is composed of 8 in. of fire-clay brick, 6 in. of chrome brick, and4 in. of common brick. The inside wall surface temperature is 2000"F, and the outsidesurface temperature is 300"F. Determine (a) the heat loss per ft2 of wall area; (b) thetemperatures at the brick interfaces; (c) the temperature 8 in. in from the outer surface.Consider 469 mm × 447 mm window in an aircraft. For a temperature difference of 98°C from the inner to the outer surface of the window, calculate the heat loss rate through L = 15-mm-thick polycarbonate, soda lime glass, and aerogel windows, respectively. The thermal conductivities of the soda lime glass, aerogel and polycarbonate are ksl = 1.960 W/m, kag = 0.011 W/m · K and kpc = 0.201 W/m · K, respectively. If the aircraft has 110 windows and the cost to heat the cabin air is $1.8/kW · h, compare the costs associated with the heat loss through the windows for an 10-hour intercontinental flight.