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In the thermal processing of semiconductor materials, annealing is accomplished by heating a silicon wafer according to a temperature-time recipe and then maintaining a fixed elevated temperature for a prescribed period of time. For the process tool arrangement shown as follows, the wafer is in an evacuated chamber whose walls are maintained at
To avoid warping the wafer and inducing slip planes in the crystal structure, the temperature difference across the thickness of the wafer must be less than
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Chapter 1 Solutions
Introduction to Heat Transfer
- 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 1.4arrow_forward1.63 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.arrow_forwardA 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.arrow_forward
- 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?arrow_forwardA 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.arrow_forwardOne 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?arrow_forward
- 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 .arrow_forwardDetermine the power requirement of a soldering iron in which the tip is maintained at 400C. The tip is a cylinder 3 mm in diameter and 10 mm long. The surrounding air temperature is 20C, and the average convection heat transfer coefficient over the tip is 20W/m2K. The tip is highly polished initially, giving it a very low emittance.arrow_forwardb) A double glazed window, 1.3m high and 2.4m wide consists of two layers of glass each 4mm thick separated by a 23mm air gap. This window is a replacement for a single glazed unit. The double glazed unit is installed in the wall of a room in which the air temperature is maintained at 23 degreesC, the outer surface of the window is exposed to the atmospheric temperature which is 2 degreesC. The surface heat transfer coefficient of the room side glass is 5.7 W/m?K and 9.1 W/m?K on the outer surface of the window. The thermal conductivity of the glass is known to be 0.76 W/mK. i) On the assumption that the air gap between the layers may be regarded as a stationary layer of air of thermal conductivity 0.026 W/mK, calculate the heat transfer rate through the window and the temperature of the room side surface of the glass. ii) Calculate the heat transfer rate for the single glazed unit which has been replaced. The window was of the same dimensions consisting of a single pane of glass. It…arrow_forward
- Don’t use Heissler charts to answer this question Heat sterilization of lumber, timbers, and pallets is used to kill insects to prevent their transfer between countries in international trade. This is analogous to food sterilization by heat. A typical requirement here is that the slowest heating point of any woodconfiguration be held at 56 °C for 30 minutes. Consider hot air heating of wooden boards that maintains their surface temperature at 70 °C. The boards are stacked outside and in the winter time they can be considered to be at 0 °Cwhen theyare brought in for heating. The thermal diffusivity of the wood is 9*10-8m2/s. a.Calculate the time from the start of heating for a 2.5 cm thick board to reach a sterilization temperature of 56 °C at its slowest heating point .b.Calculate the heating time when four such boards are stacked together. c.Calculate the ratio of the two heating times (for a single board versus when they are stacked), and explain the ratio. Note: You’re free to…arrow_forward6. A furnace wall consists of 250 mm fiber brick,125 mm insulating brick, and 250 mm building brick. The inside wall is at a temperature of 600°C and the atmospheric temperature is 20°C. Calculate the heat loss per m' of wall area and the temperature of the outside wall surface of the furnace and the temperature at each interface throughout the wall. The heat transfer coefficient for the outside surface is 10 W/m² °k and the thermal conductivities of the fiber brick, insulating brick and the building brick are 1.4,0.2 and 0.7 W/m.°C respectively.arrow_forwardAn underwater sonar that maps the ocean bathymetry is encapsulated in a sphere with a diameter of 85 mm. During operation, the sonar generates heat at a rate of 300W. What is the sonar surface temperature when it’s located in a water column where the temperature is 15o C and the water current is 1 m/sec? The sonar was pulled out of the water without turning it off, thus, it was still working. The air temperature was 15o C and the air speed was 3 m/sec. What was the sonar surface temperature? Was there any reason for concern?arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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