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Referring to the semiconductor processing tool of Problem 5.13, it is desired at some point in the manufacturing cycle to cool the chuck, which is made of aluminum alloy 2024. The proposed cooling scheme passes air at 20°C between the air-supply head and the chuck surface.
(a) If the chuck is initially at a uniform temperature of l00°C, calculate the time required for its lower surface to reach 25°C, assuming a uniform convection coefficient of
(b) Generate a plot of the time-to-cool as a function of the convection coefficient for the range
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Chapter 3 Solutions
Introduction to Heat Transfer
- 8.71 A 50-mm-diameter, thin-walled metal pipe covered with a 25-mm-thick layer of insulation (0.085 W/m.K) and carrying superheated steam at atmospheric pressure is suspended from the ceiling of a large room. The steam temperature entering the pipe is 120°C, and the air tem- perature is 20°C. The convection heat transfer coefficient on the outer surface of the covered pipe is 10 W/m².K. If the velocity of the steam is 10 m/s, at what point along the pipe will the steam begin condensing?arrow_forwardIn the final stages of production, a pharmaceuticalis sterilized by heating it from 30°C to 75°C as it moves at0.2 m/s through a straight thin-walled stainless steeltube of 12.7-mm diameter. A uniform heat flux is maintained by an electric resistance heater wrappedaround the outer surface of the tube. If the tube is 10 m long, what is the required heat flux? If fluidenters the tube with a fully developed velocity profile and a uniform temperature profile, what is thesurface temperature at the tube exit? Fluid properties may be approximated as ? = 1000 kg/m3, cp =4000 J/kg K, ? = 2 x 10-3 kg/s m, k = 0.8 W/m K, and Pr = 10.arrow_forwardInclude drawingarrow_forward
- (B) Cylindrical Water cans (diameter 6.5cm and length 15cm) are to be cooled from initial temperature of 20°C by placing theme in a cooler with ambient temperature of 1°C. Compare the initial cooling rates when the cans are laid horizontally to when the cans are laid vertically. Take v = 15.55x10° m²/s, k=0.024 W/mK and Pr=0.7. Nu = 0.53RA' a4 for horizontal orientation Nu = 0.59 Ra"4 for vertical orientationarrow_forwardThe rate at which energy must be dissipated away from single integrated circuits (computer chips) continues to increase as transitors continue to shrink in size and more and more computations are being completed in smaller and smaller volumes. The maximum chip temperature, however, has not changed much over time and remains around Tc = 75 °C. To increase the rate of dissipation of thermal energy away from a new chip, it is proposed to add a 5 x 5 array of copper pin fins to the chip. Each fin will be individually joined to the chip surface such that there is a minimal contact resistance between the fin and the chip. The diameter of the fins is df = 1 mm and the length is Lf = 15 mm. The chip is square, with a side length of W= 15 mm. It is so thin that it can be treated as having a single temperature. A dielectric liquid flows over the outer surface of the chip and around the fins, with a temperature of T»,f= 20 °C and a convection coefficient of hf = 1150 W/m²-K. The chip is joined to…arrow_forwardplease answer asap with correct answerarrow_forward
- Answer correctly and quickly as possible please.arrow_forward(B) Cylindrical Water cans (diameter 6.5cm and length 15cm) are to be cooled from initial temperature of 20°C by placing theme in a cooler with ambient temperature of 1˚C. Compare the initial cooling rates when the cans are laid horizontally to when the cans are laid vertically. Take v = 15.55x10 m²/s, k=0.024 W/mK and Pr-0.7. Nu = 0.53 Ra¹ for horizontal orientation Nu = 0.59 Ra¹/4 for vertical orientationarrow_forward(1) A copper wire 0.8 mm diameter at 150°C is suddenly dipped into water at 35°C. If h=85.5 W/m²K, estimate the time required to cool the wire to 95°C. (ii) If the same wire were placed in air instead of water what would have been the time required to cool it to 95°C. h=11.65 W/m²K For Copper: p= 9000 kg/m³, c = 0.38 kJ/kg K, k = 373 W/mKarrow_forward
- A major objective in advancing gas turbine technologies is to increase the temperature limit associated with operation of the turbine blades. For example, it is common to use internal cooling by including flow channels within the blades and routing air through the channels. We wish to assess the effect of such a scheme by approximating the blade as a rectangular solid with rectangular channels. The blade, which has a thermal conductivity of k = 25 W /m · K, is 6 mm thick, and each channel has a 2 mm × 6 mm rectangular cross section, with a 4-mm spacing between adjoining channels. Under operating conditions for which ho = 1000 W/m2 · K, T0,0 = 1700 K, hi = 200 W/m² · K, and To,i = 400 K, determine the temperature field in the turbine blade and the rate of heat transfer per unit length to the channel. At what location is the temperature a maximum? Combustion Air channel gases 2 mm 6 mm -6 mm- 4 mm Combustion Turbine blade, k gasesarrow_forwardThe cake mix, whose initial temperature is 25C, will be baked at 120C in a cylindrical mold. It takes 802 h for the core temperature of the cake to reach 98C and this time is considered sufficient for baking the cake. Calculate the diameter of the mold in which the cake should be placed. h = 68.6 W / m2K, d = 840 kg / m3 cp = 3400 J / kgK, k = 1.2 W / mK, λ = 3.07arrow_forwardUnique characteristics of biologically active materials such as fruits, vegetables, and other products require special care in handling. Following harvest and separation from producing plants, glucose is catabolized to produce carbon dioxide, water vapor, and heat, with attendant internal energy generation. Consider a single apple, spherical in shape, diameter 80 mm, which is ventilated with air at 5°C and h= 7.5 W/m2.K. Within the apple thermal energy is uniformly generated at 4000.0J/kg.day. The density and thermal conductivity of the apple are 840 kg/m3 and 0.5 W/m.K. a. Derive an equation for temperature distribution inside the apple. Use the boundary conditions @r R, T = Ts, and @r=0, dT/dr 0. Ts is the surface temperature of sphere to be determined using convection equation. b. Determine the apple center and surface temperatures.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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