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The strength and stability of tires may be enhanced by heating both sides of the rubber
(a) If steam flow over the tire surfaces maintains a convection coefficient of
(b) To accelerate the heating process, it is recommended that the steam flow be made sufficiently vigorous to maintain the tire surfaces at 200°C throughout the process. Compute and plot the midplane and surface temperatures for this case, as well as for the conditions of part (a).
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Chapter 3 Solutions
Introduction to Heat Transfer
- How long should it take to boil an egg? Model the egg as a sphere with radius of 2.3 cm that has properties similar to water with a density of = 1000 kg/m3 and thermal conductivity of k = 0.606 Watts/(mC) and specific heat of c = 4182 J/(kg C). Suppose that an egg is fully cooked when the temperature at the center reaches 70 C. Initially the egg is taken out of the fridge at 4 C and placed in the boiling water at 100 C. Since the egg shell is very thin assume that it quickly reaches a temperature of 100 C. The protein in the egg effectively immobilizes the water so the heat conduction is purely conduction (no convection). Plot the temperature of the egg over time and use the data tooltip in MATLAB to make your conclusion on the time it takes to cook the egg in minutes.arrow_forwardQ5Two large containers A and B of the same size are filled with different fluids. The fluids in containers A and B are maintainedat 0° C and 100° C, respectively. A small metal bar, whose initial temperature is 100° C, is lowered into container A. After1 minute the temperature of the bar is 90° C. After 2 minutes the bar is removed and instantly transferred to the othercontainer. After 1 minute in container B, the temperature of the bar rises 10°. How long, measured from the start of theentire process, will it take the bar to reach 99.9° C?arrow_forwardPlease quicklyarrow_forward
- An ice chest is constructed of Styrofoam [k = 0.033 W/m.°C] with inside dimensions of 25 by 40 by 100 cm. The wall thickness is 5.0 cm The outside of the chest is exposed to air at 25°C with N=10 W/m2°C. If the chest is completely filled with ice, calculate the time for the ice to completely melt. State your assumptions. The enthalpy of fusion for water is 330 kJ/kgarrow_forwardH2arrow_forwardConsider two coffee cups A and B. Small coffee cup heaters are placed in cups A and B and heat is transferred to keep cup A at 45°C and cup B at 35°C. Room temperature is 25°C. The cups contain the same amount of water (100 grams). Which answer best describes the rates at which heat must be transferred to maintain the temperatures described above?: * A. Cup A will require heat at about five times the rate of B. B. Cup A will require heat at about twice the rate of B. C. Cup A will require heat at a slightly faster rate than B. D. Both cups will require heat at the same rate.arrow_forward
- Unreasonable Results - A slightly deranged Arctic inventor surrounded by ice thinks it would be much less mechanically complex to cool a car engine by melting ice on it than by having a water-cooled system with a radiator, water pump, antifreeze, and so on. (a) If 80% of the energy in 1.00 gal of gasoline is converted into “waste heat” in a car engine, how many kilograms of 0C ice could it melt? (b) Is this a reasonable amount of ice to carry around to cool the engine for 1.00 gal of gasoline consumption? (c) What premises or assumptions are unreasonable?arrow_forwardSuppose that as a body cools, the temperature of the surrounding medium increases because it completely absorbs the heat being lost by the body. Let T(t) and Tm (t) be the temperatures of the body and the medium at time t, respectively. If the initial temperature of the body is T1 and the initial temperature of the medium is T2, then it can be shown in this case that Newton's law of cooling is dT/dt = k(T - Tm ), k 0 is a constant. (a) The foregoing DE is autonomous. Determine the limiting value of the temperature T(t) as t→ o What is the limiting value of Tm (t) as t→o? (b) Verify your answers in part (a) by actually solving the differential equation. (c) Discuss a physical interpretation of your answers in part (a).arrow_forwardSample Problem • Four metric tons of pork are to be stored at a temperature of -12°C in 8 hours. The product enters the chiller at a temperature of 21°C and the specific heats above and below freezing are 0.86 kCal/kg-°C and 0.51 kcal/kg-°C, respectively, and its latent heat of fusion is 48 kCal/kg. If the freezing temperature of the product is -5°C, determine the product load in kCal/hr. TCLarrow_forward
- Humans are able to control their rates of heat production and heat loss to maintain a nearly constant core temperature of Tc = 37°C under a wide range of environmental conditions. This process is called thermoregulation. From the perspective of calculating heat transfer between a human body and its surroundings, we focus on a layer of skin and fat, with its outer surface exposed to the environment and its inner surface at a temperature slightly less than the core temperature, Ti = 35°C = 308 K. Consider a person with a skin/fat layer of thickness L = 2 mm and effective thermal conductivity k = 0.3 Wm ⋅ K. The person has a surface area A = 1.8 m2 and is dressed in a bathing suit. The emissivity of the skin is ε = 0.95.a). When the person is in still air at T∞ = 308 K, what is the skin surface temperature and rate of heat loss to the environment? Convection heat transfer to the air is characterized by a free convection coefficient of h = 2 W?2 ⋅ Kb). When the person is in water at T∞ =…arrow_forward3. A food-processing plant requires that two large process areas A and B be kept at constant temperature TA 12°C. The refrigeration load of area A is 175 kW. The heating load of area B is 210 kW. Conditioning of the two spaces is achieved by an (cyclic) electrical air-conditioning and heating unit (CM) that also interacts with the environment at To = 5°C, as shown in the В., 12°С 8°C and TB Work R 5°C figure. А, —8°С a. What is the least amount of electrical power required to operate the air- conditioning and heating unit? b. Determine the rate of energy exchange between the unit (CM) and the environment in case a.arrow_forwardProblem #2: A mass of ice at -4°C is needed to cool 115 kg of vegetables in a bunker for 24 hours. The initial temperature of the vegetables is assumed to be 29°C. It is also assumed that, within the 24-hr period, the average temperature inside the bunker is 7°C. If the heat gained per hour in the bunker is 30% of the heat removed to cool the vegetables from 29°C to 7°C, what would be the required mass of ice in kg? Use: Specific heat of water 4.2292 kJ/kg-°C • Specific heat of ice 1.9387 kJ/kg-°C Specific heat of vegetables 3.35 kJ/kg-°Carrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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