A person puts a few apples into the freezer at -13°C to cool them quickly for guests who are about to arrive. Initially, the apples are at a uniform temperature of 37°C, and the heat transfer coefficient on the surfaces is 6.3 W/m2 · °C. Treating the apples as 8.2-cm-diameter spheres and taking their properties to be ρ= 836 kg/m3, Cp = 4.05 kJ/kg · °C, k= 0.426 W/m · °C, and α= 1.43 ×10-7 m2/s, determine the center and surface temperatures of the apples in 1.9 h

A person puts a few apples into the freezer at -13°C to cool them quickly for guests who are about to arrive. Initially, the apples are at a uniform temperature of 37°C, and the heat transfer coefficient on the surfaces is 6.3 W/m2 · °C. Treating the apples as 8.2-cm-diameter spheres and taking their properties to be ρ= 836 kg/m3, Cp = 4.05 kJ/kg · °C, k= 0.426 W/m · °C, and α= 1.43 ×10-7 m2/s, determine the center and surface temperatures of the apples in 1.9 h

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 1.9P: Heat is transferred at a rate of 0.1 kW through glass wool insulation (density=100kg/m3) with a 5-cm...

See similar textbooks

Similar questions

A person puts a few apples into the freezer at 15°C cool them quickly for guestswho are about to arrive. Initially, the apples are at a uniform temperature of 20°C,and the heat transfer coefficient on the surfaces is 8 W/m2·K. Treating the apples as9-cm-diameter spheres and taking their properties to be 840 kg/m3, Cp 3.81 kJ/kg·K, k = 0.418 W/m·K, and α =10-7 m2/s, determine the center and surface temperatures of the apples in 1 h. Also, determine the amount of heat transfer from each apple. Solve this problem using analytical one-term approximation method (notthe Heisler charts). Answer: Center: 11.2 ℃, Surface: 2.7 ℃, heat transfer: 17.2 kJ
A person puts a few apples into the freezer at 215°C tocool them quickly for guests who are about to arrive. Initially,the apples are at a uniform temperature of 20°C, and the heattransfer coefficient on the surfaces is 8 W/m2·K. Treating theapples as 9-cm-diameter spheres and taking their properties tobe r = 840 kg/m3, cp = 3.81 kJ/kg·K, k = 0.418 W/m·K, anda = 1.3 * 1027 m2/s, determine the center and surface temperaturesof the apples in 1 h. Also, determine the amount ofheat transfer from each apple. Solve this problem using analyticalone-term approximation method (not the Heisler charts).
For heat transfer purposes, a standing man can be modeled as a 30-cm-diameter, 175-cm-long vertical cylinder with both the top and bottom surfaces insulated and with the side surface at an average temperature of 34°C. For a convection heat transfer coefficient of 10 W/m2 ·°C, determine the rate of heat loss from this man by convection in an environment at 20°C.
Consider a 2-m-high electric hot-water heater thathas a diameter of 40 cm and maintains the hot water at 55°C.The tank is located in a small room whose average temperatureis 27°C, and the heat transfer coefficients on the innerand outer surfaces of the heater are 50 and 12 W/m2·K,respectively. The tank is placed in another 46-cm-diametersheet metal tank of negligible thickness, and the spacebetween the two tanks is filled with foam insulation (k =0.03 W/m·K). The thermal resistances of the water tank andthe outer thin sheet metal shell are very small and can be neglected. The price of electricity is $0.08/kWh, and the home owner pays $280 a year for water heating. Determine the fraction of the hot-water energy cost of this household that is due to the heat loss from the tank. Hot-water tank insulation kits consisting of 3-cm-thick fiberglass insulation (k = 0.035 W/m·K) large enough to wrap the entire tank are available in the market for about $30. If such an insulation is installed on…
A 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.06 W. The board is impregnated with copper fillings and has an effective thermal conductivity of 16 W/m · °C. All the heat generated in the chips is conducted across the circuit board and is dissipated from the back side of the board to the ambient air at 30°C, which is forced to flow over the surface by a fan at a free-stream velocity of 400 m/min. Determine the temperatures on the two sides of the circuit board.
An average man has a body surface area of 1.8 m2 and a skin temperature of 330C. The convective heat transfer coefficient for a clothed person walking in still air is expressed as h= 8.6V0.53 where V is the walking velocity in m/s. Assuming the average surface temperature of the clothed person to be 300C, determine the rate of heat lost by convection from an average man walking in still air at 100C at a walking velocity of 1.2 m/s.
Consider a cold aluminum canned drink that is initially at a uniform temperature of 4°C. The can is 12.5 cm high and has a diameter of 6 cm. If the combined convection/radiation heat transfer coefficient between the can and the surrounding air at 25°C is 10 W/m2 · °C, determine how long it will take for the average temperature of the drink to rise to 15°C. In an effort to slow down the warming of the cold drink, a person puts the can in a perfectly fitting 1-cm-thick cylindrical rubber insulator (k = 0.13 W/m · °C). Now how long will it take for the average temperature of the drink to rise to 15°C? Assume the top of the can is not covered.
The net radiant-heat exchange between a 20-by-20 ft rough plaster panel-heated ceiling and a 20-by-10-ft side wall, which has an emissivity of 0.80, is 2400 Btu/hr. If the surface temperature of the ceiling is 120 deg. F, determine the average surface temperature of the side wall.
The blades of a wind turbine turn a large shaft at a relatively slow speed. The rotational speed is increased by a gearbox that has an efficiency of 0.93. In turn, the gearbox output shaft drives an electric generator with an efficiency of 0.95. The cylindrical nacelle, which houses the gearbox, generator, and associated equipment, is of length L = 6 m and diameter D = 3 m. If the turbine produces P = 2.5 MW of electrical power, and the air and surroundings temperatures are T = 25 oC and Tsur = 20 oC, respectively, determine the minimum possible operating temperature inside the nacelle. The emissivity of the nacelle is 0.83, and the convective heat transfer coefficient is h = 35 W/m2 .K. The surface of the nacelle that is adjacent to the blade hub can be considered to be adiabatic, and solar irradiation may be neglected. Use Fin or N number of fins to reduce the Ts of the nacelle less than 143 oC
A 15-cm-diameter aluminum ball is to be heated from 80°C to anaverage temperature of 220C. Taking the average density and specific heat ofaluminum in this temperature range to be ρ=2700 kg/m3and Cp=0.90kJ/kg·°C, respectively, determine the amount of energy that needs to betransferred to the aluminum ball.
The chilling room of a meat plant is 15 m × 18 m × 5.5 m in size and has a capacity of 350 beef carcasses. The power consumed by the fans and the lights in the chilling room are 22 and 2 kW, respectively, and the room gains heat through its envelope at a rate of 14 kW. The average mass of beef carcasses is 220 kg. The carcasses enter the chilling room at 35C, after they are washed to facilitate evaporative cooling, and are cooled to 16°C in 12 h. The air enters the chilling room at 2.2°C and leaves at 0.5°C. Determine (a) the refrigeration load of the chilling room and (b) the volume flow rate of air. The average specific heats of beef carcasses and air are 3.14 and 1.0 kJ/kg · °C, respectively, and the density of air can be taken to be 1.28 kg/m3 .
A cylindrical fuel rod of 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel generates heat uniformly at a rate of 150 MW/m3. The convection heat transfer coefficient on the fuel rod is 5000 W/m2∙K, and the average temperature of the cooling water, sufficiently far from the fuel rod, is 70°C. Determine the surface temperature of the fuel rod and discuss whether the value of the given convection heat transfer coefficient on the fuel rod is reasonable.