spherical container is made of plastic (k=2 W/mK, ρ=5000 kg/m) and has inner and outer radii of 10 cm and 11 cm, respectively. Hot oil (c=3000 J/kgK, ρ=800 kg/m3 ) at 80 0C is stored within the container and the heat transfer coefficient between the oil and the inner surface of the container h=5 W/m2K . The outer surface of the container is perfectly insulated. Solve the differential equation under the boundary conditions for steady one dimensional heat conduction through the plastic material. h (W/m2K)=? a) Obtain an equation for the variation of temperature within the plastic material b) Calculate the temperature of the plastic material at the inner surface c) Calculate the temperature of the plastic material at the inner surface

spherical container is made of plastic (k=2 W/mK, ρ=5000 kg/m) and has inner and outer radii of 10 cm and 11 cm, respectively. Hot oil (c=3000 J/kgK, ρ=800 kg/m3 ) at 80 0C is stored within the container and the heat transfer coefficient between the oil and the inner surface of the container h=5 W/m2K . The outer surface of the container is perfectly insulated. Solve the differential equation under the boundary conditions for steady one dimensional heat conduction through the plastic material. h (W/m2K)=? a) Obtain an equation for the variation of temperature within the plastic material b) Calculate the temperature of the plastic material at the inner surface c) Calculate the temperature of the plastic material at the inner surface

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.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.38P: 2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from...

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3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.
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
Consider a person standing in a breezy room at 20°C. Determine the total rate of heat transfer from this person if the exposed surface area and the average outer surface temperature of the person are 1.6 m2 and 29°C, respectively, and the convection heat transfer coefficient is 6 W/m2 ·°C (Fig. 2–75).
There are 3 windows in a room with a width of 100 cm and a height of 150 cm.There is a single glass (k=0. 9 W/mK) of 5 mm thickness in the windows initially. Instead of these glasses to save heatYou are considering replacing it with double glazing consisting of 5 mm glass and 12 mm air (k=0.022 W/mK). Indoor and outdoor environmenttemperatures are 20 0C and -10 0C, respectively, and the heat transfer coefficients are 7 W/m2 K and 25 W/m2 K. The total heat loss in the room is 3.5 kW.when switching to double glazing;a) Find the decrease in heat transfer. b) Considering that the heat given by the heaters remains 3.5 kW, what would the room temperature be?
The temperature of a cylindrical tank containing liquid nitrogen is -10 ° C. Tank diameter is 16 cm. The amount of heat lost by convection and radiation from the tank to the environment is 65.5 W / m. Calculate the temperature of the environment where the tank is located: h = 4.35 W / m2K, ∈ = 1.
In a multilayered rectangular wall, the thermal resistance of the first layer is 0.005 °C/W, the resistance of the second layer is 0.2° C/W, and for the third layer it is 0.1 ° C/W. The overall temperature gradient in the multilayered wall from one side to another is 70° C. a. Determine the heat flux through the wall. b. If the thermal resistance of the second layer is doubled to 0.4° C/W, what will be its influence in % on the heat flux, assuming the temperature gradient remains the same?
Consider a steam pipe of length 15 ft, inner radius 2 in., outer radius 2.4 in., and thermal conductivity 7.2 Btu/hr-ft-°F. Steam is flowing through the pipe at an average temperature of 250°F, and the average convection heat transfer coefficient on the inner surface is given to be 1.25 Btu/hr-ft2-°F. If the average temperature on the outer surfaces of the pipe is 160°F, determine the rate of heat loss from the steam through the pipe. ANSWER:______Btu/hr
Steam at 235°C is flowing inside a steel pipe (k = 61 W/m ∙ °C) whose inner and outer diameters are 10 cm and 12 cm, respectively, in an environment at 20°C. The heat transfer coefficients inside and outside the pipe are 105 W/m2 ∙ °C and 14 W/m2 ∙ °C, respectively. Determine (a) the thickness of the insulation (k = 0.038 W/m ∙ °C) needed to reduce the heat loss by 95 percent and (b) the thickness of the insulation needed to reduce the exposed surface temperature of insulated pipe to 40°C for safety reasons.
A 2 m X 1.5 m section of wall of an industrial furnace burning gas is not insulated, and the temperature at the outer surface of this section is measured to be 80oC. The temperature of the furnace room is 30oC, and the combined convection and radiation heat transfer coefficient at the surface of the outer furnace is 10 w/oC. It is proposed to insulate this section of the furnace wall with glass wool insulation (K=0.038 W/moC) in order to reduce the heat loss by 90 percent. Assuming the outer surface temperature of the section remains at about 80oC, determine i) the thickness of the insulation that is needed and ii) the outer surface temperature of the insulation after installation.
The passenger compartment of a minivan traveling at 60 mph can be modeled as a 3.2-ft-high, 6-ft-wide, and 11-ftlong rectangular box whose walls have an insulating value of R-3 (i.e., a wall thickness-to-thermal conductivity ratio of 3 h?ft2?°F/Btu). The interior of a minivan is maintained at an average temperature of 70°F during a trip at night while the outside air temperature is 90°F. The average heat transfer coefficient on the interior surfaces of the van is 1.2 Btu/h?ft2?°F. The air flow over the exterior surfaces can be assumed to be turbulent because of the intense vibrations involved, and the heat transfer coefficient on the front and back surfaces can be taken to be equal to that on the top surface. Disregarding any heat gain or loss by radiation, determine the rate of heat transfer from the ambient air to the van. Assume the air flow to be entirely turbulent because of the intense vibrations involved. Use a film temperature of 80°F for evaluations of air properties at 1 atm.
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