Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 4, Problem 4.20P
A furnace of cubical shape, with external dimensions of0.35 m, is constructed from a refractory brick (fireclay).If the wall thickness is 50 mm, the inner surface temperatureis
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c) A steel pipe of 100 mm bore, and 10 mm bore thickness, carrying dry saturated steam at 28
bars, is insulated with a 40 mm layer of moulded insulation. This insulation in turn is
insulated with a 60 mm layer of felt. The atmospheric temperature is 15 °C.
Calculate:
(i) the rate of heat loss by the steam per metre pipe length.
(ii) the temperature of the outside
Dimensions in mm
surface.zzzzzzz
h₂-15 W/m²K
Steel
k₁=50 W/mK
AVALEHT
Ø100
1₂
"
Steam 28 bar
h-550 W/m²K,
Inner heat transfer coefficient = 550 W/m² K
Outer heat transfer coefficient = 15 W/m² K
Thermal conductivity of steel = 50 W/m K
Thermal conductivity of felt = 0.07 W/m K
Moulded
insulation
Felt
Moulded insulation
K₂=0.09 W/mK
Thermal conductivity of moulded insulation = 0.09 W/m
40
10.
A
60
15°C
Felt
K₁=0.07 W/mK
zzzzzzzz
The Diamond Ring Solution. The processing chip on the computer that controls the navigation equipment on your spacecraft is
overheating. Unless you fix the problem, the chip will be damaged and the navigation system will shut down. You open the panel and
find that the small copper disk that was supposed to bridge the gap between the smooth top of the chip and the cooling plate is
missing, leaving a 2.0 mm gap between them. In this configuration, the heat cannot escape the chip at the required rate. You notice by
the thin smudge of thermal grease (a highly thermally conductive material used to promote good thermal contact between surfaces)
that the missing copper disk was 2.0 mm thick and had a díameter of 1.2 cm. You know that the chip is designed to run below 65 °C, and
the copper cooling plate is held at a constant 5.0 °C.
(a) What was the rate of heat flow from the chip to the copper plate when the original copper disk was in place and the chip was at its
maximum operating…
The Diamond Ring Solution. The processing chip on the computer that controls the navigation equipment on your spacecraft is
overheating. Unless you fix the problem, the chip will be damaged and the navigation system will shut down. You open the panel and
find that the small copper disk that was supposed to bridge the gap between the smooth top of the chip and the cooling plate is
missing, leaving a 2.0 mm gap between them. In this configuration, the heat cannot escape the chip at the required rate. You notice by
the thin smudge of thermal grease (a highly thermally conductive material used to promote good thermal contact between surfaces)
that the missing copper disk was 2.0 mm thick and had a diameter of 1.0 cm. You know that the chip is designed to run below 70 °C, and
the copper cooling plate is held at a constant 5.0 °C.
(a) What was the rate of heat flow from the chip to the copper plate when the original copper disk was in place and the chip was at its
maximum operating…
Chapter 4 Solutions
Introduction to Heat Transfer
Ch. 4 - In the method of separation of variables (Section...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Consider the two-dimensional rectangular plate...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Free convection heat transfer is sometimes...Ch. 4 - Prob. 4.8PCh. 4 - Radioactive wastes are temporarily stored in a...Ch. 4 - Based on the dimensionless conduction heat rates...
Ch. 4 - Prob. 4.11PCh. 4 - A two-dimensional object is subjected to...Ch. 4 - Prob. 4.13PCh. 4 - Two parallel pipelines spaced 0.5 m apart are...Ch. 4 - A small water droplet of diameter D=100m and...Ch. 4 - Prob. 4.16PCh. 4 - Pressurized steam at 450 K flows through a long,...Ch. 4 - Prob. 4.19PCh. 4 - A furnace of cubical shape, with external...Ch. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - A pipeline, used for the transport of crude oil,...Ch. 4 - A long power transmission cable is buried at a...Ch. 4 - Prob. 4.25PCh. 4 - A cubical glass melting furnace has exterior...Ch. 4 - Prob. 4.27PCh. 4 - An aluminum heat sink k=240W/mK, used to coolan...Ch. 4 - Hot water is transported from a cogeneration power...Ch. 4 - Prob. 4.30PCh. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - An igloo is built in the shape of a hemisphere,...Ch. 4 - Consider the thin integrated circuit (chip) of...Ch. 4 - Prob. 4.35PCh. 4 - The elemental unit of an air heater consists of a...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Prob. 4.39PCh. 4 - Prob. 4.40PCh. 4 - Prob. 4.41PCh. 4 - Determine expressions for...Ch. 4 - Prob. 4.43PCh. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - Derive the nodal finite-difference equations for...Ch. 4 - Prob. 4.47PCh. 4 - Prob. 4.48PCh. 4 - Consider a one-dimensional fin of uniform...Ch. 4 - Prob. 4.50PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - Prob. 4.54PCh. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - Steady-state temperatures at selected nodal points...Ch. 4 - Prob. 4.58PCh. 4 - Prob. 4.60PCh. 4 - The steady-state temperatures C associated with...Ch. 4 - A steady-state, finite-difference analysis has...Ch. 4 - Prob. 4.64PCh. 4 - Consider a long bar of square cross section (0.8 m...Ch. 4 - Prob. 4.66PCh. 4 - Prob. 4.67PCh. 4 - Prob. 4.68PCh. 4 - Prob. 4.69PCh. 4 - Consider Problem 4.69. An engineer desires to...Ch. 4 - Consider using the experimental methodology of...Ch. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Prob. 4.74PCh. 4 - Prob. 4.75PCh. 4 - Prob. 4.76PCh. 4 - Prob. 4.77PCh. 4 - Prob. 4.78PCh. 4 - Prob. 4.79PCh. 4 - Prob. 4.80PCh. 4 - Spheres A and B arc initially at 800 K, and they...Ch. 4 - Spheres of 40-mm diameter heated to a uniform...Ch. 4 - To determine which parts of a spiders brain are...Ch. 4 - Prob. 4.84P
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- Please solve asap, Will provide helpful ratings for complete solution. Thank u A double-glazed window is constructed such that it has 5 mm thick glass as the inside layer, 4 mm layer of gas, and finally 5 mm thick glass as the outer layer. Which have thermal conductivies of 0.7, 2.120, and 5.9 W m-1 K-1, respectively. Calculate the heat loss per unit area, Wm-2 through the glass if the inside temperature of the glass is 11.09 °C and the outside temperature is 6.47 °C Report your answer to 2 decimal places.arrow_forwardQuestion(2): The ceiling outer surface temperature of an oven is 60°C. If the oven is in an environment of 20 °C and the ceiling is 1 m wide and 2 m long. find the heat loss from the furnace ceiling surface. NOTE: Use the physical properties of the air at 40°C for the environment.arrow_forward5. A horizontal disc of 9 cm diameter, which is at a temperature of 45°C, is immersed facing upward in a pool of 25°C water. Calculate the total heat transfer from the surface to the water.arrow_forward
- An oil storage tank has 20mm steel walls covered with 50mm of fiber glass insulation. if the oil temperature is kept at 150 degree Celsius, what is the rate of heat loss when the outside temperature is 20 degree Celsius and external air coefficient is 20W/m². How much would the heat loss be reduced by doubling the thickness of the insulation?arrow_forwardA cold storage room has a wall consists of an inside finish of 0.60 in cement plaster(k = 0.67), two layers of corkboard each 2.5 in thick (k = 0.03) and an outside layer of building tile. The value of U for the entire wall is 0.058, the internal air filmcoefficient is 1.65, the inner temperature is 23°F and the outside temperature is85°F. Calculate the heat flow through the unit wall area, Btu/hr.ft2A. 1.47 B. 2.47 C. 3.47 D. 4.47arrow_forwardProblem 1 A hot water pipe is used for domestic applications is insulated with a layer of calcium silicate. If the insulation is 25 mm thick and its inner and outer surfaces are maintained at Ts,1 = 800 K and Ts,2 = 400 K, respectively. The outside diameter is 0.12 m. Given the thermal conductivity calcium silicate insulation equals to 0.09 W/m.K. A. Define the difference between lagged and unlagged pipes. B. Calculate the heat loss per unit length for this pipe.arrow_forward
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- An 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_forwardA composite wall is composed of 8 in. of fire-clay brick, 6 in. of chrome brick, and4 in. of common brick. The inside wall surface temperature is 2000"F, and the outsidesurface temperature is 300"F. Determine (a) the heat loss per ft2 of wall area; (b) thetemperatures at the brick interfaces; (c) the temperature 8 in. in from the outer surface.arrow_forwardA composite wall is formed of a 2.5 cm copper plate, a 3.2 mm layer of asbestos,and a 5 cm layer of fiberglass. The wall is subjected to an overall temperaturedifference of 560oC. Calculate the heat flux through the composite structure.arrow_forward
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