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 3, Problem 3.34P
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Problem 1. (Taken from Bergman et.al. 2011*) An igloo is built in the shape of a hemisphere,
with an inner radius of 1.8 m and walls of compacted snow that are 0.5 m thick. On the inside of
the igloo the surface heat transfer coefficient is 6 W/m².K; on the outside, under normal wind
conditions, it is 15 W/m².K. The thermal conductivity of compacted snow is 0.15 W/m.K. The
temperature of the ice cap on which the igloo sits is -20 °C and has the same thermal conductivity
as the compacted snow.
Artic wind Too
Tair
Ice cap Tice
Igloo
Assuming that the occupants' body heat provides a continuous source of 320 W within the igloo,
calculate the inside air temperature when the outside air temperature is T∞ = -40 °C draw a thermal
circuit for the heat transfer from the igloo. Be sure to consider heat losses through the floor of igloo
where the heat transfer coefficient is 6 W/m²K.
Question 1
An industrial cold room has four 200 mm thick walls made of concrete. The walls are
insulated on the outside with a layer of foam 60 mm thick. Cladding with a thickness of
15 mm protects the foam on the outside from the elements. The composite wall surface
temperatures are -3 °C on the inside and 18 °C on the outside of the room respectively.
The thermal conductivities of concrete, foam and cladding are 0.75, 0.35 and 0.5 W/m K
respectively.
a) Assuming perfect thermal contact between the layers of the composite walls, draw
the typical temperature distribution across the layers and determine the heat energy
gained per hour through all 4 walls of the room with a total surface area of 20 m².
What does this heat energy represent in terms of the refrigeration system of the cold
room?
Question 1
An industrial cold room has four 200 mm thick walls made of concrete. The walls are
insulated on the outside with a layer of foam 60 mm thick. Cladding with a thickness of
15 mm protects the foam on the outside from the elements. The composite wall surface
temperatures are -3 °C on the inside and 18 °C on the outside of the room respectively.
The thermal conductivities of concrete, foam and cladding are 0.75, 0.35 and 0.5 W/m K
respectively.
a) Assuming perfect thermal contact between the layers of the composite walls, draw
the typical temperature distribution across the layers and determine the heat energy
gained per hour through all 4 walls of the room with a total surface area of 20 m².
What does this heat energy represent in terms of the refrigeration system of the cold
room?
b)
c)
Without any
calculations, how would you expect the internal and external air
temperatures to be relative to the wall surface temperatures? Explain your answer.
How do you expect the heat gain…
Chapter 3 Solutions
Introduction to Heat Transfer
Ch. 3 - Consider the plane wall of Figure 3.1, separating...Ch. 3 - A new building to be located in a cold climate is...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - A dormitory at a large university, built 50 years...Ch. 3 - In a manufacturing process, a transparent film is...Ch. 3 - Prob. 3.7PCh. 3 - A t=10-mm-thick horizontal layer of water has a...Ch. 3 - Prob. 3.9PCh. 3 - The wind chill, which is experienced on a cold,...
Ch. 3 - Prob. 3.11PCh. 3 - A thermopane window consists of two pieces of...Ch. 3 - A house has a composite wall of wood, fiberglass...Ch. 3 - Prob. 3.14PCh. 3 - Prob. 3.15PCh. 3 - Work Problem 3.15 assuming surfaces parallel to...Ch. 3 - Consider the oven of Problem 1.54. The walls of...Ch. 3 - The composite wall of an oven consists of three...Ch. 3 - The wall of a drying oven is constructed by...Ch. 3 - The t=4-mm-thick glass windows of an...Ch. 3 - Prob. 3.21PCh. 3 - In the design of buildings, energy conservation...Ch. 3 - Prob. 3.23PCh. 3 - Prob. 3.24PCh. 3 - Prob. 3.25PCh. 3 - A composite wall separates combustion gases at...Ch. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - Prob. 3.29PCh. 3 - The performance of gas turbine engines may...Ch. 3 - A commercial grade cubical freezer, 3 m on a...Ch. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A batt of glass fiber insulation is of density...Ch. 3 - Air usually constitutes up to half of the volume...Ch. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - The diagram shows a conical section fabricatedfrom...Ch. 3 - Prob. 3.40PCh. 3 - From Figure 2.5 it is evident that, over a wide...Ch. 3 - Consider a tube wall of inner and outer radii ri...Ch. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.46PCh. 3 - To maximize production and minimize pumping...Ch. 3 - A thin electrical heater is wrapped around the...Ch. 3 - Prob. 3.50PCh. 3 - Prob. 3.51PCh. 3 - Prob. 3.52PCh. 3 - A wire of diameter D=2mm and uniform temperatureT...Ch. 3 - Prob. 3.54PCh. 3 - Electric current flows through a long rod...Ch. 3 - Prob. 3.56PCh. 3 - A long, highly polished aluminum rod of diameter...Ch. 3 - Prob. 3.58PCh. 3 - Prob. 3.59PCh. 3 - Prob. 3.60PCh. 3 - Prob. 3.61PCh. 3 - Prob. 3.62PCh. 3 - Consider the series solution, Equation 5.42, for...Ch. 3 - Prob. 3.64PCh. 3 - Copper-coated, epoxy-filled fiberglass circuit...Ch. 3 - Prob. 3.66PCh. 3 - A constant-property, one-dimensional Plane slab of...Ch. 3 - Referring to the semiconductor processing tool of...Ch. 3 - Prob. 3.69PCh. 3 - Prob. 3.70PCh. 3 - Prob. 3.71PCh. 3 - The 150-mm-thick wall of a gas-fired furnace is...Ch. 3 - Steel is sequentially heated and cooled (annealed)...Ch. 3 - Prob. 3.74PCh. 3 - Prob. 3.75PCh. 3 - Prob. 3.76PCh. 3 - Prob. 3.77PCh. 3 - Prob. 3.78PCh. 3 - The strength and stability of tires may be...Ch. 3 - Prob. 3.80PCh. 3 - Prob. 3.81PCh. 3 - A long rod of 60-mm diameter and thermophysical...Ch. 3 - A long cylinder of 30-min diameter, initially at a...Ch. 3 - Work Problem 5.47 for a cylinder of radius r0 and...Ch. 3 - Prob. 3.85PCh. 3 - Prob. 3.86PCh. 3 - Prob. 3.87PCh. 3 - Prob. 3.88PCh. 3 - Prob. 3.89PCh. 3 - Prob. 3.90PCh. 3 - Prob. 3.91PCh. 3 - Prob. 3.92PCh. 3 - In Section 5.2 we noted that the value of the Biot...Ch. 3 - Prob. 3.94PCh. 3 - Prob. 3.95PCh. 3 - Prob. 3.96PCh. 3 - Prob. 3.97PCh. 3 - Prob. 3.98PCh. 3 - Work Problem 5.47 for the case of a sphere of...Ch. 3 - Prob. 3.100PCh. 3 - Prob. 3.101PCh. 3 - Prob. 3.102PCh. 3 - Prob. 3.103PCh. 3 - Consider the plane wall of thickness 2L, the...Ch. 3 - Problem 4.9 addressed radioactive wastes stored...Ch. 3 - Prob. 3.106PCh. 3 - Prob. 3.107PCh. 3 - Prob. 3.108PCh. 3 - Prob. 3.109PCh. 3 - Prob. 3.110PCh. 3 - A one-dimensional slab of thickness 2L is...Ch. 3 - Prob. 3.112PCh. 3 - Prob. 3.113PCh. 3 - Prob. 3.114PCh. 3 - Prob. 3.115PCh. 3 - Derive the transient, two-dimensional...Ch. 3 - Prob. 3.117PCh. 3 - Prob. 3.118PCh. 3 - Prob. 3.119PCh. 3 - Prob. 3.120PCh. 3 - Prob. 3.121PCh. 3 - Prob. 3.122PCh. 3 - Consider two plates, A and B, that are each...Ch. 3 - Consider the fuel element of Example 5.11, which...Ch. 3 - Prob. 3.125PCh. 3 - Prob. 3.126PCh. 3 - Prob. 3.127PCh. 3 - Prob. 3.128PCh. 3 - Prob. 3.129PCh. 3 - Consider the thick slab of copper in Example 5.12,...Ch. 3 - In Section 5.5, the one-term approximation to the...Ch. 3 - Thermal energy storage systems commonly involve a...Ch. 3 - Prob. 3.133PCh. 3 - Prob. 3.134PCh. 3 - Prob. 3.135PCh. 3 - A tantalum rod of diameter 3 mm and length 120 mm...Ch. 3 - A support rod k=15W/mK,=4.0106m2/s of diameter...Ch. 3 - Prob. 3.138PCh. 3 - Prob. 3.139PCh. 3 - A thin circular disk is subjected to induction...Ch. 3 - An electrical cable, experiencing uniform...Ch. 3 - Prob. 3.142PCh. 3 - Prob. 3.145PCh. 3 - Consider the fuel element of Example 5.11, which...Ch. 3 - Prob. 3.147PCh. 3 - Prob. 3.148PCh. 3 - Prob. 3.149PCh. 3 - Prob. 3.150PCh. 3 - In a manufacturing process, stainless steel...Ch. 3 - Prob. 3.153PCh. 3 - Carbon steel (AISI 1010) shafts of 0.1-m diameter...Ch. 3 - A thermal energy storage unit consists of a large...Ch. 3 - Small spherical particles of diameter D=50m...Ch. 3 - A spherical vessel used as a reactor for producing...Ch. 3 - Batch processes are often used in chemical and...Ch. 3 - Consider a thin electrical heater attached to a...Ch. 3 - An electronic device, such as a power transistor...Ch. 3 - Prob. 3.161PCh. 3 - In a material processing experiment conducted...Ch. 3 - Prob. 3.165PCh. 3 - Prob. 3.166PCh. 3 - Prob. 3.167PCh. 3 - Prob. 3.168PCh. 3 - Prob. 3.173PCh. 3 - Prob. 3.174PCh. 3 - Prob. 3.175PCh. 3 - Prob. 3.176PCh. 3 - Prob. 3.177P
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- Bebang owns a 830-mm-thick concrete brick table top that has an area of 10,000,000 mm^2 and a 0.750-cm-thick glass plate that has an area of 20,000 cm^2. Assuming the same temperature difference across each, what is the ratio of the rate of heat conduction through the plate with respect to the rate of heat conduction through the table top? Use Table 10.1(given below) for the value of Thermal Conductivity k. Table 10.1 Thermat Conductivities of Common Substances Values are given for temperatures near o °C. Substance Thermal Conductivity k (W/m-O Diamond 2000 Silver 420 Copper 390 Gold 318 Aluminum 220 Steel iron Steel (stainless) 14 Ice 2.2 Glass (average) 0.84 Concrete brick O.84 water 0.6 Fatty tissue (without blood) 0.2 Asbestos 0.16 Plasterboard 0.16 wood 0.08-0.16 Snow (dry) 0.10 Cork 0.042 Glass wool 0.042 wool 0.04 Down feathers 0.025 Air 0.023 Polystyrene foam 0.010arrow_forwardDetermine the heat flux through the composite walls as shown in Figure. The frontal area (normal to heat flow) for the layers of Fir brick and Brick is 1 sq.m. The frontal area for Asbestos and Earth layers are equal and the summation of the frontal areas of them is 1 sq.m. as shown required to answer. OPTIONS: 1.Heat flux is around 487.3 Watt 2.Heat flux is around 742.7 Watt 3.Heat flux is around 305.4 Watt 4.Nonearrow_forwardI need answers with clear hand writing or using Microsoft word . ASAP INTRODUCTION: for (HEAT TRANSFER THROUGH COMPOSITE WALLS) note: i want a lot of informationarrow_forward
- An electrical resistance wire made of tungsten dissipates heat to the surroundings at a constant rate. Which of the following equations are you going to use to compute for the temperature at any point within the wire when the temperature throughout the whole wire no longer changes with time? Assume that the wire can be approximated as a thin cylinder. a. Fourier-Biot equation b. Poisson equation c. Diffusion equation d. Laplace equationarrow_forward2. One end of a 40 cm metal rod 2.0 cm2 in cross section is in a steam bath while the other end is embedded in ice. It is observed that 13.3 grams of ice melted in 15 minutes from the heat conducted by the rod. What is the thermal conductivity of the rod.arrow_forwardQuestion 1 A composite component is comprised of a tube and a concentric rod running inside it, both with a length of 1.5 meters. The tube is made of copper and has inner and outer diameters of 60 mm and 100 mm, respecti vely, a coefficient of thermal expansion and elastic modulus of 17 x10-6C and 117 GPa, respectively. The rod is made of aluminium with a diameter, coefficient of thermal expansion and elastic modulus of 50 mm, 23 x10-6C and 80 GPa, respectively. If the composite is exposed to a temperature rise of 120°C, determine: The sense and magnitude of the stresses induced in the composite if it is not restrained. 1.1 1.2 The sense and magnitude of the stresses induced in the composite ifit is partially restrained with an allowed free expansion of 0.3 mm.arrow_forward
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