Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2, Problem 2.58P
Consider the steady-state temperature distributions within a composite wall composed of Material A and Material B for the two cases shown. There is no internal generation. and the conduction process is one-dimensional. 
Answer the following questions for each case. Which material has the higher thermal conductivity? Does the thermal conductivity vary significantly with temperature? If so, how? Describe the heat flux distribution
Case l. Linear temperature distributions exist in both materials, as shown.
Case 2. Nonlinear temperature distributions exist in both materials. as shown.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A hollow aluminum sphere, with an electrical heater in the center, is used in tests to determine the thermal conductivity of insulating materials. The inner and outer radii of the sphere are o.18 and o.21 m, respectively, and testing is done under steady-state conditions with the inner surface of the aluminum maintained at 250°C. In a particular test, a spherical shell of insulation is cast on the outer surface of the sphere to a thickness of o.15 m. The system is in a room for which the air temperature is 20°C and the convection coefficient at the outer surface of the insulation is 30 W/m2. K. If 80 W is dissipated by the heater under steady-state conditions, what is the thermal conductivity of the insulation?
What is the analogical reason between heat transfer by conduction and flow of electricity through ohmic resistance? Use a composite wall of a building to illustrate the concept. A composite slab with three layers of thermal conductivities k1, k2, k3 and thickness ti, t2, të respectively, are placed in a close contact. Derive an expression from the first principle for the heat flow through the composite slab per unit surface area in terms of the overall temperature difference across the slab.
Sputnik 1, the first satellite launched into space by the Russians in 1957, is a 2-shell aluminum alloy (2024-T6) sphere. The highly polished outer shell (seeing deep space) is 585 mm in diameter, and has thickness of 1 mm (ID = 583 mm). The inside shell is 2 mm thick. There is a contact resistance between the two aluminum shells of value Rc"= 200 m2·K/W. Inside the shell, there is a radio unit that is uniformly dissipating thermal energy of Qradio = 1 W. Determine the steady-state temperature on the inner shell’s inner wall (ignore the effects of the antennas).
Hint: You can use a radiation heat transfer coefficient hr = εσTshell3
Chapter 2 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - Assume steady-state, one-dimensional conduction in...Ch. 2 - A hot water pipe with outside radius r, has a...Ch. 2 - A spherical shell with inner radius r1 and outer...Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - A composite rod consists of two different...Ch. 2 - A solid, truncated cone serves as a support for a...Ch. 2 - To determine the effect of the temperature...Ch. 2 - A young engineer is asked to design a thermal...Ch. 2 - A one-dimensional plane wall of thickness 2L=100mm...
Ch. 2 - Consider steady-state conditions for...Ch. 2 - Consider a plane wall 100 mm thick and of thermal...Ch. 2 - A cylinder of radius ro, length L, and thermal...Ch. 2 - In the two-dimensional body illustrated, the...Ch. 2 - Consider the geometry of Problem 2.14 for the case...Ch. 2 - Steady-state, one-dimensional conduction occurs in...Ch. 2 - An apparatus for measuring thermal conductivity...Ch. 2 - An engineer desires to measure the thermal...Ch. 2 - Consider a 300mm300mm window in an aircraft. For a...Ch. 2 - Consider a small but known volume of metal that...Ch. 2 - Use INT to perform the following tasks. Graph the...Ch. 2 - Calculate the thermal conductivity of air,...Ch. 2 - A method for determining the thermal conductivity...Ch. 2 - Compare and contrast the heat capacity cp of...Ch. 2 - A cylindrical rod of stainless steel is insulated...Ch. 2 - At a given instant of time, the temperature...Ch. 2 - A pan is used to boil water by placing it on a...Ch. 2 - Uniform internal heat generation at q=5107W/m3 is...Ch. 2 - Consider a one-dimensional plane wall with...Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - The temperature distribution across a wall 0.3 m...Ch. 2 - Prob. 2.33PCh. 2 - One-dimensional, steady-state conduction with...Ch. 2 - Derive the heat diffusion equation, Equation 2.26,...Ch. 2 - Derive the heat diffusion equation, Equation 2.29....Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - cylindrical system illustrated has negligible...Ch. 2 - Beginning with a differential control volume in...Ch. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - For a long circular tube of inner and outer radii...Ch. 2 - Passage of an electric current through a long...Ch. 2 - Two-dimensional. steady-state conduction occurs in...Ch. 2 - An electric cable of radius r1 and thermal...Ch. 2 - A spherical shell of inner and outer radii ri and...Ch. 2 - A chemically reacting mixture is stored in a...Ch. 2 - A thin electrical heater dissipating 4000W/m2 is...Ch. 2 - The one-dimensional system of mass M with constant...Ch. 2 - Consider a one-dimensional plane wall of thickness...Ch. 2 - A large plate of thickness 2L is at a uniform...Ch. 2 - The plane wall with constant properties and no...Ch. 2 - Consider the steady-state temperature...Ch. 2 - A plane wall has constant properties, no internal...Ch. 2 - A plane wall with constant properties is initially...Ch. 2 - Consider the conditions associated with Problem...Ch. 2 - Consider the steady-state temperature distribution...Ch. 2 - A spherical particle of radius r1 experiences...Ch. 2 - Prob. 2.64PCh. 2 - A plane wall of thickness L=0.1m experiences...Ch. 2 - Prob. 2.66PCh. 2 - A composite one-dimensional plane wall is of...Ch. 2 - Typically, air is heated in a hair dryer by...Ch. 2 - Prob. 2.69P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- A section of a composite wall with the dimensions shown below has uniform temperatures of 200C and 50C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA=70W/mK,kB=60W/mK, kC=40W/mK, and kP=20W/mK, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces. Repeat Problem 1.34, including a contact resistance of 0.1 K/W at each of the interfaces.arrow_forwardHeat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of TiandTo, respectively. Derive an expression for the temperature distribution.arrow_forwardA hollow sphere with inner and outer radii of R1 and R2, respectively, is covered with a layer of insulation having an outer radius of R3. Derive an expression for the rate of heat transfer through the insulated sphere in terms of the radii, the thermal conductivities, the heat transfer coefficients, and the temperatures of the interior and the surrounding medium of the sphere.arrow_forward
- 1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.arrow_forwardAn important concern in the study of heat transfer is to determine the steady-state temperature distribution of the thin plate when the temperature around the boundary is known. Assume the plate shown in the figure represents the cross section of metal beam with negligible heat flow in the direction perpendicular to the plate. Let denotes the temperature at the four interior nodes of the mesh in the figure. The temperature in the node is approximately equal to the average of the four nearest nodes-to the left, above, to right and below. Write the system of four equations whose solution gives the estimate for the temperature Solve the system for four equations to calculate .T1,T2,T3,T4.arrow_forwardAn 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. 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?arrow_forward
- 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 m^2. What does this heat energy represent in terms of the refrigeration system of the cold room? b) Without any calculations, how would you expect the internal and external air temperatures to be relative to the wall surface temperatures?c) How do you expect the heat gain calculated in question 1a) above…arrow_forwardA plane wall of thickness L and conductivity of k is covered with an insulation layer of thickness L’ and conductivity k’. With the insulation it is aimed to reduce heat loss up to 20%. If the conductivity ratio of wall to insulation is 20 what will be the thickness ratio of wall to insulation to achieve the aimed heat loss reduction?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Understanding Conduction and the Heat Equation; Author: The Efficient Engineer;https://www.youtube.com/watch?v=6jQsLAqrZGQ;License: Standard youtube license