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
Textbook Question
Chapter 2, Problem 2.6P
A composite rod consists of two different materials, A and B, each of length 0.5L.
The thermal conductivity of Material A is half that of Material B, that is,
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A new 1 ft thick insulating material was recently tested for heat resistant properties. The data recorded temperatures of 70 deg. F and 210 deg. F on the cold and hot sides, respectively. If the thermal conductivity of the insulating material is 0.026 Btu/ft . h .⁰ F, calculate the rate of the heat flux,Q/A, through the wall in Btu/ft^2 . h. Resolve the problem in SI units.
The cross-sectional area of a conical piece made of pure aluminum has a diameter D = a.x ^ 1/2 and a = 0.5m ^ 1/2.The left edge surface of the part is at x1 = 25 mm, and the right edge surface is x2 = 125 mm. Edge temperatures are T1 = 600K and T2 = 400K and the side surface is completely insulated.a) Assuming that the heat conduction is one dimensional, write a relation for the temperature distribution T (x).b) Calculate the heat transfer.
The cross section radius of a bar of metal of length L and uniform coefficient of thermal conductivity k is expressed as r = (1 + x)1/2, where x is the distance from one end of the bar. Calculate the rate of heat transfer H if the two ends are kept at temperatures TH and TL respectively
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
- 1.4 To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in W/m K. Problem 1.4arrow_forward1.63 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_forwardA 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_forward
- An experiment was conducted to measure thermal conductivity of a formulated food. The measurement was made by using a large plane plate of the food material, which was 5 mm thick. It was found, under steady-state conditions,that when a temperature difference of 35°C was maintained between the two surfaces of the plate, a heat-transfer rate per unit area of 4700 W/m 2 was measured near the center of either surface. Calculate the thermal conductivity of the product, and list two assumptions used in obtaining the result.arrow_forwardWhat 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.arrow_forwardThe composite wall of a furnace consists of three different materials, two of which have known thermal conductivity (ka = 20 W/m°C and kc = 50 W/m°C) and thicknesses La = 0.30 m and Lb = 0.15 m. The third material (B) is between A and C, with a thickness of 0.15 m, but its thermal conductivity (kb) is unknown. Under steady-state operating conditions, measurements reveal a temperature of 20 °C on the external surface, 600 °C on the internal surface, and a furnace ambient temperature of 800 °C. The internal convection coefficient is 25 W/m²°C. What is the value of kb?arrow_forward
- An aluminum pipe has a length of 75 m at a temperature of 18°C. An adjacent steel pipe at the same temperature is 5 mm longer than the aluminum pipe. At what temperature (°C) will the aluminum pipe be 15 mm longer than the steel pipe? (Assume that the coefficients of thermal expansion of aluminum and steel are αa = 23 x 10^–6/°C and αs = 12 x 10^–6/°C, respectively.)arrow_forwardThe temperatures on the faces of a plane wall 20 cm thick are 400 and 90 ℃. The wall is constructed of a special glass with the following properties: k = 0.8 W∙m-1K-1, ρ = 2750 kgm-3, cP = 0.86 kJkg-1K-1. What is the heat flux (q") through the wall at steady-state conditions?arrow_forwardThe diagram below shows a composite wall 1 m deep. The first layer of thickness LA is made of special refractory material (kA=0.50 W/m.K). The second layer, 0.30 m thick, consists of insulating material A (kB=0.1 W/m.K) and insulating material B (kC = 0.35 W/m.K). The temperature on the inner face of A (Tsup) is equal to 900°C and the ambient temperature (Tamb) is equal to 25°C. The heat transfer coefficient h is equal to 10 W/m2.K. The rate of heat through the oven wall is constant and equal to 2500 W. Determine the thickness of the layer LA that forms wall A.arrow_forward
- The diagram below shows a composite wall 1 m deep. The first layer of thickness LA is made of special refractory material (kA=0.50 W/m.K). The second layer, 0.30 m thick, consists of insulating material A (kB=0.1 W/m.K) and insulating material B (kC = 0.35 W/m.K). The temperature on the inner face of A (Tsup) is equal to 900°C and the ambient temperature (Tamb) is equal to 25°C. The heat transfer coefficient h is equal to 10 W/m2.K. The rate of heat through the oven wall is constant and equal to 2500 W. Determine the thickness of the layer LA that forms wall A. What is the correct option? Present the calculation. a. 1,02 m b. 56 cm c. 27 cm d. 70 cm e. 12 cmarrow_forwardA square silicon chip (k = 150 W/m • K) has side width w = 5 mm and thickness z = 1 mm.The chip is mounted on a substrate so that its sides and interior surface are insulated. whilethat the front surface is exposed to a cooling fluid.If 4 W is dissipated from the circuitry mounted on the back surface of the chip, what is the difference insteady-state temperatures between the bottom and front surfaces?arrow_forward5. A 10-in nominal pipe (outside diameter = 10.75in) is covered with a composite pipe insulation consisting of 2.0 in of insulation I placed next to the pipe and 1.5 in of insulation II placed upon insulation I. Assume that the inner and outer surface temperatures of the composite insulation are 900F and 150F respectively, and that the thermal conductivity of material I is 0.05 BTU/hr-ft-F and for material II is 0.039 BTU/hr-ft-F. What is the individual thermal resistance of insulation I?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
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
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license