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 1, Problem 1.14P
To determine
The expression for the temperature gradient and the temperature distribution.
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A wall is made from an inhomogeneous (nonuniform) material for which the thermal conductivity varies through the thickness according to k = ax + b, where a and b are constants. The heat flux q"q" is known to be constant.
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Use the following values
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Chapter 1 Solutions
Introduction to Heat Transfer
Ch. 1 - The thermal conductivity of a sheet of rigid,...Ch. 1 - The heat flux that is applied to the left face of...Ch. 1 - A concrete wall, which has a surface area of 20m2...Ch. 1 - The concrete slab of a basement is 11 m long, 8 m...Ch. 1 - Consider Figure 1.3. The heat flux in the...Ch. 1 - Prob. 1.6PCh. 1 - The inner and outer surface temperatures of a...Ch. 1 - A thermodynamic analysis of a proposed Brayton...Ch. 1 - A glass window of width W=1m and height H=2m is 5...Ch. 1 - Prob. 1.10P
Ch. 1 - The heat flux that is applied to one face of a...Ch. 1 - Prob. 1.12PCh. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - The 5-mm-thick bottom of a 200-mm-diameter pan may...Ch. 1 - Prob. 1.16PCh. 1 - For a boiling process such as shown in Figure...Ch. 1 - You've experienced convection cooling if you've...Ch. 1 - Prob. 1.19PCh. 1 - A wall has inner and outer surface temperatures of...Ch. 1 - An electric resistance heater is embedded in a...Ch. 1 - Prob. 1.22PCh. 1 - A transmission case measures W=0.30m on a side and...Ch. 1 - Prob. 1.24PCh. 1 - A common procedure for measuring the velocity of...Ch. 1 - Prob. 1.26PCh. 1 - Prob. 1.27PCh. 1 - Prob. 1.28PCh. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Prob. 1.31PCh. 1 - Prob. 1.32PCh. 1 - Prob. 1.33PCh. 1 - Prob. 1.34PCh. 1 - An electrical resistor is connected to a battery,...Ch. 1 - Pressurized water pin=10bar,Tin=110C enters the...Ch. 1 - Consider the tube and inlet conditions of Problem...Ch. 1 - An internally reversible refrigerator has a...Ch. 1 - A household refrigerator operates with cold- and...Ch. 1 - Chips of width L=15mm on a side are mounted to a...Ch. 1 - Consider the transmission case of Problem 1.23,...Ch. 1 - One method for growing thin silicon sheets for...Ch. 1 - Heat is transferred by radiation and convection...Ch. 1 - Radioactive wastes are packed in a long,...Ch. 1 - An aluminum plate 4 mm thick is mounted in a...Ch. 1 - A blood warmer is to be used during the...Ch. 1 - Consider a carton of milk that is refrigerated at...Ch. 1 - The energy consumption associated with a home...Ch. 1 - Liquid oxygen, which hems a boiling point of 90 K...Ch. 1 - The emissivity of galvanized steel sheet, a common...Ch. 1 - Three electric resistance heaters of length...Ch. 1 - A hair dryer may be idealized as a circular duct...Ch. 1 - In one stage of an annealing process, 304...Ch. 1 - Convection ovens operate on the principle of...Ch. 1 - Annealing, an important step in semiconductor...Ch. 1 - In the thermal processing of semiconductor...Ch. 1 - A furnace for processing semiconductor materials...Ch. 1 - Single fuel cells such as the one of Example 1.5...Ch. 1 - Prob. 1.59PCh. 1 - Prob. 1.60PCh. 1 - Prob. 1.61PCh. 1 - A small sphere of reference-grade iron with a...Ch. 1 - A 50mm45mm20mm cell phone charger has a surface...Ch. 1 - A spherical, stainless steel (AISI 302) canister...Ch. 1 - Prob. 1.65PCh. 1 - Prob. 1.66PCh. 1 - A photovoltaic panel of dimension 2m4m is...Ch. 1 - Following the hot vacuum forming of a paper-pulp...Ch. 1 - Prob. 1.69PCh. 1 - Prob. 1.70PCh. 1 - Prob. 1.71PCh. 1 - The roof of a car in a parking lot absorbs a solar...Ch. 1 - Prob. 1.73PCh. 1 - Prob. 1.74PCh. 1 - Consider Problem 1.1. If the exposed cold surface...Ch. 1 - Prob. 1.76PCh. 1 - Prob. 1.77PCh. 1 - A thin electrical heating element provides a...Ch. 1 - Prob. 1.79PCh. 1 - Prob. 1.80PCh. 1 - Prob. 1.81PCh. 1 - The curing process of Example 1.9 involves...Ch. 1 - The diameter and surface emissivity of an...Ch. 1 - Bus bars proposed for use in a power transmission...Ch. 1 - A solar flux of 700W/m2 is incident on a...Ch. 1 - In considering the following problems involving...
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- 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_forwardIn the design of a certain computer application, a heat flow simulation is required. In the simulation, the heat conductor, which is of length 10m, has a perfectly insulated surface. The temperature at both ends of the conductor is kept consistently at zero. The initial temperature at any point of the conductor is uniform at 25°C. The 1-dimensional heat equation is given as follows: for all 0arrow_forwardA two dimensional rectangular plate is subjected to prescribed boundary conditions. Using the results of the analytical solution for the heat equation presented in class, calculate the temperature at the midpoint (1,0.5) by considering the first five nonzero terms of the infinite series that must be evaluated. T₁ = 50°C y (m) 1 T₂ = 150°C T₁ = 50°C ►x (m) 2 -T₁ = 50°Carrow_forwardSolve using the methodology : Known, Find, Schematic Diagram, Assumptions, Properties, Analysis and Comments.arrow_forwardQ1/ The fumace wall consists of 120 mm wide Reftactory bricks Air gap Insulating fire bricks -Plaster refractory brick and 120 mm wide insulating fire brick separated by an air gap. The outside wall is covered with a 12 mm thickness of plaster. The inner surface of the wall is at 1090°C and the - 1090°C room temperature is 20°C. The heat transfer coefficient from the outside wall surface to the air in the room is 18 W/m² °C, and the resistance to heat flow of the air gap is 0.16 °C /W. If the thermal conductivities of the refractory brick, insulating fire brick, and plaster are 1.6, 0.3 and 0.14 W/m. °C, respectively calculates: (i) Rate at which heat is lost per m of the wall surface; (ii) Each interface temperature. -20°C - 120 mm 120 mm12 mmarrow_forwardThe temperature distribution for the plane wall is given in Fig. and here T1 and T2 are the temperatures on both sides of the 2 walls. The thermal conductivity of the wall is constant and its thickness is L. T=T1 Subtract the expression for heat generation per unit volume based on x, which represents the distance from the wall for which the equation is satisfied. At x=0, take the heat generation rate as q0. T -T, - = C, +C,x² +C¸x' T, -T, | %3D |arrow_forwardQUESTION 2 hot steam pipe (k =16 W/m K) has an inside and outside diameter of 80 mm and 190 mm. If the temperature of the steam is 523 K with h 3000 W/m² K and the outside temperature of the pipe is 353 K. If the pipe is 2 m long compelete the following the thermal resistance of heat transfer by convection is = the conductive heat resistance is the heat transfer per unit length isarrow_forwardProblem 4 A cork board (k = 0.039W/m K) 3 cm thick is exposed to air with an average temperature T.. = 30°C with a convection heat transfer coefficient, h = 25 W/m².K. The other surface of the board is held at a constant temperature of 15°C. A volumetric heat generation of 5 W/m³ is occurring inside the wall. Assuming one dimensional conduction, write the governing equation and express the boundary conditions for the wall. (solve the equation is not required) Problomarrow_forwardA 1-D conduction heat transfer problem with internal energy generation is governed by the following equation: +-= dx2 =0 W where è = 5E5 and k = 32 If you are given the following node diagram with a spacing of Ax = .02m and know that m-K T = 611K and T, = 600K, write the general equation for these internal nodes in finite difference form and determine the temperature at nodes 3 and 4. Insulated Ar , T For the answer window, enter the temperature at node 4 in Kelvin (K). Your Answer: EN SORN Answer units Pri qu) 232 PM 4/27/2022 99+ 66°F Sunny a . 20 ENLARGED oW TEXTURE PRT SCR IOS DEL F8 F10 F12 BACKSPACE num - %3D LOCK HOME PGUP 170arrow_forward1- Microwave radiation is incident on one side of a planar wall with a heat conductivity coefficient k. (x=0) -D°b=(x)b leads to volumetric heating. While this surface is 9(W/m²) microwave radiation is fixed. kept at a constant temperature To, the other surface at x=L is very well insulated. Determine the temperature distribution T(x) in terms of x, L, k, qo and To.arrow_forwardHeat is transferred at the rate of 10 kW at the left end of a metal rod as shown in Figure 7.17. Determine the temperature distribution in the rod if the right end of the rod at x-2m is held at 50°C. The cross sectional area of the rod is 1200 mm? and the thermal conductivity k = 100 kW/m-°Carrow_forwardThe rate of heat flow (q) through a plane wall of thickness x = 50 mm is 700 watt/m2 . Determine the difference between the temperatures of wall surfaces and the numerical values of the temperature gradient through the wall if it is made from (a) Brass whose k = 78 watt/m-C, (b) If wall is made of red brick whose k = 0.77 watt/m-Carrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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