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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Question
Chapter 1, Problem 1.14P
To determine
The expression for the temperature gradient and the temperature distribution.
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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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- Repeat Problem 1.35 but assume that instead of surface temperatures, the given temperatures are those of the air on the left and right sides of the wall and that the convection heat transfer coefficients on the left and right surfaces are 6 and 10W/m2K, respectively.arrow_forward1.4 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_forward1.12 A wall with a thickness is made of a material with a thermal conductivity that varies with its thickness according to the equation, , where and are constants. If the heat flux applied at the surface of one end of the wall is , derive an expression for the temperature gradient and the temperature distribution across the wall thickness (between and ). Use and define appropriate notations for the surface temperatures at each end of the wall.arrow_forward
- A copper pipe is used as electrical resistance to generate heat. This generation is equal to A/r per unit ofvolume, where “r” is the measured distance from the pipe axis. determine the profile of temperatures if the temperatures in the pipe walls are respectively T1 and T2.arrow_forwardThe walls of the flat furnace are connected by two insulating layers A and B. The temperature of the insulating layer A facing the inside of the Furnace is 800°C and the temperature of the outside air is 60°C. Find the temperature of the interface between the two insulation layers when the thickness of insulation layer A is 150 mm, its thermal conductivity is 0.05 W/m℃, the thickness of insulation layer B is 240 mm, and its thermal conductivity is 0.15 W/m℃arrow_forwardTwo sides AB and AD of a reetangular plate ABCD lie along the xand y axes respectively. The remaining two sides are the lines x = 5and y = 2. The sides BC, CD and DA are maintained at zerotemperature. The temperature distribution along AB is defined byf (x) = x (x - 5). Determine an expression for the steady statetemperature at any point in the plate.arrow_forward
- A coil-shaped cooling pipe is made of SS-304 material. This pipe is 1 ft long, 0.4 inch outside diameter, and inch inside diameter. This coil cooling pipe is used to cool the water in the bath. The temperature of the inner coil pipe is 40oF while the outer coil in contact with water is 80oF. The thermal conductivity of SS-304 is a function of temperature where k(T) = 7.75 + (7.78 x 10-3).T where k is in Btu/h.ft.oF and T is in oF. Calculate the rate of heat dissipation in watts! (1287.7)arrow_forwardWhat is the rate of heat transfer through a piece of Celotex 3 ft by 8 ft by 1 in. in thickness, if the temp of one surface is 80°F and of the other side is 60°F? thermal conductivity of Celotex in AES = 0.028. Pls determine the temperature gradient and the direction of the heat transfer as well.arrow_forwardA spherical container having an outer radius r2 and inner radius r1 (with thermal conductivity, k) is filled with radioactive material generating constant heat at a rate of qdot. Fluid flows across the container at Tinfinity and convection coefficient h. Obtain a relation for the variation of temperature through the spherical container assuming steady state.arrow_forward
- 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. Determine expressions for the temperature gradient and the temperature distribution when the surface at x = 0 is at temperature T1. Use the following values a = 11 W/K b = 25 W/m-K k = 11x + 25 W/m-K q"q" = 104 W/m^2 T1 = 60 Carrow_forwardThe heat conducts through the shape below. The temperature of the right face is 93 °C, while the left face is at 23 °C. If the top and bottom faces are completely insulated, and the thermal conductivity of the material decreases with decreasing temperature. * Assume that the thermal conductivity is 100 at 23, decreased to 10 at 93. A) Sketch the temperature profile inside the plate. B) If both sides of the plate in the above problem is exposed to air: Left side (h = 20 W/m2K, TL = 20 °C) and right side (h = 90 W/m2K). Calculate the temperature of the air on the right side.arrow_forwardA 100 mm diameter steam pipe is covered by two layers of lagging (insulation). The inside layer is 40 mm thick and has a thermal conductivity of 0.07 W/m K. The outside layer is 25 mm thick and has a thermal conductivity of 0.1 W/mK. The pipe carries steam at a temperature of 234°C , where the outside temperature of lagging is 24°C. If the steam pipe is 20 m long, determine (a) The heat lost per hour, (b) The interface temperature of lagging. Neglect the resistance of steam pipe as well as the convection resistances.arrow_forward
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