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 1.10P
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Minimum thickness of Styrofoam insulation.
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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
include diagram.
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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- 1.1 On a cold winter day, the outer surface of a 0.2-m-thick concrete wall of a warehouse is exposed to temperature of –5°C, while the inner surface is kept at 20°C. The thermal conductivity of the concrete is 1.2 W/m K. Determine the heat loss through the wall, which is 10-m long and 3-m high. Problem 1.1arrow_forwardA boiler furnace wall must have a heat loss no greater than 700 Btu/hr~ft2 and is madeof a material with a thermal conductivity of 0.60 Btu/hr~ft~F. The inner wall surfacetemperature is '2000°F, and the outer surface temperature is 800°F. What wall thick~ness is required?arrow_forwardA hot water pipe is used for domestic applications is insulated with a layer of calcium silicate. If the insulation is 25 mm thick and its inner and outer surfaces are maintained at Ts,1 = 800 K and Ts,2 = 400 K, respectively. The outside diameter is 0.12 m. Calculate the heat loss per unit length of the pipe. Given the thermal conductivity of calcium silicate insulation equals to 0.09 W/m.K.arrow_forward
- 2. Calculate insulation thickness (minimum value) required for a pipe carrying steam at 180°C. The pipe size is 8" and the maximum allowable temperature of outer wall of insulation is 50 °C. Thermal conductivity of the insulation material for the temperature range of the pipe can be taken as 0.04 W/m K. The heat loss from steam per meter of pipe length has to be limited to 80 W/m. ANSWER: 102.5 mmarrow_forwardQUESTION 2 The wall of a refrigerated truck consists of 1.5mm sheet steel outer surface, 10mm plywood at the inner surface and 20mm of glass wool in between. The inside temperature is -15°C and outside temperature is 240C. Take the thermal conductivities of the materials as follows: - 0,052W/mK = 23,2W/mK k for glass-wool = 0,14W/mK k for plywood k for steel %3D %3D %3D Calculate: 2.1. the rate of heat flow per unit area; 2.2. the interface temperature. If the glass-wool is replaced by a 5mm cork board with a thermal conductivity of 0.043W/mK; 2.3. What percentage change in heat flow is obtained? 2.4. What must be the thickness of the cork board be, to achieve the same heat flow as in (2.1.).arrow_forward3. A composite plain wall is to be constructed of (1/4)-in. stainless steel (k-17.03 W/m-K), 3-in. of corkboard (k=0.04 W/m-K) and (1/2)-in. of plastic (k=2.6 W/m-K). (a) Draw a thermal circuit for the steady-state heat conduction through this wall; (b) Evaluate the individual thermal resistances of each material layer; (c) Determine the heat flux if the inside steel surface is maintained at 400 K and the outer surface of plastic surface is held at 300 K; and (d) What are the temperatures on each surface of the corkboard under these conditions?arrow_forward
- A dormitory at a large university, built 50 years ago, has exterior walls constructed of L, = 25-mm-thick sheathing with a thermal conductivity of k, = 0.1 W/m-K. To reduce heat losses in the winter, the university decides to encapsulate the entire dormitory by applying an L; = 25-mm-thick layer of extruded insulation characterized by k; = 0.029 W/m-K to the exterior of the original sheathing. The extruded insulation is, in turn, covered with an Lg = 5-mm-thick architectural glass with kg = 1.4 W/m-K. Determine the heat flux through the original and retrofitted walls when the interior and exterior air temperatures are Ti = 22°C and T.0 -17.5°C, respectively. The inner and outer convection heat transfer coefficients are h; = 5W/m?-K and h, = 25 W/m²-K, respectively. The heat flux through the original walls is i W/m?. The heat flux through the retrofitted walls is i W/m?.arrow_forwardA dormitory at a large university, built 50 years ago, has exterior walls constructed of L, = 25-mm-thick sheathing with a thermal conductivity of k, = 0.1 W/m-K. To reduce heat losses in the winter, the university decides to encapsulate the entire dormitory by applying an L; = 25-mm-thick layer of extruded insulation characterized by k; = 0.029 W/m-K to the exterior of the original sheathing. The extruded insulation is, in turn, covered with an L, = 5-mm-thick architectural glass with kg = 1.4 W/m-K. Determine the heat flux through the original and retrofitted walls when the interior and exterior air temperatures are Ti = 22°C and T0 -15°C, respectively. The inner and outer convection heat transfer coefficients are h; = 5 W/m?-K and h, = 25 W/m²-K, respectively. The heat flux through the original walls is i W/m?. The heat flux through the retrofitted walls is i W/m?.arrow_forwardAn insulation layer of 20 mm thick refractory material is placed on top of a layer of mineral wool to insulate a hollow, spherical steel ball with an outside diameter of 60 mm and an internal diameter of 50 mm wool. The table below lists the thermal conductivities: Substance a. 6.0 mm above Steel Refractory Mineral wool b. 6.1 mm k (W/m-K) c. 6.2 mm 48 While the outside temperature is 30 °C, the temperature within the steel is 200 °C. Heat effects from convection and radiation are disregarded. Find the needed thickness of the mineral wool if the heat loss is 50 W. 0.346 0.047 d. 6.3 mm e. No to all of thearrow_forward
- A dormitory at a large university, built 50 years ago, has exterior walls constructed of Ls a thermal conductivity of k, = 25-mm-thick sheathing with = 0.1 W/m-K. To reduce heat losses in the winter, the university decides to encapsulate the = 0.029 W/m:K to entire dormitory by applying an L; = 25-mm-thick layer of extruded insulation characterized by k; the exterior of the original sheathing. The extruded insulation is, in turn, covered with an Lg = 5-mm-thick architectural glass with kg exterior air temperatures are T; 1.4 W/m-K. Determine the heat flux through the original and retrofitted walls when the interior and = 22°C and T. 0°C, respectively. The inner and outer convection heat transfer 0,i coefficients are h; = 5 W/m2.K and ho 25 W/m2-K, respectively. The heat flux through the original walls is i W/m?. The heat flux through the retrofitted walls is i W/m?.arrow_forwardPlease include a fbd of the problemarrow_forwardParts d though f please: Consider a multi-layered walls of a storage building (no windows) that is made of three layers as shown in the figure. The inside layer is a gypsum material that is 1.0 cm thick and has a thermal conductivity of 0.5 W/m.K. We then have a dense brick layer that is 15.0 cm thick and has a thermal conductivity of k = 5 W/m.K The outside wall is made of a wood panel that is 2.0 cm thick and has a thermal conductivity of k = 1.0 W/m.K In a cold day, the outside can be at -10oC and the convective heat transfer coefficient can be hout = 25 W/m2.K due to wind. Inside air of the building is kept at 10oC and the convective heat transfer coefficient over the inside surfaces is rather low with hin = 5 W/m2.K a) Show the thermal resistance diagram with all the temperature nodes. b) What is the rate of heat loss in kW per m2 under these conditions? c) What would be the temperature of the inside surface of the wall? d) What is the temperature at the interface between the…arrow_forward
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