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
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Chapter 4, Problem 4.72P
To determine
Temperature distribution across the foil.
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Chapter 4 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 4 - In the method of separation of variables (Section...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Consider the two-dimensional rectangular plate of...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Using the thermal resistance relations developed...Ch. 4 - Free convection heat transfer is sometimes...Ch. 4 - Consider Problem 4.5 for the case where the plate...Ch. 4 - Prob. 4.9PCh. 4 - Based on the dimensionless conduction heat rates...
Ch. 4 - Determine the heat transfer rate between two...Ch. 4 - A two-dimensional object is subjected to...Ch. 4 - An electrical heater 100 mm long and 5 mm in...Ch. 4 - Two parallel pipelines spaced 0.5 m apart are...Ch. 4 - A small water droplet of diameter D=100m and...Ch. 4 - A tube of diameter 50 mm having a surface...Ch. 4 - Pressurized steam at 450K flows through a long,...Ch. 4 - The temperature distribution in laser-irradiated...Ch. 4 - Hot water at 85°C flows through a thin-walled...Ch. 4 - A furnace of cubical shape, with external...Ch. 4 - Laser beams are used to thermally process...Ch. 4 - A double-glazed window consists of two sheets of...Ch. 4 - A pipeline, used for the transport of crude oil,...Ch. 4 - A long power transmission cable is buried at a...Ch. 4 - A small device is used to measure the surface...Ch. 4 - A cubical glass melting furnace has exterior...Ch. 4 - An aluminum heat sink (k=240W/mK), used to cool an...Ch. 4 - Hot water is transported from a cogeneration power...Ch. 4 - A long constantan wire of 1-mm diameter is butt...Ch. 4 - A hole of diameter D=0.25m is drilled through the...Ch. 4 - In Chapter 3 we that, whenever fins are attached...Ch. 4 - An igloo is built in the shape of a hemisphere,...Ch. 4 - Prob. 4.34PCh. 4 - An electronic device, in the form of a disk 20 mm...Ch. 4 - The elemental unit of an air heater consists of a...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Prob. 4.39PCh. 4 - Prob. 4.40PCh. 4 - One of the strengths of numerical methods is their...Ch. 4 - Determine expressionsfor...Ch. 4 - Consider heat transfer in a one-dimensional...Ch. 4 - In a two-dimensional cylindrical configuration,...Ch. 4 - Upper and lower surfaces of a bus bar are...Ch. 4 - Derive the nodal finite-difference equations for...Ch. 4 - Consider the nodal point 0 located on the boundary...Ch. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Consider the network for a two-dimensional system...Ch. 4 - An ancient myth describes how a wooden ship was...Ch. 4 - Consider the square channel shown in the sketch...Ch. 4 - A long conducting rod of rectangular cross section...Ch. 4 - A flue passing hot exhaust gases has a square...Ch. 4 - Steady-state temperatures (K) at three nodal...Ch. 4 - Functionally graded materials are intentionally...Ch. 4 - Steady-state temperatures at selected nodal points...Ch. 4 - Consider an aluminum heat sink (k=240W/mK), such...Ch. 4 - Conduction within relatively complex geometries...Ch. 4 - Prob. 4.60PCh. 4 - The steady-state temperatures (°C) associated with...Ch. 4 - A steady-state, finite-difference analysis has...Ch. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Consider a two-dimensional. straight triangular...Ch. 4 - A common arrangement for heating a large surface...Ch. 4 - A long, solid cylinder of diameter D=25mm is...Ch. 4 - Consider Problem 4.69. An engineer desires to...Ch. 4 - Prob. 4.71PCh. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Refer to the two-dimensional rectangular plate of...Ch. 4 - The shape factor for conduction through the edge...Ch. 4 - Prob. 4.77PCh. 4 - A simplified representation for cooling in very...Ch. 4 - Prob. 4.84PCh. 4 - A long trapezoidal bar is subjected to uniform...Ch. 4 - Consider the system of Problem 4.54. The interior...Ch. 4 - A long furnace. constructed from refractory brick...Ch. 4 - A hot pipe is embedded eccentrically as shown in a...Ch. 4 - A hot liquid flows along a V-groove in a solid...Ch. 4 - Prob. 4S.5PCh. 4 - Hollow prismatic bars fabricated from plain carbon...
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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_forward2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.arrow_forwardConsider a flat plate or a plane wall with a thickness L and a long cylinder of radius r0. Both of these are made of materials such that they can be treated as lumped capacitances (Bi0.1). Show that in each case, the characteristic length lc, defined lc=(V/As), can be approximated as (L/2) and (ro/2), respectively.arrow_forward
- 1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.arrow_forward1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.arrow_forward2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)arrow_forward
- A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6arrow_forwardA cubical furnace 50 by 50 by 50 cm on the inside is built of fireclay brick [k =1.04 W/m. •C] with a wall thickness of 5 cm. The inside of the furnace is maintained at 500•C, and the outside is maintained at 50.C. Calculate the heat lost through the walls.arrow_forward
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