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 4.70P
Consider Problem 4.69. An engineer desires to measure the surface temperature of the thin sheathing by painting it black
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A horizontal steam pipe with an outside diameter of 60.0 mm passes through a large room whose walls are at a temperature of 298 K. The outer surface of the pipe wall has a surface temperature of 443 K and an emissivity of 0.8. The air temperature in the room is 303 K. Calculate the rate of heat loss per unit length of the pipe by radiation and natural convection.
A small, oxidized, horizontal metal tube with an OD of 0.0254 m (1 in.), 0.61 m (2 ft) long, and with a surface temperature at 588 K (600°F) is in a very large furnace enclosure with fire-brick walls and the surrounding air at 1088 K (1500°F). The emissivity of the metal tube is 0.60 at 1088 K and 0.46 at 588 K. Calculate the heat transfer to the tube by radiation using SI units and AES units.
A circular grill of diameter 0.35 m and emissivity 0.7 is maintained at a constant surface temperature of 130 °C in a horizontal position. What electrical power is required when the room air and surroundings are at 24 °C?
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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- 1.13 If the outer air temperature in Problem is –2°C, calculate the convection heat transfer coefficient between the outer surface of the window and the air, assuming radiation is negligible.arrow_forwardA long wire 0.7 mm in diameter with an emissivity of 0.9 is placed in a large quiescent air space at 270 K. If the wire is at 800 K, calculate the net rate of heat loss. Discuss your assumptions.arrow_forward1.11 Calculate the heat loss through a glass window 7-mm thick if the inner surface temperature is 20°C and the outer surface temperature is 17°C. Comment on the possible effect of radiation on your answer.arrow_forward
- Determine the power requirement of a soldering iron in which the tip is maintained at 400C. The tip is a cylinder 3 mm in diameter and 10 mm long. The surrounding air temperature is 20C, and the average convection heat transfer coefficient over the tip is 20W/m2K. The tip is highly polished initially, giving it a very low emittance.arrow_forwardThree thin sheets of polished aluminum are placed parallel to each other so that the distance between them is very small compared to the size of the sheets. If one of the outer sheets is at 280C and the other outer sheet is at 60C, calculate the temperature of the intermediate sheet and the net rate of heat flow by radiation. Convection can be ignored.arrow_forwardThermal comfort in a house is strongly affected by the so called radiation effect,which is due to radiation heat transfer between the person and the surrounding surfaces,a person feels much colder in the morning.For example ,because of the lower surface temperature of the walls at that time,although the thermostat setting of the house is fixed.Write an essay on the radiation effect,how it affects human comfort,and how it is accounted for in heating and air-conditioning applicationsarrow_forward
- A 4.0-cm-diameter sphere is heated to a temperature of 200°C and is enclosed in a large room at 20 C. Calculate the radiant heat loss if the surface emissivity is 0.6.arrow_forwardHeat is generated in a sphere of radius 1 m at a rate of 1000 W/m3. The sphere is surrounded by air at 27 oC.A. Balance total energy produced by the total energy lost from the surface by convection and radiation tocalculate the surface temperature.B. Solve the heat transfer problem in the sphere and use the temperature calculated in A as the boundarycondition to determine the temperature at the center of the sphere.Assume that the sphere can be treated as a black body for calculating radiation losses.Properties The thermal conductivity is given to be k =2.5 W/m°C.σ = 5.67 × 10−8 W / (m2 x K4). Heat transfer coefficient h = 10 W/(m2 K)arrow_forwardA loaf of bread having a surface temperature of 373 K is being baked in an oven whose walls and the air are at 477.4 K. The bread moves continuously through the large oven on an open chain belt conveyor. The emissivity of the bread is estimated to be 0.85, and the loaf can be assumed to be a rectangular solid 114.3 mm high × 114.3 mm wide × 330 mm long. Calculate the radiation heat-transfer rate (in SI and AES units) to the bread, assuming that it is small compared to the oven and neglecting natural convection heat transfer.arrow_forward
- A long electrical conductor of 10 mm diameter is concentric with a refrigerated cylindrical tube of 50 mm diameter whose surface has an emissivity of 0.9 and temperature of 27 °C. The electrical conductor has a surface emissivity of 0.6 and dissipates 6.0 W per meter length. Assuming that the space between the two surfaces is empty, calculate the surface temperature of the conductor.arrow_forwardThe production line of a special biscuit at 30 ̊C and 1 atm has a 0.8 X 0.8 (m) square plate. One side of the plate is maintained at a temperature of 100 ̊C, while the other side is insulated. Determine the rate of heat transfer from the plate by natural convection if the plate (i) Is horizontal with the hot surface facing down; (ii) Is horizontal with the hot surface facing up; Data: The properties of air at the film temperature are: thermal conductivity, k= 0.0279 W/m.k); kinematic viscosity= 1.815 x 10-5 m2/s; Pr = 0.709arrow_forwardThe small horizontal metal tube with an OD of 0.05 m, 0.1 m long, and with a surface temperature of 25 C is in a very large furnace enclosure with firebrick walls and the surrounding air at 500 C. The emissivity of the metal tube is 0.6. Calculate the net heat transfer to the tube by radiation in Watts.arrow_forward
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