Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 13, Problem 13.67P
Two parallel, aligned disks, 0.4 m in diameter and separated by 0.1 m, are located in a large room whose walls are maintained at 300 K. One of the disks is maintained at a uniform temperature of 500 K with an emissivity of 0.6, while the back side of the second disk is well insulated. If the disks are diffuse, gray surfaces, determine the temperature of the insulated disk.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Two large parallel surfaces (surface 1 and surface 2) kept at constant surface temperature of T1= 300 °C
and T2= 100 °C. The two surfaces have emissivity of ɛ1= 0.8 and ɛ2= 0.5 respectively. The top surface
(surface 2) is cooled by convective heat transfer with surrounding air temperature of 20 °C. The bottom
surface (surface 1) is well insulated at the backside. Assume the surfaces are diffuse and gray, and the
space between the surfaces is vacuum.
a. Calculate the radiation heat transfer between the surfaces per unit area [W/m?].
b. Calculate the convective heat transfer coefficient for the top surface [W/m2 K].
Two parallel black disks are positioned coaxially with a distance of 0.25 m apart in a surrounding with a constant temperature of 300 K. The lower disk is 0.2 m in diameter and the upper disk is 0.4 m in diameter. If the lower disk is heated electrically at 100 W to maintain a uniform temperature of 500 K, determine the temperature of the upper disk.
An opaque, diffuse, gray, square (200 mm x 200 mm) plate with an emissivity of 0.8 is placed over the opening of a furnace (L = 200
mm) and the plate temperature is known to be 400 K at a certain instant. The bottom of the furnace, having the same dimensions as
the plate, is black and operates at 1040 K. The sidewalls of the furnace are well insulated. The top of the plate is exposed to ambient air
with a convection coefficient of 25 W/m².K and to large surroundings. The air and surroundings are each at 300 K.
Air
9₁ =
To
h
=
W
-Plate
(a) Evaluate the net radiative heat transfer to the bottom surface of the plate, in W.
T SUT
-Insulated sidewalls
-Furnace bottom
O
(b) If the plate has mass and specific heat of 2 kg and 900 J/kg-K, respectively, what will be the change in temperature of the plate with
time, dTp/dt, in K/s? Assume convection to the bottom surface of the plate to be negligible.
dT₁ =
K/s
dt
Chapter 13 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 13 - Determine F12 and F21 for the following...Ch. 13 - Drive expressions for the view factor F12...Ch. 13 - A right-circular cone and a right-circular...Ch. 13 - Consider the two parallel, coaxial, ringshaped...Ch. 13 - The “crossed-strings” method of Hottel [13]...Ch. 13 - Consider the rightcircular cylinder of diameter D,...Ch. 13 - Consider the parallel rectangles shown...Ch. 13 - Consider the perpendicular rectangles shown...Ch. 13 - The reciprocity relation, the summation rule, and...Ch. 13 - Determine the shape factor, F12, for the...
Ch. 13 - Consider parallel planes of infinite extent normal...Ch. 13 - Consider the parallel planes of infinite extent...Ch. 13 - Consider two diffuse surfaces A1 and A2 on the...Ch. 13 - As shown in the sketch, consider the disk A1...Ch. 13 - A heat flux gage of 4mm diameter is positioned...Ch. 13 - A circular ice rink 25 m in diameter is enclosed...Ch. 13 - A drying oven consists of a long semicircular duct...Ch. 13 - Consider the arrangement of the three black...Ch. 13 - A long, Vshaped pan is heat treated by suspending...Ch. 13 - Consider coaxial, parallel, black disks separated...Ch. 13 - A tubular healer with a black inner surface of...Ch. 13 - A circular plate of 500-mm diameter is maintained...Ch. 13 - To enhance heat rejection from a spacecraft, an...Ch. 13 - Determine the temperatures of surfaces 1 through 4...Ch. 13 - A cylindrical cavity of diameter D and depth L is...Ch. 13 - In the arrangement shown, the tower disk has a...Ch. 13 - Two plane coaxial disks are separated by a...Ch. 13 - A radiometer views a small target (1) that is...Ch. 13 - A meter to measure the power of a laser beam is...Ch. 13 - The arrangement shown is to be used to calibrate a...Ch. 13 - A long, cylindrical heating element of 20-mm...Ch. 13 - Water flowing through a large number of long,...Ch. 13 - A row of regularly spaced, cylindrical heating...Ch. 13 - A manufacturing process calls for heating long...Ch. 13 - Consider the very long, inclined black surfaces...Ch. 13 - Many products are processed in a manner that...Ch. 13 - Consider two very large parallel plates with...Ch. 13 - A flat-bottomed hole 6 mm in diameter is bored to...Ch. 13 - In Problems 12.20 and 12.25, we estimated the...Ch. 13 - Consider the cavities formed by a cone, cylinder,...Ch. 13 - Consider the attic of a home located in a hot...Ch. 13 - A long, thin-walled horizontal tube 100 mm in...Ch. 13 - A t=5-mm -thick sheet of anodized aluminum is used...Ch. 13 - Consider the spacecraft heat rejection scheme of...Ch. 13 - A very long electrical conductor 10 mm in diameter...Ch. 13 - Liquid oxygen is stored in a thin-walled,...Ch. 13 - Two concentric spheres of diameter D1=0.8m and...Ch. 13 - Determine the steady-stale temperatures of two...Ch. 13 - Consider two large (infinite) parallel planes that...Ch. 13 - Consider two large, diffuse, gray, parallel...Ch. 13 - Heat transfer by radiation occurs between two...Ch. 13 - The end of a cylindrical liquid cryogenic...Ch. 13 - At the bottom of a very large vacuum chamber whose...Ch. 13 - A furnace is located next to a dense array of...Ch. 13 - A cryogenic fluid flows through a tube 20 mm in...Ch. 13 - A diffuse, gray radiation shield of 60mm diameter...Ch. 13 - Consider the three-surface enclosure shown. The...Ch. 13 - Two parallel, aligned disks, 0.4 m in diameter and...Ch. 13 - Coatings applied to long metallic strips are cured...Ch. 13 - A molten aluminum alloy at 900 K is poured into a...Ch. 13 - A long, hemicylindrical (1-m radius) shaped...Ch. 13 - The bottom of a steam-producing still of 200-mm...Ch. 13 - A long cylindrical healer element of diameter...Ch. 13 - A radiative heater consists of a bank of ceramic...Ch. 13 - Consider a long duct constructed with diffuse,...Ch. 13 - A solar collector consists of a long duct through...Ch. 13 - The cylindrical peephole in a furnace wall of...Ch. 13 - A composite wall is comprised of two large plates...Ch. 13 - A small disk of diameter D1=50mm and emissivity...Ch. 13 - Consider a cylindrical cavity of diameter D=100mm...Ch. 13 - Consider a circular furnace that is 0.3 m long and...Ch. 13 - Consider two very large metal parallel plates. The...Ch. 13 - Two convex objects are inside a large vacuum...Ch. 13 - the diffuse, gray, four-surface enclosure with all...Ch. 13 - A cylindrical furnace for heal-treating materials...Ch. 13 - A laboratory oven bas a cubical interior chamber 1...Ch. 13 - A small oven consists of a cubical box of...Ch. 13 - An opaque, diffuse, gray (200mm200mm) plate with...Ch. 13 - A tool for processing silicon waters is housed...Ch. 13 - Consider Problem 6.17. The stationary plate,...Ch. 13 - Most architects know that the ailing of an...Ch. 13 - Boiler tubes exposed to the products of coal...Ch. 13 - Consider two very large parallel plates. The...Ch. 13 - Coated metallic disks are cured by placing them at...Ch. 13 - A double-glazed window consists of two panes of...Ch. 13 - Electrical conductors, in the form of parallel...Ch. 13 - The spectral absorptivity of a large diffuse...Ch. 13 - The cross section of a long circular tube, which...Ch. 13 - Cylindrical pillars similar to those of Problem...Ch. 13 - A row of regularly spaced, cylindrical healing...Ch. 13 - The composite insulation shown, which was...Ch. 13 - Hot coffee is contained in a cylindrical thermos...Ch. 13 - Consider a vertical, double-pane window for the...Ch. 13 - Consider the double-pane window of Problem 9.95,...Ch. 13 - A flat-plate solar collector, consisting of an...Ch. 13 - Consider the tube and radiation shield of Problem...Ch. 13 - Consider the tube and radiation shield of Problem...Ch. 13 - Consider the flatplate solar collector of Problem...Ch. 13 - The lower side of a 400-mm-diameter disk is heated...Ch. 13 - The surface of a radiation shield facing a black...Ch. 13 - The fire tube of a hot water heater consists of a...Ch. 13 - Consider the conditions of Problem 9.107....Ch. 13 - A special surface coating on a square panel that...Ch. 13 - A long rod heater of diameter D1=10mm and...Ch. 13 - A radiant heater, which is used for surface...Ch. 13 - A steam generator consists of an in-line array of...Ch. 13 - A furnace having a spherical cavity of 0.5-m...Ch. 13 - A gas turbine combustion chamber may be...Ch. 13 - A flue gas at 1-atm total pressure and a...Ch. 13 - A furnace consists of two large parallel plates...Ch. 13 - In an industrial process, products of combustion...Ch. 13 - A grain dryer consists of a long semicircular duct...Ch. 13 - A novel infrared recycler has been proposed for...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- 11.31 A large slab of steel 0.1 m thick contains a 0.1 -m-di- ameter circular hole whose axis is normal to the surface. Considering the sides of the hole to be black, specify the rate of radiative heat loss from the hole. The plate is at 811 K, and the surroundings are at 300 K.arrow_forwardTwo large parallel plates with surface conditions approximating those of a blackbody are maintained at 816C and 260C, respectively. Determine the rate of heat transfer by radiation between the plates in W/m2 and the radiative heat transfer coefficient in W/m2K.arrow_forwardDetermine the total average hemispherical emissivity and the emissive power of a surface that has a spectral hemispherical emissivity of 0.8 at wavelengths less than 1.5m, 0.6 at wavelengths from 1.5to2.5m, and 0.4 at wavelengths longer than 2.5m. The surface temperature is 1111 K.arrow_forward
- 11.68 Two infinitely large, black, plane surfaces are 0.3 m apart, and the space between them is filled by an isothermal gas mixture at 811 K and atmospheric pressure. The gas mixture consists of by volume. If one of the surfaces is maintained at 278 K and the other at 1390 K, calculate (a) the effective emissivity of the gas at its temperature, (b) the effective absorptivity of the gas to radiation from the 1390 K surface, (c) the effective absorptivity of the gas to radiation from the 278 K surface, and (d) the net rate of heat transfer to the gas per square meter of surface area.arrow_forwardA tungsten filament is heated to 2700 K. At what wavelength is the maximum amount of radiation emitted? What fraction of the total energy is in the visible range (0.4to0.75m)? Assume that the filament radiates as a graybody.arrow_forwardLiquid oxygen is stored in a thin-walled, spherical container 0.8 m in diameter, which is enclosed within a second thin-walled, spherical container 1.4 m in diameter. The opaque, diffuse, gray container surfaces have an emissivity of 0.05 and are separated by an evacuated space. If the outer surface is at 275 K and the inner surface is at 95 K, what is the mass rate of oxygen lost due to evaporation, in kg/s? (The latent heat of vaporization of oxygen is 2.13 × 105 J/kg.)arrow_forward
- Liquid oxygen is stored in a thin-walled, spherical container 0.8 m in diameter, which is enclosed within a second thin-walled, spherical container 1.4 m in diameter. The opaque, diffuse, gray container surfaces have an emissivity of 0.05 and are separated by an evacuated space. If the outer surface is at 270 K and the inner surface is at 95 K, what is the mass rate of oxygen lost due to evaporation, in kg/s? (The latent heat of vaporization of oxygen is 2.13 × 105 J/kg.)arrow_forwardDetermine the view factor between two gray surfaces A and B. Their emissivities are εA = 0.90 and εB = 0.25 at temperatures 450°C and 50°C, respectively, if (1) surfaces are infinite black parallel planes, (2) surfaces are infinite gray parallel planes, (3) surface A is a spherical shell 3 m in diameter and surface B is a similar shell concentric with A and 0.3 m in diameter, (4) surfaces A and B concentric cylindrical tubes with diameters of 300 mm and 275 mm, respectively, (5) both surfaces are discs with diameter 2 m one exactly above the other, 1 m apart.arrow_forwardA horizontal opaque flat plate is well insulated on the edges and the lower surface. The top surface has an area of 5 m2, and it experiences uniform irradiation at a rate of 5000 W. The plate absorbs 4000 W of the irradiation, and the surface is losing heat at a rate of 500 W by convection. If the plate maintains a uniform temperature of 350 K, determine the absorptivity, reflectivity, and emissivity of the plate.arrow_forward
- Liquid oxygen is stored in a thin-walled, spherical container 0.8 m in diameter, which is enclosed within a second thin-walled, spherical container 1.6 m in diameter. The opaque, diffuse, gray container surfaces have an emissivity of 0.05 and are separated by an evacuated space. If the outer surface is at 275 K and the inner surface is at 95 K, what is the mass rate of oxygen lost due to evaporation, in kg/s? (The latent heat of vaporization of oxygen is 2.13 x 105 J/kg.) m = i kg/sarrow_forwardLiquid oxygen is stored in a thin-walled, spherical container 0.8 m in diameter, which is enclosed within a second thin-walled, spherical container 1.2 m in diameter. The opaque, diffuse, gray container surfaces have an emissivity of 0.05 and are separated by an evacuated space. If the outer surface is at 270 K and the inner surface is at 95 K, what is the mass rate of oxygen lost due to evaporation, in kg/s? (The latent heat of vaporization of oxygen is 2.13 x 105 J/kg.) m = kg/s Physical Properties Mathematical Functionsarrow_forwardKeep in mind that both the bottom and top surfaces of the workpiece are exposed to radiation and convection. The workpiece is suspended in air in the furnace.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Understanding Thermal Radiation; Author: The Efficient Engineer;https://www.youtube.com/watch?v=FDmYCI_xYlA;License: Standard youtube license