Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Textbook Question
Chapter 13, Problem 13.24P
A circular plate of 500-mm diameter is maintained at
(a) What is the temperature of the conical surface, T2?
(b) What is the electrical power that would be required to maintain the circular plate at 600 K?
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Question #9
A circular ceramic plate that can be modelled as a blackbody is being heated by an electrical
heater. The plate is 30cm in diameter and is situated in a surrounding ambient temperature
of 15°C where the natural convection heat transfer coefficient is 12W/m² K. The efficiency
of the electrical heater to transfer heat to the plate is 80%, the electric power is required
such that the heater needs to keep the surface temperature of the plate at 200°C.
Ambient 15°C Tsurr = 15°C
h = 12 W/m².K
Ceramic plate
-T₂ = 200°C
Welec
(A) Determine the heat emitted from the plate, as a blackbody.
(B) Determine the radiation incident on the plate from the surroundings.
(C) Determine the heat transfer from the plate to the surroundings.
(D) Determine the required electric power.
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
An enclosure has an inside area of 50 m², and its inside surface is black and is maintained at a constant temperature. A small opening in
the enclosure has an area of 0.03 m². The radiant power emitted from this opening is 52 W. What is the temperature of the interior
enclosure wall, in K? If the interior surface is maintained at this temperature, but is now polished so that its emissivity is 0.15, what will
be the value of the radiant power emitted from the opening, in W?
T, =
grad =
i
K
W
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...
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