Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 13, Problem 13.33P
A meter to measure the power of a laser beam is constructed with a thin-walled, black conical cavity that is well insulated from its housing. The cavity has an opening of
A fine-wire thermocouple attached to the surface indicates a temperature rise of 10.1°C when a laser beam is incident upon the meter. What is the radiant flux of the laser beam,
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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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- 29. Gamma radiation is bombarding an iron plate as shown in the figure. A con- vection boundary condition of T;= 150 C and h = 200 W/m-K removes heat from the plate. Find the maximum temperature and its location in the plate. Also find temperature at 1 cm from the side facing irradiation and the rate of heat removal from the side not being irradiated. k= 48.5 kW/m K, µ= 24.6 m'. Questions and Problems 507 40 = 19,600 kW/m³ 15 cm T, = 150 C h= 200 W/m K T = 150 C h= 200 W/m Karrow_forwardConsider a silicon wafer positioned in a furnace that is zone-heated on the top section and cooled on the lower section. The wafer is placed such that the top and bottom surfaces of the wafer exchange radiation with the hot and cold zones respectively of the furnace. The zone temperatures are Tsur,h = 1050 K and Tsur.e = 330 K. The emissivity and thickness of the wafer are e = 0.65 and d = 0.78 mm, respectively. With the ambient gas at T. = 700 K, convection heat transfer coefficients at the upper and lower surfaces of the wafer are 8 and 4 W/m²-K. Find the steady-state temperature of the wafer, in K. Tw i Karrow_forwardConsider a silicon wafer positioned in a furnace that is zone-heated on the top section and cooled on the lower section. The wafer is placed such that the top and bottom surfaces of the wafer exchange radiation with the hot and cold zones respectively of the furnace. The zone temperatures are Tsur,h = 950 K and Tsur.c = 330 K. The emissivity and thickness of the wafer are e = 0.65 and d = 0.78 mm, respectively. With the ambient gas at T = 700 K, convection heat transfer coefficients at the upper and lower surfaces of the wafer are 8 and 4 W/m2-K. Find the steady-state temperature of the wafer, in K. i K Save for Laterarrow_forward
- An electric heating system is installed in the ceiling of a room 5 m (length) × 5 m (width) ×2.5 m (height). The temperature of the ceiling is 315 K whereas under equilibrium conditions the walls are at 295 K. If the floor is non-sensitive to radiations and the emissivities of the ceiling and wall are 0.75 and 0.65, respectively. Calculate the radiant heat loss from the ceiling to the walls. The answer should be 1595 W. Please show steps in your solutionarrow_forwardConsider a silicon wafer positioned in a furnace that is zone-heated on the top section and cooled on the lower section. The wafer is placed such that the top and bottom surfaces of the wafer exchange radiation with the hot and cold zones respectively of the furnace. The zone temperatures are Tsur,h = 1150 K and Tsur,c = 330 K. The emissivity and thickness of the wafer are e = 0.65 and d = 0.78 mm, respectively. With the ambient gas at T, = 700 K, convection heat transfer coefficients at the upper and lower surfaces of the wafer are 8 and 4 W/m2-K. Find the steady-state temperature of the wafer, in K. K Tw iarrow_forwardI need answer within 20 minutes please please with my best wishesarrow_forward
- An electrical cable with 20 mm in diameter and emissivity equal to 0.85 is installed inside a conduit whose inner surface and air in the its interior is at 30oC. The electrical resistivity of the cable, ρe (µΩ.m), is a function of its temperature, given by ρe=a[1+b(T-T0)], where a=0.0171 µΩ.m, b=0.00396 K-1 and T0= 25oC. The natural convection heat transfer coefficient is expressed by the relation h=cD-0.25(T-Tꚙ)0.25where c=1.21 W/(m1.75.K1.25) and D is the cable diameter. Electrical resistance per unit of cable length is R’e=ρe/Ac (Ac is the cross-sectional area). (a) For steady state operating conditions, estimate the maximum current that can be dissipated in the wire so that its temperature does not exceed 65oC;arrow_forwardA small sphere (emissivity =0.503 radius=r1) is located at the center of a spherical abestos shell ( thickness =1.74 cm, outer radius= r2; thermal conductivity of abestos is 0.090 J/ (sm c degrees) The thickness of the shell is small compared to the inner and outer radii of the shell. The temperature of the small sphere is 695 degrees Celsius while the temperature of the inner surface of the shell is 352 degrees Celsius, both temperatures remaining constant. Assuming that r2/r1 =8.75 and ignoring any air inside the shell, find the temperature in degrees Celsius of the outer surface of the shell.arrow_forwardA furnace wall is constructed of an inner layer of 12.7 mm of refracter material, a middle layer of 101.6 mm of insulation material and outer layer of 76.2 mm of steel. The wall surface temperature is 1370 °C inside the refracter material (T0) and 37.8 °C at the outside surface of the steel (T3). Use thermal conductivity for refractor kref = 6.64 W/mK, for insulation, kins= 2.34 W/mK and for steel kste = 45 W/mK. Calculate the heat loss in W for 1 m2 (heat flux)? The temperature at the inter face between the insulation material and steel board?arrow_forward
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