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
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 13, Problem 13.39P
A manufacturing process calls for heating long copper rods, which are coated with a thin film having
(a) What is the initial rate of change of the rod temperature!
(b) How long must the rods remain in the oven to achieve a temperature of 1000 K?
(c) The heating process may be accelerated by routing combustion gases, also at 1650 K, through the oven. For convection coefficients of 10, 100, and
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A brass plate has a circular hole whose diameter is slightly smaller than the diameter of an aluminum ball. Ifthe ball and the plate are always kept at the same temperature,(a) should the temperature of the system be increased or decreasedin order for the ball to fit through the hole? (b) Choose the bestexplanation from among the following:I. The aluminum ball changes its diameter more with temperature than the brass plate, and therefore the temperatureshould be decreased.II. Changing the temperature won’t change the fact that the ballis larger than the hole.III. Heating the brass plate makes its hole larger, and that willallow the ball to pass through.
The surface temperature of the hot side of the furnace wall is 1200 degrees C. It is desired to maintain the outside of the wall at 38 degrees C. A 152 mm of refractory silica is used adjacent to the combustion chamber and 10 mm of steel covers the outside. What thickness of insulating bricks is necessary between refractory and steel, if the heat loss should be kept at 788 W/m2? Use k=13.84 W/m-K for refractory silica; 0.15 for insulating brick, and 45 for steel.
A solid sphere made of polished copper has a diameter of 2 cm and is at 100 C. We now expose the solid sphere to are at 50 C and 1 atm. Use the lumped capacitance method to plot the temperature of the solid sphere versus time after five minutes of exposure. The air is quiescent.
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
- The Diamond Ring Solution. The processing chip on the computer that controls the navigation equipment on your spacecraft is overheating. Unless you fix the problem, the chip will be damaged and the navigation system will shut down. You open the panel and find that the small copper disk that was supposed to bridge the gap between the smooth top of the chip and the cooling plate is missing, leaving a 2.0 mm gap between them. In this configuration, the heat cannot escape the chip at the required rate. You notice by the thin smudge of thermal grease (a highly thermally conductive material used to promote good thermal contact between surfaces) that the missing copper disk was 2.0 mm thick and had a díameter of 1.2 cm. You know that the chip is designed to run below 65 °C, and the copper cooling plate is held at a constant 5.0 °C. (a) What was the rate of heat flow from the chip to the copper plate when the original copper disk was in place and the chip was at its maximum operating…arrow_forwardThe Diamond Ring Solution. The processing chip on the computer that controls the navigation equipment on your spacecraft is overheating. Unless you fix the problem, the chip will be damaged and the navigation system will shut down. You open the panel and find that the small copper disk that was supposed to bridge the gap between the smooth top of the chip and the cooling plate is missing, leaving a 2.0 mm gap between them. In this configuration, the heat cannot escape the chip at the required rate. You notice by the thin smudge of thermal grease (a highly thermally conductive material used to promote good thermal contact between surfaces) that the missing copper disk was 2.0 mm thick and had a diameter of 1.0 cm. You know that the chip is designed to run below 70 °C, and the copper cooling plate is held at a constant 5.0 °C. (a) What was the rate of heat flow from the chip to the copper plate when the original copper disk was in place and the chip was at its maximum operating…arrow_forward9.3 A 5 cm? thin film solar cell has a reverse saturation or dark current 1, = 5.9 x 10-15 mA. Under the insolation Ia of 900 W/m?, the short-circuit current Ie is 124 mA. At the cell temperature of 25°C, V,= kT/q = 0.026 V. Determine: (i) open-circuit voltage Voc, (ii) MPP voltage Vm and current Im, (iii) maximum power output Pm, (iv) fill factor FF of cell I–V characteris- tics, and (v) cell efficiency n..arrow_forward
- Spacecraft must be cooled via radiative mechanisms, and one means of doing this is by using radiation fins. In many instances, these fins are heated rods that protrude from the spacecraft. Assume that the rod is of length, L; cross-sectional are, Ac; and perimeter, Pā. Its base temperature is T, and the rod has thermal conductivity and emissivity, λ and ɛ, respectively. Set up the differential equation describing the temperature profile within the rod assuming that space is a blackbody at Ts.arrow_forwardA long, horizontal, cylindrical steel reactor, 1 m in diameter, has a surface temperature of 300ºC. The emissivity of the steel is 0.6, and the heat transfer coefficient for natural convection is 5 W m−2 K−1 . Heat is lost by convection to the air at 15ºC, and also by radiation to the surroundings, which can be considered to be a black body at 15ºC. a) Calculate the total heat loss per metre length of the reactor, and the proportions lost by convection and radiation b) The reactor is then insulated with a thin layer of insulation material to reduce the total heat loss to one-tenth of its original value. This causes the surface temperature of the steel to rise to 400ºC. The thermal conductivity of the insulation is 0.01 W m−1 K−1 , and its surface emissivity is 0.2. Show that the resulting surface temperature of the insulation is about 89ºC, and calculate the thickness of insulation required, stating any assumptions made. Specifically need help with part barrow_forwardA long, horizontal, cylindrical steel reactor, 1 m in diameter, has a surface temperature of 300ºC. The emissivity of the steel is 0.6, and the heat transfer coefficient for natural convection is 5 W m−2 K−1 . Heat is lost by convection to the air at 15ºC, and also by radiation to the surroundings, which can be considered to be a black body at 15ºC. a) Calculate the total heat loss per metre length of the reactor, and the proportions lost by convection and radiation. b) The reactor is then insulated with a thin layer of insulation material to reduce the total heat loss to one-tenth of its original value. This causes the surface temperature of the steel to rise to 400ºC. The thermal conductivity of the insulation is 0.01 W m−1 K−1 , and its surface emissivity is 0.2. Show that the resulting surface temperature of the insulation is about 89ºC, and calculate the thickness of insulation required, stating any assumptions made. can you solve part b please?arrow_forward
- 3. An electric immersion heater, 10 mm in diameter and 300 mm long, is rated at 550 W. The emissivity of the heater is ε = 0.85. a) If the heater is horizontally positioned in a large tank of water at 20°C, estimate its surface temperature. b) If the heater is accidentally operated in air at 20°C, estimate the surface temperature. Hint: Radiation heat transfer can be neglected in liquids, but not in gases like air.arrow_forward2 inch OD during a visit to a plastic sheet factory 60 m long section of a horizontal steam pipe passes from one end to the other without insulation is observed. While the temperature of the ambient air and its surfaces is 20 °C, the temperature measurements at several points are the average of the exposed surfaces of the steam pipe. indicates that the temperature is 160 °C. It is seen that the outer surface of the pipe is oxidized and The emissivity can be taken as 0.59. According to this; a) Calculate the heat loss in the steam pipe. b) The steam used is produced in a gas furnace operating with an efficiency of 59%. Factory 105500 It pays $1.10 per kJ of natural gas. If it is assumed that the factory works all year (365 days), for this facility Calculate the annual cost of heat losses in the steam pipe.arrow_forwardPROBLEM 4: A black thermocouple is inside a chamber with black walls. If the air around the thermocouple is at 20°C, the walls are at 100-C, and the heat transfer coefficient between the thermocouple and the air is 75 W/m²K, what temperature will the thermocouple read?arrow_forward
- An infrared camera is used to measure a temperature at a tissue location. The infrared camera uses the same equation as that in the lecture notes. When the total hemispherical emissivity is selected as &=1.0, the temperature reading on the camera is 45°C. (a) Based on the equation given in the notes, please calculate the radiation heat flux received by the camera qck. The Stefan-Boltzmann's constant ois 5.67*108 W/(m²K¹). (b) However, you notice that the actual emissivity of the tissue surface should be 0.95. The room temperature is 20°C. Use the equation again to calculate the temperature of the tissue location, note that qck should be the same as in (a). What is the absolute error of the measurement if both the room temperature and deviation from a perfect blackbody surface are not considered?arrow_forwardThe surface temperature of the hot side of the furnace wall is 1200°C. It is desired to maintain the outside of the wall at 38°C. A 152 mm refractory silica is used adjacent to the combustion chamber and 10 mm of steel covers the outside. What thickness of insulating bricks is necessary between refractory and steel, If the heat loss should be kept at 788 W/m2? use k = 13.84 W/m-K fro refractory silica; 0.15 for insulating brick, and 45 for steel. O 260 mm 280 mm O 240 mm 220 mmarrow_forwardExplain in your own words: (a) In what way is the heat transfer through a large steel plate that has its surfaces at specific temperatures? (B) What are the patterns in which the temperature at one surface of the steel plate is not specified, but the surface is exposed to a fluid at a specified temperature?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
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license