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 1, Problem 1.41P
Consider the transmission case of Problem 1 .23,butnow allow for radiation exchange with the ground/chassis, which may be approximated as large surroundings at
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1. Consider a spaceship that has a volume V = 3000 m³, is
effectively spherical in shape and has a density comparable to
water (p = 1000 kg m-3). It absorbs CMB radiation (TCMB =
2.73K) and radiates its own radiation with a blackbody
spectrum of T = 300K.
What is its mass, radius and surface area?
At what rate does it absorb energy from the
CMB? (Hint: You can use the Stefan-Boltzmann law.)
How many CMB photons are absorbed per
а.
b.
с.
second?
d.
At what rate does it emit energy through
blackbody radiation?
What is the net rate that the spaceship
temperature would change if the spaceship has an
е.
effective heat capacity of pure water:
C = 4200 J kg-1K-1 ?
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 solution
A 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.
Chapter 1 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 1 - The thermal conductivity of a sheet of rigid,...Ch. 1 - The heat flux that is applied to the left face of...Ch. 1 - A concrete wall, which has a surface area of 20m2...Ch. 1 - The concrete slab of a basement is 11 in long. 8...Ch. 1 - Consider Figure 1.3. The heat flux in the...Ch. 1 - The heal flux through a wood slab 50 mm thick,...Ch. 1 - The inner and outer surface temperatures of a...Ch. 1 - A thermodynamic analysis of a proposed Brayton...Ch. 1 - A glass window of width W=1m and height H=2m is 5...Ch. 1 - A freezer compartment consists of a cubical cavity...
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- A 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_forward1.26 Repeat Problem 1.25 but assume that the surface of the storage vessel has an absorbance (equal to the emittance) of 0.1. Then determine the rate of evaporation of the liquid oxygen in kilograms per second and pounds per hour, assuming that convection can be neglected. The heat of vaporization of oxygen at –183°C is .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
- An electric heating system is installed in the ceiling of a room 5 m (length), 5 m (width) and 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?arrow_forwardQ.4 Determine radiation heat loss from a steel tube of outside diameter 60 mm and 5m long at a temperature of 327 °C if the tube is inside a square conduit made of brick having 0.4 m side as shown in given figure and temperature of 25 °C. (Take, ɛ(steel)= 0.8, e(brick)= 0.9. Steel tube(1) Brick(2) A 5889.25W 5656.47W C 5149.41W D 6125.84Warrow_forwardAn 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_forward
- Molten metal at 2000 C is poured using crucible. The liquid metal jet has a diameter of 3 mm with an insulation shield of 5 cm diameter. There is a slit of 30 degrees around the insulation shield. The temperature inside the room is 30 C and the shield is 700 C. Assuming black bodies, find the net heat transfer between jet and shield, jet and room, shield and the room. One of the steps is wrong? Slit doesnot participate in radiation To find the view factor between metal and shield , ratio of the angles is used View factors are one of the most important steps to solve the problem None of the given Resistance network is required to be builtarrow_forwardA small sphere (emissivity = 0.745, radius = r1) is located at the center of a spherical asbestos shell (thickness = 1.72 cm, outer radius = r2; thermal conductivity of asbestos is 0.090 J/(s m Co)). The thickness of the shell is small compared to the inner and outer radii of the shell. The temperature of the small sphere is 727 °C, while the temperature of the inner surface of the shell is 406 °C, both temperatures remaining constant. Assuming that r2/r1 = 6.54 and ignoring any air inside the shell, find the temperature in degrees Celsius of the outer surface of the shell.arrow_forwardLiquefied natural gas (LNG) is transported around the globe using ships similar to thatshown in Figure QA3. This ship has four pressurised cylindrical steel tanks each ofradius of 20 m. The tanks are internally insulated with 30 cm of polyurethane foamwhich keeps the LNG at a constant -162 ºC. Take the effective sky temperature is 265K and the net radiative thermal energy exchange with the sky as 1x10^6 W. (a) Calculate the surface temperature of the end (facing the sun) of a tank.(b) Calculate the conductive heat transfer through the end (facing the sun)of a tank. DATA FOR QUESTION: Thermal conductivity, polyurethane foam = 0.02 W/mKStefan’s Constant = 5.67x10^-8 W/m^2K^4Emissivity, steel = 0.95 answers: a) 375K b) 22.1kWarrow_forward
- Liquefied natural gas (LNG) is transported around the globe using ships similar to thatshown in Figure QA3. This ship has four pressurised cylindrical steel tanks each ofradius of 20 m. The tanks are internally insulated with 30 cm of polyurethane foamwhich keeps the LNG at a constant -162 ºC. Take the effective sky temperature is 265K and the net radiative thermal energy exchange with the sky as 1x106 W. Calculate the surface temperature of the end (facing the sun) of a tank. Calculate the conductive heat transfer through the end (facing the sun)of a tank.arrow_forwardLiquefied natural gas (LNG) is transported around the globe using ships similar to thatshown in Figure QA3. This ship has four pressurised cylindrical steel tanks each ofradius of 20 m. The tanks are internally insulated with 30 cm of polyurethane foamwhich keeps the LNG at a constant -162 ºC. Take the effective sky temperature is 265K and the net radiative thermal energy exchange with the sky as 1x10^6 W. (a) Calculate the surface temperature of the end (facing the sun) of a tank.(b) Calculate the conductive heat transfer through the end (facing the sun)of a tank. answers: a) 375K b) 22.1kWarrow_forward2. A heater is a thin vertical panel 1.0m long and 0.7m high and is used in a warehouse to keep workers warm. The heater has air circulating on each side. Assume the maximum temperature of the panel is 60°C (already above the board line that is safe for human hands to touch briefly without getting hurt). Assume the room air temperature is 18°C but the warehouse wall temperature is 5°C. Model the surface with an emittance of 0.9 and Vair = 1.57x105 m²/s. a. Determine the maximum power rating for the heater. b. Now if you run the heat by standing on its side (it will be 1.0 m high and 0.7 m long), determine the surface temperature. c. Compare case a and b and explain any differences you see.arrow_forward
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