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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Textbook Question
Chapter 13, Problem 13.115P
Consider the tube and radiation shield of Problem 13.49, hut now account for free convection in the gap between the tube and the shield.
(a) What is the total rate of heat transfer per unit length between the tube and the shield?
(b) Explore the effect of variations in the shield diameter on the total heat rate, as well as on thecontributions due to convection and radiation.
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A 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?
A 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 b
A long electrical conductor of 10 mm diameter is concentric with a refrigerated cylindrical tube of 50 mm diameter whose surface has an emissivity of 0.9 and temperature of 27 °C. The electrical conductor has a surface emissivity of 0.6 and dissipates 6.0 W per meter length. Assuming that the space between the two surfaces is empty, calculate the surface temperature of the conductor.
Chapter 13 Solutions
Fundamentals of Heat and Mass Transfer
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