Introduction to Heat Transfer
Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 2, Problem 2.28P

Uniform internal heat generation at q . = 5 × 10 7 W/m 3 is occurring in a cylindrical nuclear reactor fuel rod of 50-mm diameter, and under steady-state conditions the temperature distribution is of the form T r = a + b r 2 , where T is in degrees Celsius and r is in meters, while a = 800 ° C and b = 4.167 × 10 5 ° C/m 2 . The fuel rod properties are k = 30 W/m K, ρ = 1100 kg/m 3 , and c p = 800 J/kg K .

  1. What is the rate of heat transfer per unit length of the rod at r = 0 (the centerline) and at r = 25 mm (the surface)?
  2. If the reactor power level is suddenly increased to q . 2 = 10 8 W/m 3 , what is the initial time rate of temperature change at r = 0 and r = 25 mm?

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Use the alternative conduction analysis of Section 3.2 to derive an expression relating the radial heat rate, q,, to the wall temperatures Ts,1 and Ts,2, for the hollow cylinder show in the figure below. Cold fluid Too,2, h₂ Ts,1 Hot fluid Too,1, h₁1 Ts,1 Ts2 r1 12 Ts.2 Use your expression to calculate the heat transfer rate, in W, associated with a L = 1.25 m long cylinder of inner and outer radii of r₁ = 50 mm and r₂ = 75 mm, respectively. The thermal conductivity of the cylindrical wall is k 2.5 W/m-K, and the inner and outer surface temperatures are Ts,1 100°C and Ts2 = 67°C, respectively. = 9r = i W

Chapter 2 Solutions

Introduction to Heat Transfer

Ch. 2 - Consider steady-state conditions for...Ch. 2 - Consider a plane wall 100 mm thick and of thermal...Ch. 2 - Prob. 2.13PCh. 2 - In the two-dimensional body illustrated, the...Ch. 2 - Consider the geometry of Problem 2.14 for the case...Ch. 2 - Steady-state, one-dimensional conduction occurs in...Ch. 2 - Prob. 2.17PCh. 2 - Prob. 2.18PCh. 2 - Consider a 300mm300mm window in an aircraft. For a...Ch. 2 - Prob. 2.20PCh. 2 - Use IHT to perform the following tasks. Graph the...Ch. 2 - Calculate the thermal conductivity of air,...Ch. 2 - A method for determining the thermal conductivity...Ch. 2 - Prob. 2.24PCh. 2 - Prob. 2.25PCh. 2 - At a given instant of time, the temperature...Ch. 2 - Prob. 2.27PCh. 2 - Uniform internal heat generation at q.=5107W/m3 is...Ch. 2 - Prob. 2.29PCh. 2 - The steady-state temperature distribution in a...Ch. 2 - The temperature distribution across a wall 0.3 m...Ch. 2 - Prob. 2.32PCh. 2 - Prob. 2.33PCh. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.43PCh. 2 - Prob. 2.44PCh. 2 - Beginning with a differential control volume in...Ch. 2 - A steam pipe is wrapped with insulation of inner...Ch. 2 - Prob. 2.47PCh. 2 - Prob. 2.48PCh. 2 - Two-dimensional, steady-state conduction occurs in...Ch. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - A chemically reacting mixture is stored in a...Ch. 2 - A thin electrical heater dissipating 4000W/m2 is...Ch. 2 - The one-dimensional system of mass M with constant...Ch. 2 - Consider a one-dimensional plane wall of thickness...Ch. 2 - A large plate of thickness 2L is at a uniform...Ch. 2 - Prob. 2.57PCh. 2 - Prob. 2.58PCh. 2 - A plane wall has constant properties, no internal...Ch. 2 - A plane wall with constant properties is initially...Ch. 2 - Consider the conditions associated with Problem...Ch. 2 - Prob. 2.62PCh. 2 - A spherical particle of radius r1 experiences...Ch. 2 - Prob. 2.64PCh. 2 - A plane wall of thickness L=0.1m experiences...Ch. 2 - Prob. 2.66PCh. 2 - A composite one-dimensional plane wall is of...Ch. 2 - Prob. 2.68PCh. 2 - The steady-state temperature distribution in a...
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