Fundamentals of Heat and Mass Transfer
Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 2, Problem 2.43P

cylindrical system illustrated has negligible variation of temperature in the r- and z-directions. Assume that Δ r = r o r i is small compared to r i , and the length in the z-direction, normal to the page, as L.
Chapter 2, Problem 2.43P, cylindrical system illustrated has negligible variation of temperature in the r- and z-directions.

  1. Beginning with a properly defined control volume and considering energy generation and storage effects, derive the differential equation that prescribe: the variation in temperature with the angular coordinate ϕ . Compare your result with Equation 2.26.
  2. For conditions with no internal heat generation and constant properties, determine the temperature distribution T ( ϕ ) in terms of the constant, T 1 , T 2 , r i , and r o . Is this distribution linear in ϕ ?
  3. For the conditions of part (b) write the expression for the heat rate q ϕ .

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under steady-state conditions. If you are given T1 = 200 °C and T2 = 164 °C, determine: a) the conduction heat flux, q,.cond, in m2 W from x = 0 to x = L b) if the dimensions of the triangle ares 15 mm and h 13 mm, calculate the heat transfer due to convection, q,y, in W at x = L Finsulation T2 T T = 20°C h = 500 W/m2.K Triangular Prism x L x 0 L= 50 mm k = 100 W/m-K
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Chapter 2 Solutions

Fundamentals of Heat and Mass Transfer

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