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 2.56P

A large plate of thickness 2 L is at a uniform temperature of T i = 200 ° C, when it is suddenly quenched by dipping it in a liquid bath of temperature T = 20 ° C . Heat transfer to the liquid is characterized by the convection coefficient h.

  1. If x = 0 corresponds to the midplane of the wall, on T x coordinates, sketch the temperature distributions for the following conditions: initial condition t 0 , steady-state condition t , and two intermediate times.
  2. On q x " t coordinates, sketch the variation with time of the heat flux at x = L . If h = 100 W/m 2 K, what is the heat flux at x = L and t = 0 ? If the wall has a thermal conductivity of k = 50 W/m K what is the corresponding temperature gradient at x = L ? Consider a plate of thickness 2 L = 20 mm with a density of ρ = 2770 kg/m 3 and a specific heat c p = 875 J/kg K . By performing an energy balance on the plate, determine the amount of energy per unit surface area of the plate J/m 2 that is transferred to the bath over the time required to reach steady-state conditions.
  3. From other considerations, it is known that, during the quenching process, the heat flux at x = + L and x = L decays exponentially with time according to the relation, q x " = A exp B t , where t is in seconds, A = 1.80 × 10 4 W/m 2 , and B = 4.126 × 10 3 s 1 . Use this information to determine the energy per unit surface area of the plate that is transferred to the fluid during the quenching process.

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Chapter 2 Solutions

Introduction to Heat Transfer

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