A plane wall of thickness 2L=40 mm and thermal conductivity k=5 W/m·K experiences uniform volumetric heat generation at a rate q, while convection heat transfer occurs at both of its surfaces (x=-L, +L), each of which is exposed to a fluid of temperature T=20 °C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a+bx+cx² where a = 82.0 °C, b=-210 °C/m, c = -2x10 °C/m², and x is in meters. The origin of the x- coordinate is at the midplane of the wall. -L x -L (a) Determine the surface heat fluxes, qx(-L) and qx(+L). (b) What is the volumetric rate of heat generation & in the wall? (c) What is the convection heat transfer coefficient for the surfaces at x = +L? (d) Obtain an expression for the heat flux distribution q (as a function of x). Is the heat flux zero at any location? (e) If the source of the heat generation is suddenly deactivated (i. e. q = 0), what temperature will the wall eventually reach with q = 0?

A plane wall of thickness 2L=40 mm and thermal conductivity k=5 W/m·K experiences uniform volumetric heat generation at a rate q, while convection heat transfer occurs at both of its surfaces (x=-L, +L), each of which is exposed to a fluid of temperature T=20 °C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a+bx+cx² where a = 82.0 °C, b=-210 °C/m, c = -2x10 °C/m², and x is in meters. The origin of the x- coordinate is at the midplane of the wall. -L x -L (a) Determine the surface heat fluxes, qx(-L) and qx(+L). (b) What is the volumetric rate of heat generation & in the wall? (c) What is the convection heat transfer coefficient for the surfaces at x = +L? (d) Obtain an expression for the heat flux distribution q (as a function of x). Is the heat flux zero at any location? (e) If the source of the heat generation is suddenly deactivated (i. e. q = 0), what temperature will the wall eventually reach with q = 0?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.5P: To determine the thermal conductivity of a structural material, a large 15-cm-thick slab of the...

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A plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where T is in kelvin. If one surface of this wall is maintained at 150C and the other at 50C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.
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