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 2.34P
(a)
To determine
The volumetric energy generation rate.
(b)
To determine
The coefficients a, b and c.
(c)
To determine
The coefficients a, b and c.
(d)
To determine
The effect of
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A plane wall of thickness 2L = 30 mm and thermal conductivity k = 7 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 = -2x 10°C/m², and x is in meters. The origin of the x-coordinate is at
the midplane of the wall.
(a) What is the volumetric rate à of heat generation in the wall?
(b) Determine the surface heat fluxes, q" (L)and q ( + L).
(c) What are the convection coefficients for the surfaces at x = - Land x = + L?
The volumetric rate of heat generation in the wall, in W/m³:
q = i
W/m³
The surface heat flux, in W/m²:
qx ( - L) = i
The surface heat flux, in W/m²:
q (+ L) = i
W/m²
W/m²
The convection coefficients for the surface at x = - L, in W/m²-K:
h(- L) = i
W/m².K
The convection…
A plane wall of thickness 2L = 2*33 mm and thermal conductivity k = 7 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∞ = 31°C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a + bx + cx2 where a = 85°C, b = −-218°C/m, c = −-23,942°C/m2, and x is in meters. The origin of the x-coordinate is at the midplane of the wall.
(a) Sketch the temperature distribution and identify significant physical features.
(b) What is the volumetric rate of heat generation q˙ in the wall?
(c) Obtain an expression for the heat flux distribution qx″(x). Is the heat flux zero at any location? Explain any significant features of the distribution.
(d) Determine the surface heat fluxes, qx″(−L) and qx″(+L). How are these fluxes related to the heat generation rate?
(e) What are the convection coefficients…
1-D, steady-state conduction with uniform internal energy generation occurs in a plane wall with
a thickness of 50 mm and a constant thermal conductivity of 5 W/m/K. The temperature
distribution has the form T = a + bx + cx² °C. The surface at x=0 has a temperature of To =
120 °C and experiences convection with a fluid for which T..
surface at x= 50 mm is well insulated (no heat transfer). Find:
(a) The volumetric energy generation rate q. (15)
(b) Determine the coefficients a, b, and c.
20 °C and h 500 W/m² K. The
To:
= 120°C
T = 20°C
h = 500 W/m².K
111
Fluid
T(x)-
=
q, k = 5 W/m.K
L = 50 mm
Chapter 2 Solutions
Introduction to Heat Transfer
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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.arrow_forwardA 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?arrow_forwardYou are asked to estimate the maximum human body temperature if the metabolic heat produced in your body could escape only by tissue conduction and later on the surface by convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in radius. Further, simplify the heat transfer process inside the human body as a 1-D situation when the temperature only depends on the radial coordinater from the centerline. The governing dT +q""=0 dr equation is written as 1 d k- r dr r = 0, dT dr =0 dT r=ro -k -=h(T-T) dr (k-0.5 W/m°C), ro is the radius of the cylinder (0.15 m), h is the convection coefficient at the skin surface (15 W/m² °C), Tair is the air temperature (30°C). q" is the average volumetric heat generation rate in the body (W/m³) and is defined as heat generated per unit volume per second. The 1-D (radial) temperature distribution can be derived as: T(r) = q"¹'r² qr qr. + 4k 2h + 4k +T , where k is thermal conductivity of tissue air (A) q" can be calculated…arrow_forward
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