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 2.12P
Consider a plane wall 100 mm thick and of thermal conductivity
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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
Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are ρ =1200
kg/m 3, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux q =1000 W/m 2 is applied to the upper surface. The right and left surfaces are also kept at 0oC. Bottom surface is insulated.
You 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…
Chapter 2 Solutions
Introduction to Heat Transfer
Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - Assume steady-state, one-dimensional conduction in...Ch. 2 - A hot water pipe with outside radius r1 has a...Ch. 2 - A spherical shell with inner radius r1 and outer...Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - A composite rod consists of two different...Ch. 2 - A solid, truncated cone serves as a support for a...Ch. 2 - To determine the effect of the temperature...Ch. 2 - Prob. 2.9PCh. 2 - A one-dimensional plane wall of thickness 2L=100mm...
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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- 4x F2 # 3 E 4, F3 54 $ R F4 Ac = 1m² ▬ H DII x= 1 m (4) Consider a wall (as shown above) of thickness L-1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h= 1 W/m²K and an ambient temperature T. 1 K. There is no heat generation inside the wall. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). % To,1 = 1 K h₁ = 1 W/m²K 5 Q Search F5 T T₁ A 6 x=0 F6 à = 0 W/m³ k= 1W/mK L=1m Y 994 F7 & 7 T₂ U Ton2 = 1 K h₂ = 1 W/m²K1 PrtScn F8 Page of 7 ) 0 PgUp F11 Parrow_forwardA curved surface of a rod of length L is perfectly insulated against the flow of heat . The rod , which is so thin that heat flow in it can be assumed to be one dimensional , is initially at the temperature U(x,0 ) = 20 x / 3L ° C . Find the temperature at any point in the road at any subsequent time if at t = 0 the temperature at each end of the rod is suddenly reduced to 0 ° C and maintained at that temperature thereafter .arrow_forwardThe temperature gradient is inversely proportional to the cross sectional area for one dimensional flow of heat in a solid material of contact thermal conductivity. Select one: a. True O b. Falsearrow_forward
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