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 2.25P
To determine
The heat flux along the rod.
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Students have asked these similar questions
Find the temperature of a rod 0 < x < 1 thermally insulated along the surface, if
heat sources of density equal to (t) sin (7) are continuously distributed over the
rod, and the initial temperature of the rod is an arbitrary function f(x) and the
temperature of the ends is maintained equal to zero.
A wall is made from an inhomogeneous (nonuniform) material for which the thermal conductivity varies through the thickness according to k = ax + b, where a and b are constants. The heat flux q"q" is known to be constant.
Determine expressions for the temperature gradient and the temperature distribution when the surface at x = 0 is at temperature T1.
Use the following values
a = 11 W/K
b = 25 W/m-K
k = 11x + 25 W/m-K
q"q" = 104 W/m^2
T1 = 60 C
1. The four sides of a square plate of side 12 cm, made of homogeneous material,
are kept at constant temperature and as shown in Fig. Using a (very wide) grid
of mesh 4 cm and applying Gauss-Seidel iteration with ek < 0.0001, find the
(steady-state) temperature at the mesh (interior) points.
y
u = 0
12
u = 100
u = 100
R
12
u = 100
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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- 1.4 To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in W/m K. Problem 1.4arrow_forward2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.arrow_forwardA section of a composite wall with the dimensions shown below has uniform temperatures of 200C and 50C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA=70W/mK,kB=60W/mK, kC=40W/mK, and kP=20W/mK, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces. Repeat Problem 1.34, including a contact resistance of 0.1 K/W at each of the interfaces.arrow_forward
- 2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)arrow_forwardA section of a composite wall with the dimensions shown below has uniform temperatures of 200C and 50C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA=70W/mK,kB=60W/mK, kC=40W/mK, and kD=20W/mK, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces.arrow_forwardHeat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of TiandTo, respectively. Derive an expression for the temperature distribution.arrow_forward
- In this question, we are concerned with the evolution of the temperature u(x, t) in a homogeneous thin heat conducting rod of length L = 1. We can consider that the rod is laterally insulated as to have a one-dimensional problem. The evolution of the temperature is governed by the one-dimensional heat equation ди 0 0 = K Ət Əx2' Assume that this equation is subject to the following initial conditions u(x,0) = f(x) and boundary conditions (0, t) = 0 and ди (1,t) + и(1,t) — 0 (i) Discuss briefly the physical meaning of the boundary conditions.arrow_forward2. The lateral surface of a 50-units-long, thin vertical rod is insulated. When 0arrow_forward1. Question 1- Laplace Equation: Leibmann's Method The four sides of a square plate of side 12cm, made of homogenous material, are kept at a constant temperature 0°C and 100°C as shown in Figure 1. Using a grid of mesh 4cm and applying Leibmann's method, perform up to four (4) iteration to find the temperature at the various mesh points. 12cm U=100 ➤U=0 R u=100 U=100 ·X 12cm Figure 1 Showing Boundary Conditions for Given Problem.arrow_forwardThe temperature distribution for the plane wall is given in Fig. and here T1 and T2 are the temperatures on both sides of the 2 walls. The thermal conductivity of the wall is constant and its thickness is L. T=T1 Subtract the expression for heat generation per unit volume based on x, which represents the distance from the wall for which the equation is satisfied. At x=0, take the heat generation rate as q0. T -T, - = C, +C,x² +C¸x' T, -T, | %3D |arrow_forwardQ2/ A metal plate of 4mm thickness (k = 95.5 W/m°C) is exposed to vapor at 100°C on one side and cooling water at 25°C on the opposite side. The heat transfer coefficients on vapor side and waterside are 14500 W/m^2°C and 2250 W/m^2 °C respectively. Determine the overall heat transfer coefficient *arrow_forwardquestion A B and Carrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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