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 4, Problem 4.74P
(a)
To determine
The unknown nodal temperature and heat transfer rate.
(b)
To determine
The temperatures and heat rate with grid spacing 10mm. Also, the temperature field and heat rate for values of h = 5, 200 and 1000 W/m2K as well as h tends to infinity.
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H.W.:
Q1: Consider steady two-dimensional heat transfer in a long solid body whose cross section is
given in the figure. The temperatures at the selected nodes and the thermal conditions at the
boundaries are as shown. The thermal conductivity of the body is k = 45 W/m. °C, and heat is
generated in the body uniformly at a rate of g = 6 x 106 W/m3. Using the finite difference
method with a mesh size of Ax = Ay = 5.0 cm, determine (a) the temperatures at nodes 1, 2, and
3 and (b) the rate of heat loss from the bottom surface through a 1-m-long section of the body.
.
200°C
5 cm
5 cm
g=6x 10 W/m²
260
3
240
305
290
Insulation
1
Convection
T₂= 20°C, h= 50 W/m² °C
350°C
325
A vertical cylinder 1.75 m tall and 0.3 m in diameter might be used to approximate a man
for heat-transfer purposes (thermal conductivity, k-0.8 /m°C). Suppose the center temperature of
the cylinder is 37°C, the surface emissivity is 0.9, and the cylinder is placed in a large room
where the air temperature is 20°C and the heat transfer coefficient is 20W /m2°C and the wall
temperature is 10°C.
1-Sketch the equivalent thermal resistance network.
2-Neglect the radiation and:
-Cakculate the heat lost from the from the cylinder.
-Determine the surface temperatures of the cylinder.
A very long, rectangular cross-section block is made from metal with the following properties: thermal conductivity = 130 W/mK, density = 2771 kg/m³, and specific heat
capacity = 703 J/kgK. Initially all 4 sides of the cross section are maintained at 373 K. Then the temperature of one side is suddenly increased to 473 K. The temperature
profile in the block will be investigated using an explicit finite difference model. If the time step is fixed at 5.5 seconds, what is the limit for node spacing that should be
used to ensure stability of the solution? Give your numerical answer in mm to 1 decimal place.
Chapter 4 Solutions
Introduction to Heat Transfer
Ch. 4 - In the method of separation of variables (Section...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Consider the two-dimensional rectangular plate...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Free convection heat transfer is sometimes...Ch. 4 - Prob. 4.8PCh. 4 - Radioactive wastes are temporarily stored in a...Ch. 4 - Based on the dimensionless conduction heat rates...
Ch. 4 - Prob. 4.11PCh. 4 - A two-dimensional object is subjected to...Ch. 4 - Prob. 4.13PCh. 4 - Two parallel pipelines spaced 0.5 m apart are...Ch. 4 - A small water droplet of diameter D=100m and...Ch. 4 - Prob. 4.16PCh. 4 - Pressurized steam at 450 K flows through a long,...Ch. 4 - Prob. 4.19PCh. 4 - A furnace of cubical shape, with external...Ch. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - A pipeline, used for the transport of crude oil,...Ch. 4 - A long power transmission cable is buried at a...Ch. 4 - Prob. 4.25PCh. 4 - A cubical glass melting furnace has exterior...Ch. 4 - Prob. 4.27PCh. 4 - An aluminum heat sink k=240W/mK, used to coolan...Ch. 4 - Hot water is transported from a cogeneration power...Ch. 4 - Prob. 4.30PCh. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - An igloo is built in the shape of a hemisphere,...Ch. 4 - Consider the thin integrated circuit (chip) of...Ch. 4 - Prob. 4.35PCh. 4 - The elemental unit of an air heater consists of a...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Prob. 4.39PCh. 4 - Prob. 4.40PCh. 4 - Prob. 4.41PCh. 4 - Determine expressions for...Ch. 4 - Prob. 4.43PCh. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - Derive the nodal finite-difference equations for...Ch. 4 - Prob. 4.47PCh. 4 - Prob. 4.48PCh. 4 - Consider a one-dimensional fin of uniform...Ch. 4 - Prob. 4.50PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - Prob. 4.54PCh. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - Steady-state temperatures at selected nodal points...Ch. 4 - Prob. 4.58PCh. 4 - Prob. 4.60PCh. 4 - The steady-state temperatures C associated with...Ch. 4 - A steady-state, finite-difference analysis has...Ch. 4 - Prob. 4.64PCh. 4 - Consider a long bar of square cross section (0.8 m...Ch. 4 - Prob. 4.66PCh. 4 - Prob. 4.67PCh. 4 - Prob. 4.68PCh. 4 - Prob. 4.69PCh. 4 - Consider Problem 4.69. An engineer desires to...Ch. 4 - Consider using the experimental methodology of...Ch. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Prob. 4.74PCh. 4 - Prob. 4.75PCh. 4 - Prob. 4.76PCh. 4 - Prob. 4.77PCh. 4 - Prob. 4.78PCh. 4 - Prob. 4.79PCh. 4 - Prob. 4.80PCh. 4 - Spheres A and B arc initially at 800 K, and they...Ch. 4 - Spheres of 40-mm diameter heated to a uniform...Ch. 4 - To determine which parts of a spiders brain are...Ch. 4 - Prob. 4.84P
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