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 4.76P
(a)
To determine
The temperature distribution in the element, the heat rate and shape factor for the edge.
(b)
To determine
The temperature field assess the validity of assuming linear temperature distribution across section a-a and b-b.
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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
Q1
Passage of an electric current through a long conducting
rod of radius r; and thermal conductivity k, results in
uniform volumetric heating at a rate of ġ. The conduct-
ing rod is wrapped in an electrically nonconducting
cladding material of outer radius r, and thermal conduc-
tivity k, and convection cooling is provided by an
adjoining fluid.
Conducting
rod, ġ, k,
11
To
Čladding, ke
For steady-state conditions, write appropriate forms of
the heat equations for the rod and cladding. Express ap-
propriate boundary conditions for the solution of these
equations.
Q2/
A (2 cm) thick steel plate of thermal conductivity (50 W/m.°C) has a uniform heat generation of
(40 x 106 W/m³). The temperature at the left surface of the plate is (160 °C) and at the right surface is
(100 °C) start from principle to find the place and the value of the maximum temperature.
(25 marks)
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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- a. A slab of thermal insulator is 100 cm² in cross section and 2 cm thick. Its thermal conductivity is 2.4 x 10 -+ cal/(s cm C"). If the temperature difference between opposite faces is 180 F', how much heat flows through the slab in one day?arrow_forward3.112 A metal rod of length 21, diameter D. and thermal conductivity is inserted into a perfectly insulating wall, exposing one-half of its length to an air stream that is of temperature and provides a convection co- efficient h at the surface of the rod. An electro- magnetic field induces volumetric energy generation at a uniform rate q within the embedded portion of the rod. T=20°C h=100 W/m²K Rod, D. & T L 50 mm D-5 mm 25 W/m-K q=1 x 100 W/m² (a) Derive an expression for the steady-state tempera- ture 7, at the base of the exposed half of the rod. The exposed region may be approximated as a very long fin. (b) Derive an expression for the steady-state tempera- ture T at the end of the embedded half of the rod. (c) Using numerical values provided in the schematic plot the temperature distribution in the rod and de- scribe key features of the distribution. Does the rod behave as a very long fin?arrow_forward4x 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_forward
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