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 4.15P
A small water droplet of diameter
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THERMODYNAMICS
A 1.5kW iron has a 0.5 cm thick brass base plate (p=8,310 kg/m3 and cp = 400 J/kg C) with a surface area of 0.03 m^2. At the start, the iron is in thermal equilibrium with the ambient air temperature of 22 degrees Celsius. What is the shortest time required for the plate temperature to reach 200 degrees Celsius if 95 percent of the heat generated in the resistance wires is transmitted to the plate?
A wood stove is used to heat a single room. The stove is cylindrical in shape, with a
diameter of D = 0.400 m and a length of L = 0.500 m, and operates at a temperature
of T, = 200 °C.
(a) If the temperature of the room is T, = 20°C, determine the amount of radiant
energy delivered to the room by the stove each second if the emissivity of the
stove is e = 0.920.
(b) By definition, the R-value of a conducting slab is given by
Atot(Th – To)
Poond
R =
where Atot is the total surface area, Pcond is the power loss by conduction through
the slab, Th and Te are the temperatures on the hotter and cooler sides of the
slab. If the room has a square shape with walls of height H = 2.40 m and width
W = 7.60 m, determine the R-value of the walls and ceiling required to maintain
the room temperature at T = 20°C if the outside temperature is T, = 0°C.
Note that we are ignoring any heat conveyed by the stove via convection and any
energy lost through the walls and windows via convection or radiation.
Suppose that as a body cools, the temperature of the surrounding medium increases because it
completely absorbs the heat being lost by the body. Let T(t) and Tm (t) be the temperatures of
the body and the medium at time t, respectively. If the initial temperature of the body is T1 and
the initial temperature of the medium is T2, then it can be shown in this case that Newton's law
of cooling is dT/dt = k(T - Tm ), k 0 is a constant.
(a) The foregoing DE is autonomous. Determine the limiting value of the temperature T(t)
as t→ o What is the limiting value of Tm (t) as t→o?
(b) Verify your answers in part (a) by actually solving the differential equation.
(c) Discuss a physical interpretation of your answers in part (a).
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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