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 4.13P
To determine
The temperature reached by the heater.
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2. A steel plate of k=50w/mk and thickness 10cm passes a heat flux by conduction of 25kW/m² . If the
temperature of hot surface of plate is 100C, then what is the temperature of the cooler side of plate?
The temperature distribution across a wall 0.25 m thick at a certain instant of time is T(x) = a + bx + cx², where T is in degrees Celsius and x is
in meters, a = 200 C, b = -200 C/m, and c = 30 C/m². The wall has a thermal conductivity of 2.5 W/m.K. (a) Determine the heat flux into and
out of the wall (q"in and q'out). (b) If the cold surface is exposed to a fluid at 100 C, what is the convection coefficient h?
- Degree Celsius
200°C
q" In-
q'in
q'out=
h =
Choose...
Choose....
Choose...
L₂x
K = 2.5 W/m.k
T(x)-200-200 x +30x²
q" Out
142.7 C
11
L=0.25 m
Fluid
Too = 100 °C
h
Problem 2
Suppose that heat conduction occurs at a
constant rate of đQ/dt in a hollow sphere with
an inner radius of r, at temperature T, and an
inner radius of r, at temperature T,. Show
that for constant thermal conductivity K, the
temperature difference between the two
surfaces is given by
dQ I dT ( 1
т, - т,
1
4л К
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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- 1.67 In beauty salons and in homes, a ubiquitous device is the hairdryer. The front end of a typical hairdryer is idealized as a thin-walled cylindrical duct with a 6-cm diameter with a fan at the inlet that blows air over an electric heating coil as schematically shown in the figure. The design of this appliance requires two power settings, with which the air blown over the electric heating coil is heated from the ambient temperature of to an outlet temperature of and with exit air velocities of 1.0 m/s and 1.5 m/s. Estimate the electric power required for the heating coil to meet these conditions, assuming that heat loss from the outside of the dryer duct is neglected.arrow_forward2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.arrow_forward3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.arrow_forward
- Heat is generated in a sphere of radius 1 m at a rate of 1000 W/m3. The sphere is surrounded by air at 27 oC.A. Balance total energy produced by the total energy lost from the surface by convection and radiation tocalculate the surface temperature.B. Solve the heat transfer problem in the sphere and use the temperature calculated in A as the boundarycondition to determine the temperature at the center of the sphere.Assume that the sphere can be treated as a black body for calculating radiation losses.Properties The thermal conductivity is given to be k =2.5 W/m°C.σ = 5.67 × 10−8 W / (m2 x K4). Heat transfer coefficient h = 10 W/(m2 K)arrow_forwardCalculate the quantity of heat conducted per minute through a duralumin circular disc 127 mm diameter and 19 mm thick when the temperature drop across the thickness of the plate is 5 degrees Celsius. Take the coefficient of thermal conductivity of duralumin as 150 W/(m-K).arrow_forwardA metal cube of 0.1 m sides is being cooled down uniformly from 300°C to 30°C by placing it in cold water at 10°C. The convection coefficient of water around the cube is 40 W/m².K. The properties of the cube material are as follows - thermal conductivity: 137 W/m-K, density: 1600 kg/m³; specific heat: 800 J/kg.K. Neglect radiation. Find the time required for coo cooling. 1426-2arrow_forward
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