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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Textbook Question
Chapter 2, Problem 2.3P
A hot water pipe with outside radius
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A plane wall of thickness 8cm and thermal conductivity k=5W/mK experiences uniform volumetric heat generation, while convection heat transfer occurs at both of its surfaces (x= -L, x= + L), each of which is exposed to a fluid of temperature T∞ = 20˚C. The origin of the x-coordinate is at the midplane of the wall. Under steady-state conditions, the temperature distribution in the wall is of the form T(˚C) = a + bx - cx^2, where x is in meters, a =86˚C, b = -500˚C/m, and c=4459.
1) Heat Flux Entering the wall is ?
2) Temperature at the left face is /
Consider a solid sphere of radius R with a fixed surface temperature, TR. Heat is generated within
the solid at a rate per unit volume given by q = ₁ + ₂r; where ₁ and ₂ are constants.
(a) Assuming constant thermal conductivity, use the conduction equation to derive an expression
for the steady-state temperature profile, T(r), in the sphere.
(b) Calculate the temperature at the center of the sphere for the following parameter values:
R=3 m 1₁-20 W/m³ TR-20 °C k-0.5 W/(m K) ₂-10 W/m³
2. The slab shown is embedded in insulating materials on five
sides, while the front face experiences convection off its face.
Heat is generated inside the material by an exothermic
reaction equal to 1.0 kW/m'. The thermal conductivity of the
slab is 0.2 W/mk.
a. Simplify the heat conduction equation and integrate
the resulting ID steady form of to find the
temperature distribution of the slab, T(x).
b. Present the temperature of the front and back faces of
the slab.
n-20-
10 cm
IT- 25°C)
100 cm
100 cm
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6arrow_forward1.4 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_forward1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.arrow_forward
- A solid cylinder of radius R and length L is made from material with thermal conductivity 2. Heat is generated inside the cylinder at a rate S (energy per unit volume per unit time). (a) Neglecting conduction along the axis of the cylinder, find the steady-state temperature distribution in the cylinder, given that the surface temperature is Ts. (b) Consider a crude approximation of a mouse modeled as a cylinder of radius 1 cm and length 5 cm. If the ambient air temperature is 10°C and the internal rate of heat generation in the animal is 10-³ W/cm³, find the skin temperature (Ts) for the mouse. The external heat-transfer coefficient is h = 0.2 W/m².K. (You can neglect conduction along the axis of the mouse, as in part a.)arrow_forwardSteel pipe 5 cm thick, 1.0 m long and 12 cm deep, covered with 8 cm thick insulation. The wall temperature in the steel pipe is 100 ° C. The ambient temperature around the insulated pipe is 24 ° C. The convection heat transfer coefficient outside the insulation surface is 50 W / (m² K). The thermal conductivity of steel is 54 W / (m K), and the thermal conductivity of the insulation is 0.04 W / (m K). Count; a. Heat loss per meter of pipe = watt. b. Temperature between steel pipe and insulation. = ° C.arrow_forwardA 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.arrow_forward
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