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
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 3, Problem 3.77P
To determine
The general expression for the substrate temperature distribution and find the surface temperature of heat source for
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Q4. Two long rods of the same diameter, one of brass(k= 85 W/mK) and the other of
copper (k=375 W/mK) have one of their ends inserted in a furnace and the other ends
exposed to the same atmosphere. At a distance of 105mm away from the furnace, the
temperature of the brass rod is 120' C. Find the distance from the furnace in which the
copper rod have the same temperature.
Which of the following types of thermometershave to be in thermal equilibrium with the object being measured in order to giveaccurate readings? (i) A bimetallic strip; (ii) a resistance thermometer; (iii) a temporal artery thermometer;(iv) both (i) and (ii); (v) all of (i), (ii), and (iii).
Find the steady-state temperature distribution in a (very long) solid cylinder if the boundary temperatures are T(s=0, θ, z)=0 and T(s, θ, z=0)=s*sinθ
Chapter 3 Solutions
Introduction to Heat Transfer
Ch. 3 - Consider the plane wall of Figure 3.1, separating...Ch. 3 - A new building to be located in a cold climate is...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - A dormitory at a large university, built 50 years...Ch. 3 - In a manufacturing process, a transparent film is...Ch. 3 - Prob. 3.7PCh. 3 - A t=10-mm-thick horizontal layer of water has a...Ch. 3 - Prob. 3.9PCh. 3 - The wind chill, which is experienced on a cold,...
Ch. 3 - Prob. 3.11PCh. 3 - A thermopane window consists of two pieces of...Ch. 3 - A house has a composite wall of wood, fiberglass...Ch. 3 - Prob. 3.14PCh. 3 - Prob. 3.15PCh. 3 - Work Problem 3.15 assuming surfaces parallel to...Ch. 3 - Consider the oven of Problem 1.54. The walls of...Ch. 3 - The composite wall of an oven consists of three...Ch. 3 - The wall of a drying oven is constructed by...Ch. 3 - The t=4-mm-thick glass windows of an...Ch. 3 - Prob. 3.21PCh. 3 - In the design of buildings, energy conservation...Ch. 3 - Prob. 3.23PCh. 3 - Prob. 3.24PCh. 3 - Prob. 3.25PCh. 3 - A composite wall separates combustion gases at...Ch. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - Prob. 3.29PCh. 3 - The performance of gas turbine engines may...Ch. 3 - A commercial grade cubical freezer, 3 m on a...Ch. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A batt of glass fiber insulation is of density...Ch. 3 - Air usually constitutes up to half of the volume...Ch. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - The diagram shows a conical section fabricatedfrom...Ch. 3 - Prob. 3.40PCh. 3 - From Figure 2.5 it is evident that, over a wide...Ch. 3 - Consider a tube wall of inner and outer radii ri...Ch. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.46PCh. 3 - To maximize production and minimize pumping...Ch. 3 - A thin electrical heater is wrapped around the...Ch. 3 - Prob. 3.50PCh. 3 - Prob. 3.51PCh. 3 - Prob. 3.52PCh. 3 - A wire of diameter D=2mm and uniform temperatureT...Ch. 3 - Prob. 3.54PCh. 3 - Electric current flows through a long rod...Ch. 3 - Prob. 3.56PCh. 3 - A long, highly polished aluminum rod of diameter...Ch. 3 - Prob. 3.58PCh. 3 - Prob. 3.59PCh. 3 - Prob. 3.60PCh. 3 - Prob. 3.61PCh. 3 - Prob. 3.62PCh. 3 - Consider the series solution, Equation 5.42, for...Ch. 3 - Prob. 3.64PCh. 3 - Copper-coated, epoxy-filled fiberglass circuit...Ch. 3 - Prob. 3.66PCh. 3 - A constant-property, one-dimensional Plane slab of...Ch. 3 - Referring to the semiconductor processing tool of...Ch. 3 - Prob. 3.69PCh. 3 - Prob. 3.70PCh. 3 - Prob. 3.71PCh. 3 - The 150-mm-thick wall of a gas-fired furnace is...Ch. 3 - Steel is sequentially heated and cooled (annealed)...Ch. 3 - Prob. 3.74PCh. 3 - Prob. 3.75PCh. 3 - Prob. 3.76PCh. 3 - Prob. 3.77PCh. 3 - Prob. 3.78PCh. 3 - The strength and stability of tires may be...Ch. 3 - Prob. 3.80PCh. 3 - Prob. 3.81PCh. 3 - A long rod of 60-mm diameter and thermophysical...Ch. 3 - A long cylinder of 30-min diameter, initially at a...Ch. 3 - Work Problem 5.47 for a cylinder of radius r0 and...Ch. 3 - Prob. 3.85PCh. 3 - Prob. 3.86PCh. 3 - Prob. 3.87PCh. 3 - Prob. 3.88PCh. 3 - Prob. 3.89PCh. 3 - Prob. 3.90PCh. 3 - Prob. 3.91PCh. 3 - Prob. 3.92PCh. 3 - In Section 5.2 we noted that the value of the Biot...Ch. 3 - Prob. 3.94PCh. 3 - Prob. 3.95PCh. 3 - Prob. 3.96PCh. 3 - Prob. 3.97PCh. 3 - Prob. 3.98PCh. 3 - Work Problem 5.47 for the case of a sphere of...Ch. 3 - Prob. 3.100PCh. 3 - Prob. 3.101PCh. 3 - Prob. 3.102PCh. 3 - Prob. 3.103PCh. 3 - Consider the plane wall of thickness 2L, the...Ch. 3 - Problem 4.9 addressed radioactive wastes stored...Ch. 3 - Prob. 3.106PCh. 3 - Prob. 3.107PCh. 3 - Prob. 3.108PCh. 3 - Prob. 3.109PCh. 3 - Prob. 3.110PCh. 3 - A one-dimensional slab of thickness 2L is...Ch. 3 - Prob. 3.112PCh. 3 - Prob. 3.113PCh. 3 - Prob. 3.114PCh. 3 - Prob. 3.115PCh. 3 - Derive the transient, two-dimensional...Ch. 3 - Prob. 3.117PCh. 3 - Prob. 3.118PCh. 3 - Prob. 3.119PCh. 3 - Prob. 3.120PCh. 3 - Prob. 3.121PCh. 3 - Prob. 3.122PCh. 3 - Consider two plates, A and B, that are each...Ch. 3 - Consider the fuel element of Example 5.11, which...Ch. 3 - Prob. 3.125PCh. 3 - Prob. 3.126PCh. 3 - Prob. 3.127PCh. 3 - Prob. 3.128PCh. 3 - Prob. 3.129PCh. 3 - Consider the thick slab of copper in Example 5.12,...Ch. 3 - In Section 5.5, the one-term approximation to the...Ch. 3 - Thermal energy storage systems commonly involve a...Ch. 3 - Prob. 3.133PCh. 3 - Prob. 3.134PCh. 3 - Prob. 3.135PCh. 3 - A tantalum rod of diameter 3 mm and length 120 mm...Ch. 3 - A support rod k=15W/mK,=4.0106m2/s of diameter...Ch. 3 - Prob. 3.138PCh. 3 - Prob. 3.139PCh. 3 - A thin circular disk is subjected to induction...Ch. 3 - An electrical cable, experiencing uniform...Ch. 3 - Prob. 3.142PCh. 3 - Prob. 3.145PCh. 3 - Consider the fuel element of Example 5.11, which...Ch. 3 - Prob. 3.147PCh. 3 - Prob. 3.148PCh. 3 - Prob. 3.149PCh. 3 - Prob. 3.150PCh. 3 - In a manufacturing process, stainless steel...Ch. 3 - Prob. 3.153PCh. 3 - Carbon steel (AISI 1010) shafts of 0.1-m diameter...Ch. 3 - A thermal energy storage unit consists of a large...Ch. 3 - Small spherical particles of diameter D=50m...Ch. 3 - A spherical vessel used as a reactor for producing...Ch. 3 - Batch processes are often used in chemical and...Ch. 3 - Consider a thin electrical heater attached to a...Ch. 3 - An electronic device, such as a power transistor...Ch. 3 - Prob. 3.161PCh. 3 - In a material processing experiment conducted...Ch. 3 - Prob. 3.165PCh. 3 - Prob. 3.166PCh. 3 - Prob. 3.167PCh. 3 - Prob. 3.168PCh. 3 - Prob. 3.173PCh. 3 - Prob. 3.174PCh. 3 - Prob. 3.175PCh. 3 - Prob. 3.176PCh. 3 - Prob. 3.177P
Knowledge Booster
Learn more about
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
- What will be the rise in temperature in 30 minutes of a block of copper of 500-gram mass if it is joined to a cylindrical copper rod 20 cm long and 3.0 mm in diameter when a temperature difference of 80 degree Celsius is maintained between ends of the rod? The thermal conductivity of copper is 1.02 cal/cm2-sec-°C/cm (neglect heat losses). Please include FBDarrow_forward2. The 40mm diameter steel rod AB shown in Figure 2 is resting on frictionless rollers between two steel plates. End A is just touching the left hand steel plate. Steel plate Steel plate А 1500mm Imm Figure 2 There is a gap of 1mm between the end B and the right hand side steel plate. The temperature of the rod increases by an amount AT and this increase in temperature causes the two ends of the rod to press against the steel plates. This action causes the right hand steel plate to move to the right by 0.5mm while the left hand plate does not move. The Young's modulus value for steel is 210,00ON/mm?. Taking any assumptions that you deem necessary calculate the increase in temperature AT required to cause the rod to buckle.arrow_forwardAn ideal mono-atomic gas is confined in a cylinder with the help of a piston that can slide inside the cylinder without friction. The cylinder I placed on a horizontal platform in a vacuum chamber. The walls of the cylinder and the piston are made of heat insulating materials. Initially the temperature of the gas is 'T, and the piston stays in equilibrium. The temperature of the gas is quickly increased n times and then the gas is allowed to expand. If the piston rises and again acquires an equilibrium state, find the temperature of the gas in this new equilibrium state.arrow_forward
- A rectangular nylon [E = 8 GPa; v = 0.35; d = 29 x 10-6/°C] plate has a circular hole in its center. At an initial temperature of T; = 19°C, the plate width is b = 360 mm, the plate height is h = 190 mm, the diameter of the central hole is d = 55 mm, and the thickness of the plate is t = 21 mm. At a final temperature of T=45°C, determine (a) the diameter d of the central hole. (b) the thickness t of the plate. Answers: (a) df = i (b) t= i b Save for Later d eTextbook and Media mm mm Attempts: 0 of 5 used Submit Answerarrow_forwardQuestion 5: Z=62 a. An iron sphere of mass (Z + 300)g is kept in a container having boiling water (100 °C). If the temperature of the sphere is 25.5°C, how much heat energy is absorbed by the iron sphere? Consider the specific heat of iron as 452J/kg. b. The wall of an industrial furnace is constructed from (Z + 3) cm thick fireclay brick having a thermal conductivity of 1.7 W/mK. Measurements made during steady-state operation reveal temperatures of 530°C and 375°C at the inner and outer surfaces, respectively. Find the rate of heat loss through a wall which is (Z + 5) cm by (Z + 3) m on a side.arrow_forward50 mm PROBLEM 2.55 Brass 37.5 mm A brass link (E, = 105 GPa, a, = 20.9x10/°C) and a steel rod (E, = 200 GPa, a =11.7x10/°C) have the dimensions shown at a temperature of 20°C. The steel rod is cooled until it fits freely into the link. The temperature of the whole assembly is then raised to 45°C. Determine (a) the final stress in the steel rod, (b) the final length of the steel rod. 37.5 mm 0.12 mm -250 mm 30-mm diameter Steel A Section A-A 0, =-36.8 MPa L, = 250.147 mm %3Darrow_forward
- a metal bar is made up of 3.0 cm of aluminum and 5.0 cm of steel. the free end of the aluminum bar is placed in contact with steam at 100 degree Celsius. at the other side, the free end of the steel bar maintained at 0 degree Celsius by placing it in contact with the ice. find the temperature at the point that connect the aluminum and the steal (junction)arrow_forwardTwo large containers A and B of the same size are filled with different fluids. The fluids in containers A and B are maintained at 0° C and 100° C, respectively. A small metal bar, whose initial temperature is 100° C, is lowered into container A. After 1 minute the temperature of the bar is 90° C. After 2 minutes the bar is removed and instantly transferred to the other container. What is the temperature of the bar at the instant it is transferred?arrow_forward3. Thermal expansion is a second rank tensor property. A particular material has principal thermal expansion coefficients a11 = am = -2 x 10* K'and a33 = 5 x 10* K1 Along which direction, measured from xạ towards x1 in the x,X3 plane, will the thermal expansion coefficient be zero?arrow_forward
- A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 300 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant O degrees C. Let u(x, t) be the temperature in the bar at x at timet, with t measured in seconds. Find u(x, t) and then u7 (2, 0.1). Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.arrow_forward2. The drawing shows two thin rods, one made from aluminum Midpoint [a = 23 x 10-6 (C°)-'] and the other from steel [a = 12 × 10-“ (C°)-']. Each rod has the same length and the same initial temperature and is attached at one end to an immovable wall, as shown. The temperatures of the rods are increased, both by the same amount, until the gap be- tween the rods is closed. Where do the rods meet when the gap is closed? (a) The rods meet exactly at the midpoint. (b) The rods meet to the right of the midpoint. (c) The rods meet to the left of the midpoint. Aluminum Steelarrow_forwardA solid nylon [E = 8 GPa; v = 0.35; a = 29x106/°C] rod is initially unconstrained. The initial length of the rod is L = 600 mm and its diameter is d = 24 mm. If the temperature of the unconstrained rod is increase by 33°C above the initial temperature, determine (a) the change in the rod's length. (b) the change in the rod's diameter. Answers: (a) AL = i (b) Δd = i eTextbook and Media Save for Later mm mm Attempts: 0 of 5 used Submit Answerarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Understanding Conduction and the Heat Equation; Author: The Efficient Engineer;https://www.youtube.com/watch?v=6jQsLAqrZGQ;License: Standard youtube license