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
Videos
Textbook Question
Chapter 3, Problem 3.82P
A long rod of 60-mm diameter and thermophysical properties
(a) What is the centerline temperature of the rod when the surface temperature is 550 K?
(b) In a heat-treating process, the centerline temperature of the rod must be increased from
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
19 mm diameter steel balls are quenched by heating to 989 K followed by slow cooling to 400 K in an environment with air at T∞ = 325 K and h = 39 W/m2.K. Assuming that the steel properties are k = 40 W/m.K, ρ = 7800 kg/m3 and C = 600 J/kg.K, estimate the time (in "minutes") required for the cooling process.
Bolas de aço com 19 mm de diâmetro são temperadas pelo aquecimento a 989 K seguido pelo resfriamento lento até 400 K em um ambiente com ar a T∞ = 325 K e h = 39 W/m2.K. Admitindo que as propriedades do aço sejam k = 40 W/m.K, ρ = 7800 kg/m3 e C = 600 J/kg.K, estime o tempo (em "minutos") necessário para o processo de resfriamento.
t = 30 + 0.9563 (62.2- 30) = 60.79°C (Ans.)
Example 4.14. A very thin glass walled 3 mm diameter mercury thermometer is placed in a
stream of air, where heat transfer coefficient is 55 W/m2°C, for measuring the unsteady temperature
of air. Consider cylindrical thermometer bulb to consist of mercury only for which k
and a = 0.0166 m2/h. Calculate the time required for the temperature change to reach half its final
or,
%3D
8.8 W/m C
%3D
value.
Steel balls 12 mm in diameter are annealed by heating to 1100 K and then slowly cooling to 360 K in an air environment for which
T. = 325 Kand h = 20 W/m2-K. Assuming the properties of the steel to be k = 40 W/m-K,p = 7800 kg/m, and c = 600
J/kg-K, estimate the time required for the cooling process.
The time required for the cooling process isi
h.
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
- A cylindrical shape body of length is 1.9 m and diameter is 400 mm is inside a room where the ambient temperature is equal to 300 K. The initial temperature of the body is equal to 350 K. If the heat convective coefficient is equal to 1.3 W/m^2.K. What is the thermal conductivity K.arrow_forwardA 10.0-cm cube of stainless steel is initially at 500oC. It is suddenly immersed in a tank of oil maintained at 100oC. The convection coefficient is 1000 W/m2×oC. Calculate the temperature at the center of one face after 1 min.Data: stainless steel properties, k = 22 W/m×oC, r = 7,689 kg/m3, c = 460 J/kg×oC.arrow_forwardSteel cubes 10 mm in width are annealed by heating to 1,377 K and then slowly cooling to 469 K in an air environment for which T∞ = 301 K and h = 24 W/m2-K. Assuming the properties of the steel to be k = 24 W/m · K, ρ = 7,047 kg/m3, and c = 916 J/kg · K, estimate the time required for the cooling process.arrow_forward
- What is the temparature at depth 1 cm from the surface at t=2 minutes after the start of the coolıng ?arrow_forwardNumber 4 A food product wants to be produced in a small round shape (pellet) by freezing it in a water blast freezer freezer. Air freezer operates at -25°C. The initial product temperature is 25°C. The pellet has a diameter of 1.2 cm, and a density of 980 kg/m³. The initial freezing temperature is -2.5°C. The latent heat of freezing of the product is 280 kJ/kg. The thermal conductivity of the frozen product is 1.9 W/(m °C). The convective heat transfer coefficient is 40 W/(m² K). Calculate the freeze time. tf = answer in hourarrow_forwardQ1/ The center to surface temperature difference in a heat generating cylindrical rod of 4 m diameter was 30°C. What is the difference temperature between the center and surface in the case of a sphere of 2 m diameter under similar conditions? * Your answer Q2/ A metal plate of 4mm thickness (k = 95.5 W/m°C) is exposed to vapor at 100°C on one side and cooling water at 25°C on the opposite side. The heat transfer coefficients on vapor side and waterside are 14500 W/m^2°C and 2250 W/m^2 °C respectively. Determine the overall heat transfer coefficient * Your answerarrow_forward
- A composite plane wall consisting of materials, 1.5-in steel (k = 312 BTU-in/HR.ft2.0F) and 2-in aluminum (k = 1400 BTU-in/HR.ft2.0F), separates a hot gas at Ti = 2000F, hi = 2 BTU/HR.ft2.0F, from cold gas at To = 80 deg F, ho = 5. If the hot fluid is on the aluminum side, find: a) Transmittance, U; b) The heat through 100 sq. ft of the surface under steady state condition and c) The interface temperature at the junction of the metals.arrow_forwardA glass door is used on a fireplace to reduce exfiltration of room air through the chimney. The door, 0.70m high and 1.00m wide, reaches a uniform temperature of 232oC. If the room air temperature is 23oC, estimate the rate of heat transfer to the room air due to convection. Air properties: k=0.0338W/m-K ν=26.4x10-6 m2/s Pr=0.690arrow_forwardb. Consider a large plane wall of thickness L = 0.25 m, thermal conductivity k= 0.77 W/m-K, and surface area A = 15 m. The outside wall is subjected to convection with T1 = 100 °C and h, = 5 W/m? · K and the inside wall is maintained at constant temperatures of T2 = 50 °C, respectively, as shown in Fig. 2. Determine: i. express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, and obtain a relation for the variation of temperature in the wall by solving the differentiai equation 11. -T2arrow_forward
- It is required to perform a heat treatment for gas turbine applications, for them it is required to analyze a sample of the material to be used. The analysis will be performed using the method of a semi-infinite cylinder of stainless steel 12Awith the following thermal properties; (ρ=8700 kg/m3, Cp = 897 J/kg. °C and k = 242 W/m. °C. Of diameter D=12 cm is initially at a uniform temperature of 120 °C. Then the cylinder is placed in a furnace at a constant heat flux of 3800 W/m2, a temperature of 60 °C andh= 170 W/m2. Determine the temperature at the center of the cylinder 3.5 cm from the end surface 6 minutes after placing it in the furnace.arrow_forwardA 3 cm diameter Aluminum sphere (k = 204 W / mK, p = 2700 kg / m² and C = 896 J / Kg.K initially at 175 ° C. It is suddenly immersed in a well stirred fluid at 25 ° C. The temperature of the sphere is lowered to 100 ° C in 42 second, calculate the heat transfer coefficient and the rate of heat transfer.arrow_forwardThe temperature of a gas stream is measured by a thermocouple whose junction can be approximated as a 1-mm-diameter sphere. Take the junction’s properties as: k of 32 W/m K, density of 8.2 kg/m^3, c of 300 J/Kg K. On its surface, the overall heat transfer coefficient is 200 W/m^2 K. Neglect any conduction loss from the sphere to other parts of the thermocouple. Create a plot of measurement error as a function of time for the thermocouple.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license