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 4, Problem 4.82P
Spheres of 40-mm diameter heated to a uniform temperature of 400°C are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of
(a) How long must the spheres remain in the air bath for 80% of the thermal energy to be removed?
(b) The spheres are then placed in a packing carton that prevents further heat transfer to the environment. What uniform temperature will the spheres eventually reach?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Number 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 hour
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.
Steel 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.
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
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
- Steel balls 12 mm in diameter are annealed by heating to 1200 K and then slowly cooling to 350 K in an air environment for which T∞ = 325 K and h = 20 W/m².K. Assuming the properties of the steel to be k = 40 W/m-K, p = 7800 kg/m³, and c = 600 J/kg-K, estimate the time required for the cooling process. The time required for the cooling process is i h.arrow_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_forward3 Brass cube "p = 8530 kg/m , c= side length =9 mm, are annealed by heating them first to 813°C in a furnace and then allowing them to cool slowly to 130°C in ambient air at 28°C. If the average heat transfer coefficient is 19.9 W/m .°C, If 2204 balls are to be annealed per hour, what is the total rate of heat transfer (watts) from the balls to the ambient air? 380 J/kg.°C, k = 110 W/m.°C, a = 33.9E-6 W/m.°C",arrow_forward
- 3. A food product with 73% moisture content in a 10 cm diameter can wants to be frozen. The density of the product is 970 kg / m³, the thermal conductivity is 1.2 W / (m K), and the initial freezing temperature is -2 ° C. After 14 hours in the freezing medium -30 ° C, the product temperature becomes -10 ° C. Estimate the convection heat transfer coefficient of the freezing medium. Assume the can as an infinite cylinder. h = Answer W / (m² K).arrow_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_forwardYou are cooling the door to a large heat-treating oven, which is 3.50 m tall by 1.30 m wide, with a large fan blowing air at 25.0°C over the outside of the door. The convection coefficient associated with this cooling process is h = 57.0 W/(m2-K). The outside surface temperature of the door is 58.0°C. Find the heat transfer rate q, in units of Watts, associated with this cooling process.arrow_forward
- Consider a wall that is 5 m high, 8 m long, and 0.22 m thick. The thermal conductivities of the various materials used, in W/m °C, are kA = kF = 2, kB = 8, kC = 20, kD = 15 and kE = 35. The left and right surfaces of the wall are maintained at uniform temperatures of 300 °C and 100 °C, respectively. If the heat transfer through the wall is one-dimensional, determine (a) the rate of heat transfer through the wall; b) the temperature at the point where sections B, D, and E meet, and c) the temperature drop across section F. Disregard any contact resistances between the interfaces.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, expressed as a fraction of the initial temperature difference.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
- Problem: Conduction related Steel balls 10 mm in diameter are annealed by heating to 1,150 K and then slowly cooling to 450 K in an air environment for which T∞ = 325 K + at, where a = 0.1875 K/s and h = 25 W/m2 · K. Assuming the properties of the steel to be k = 40 W/m · K, ρ = 7,800 kg/m3, and c = 600 J/kg · K, estimate the time required for the cooling process. Find an expression for the ball temperature as a function of time T(t), and plot the ball temperature for 0 ≤ t ≤ 1 h and ambient temperature.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_forward3) The two sides of a large plan wall are maintained at constant temperatures of T₁ = 120°C and T₂ = 50°C, respectively. If you know that the wall thickness L = 0.2 m, thermal conductivity k = 1.2 W/m.K, and surface area A= 15 m². Determine (a) the variation of temperature within the wall and the value of temperature at x = 0.1 m and (b) the rate of heat conduction through the wall under steady conditions. -02-1arrow_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 Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering 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
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license