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
Videos
Textbook Question
Chapter 2, Problem 2.38P
One-dimensional, steady-state conduction with no energy generation is occurring in a cylindrical shell of inner radius
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
In the given figure, the two-dimensional steady state heat conduction has a square network structure with dimensions 0≤x≤L and 0≤y≤L. Find the temperature values at m=1,2,3 and 4 nodes by subtracting the finite difference heat conduction equations for the given network structure with dimensions ∆x=∆y=L/3.
Derive the combined one-dimensional heat conduction equation.
Consider steady-state, one-dimensional heat conduction throughthe shape shown in the figure. Cross-sectional area is variable(Ax(x)=Aoeax).The lateral surface of the rod is well-insulated. Left and right surfaceof the rod are maintained at constant temperature of T1 and T2,respectively. Assuming that thermal conductivity is constant,express an equation to determine the heat transfer rate through thewall.
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...
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
- 2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .arrow_forward2.3 The shield of a nuclear reactor is idealized by a large 25-cm-thick flat plate having a thermal conductivity of . Radiation from the interior of the reactor penetrates the shield and there produces heat generation that decreases exponentially from a value of at the inner surface to a value of at a distance of 12.5 cm from the interior surface. If the exterior surface is kept at 38°C by forced convection, determine the temperature at the inner surface of the field. Hint: First set up the differential equation for a system in which the heat generation rate varies according to .arrow_forwardOne end of a 0.3-m-long steel rod is connected to a wall at 204C. The other end is connected to a wall that is maintained at 93C. Air is blown across the rod so that a heat transfer coefficient of 17W/m2 K is maintained over the entire surface. If the diameter of the rod is 5 cm and the temperature of the air is 38C, what is the net rate of heat loss to the air?arrow_forward
- The rear window of a car is defrosted by the passage of warm air on the internal surface. If the warm air is at 40 °C and the internal convection transfer coefficient is 30 W/m²°C, what are the temperatures of the internal and external surfaces of the glass (4 mm thick) if the external air temperature is -10 °C and the convection coefficient is 65 W/m²°C?arrow_forwardIf the surface of a plane wall with heat conduction coefficient k is under constant heat flux (q0 ") condition at x = 0 and its surface at x = L is at temperature Ts, which of the following is the temperature distribution of this plane wall?arrow_forwardA heat-conducting rod, that is wrapped in insulation, is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have a cross-sectional area of 0.0020 m2. The thermal conductivity of alloy B is known to be 1.8 times as great as that of alloy A. The end of the rod in alloy A is maintained at a temperature of 10 degrees Celcius, and the other end of the rod is maintained at an unknown temperature. When the steady-state flow has been established, the temperature at the junction of the alloys is measured to be 40 degrees Celcius, and the rate of heat flow in the rod is measured at 56 W. What is the temperature of the end of the rod in alloy B.arrow_forward
- Two large stainless steel plates at temperatures of 90°C and 70°C are separated by a stainless steel rod0.3 m long and 2.5 cm in diameter. The thermal conductivity of type 304 stainless steel is k = 16.2W/m K. The rod is welded to each plate. The space between the plates is filled with insulation so thatno heat is lost from the circumference of the rod. Because of a voltage difference between the twoplates, current flows through the rod, resulting in a uniform heat generation rate of 1.5 x 105 W/m3.a) Solve for the temperature distribution in the rod as a function of position x analytically (integratethe equation).b) Determine the maximum temperature in the rod. Where does it occur?c) Solve for the temperature distribution in the rod as a function of position x using the finitedifference method. Assume a ∆x of 0.05 m. How does this compare to the exact solution?arrow_forwardExplain how Fourier’s law of conduction canbe applied to experimentally measure the thermal conductivity of solid materials.What are the necessary conditions and assumptions?arrow_forwardDetermine the steady-state heat transfer rate per unit arca through a # # mm thick homogeneous slab with its two faces maintained at uniform temperatures of 40 °C and 200 °C respectively. The thermal conductivity of the material is 0.20 W/(mK). 2arrow_forward
- It is observed that the temperature distribution, in steady-state, inside a one-dimensional wall with thermal conductivity equal to 50 W/mK and thickness of 50 mm has the form T(°C) = a + bx², where a = 200 °C and b = -2000 °C/m², and x is in meters. (a) What is the heat generation rate (q’’’) in the wall? (b) Determine the heat fluxes on both faces of the wall.arrow_forwardA sidewall of a cold storage room is 3 m high, 15 m wide, and 10 cm thick. the thermal conductivity of the wall material is k = .6 W/m°C. The air temperature in the cold storage room is 5 °C, and the outside surface of the wall is exposed to air with a temperature of 25 °C. The surface convective heat transfer coefficient on both side surfaces is 10 W/(m2K). Assuming steady-state conditions. A) How many layers of thermal resistances are presented in this problem? What are the thermal resistance values in each part of the system, and what is the total thermal resistance? B) what is the heat transfer rate C) what is the temperature of the outside wall?arrow_forwardWrite down the Fourier heat conduction equation and explain the meaning of each term in the equation in units. Find the heat conduction coefficient of a cylindrical material with a diameter of 25mm, a length of 30mm, temperatures of its two surfaces T1 = 40.2oC, T2 = 38.9oC, respectively, and a given thermal power amount of 22.4W.arrow_forward
arrow_back_ios
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
Understanding Conduction and the Heat Equation; Author: The Efficient Engineer;https://www.youtube.com/watch?v=6jQsLAqrZGQ;License: Standard youtube license