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
Question
Chapter 2, Problem 2.66P
(a)
To determine
The verification of the equations to satisfy the heat equation and boundary conditions.
(b)
To determine
The expression for the heat flux at
(c)
To determine
The sketch of temperature distribution at
The sketch of variation of heat flux with time.
(d)
To determine
The effects of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Question 2a) Give the Stefan Boltzman equation and define each term.[4]b) A electric room heater (radiator) element is 25 cm long and 4 cm in diameter. The element dissipates heat to the surroundings at 1500 W mainly by radiation, the surrounding temperature being 15°C. Determine the equilibrium temperature of the element surface.[4]c) A composite cylinder consists of 10 cm radius steel pipe of 25 mm thickness over which two layers of insulation 30 mm and 35 mm are laid. The conductivities are 25 W/mK, 0.25 W/mK and 0.65 W/mK. The inside is exposed to convection at 300°C with h 65 W/m2K.The outside is exposed to air at 30°C with h 15 W/m2K. Determinei. the heat loss/m,the interface temperatures.ii. The overall heat transfer coefficient.[4][4][2]
A steel pipe (outside diameter 100 mm) is covered with two
layers of insulation. The inside layer, 40 mm thick, has a
thermal conductivity of 0.07 W/(m K). The outside layer,
20 mm thick, has a thermal conductivity of 0.15 W/(m K).
The pipe is used to convey steam at a pressure of 600 kPa. The
outside temperature of insulation is 24°C. If the pipe is 10 m
long, determine the following, assuming the resistance to
conductive heat transfer in steel pipe and convective resistance
on the steam side are negligible:
a. The heat loss per hour.
b. The interface temperature of insulation.
Some sections of the Alaska pipeline above ground are supported by vertical steel supports (k = 25 W/mK), which have a length of 1 m and a cross-sectional area of 0.05 m². Under normal operating conditions, the temperature variation along the length of the steel support is given by the expression T = 100 – 150x + 10x², where T and x have units of °C and m, respectively. Temperature variations in the cross-sectional area of the support are negligible. Evaluate the temperature and the heat conduction rate at the pipeline-support junction (x = 0) and at the support-soil interface (x = 1 m). Explain the difference in heat rates.
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
- 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.arrow_forwardA new 1 ft thick insulating material was recently tested for heat resistant properties. The data recorded temperatures of 70 deg. F and 210 deg. F on the cold and hot sides, respectively. If the thermal conductivity of the insulating material is 0.026 Btu/ft . h .⁰ F, calculate the rate of the heat flux,Q/A, through the wall in Btu/ft^2 . h. Resolve the problem in SI units.arrow_forwardA steel rod, which is free to move, has a length of 200 mm and diameter of 20 mm at a temperature of 15°C. If the rod is heated uniformly to 115°C, determine the length and the diameter of this rod to the nearest micron at the new temperature if the linear coefficient of thermal expansion of steel is 12.5 x 10 m/m/°C. Wrong solution will be reported instantlyarrow_forward
- The temperatures on the faces of a plane wall 20 cm thick are 400 and 90 ℃. The wall is constructed of a special glass with the following properties: k = 0.8 W∙m-1K-1, ρ = 2750 kgm-3, cP = 0.86 kJkg-1K-1. What is the heat flux (q") through the wall at steady-state conditions?arrow_forward10 km of steel railroad track are placed when the temperature is 20 C. The linear coefficient of thermal expansion for the rails is 11 x 10^6 1/ C. The track is free to slide forward. How far apart will the end of the track be when the temperature reaches 50 Carrow_forwardThe outer surface of a long cylinder is kept at a constant temperature. There is no heat generation inside the cylinder. Accordingly, which of the following is correct. a.Temperature inside the cylinder increases linearly with the radius b.Temperature inside the cylinder decreases linearly with the radius c.Temperature inside the cylinder is independent of the radius d.Temperature inside the cylinder changes logarithmically with the radius e.nonearrow_forward
- A wall is made from an inhomogeneous (nonuniform) material for which the thermal conductivity varies through the thickness according to k = ax + b, where a and b are constants. The heat flux q"q" is known to be constant. Determine expressions for the temperature gradient and the temperature distribution when the surface at x = 0 is at temperature T1. Use the following values a = 11 W/K b = 25 W/m-K k = 11x + 25 W/m-K q"q" = 104 W/m^2 T1 = 60 Carrow_forwardThe walls of the flat furnace are connected by two insulating layers A and B. The temperature of the insulating layer A facing the inside of the Furnace is 800°C and the temperature of the outside air is 60°C. Find the temperature of the interface between the two insulation layers when the thickness of insulation layer A is 150 mm, its thermal conductivity is 0.05 W/m℃, the thickness of insulation layer B is 240 mm, and its thermal conductivity is 0.15 W/m℃arrow_forwardThe outer surface of a long cylinder is kept at a constant temperature. There is no heat generation inside the cylinder. Accordingly, which of the following is correct. a)Temperature inside the cylinder increases linearly with the radius b) The temperature inside the cylinder decreases linearly with the radius c) Temperature inside the cylinder is independent of the radius d) Temperature inside the cylinder changes logarithmically with the radius e) nonearrow_forward
- At a given moment in time, the temperature distribution inside an infinite homogeneous body is given by the function T(x, y, z) = x² – 2y² – xy + 2yz. Considering constant properties and no heat generation inside the body, determine the regions where the temperature varies over timearrow_forwardIn a glass plant in Cavite, a furnace has fire-brick walls made up of the following two materials in series : Non-corrosive brick as inner layer (material 1) Clay brick as outer layer (material 2) Thickness 4.5 inches 8 inches Thermal conductivity k1 k2 The temperature inside the furnace (inside wall surface of the non-corrosive brick) is found to be 1105 oF while the outside temperature (outside wall surface of clay brick) is 365 oF. This is not the desired temperature inside the furnace so engineers thought of lagging the furnace walls with another material to reduce heat loss. The additional lagging material consists of magnesia layer which is 2 inches thick and has a thermal conductivity of 0.04 Btu /h.ft.oF. During a test run on the furnace with the magnesia lagging material now, new temperature readings were recorded : Point of measurement Temperature reading Inside furnace (inside wall surface of non-corrosive brick 1355 oF Interface between…arrow_forwarda pipe with an outside diameter of 2.5 inches is insulated with 2 inches layer of asbestos ( K= 0.396(btu-in)/(hr-ft-F) followed by a layer of cork 1.5 inches thick ( K= 0.30 (btu-in)/ft (hr-ft-F). if the temperature of the outer surface of the cork and pipe is 90 F and 290 F RESPECTIVELY, calculate the heat loss per 100 ft of insulated pipe in btu/hrarrow_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