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
Question
Chapter 3, Problem 3.91P
(a)
To determine
The temperature distribution, smallest and largest temperatures and their locations.
(b)
To determine
The temperature distribution, smallest and largest temperatures and their locations, if insulation is removed and both the surfaces are maintained at the same convection.
(c)
To determine
To plot: the temperature distribution for part (a) and (b).
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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.
A 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 instantly
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 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
- The 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_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_forward5. A 10-in nominal pipe (outside diameter = 10.75in) is covered with a composite pipe insulation consisting of 2.0 in of insulation I placed next to the pipe and 1.5 in of insulation II placed upon insulation I. Assume that the inner and outer surface temperatures of the composite insulation are 900F and 150F respectively, and that the thermal conductivity of material I is 0.05 BTU/hr-ft-F and for material II is 0.039 BTU/hr-ft-F. What is the individual thermal resistance of insulation I?arrow_forward
- I want to know how much heat the tube lost due to the material it is made of. Even if it is a small difference in temperature. It is a heat transfer problem material: Aluminum temperature touching cylinder: 65 Celcius temeprature inside cylinder 64.5 celsius room temperature 24 celcius Tube measurements outer radius r1 r1 = 4 in inner radius r2 r2 = 3 in outer circumference C1 C1 = 25.132741228718 in inner circumference C2 C2 = 18.849555921539 in height h = 8 in wall thickness t = 1 inarrow_forwardA coil-shaped cooling pipe is made of SS-304 material. This pipe is 1 ft long, 0.4 inch outside diameter, and inch inside diameter. This coil cooling pipe is used to cool the water in the bath. The temperature of the inner coil pipe is 40oF while the outer coil in contact with water is 80oF. The thermal conductivity of SS-304 is a function of temperature where k(T) = 7.75 + (7.78 x 10-3).T where k is in Btu/h.ft.oF and T is in oF. Calculate the rate of heat dissipation in watts! (1287.7)arrow_forwardA manufacturer of loose-fill cellulose insulating material provides a table showing the relationship between the thickness of the material and its R-value. The manufacturer’s data is shown in the accompanying table. R -value (m2 ⋅K/W) Thickness (mm) R -40 275 R -32 225 R -24 162 R- 19 132 R -13 88 Calculate the thermal conductivity of the insulating material. Also, determine how thick the insulation should be to provide R-values of a. R-30 b. R-20 11.9arrow_forward
- To find the thermal conductivity of a material, the following experimental setup can be prepared. Two long cylinders that are identical in terms of manufacturing are prepared. One of them is of a known thermal conductivity value kA while the other is for an unknown material kB. Both cylinders are attached to a heat sink of a fixed temperature Tb and they are exposed to a fluid (typically ultra-cooled for accuracy purposes). The temperature measurements are taken along some distance (x1) away from the base. If the first measurements reads 65 C for a distance (x1) of 12 mm while the second material reads 54 C for the same distance. What is the thermal conductivity of the second material (B).Knowns: material A is made of copper. k = 390 W/m.k. Tb = 130 C, Tinf = 12 C.arrow_forwardWhat 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_forwardDetermine k, thermal conductivity of a wall if q = 1000 kcal/m2 -hr at thickness, k = 33 mm and ∆t = 30°C.arrow_forward
- Two plates, one of aluminum with a tickness of 14mm and one of brass with thickness of 9mm were attached to each other. Determine the thickness of a board of another metallic material with thermal conductivity λ= 79W / mK so that it conducts an equal heat flow as together fasten the boards at the same total temperature drop across the structure. The thermal conductivity for aluminium is λAI = 238W / mK and for brass λm = 111W / mK.arrow_forwardSteel pipe (outer diameter 100 mm) is covered with two layers of insulation. The inner layer, 40 mm thick, has a thermal conductivity of 0.07 W / (m K). The outer layer, 20 mm thick, has a thermal conductivity of 0.15 W / (m K). Pipes are used to deliver steam with a pressure of 800 kPa. The temperature on the outer insulation surface is 24 ° C. If the pipe is 10 m long, determine the following: (assuming that the conduction heat transfer resistance of the steel pipe and the vapor convection resistance are negligible). a. Heat loss per hour. = AnswerkJ / hr. b. Temperature between insulation layers. = Answer ° C.arrow_forwardSteel pipe (outer diameter 100 mm) is covered with two layers of insulation. The inner layer, 40 mm thick, has a thermal conductivity of 0.07 W / (m K). The outer layer, 20 mm thick, has a thermal conductivity of 0.15 W / (m K). Pipes are used to deliver steam with a pressure of 600 kPa. The temperature on the outer insulation surface is 24 ° C. If the pipe is 8 m long, determine the following: (assuming that the conduction heat transfer resistance of the steel pipe and the vapor convection resistance are negligible). a. Heat loss per hour. = kJ / hour. b. Temperature between insulation layers. = ° Carrow_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
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license