A hollow cylinder has length L, inner radius R, and thickness d, and the temperatures at the inner and outer surfaces are Th and T1, respectively. The thermal conductivity of the material of which the cylinder is made is k. Derive an equation for the rate of heat transfer P through the walls of the cylinder. Simplify this equation assuming that the thickness of the cylinder d is much smaller than the its inner radius R.

A hollow cylinder has length L, inner radius R, and thickness d, and the temperatures at the inner and outer surfaces are Th and T1, respectively. The thermal conductivity of the material of which the cylinder is made is k. Derive an equation for the rate of heat transfer P through the walls of the cylinder. Simplify this equation assuming that the thickness of the cylinder d is much smaller than the its inner radius R.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.34P: A section of a composite wall with the dimensions shown below has uniform temperatures of 200C and...

See similar textbooks

Related questions

Q: 2.1 A composite wall shown below has uniform temperatures. You are given that the thermal…

Q: Assume steady-state, one-dimensional heat conductionthrough the symmetric shape shown in Figure…

A: Heat transfer: The transfer of heat from one body to another due to the temperature difference…

Q: The wall of shed in which ice is stored consists of an outer layer of wood 2cm and an inner layer of…

Q: A solid block is with 0.2 m thick and 0.1 m cross section area and 100W/m C thermal conductivity.…

Q: 20-m pipe has an outside diameter of 50 mm. Pipe is insulated with a layer of asbestos, then…

Q: Two identical 7.5-cm cubes of copper at 425 and 90°C are brought into contact. Assuming that the…

Q: A section of a composite wall with the dimensions shown below has uniform temperatures of 200°C and…

Q: A plane wall is having 160 mm thickness, ‘b’ mm width and its height is three times the width is…

Q: A rectangular electrical heater is attached to a metal sheet. Measurements show the surface…

Q: A spherical steel reaction vessel has an outer radius of 2.0 m and is covered in lagging 250mm…

A: Given:r1=2 mt=250 mmkl=0.4 W/m.KT1=340°CT2=45°Ck=385 W/m.K

Q: A flat wall is exposed to an environmental temperature of 38oC. The wall is coveredwith a layer of…

A: Given: T1=41°CT2=315°CTe=38°Ck=1.4W/m°Cdx=2.5 cm = 0.025 m

Q: For one -dimension heat transfer conduction consider a shielding wall for a nuclear reactor. The…

Q: The walls of the flat furnace are connected by two insulating layers A and B. The temperature of the…

Q: wall, plastered on one face, has a thermal conductance of 0.36 m2 K/W, an inside surface

A: Handwriting.jpg

Q: A plane wall is having width ‘b’ mm and height 4 times of its width. The wall thickness is…

Q: 2. Two bars are conducting heat from a region of higher temperature to a region of lower…

A: Ans (b) Arrangement A

Q: Calculate the thermal resistance of a copper tube with diameter1=0.153 mm diameter2= 0.157 mm and…

A: Styrofoam diameter should be more than diameter 2 (0.157 mm) .it cannot be 0.09 mm ,so it should be…

Q: A representative cross-section of a 31.5-cm-thick wall is shown in the left figure below (not drawn…

A: Since you have put a question which is having more than than 3 sub-parts, thus we can provide you…

Q: Two water columns are at different ⦁ temperatures, one being at 35oC and the other being at 18oC.…

A: Given Data Thermal Conductivity of glass is 1.6 W/mK Area, A=1(2)=2 m2 thickness, t=0.005 m…

Q: Calculate the quantity of heat conducted per minute through a duralumin circular disc 127 mm…

A: Given data as per the question Diameter of the disc =127 mm The thickness of the disk = 19 mm…

Q: .A steel plate is exposed to solar heat flux of 800 W/m² on one side. The plate is exposed to air at…

Q: The outer surface of a long cylinder is kept at a constant temperature. There is no heat generation…

Q: A layer of pulverized cork 152-mm thick is used as a layer of thermal insulation in a flat wall. The…

A: GIVEN :- thick : t=152 mm The temperature of the cold side of the cork : TC= 4.4℃, The temperature…

Q: A hollow cylinder has length L, inner radius R, and thickness d, and the temperatures at the inner…

A: To determine: Relation for radial heat conduction through a hollow cylinder

Q: 5. The temperature distribution along a fin with insulated tip is given by: mx e

A: Temperature distribution along fin with insulated tip to be find out

Q: A 1.0-mm-diameter wire is maintained at a temperature of 400°C and exposed to aconvection…

Q: 2. Calculate insulation thickness (minimum value) required for a pipe carrying steam at 180°C. The…

Q: Derive an expression for heat conduction through a composite plane wall of n- layers.

Q: Stainless steel pipes with a thermal conductivity of 17 W / (m° C) are used to transport hot oil.…

Q: Why is the thermal conductivity of superinsulation orders of magnitude lower than the thermal…

A: (1) Superinsulation: Superinsulation is made by a number of layers of highly reflective sheets and…

Q: 6. A sphere of radius R2 has a concentric central cavity of radius R1. The material between R1 and…

Q: Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an…

Q: 6. A furnace wall consists of 250 mm fiber brick, 125 mm insulating brick, and 250 mm building…

Q: Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an…

Q: A plane wall is having 160 mm thickness, ‘b’ mm width and its height is three times the width is…

A: Conduction is one of the mode of heat transfer in which heat transfer occurs in any material due to…

Q: The interior of an oven is maintained at a temperature of 1500°F by means of suitable control…

A: Given data: Inside wall temperature, Ti=1500°F, Outside wall temperature, To=400°F. Wall thickness,…

Q: /The thermal conductivity 14.4w/m.k for the block of stainless steel shown below is well insulated…

Q: 1.0-mm-diameter wire is maintained at a temperature of 400°C and exposed to a convection environment…

A: h=heat transfer coefficient=120 W/m-°CT1=Temperature of wire maintained=400 °CT2=Ambient…

Q: 3. Determine the critical insulation thickness for: (i) A sphere, (ii) A cylinder Also determine the…

A: given; critical insulation thickness; (i) for sphere (ii) cylinder

Concept explainers

Mechanisms of heat transfer

Heat transfer is an essential discipline in thermal engineering that deals with the transfer, conversion, usability, and creation of heat or thermal energy. Transfer of heat occurs through various mechanisms like conduction, convection, radiation, and change of phases. All these mechanisms have distinct characteristics, but these mechanisms can simultaneously occur in an identical system.

Question

100%

Derive an equation for the rate of heat transfer.

A hollow cylinder has length L, inner radius R, and thickness d, and the temperatures at the inner and outer
surfaces are Th and T1, respectively. The thermal conductivity of the material of which the cylinder is made is k.
Derive an equation for the rate of heat transfer P through the walls of the cylinder. Simplify this equation
assuming that the thickness of the cylinder d is much smaller than the its inner radius R.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

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 hollow sphere with inner and outer radii of R1 and R2, respectively, is covered with a layer of insulation having an outer radius of R3. Derive an expression for the rate of heat transfer through the insulated sphere in terms of the radii, the thermal conductivities, the heat transfer coefficients, and the temperatures of the interior and the surrounding medium of the sphere.
Heat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of TiandTo, respectively. Derive an expression for the temperature distribution.
1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.
1.4 To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in W/m K. Problem 1.4
A section of a composite wall with the dimensions shown below has uniform temperatures of 200C and 50C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA=70W/mK,kB=60W/mK, kC=40W/mK, and kD=20W/mK, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces.
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 .
Both ends of a 0.6-cm copper U-shaped rod are rigidly affixed to a vertical wall as shown in the accompanying sketch. The temperature of the wall is maintained at 93C. The developed length of the rod is 0.6 m, and it is exposed to air at 38C. The combined radiation and convection heat transfer coefficient for this system is 34W/m2K. (a) Calculate the temperature of the midpoint of the rod. (b) What will the rate of heat transfer from the rod be?
One 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?
A plane wall of thickness 2L has internal heat sources whose strength varies according to qG=qocos(ax) Where qo is the heat generated per unit volume at the center of the wall (x=0) and a is a constant. If both sides of the wall are maintained at a constant temperature of Tw, derive an expression for the total heat loss from the wall per unit surface area.
1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.
A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6
2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.