Fundamentals of Heat and Mass Transfer
Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 13, Problem 13.105P

The cross section of a long circular tube, which is divided mw two semicylindrical ducts by a thin wall, is shown.

Chapter 13, Problem 13.105P, The cross section of a long circular tube, which is divided mw two semicylindrical ducts by a thin
Sides 1 and 2 are maintained at temperatures of T 1 = 600 K and T 2 = 400 K , respectively, while the mean temperatures of gas flows through ducts 1 and 2 are T g , 1 = 571 K and T g , 2 = 449 K , respectively. The foregoing temperatures are invariant in the axial direction. The gases provide surface convection coefficients of h 1 = h 2 = 5 W/m 2 K while all duct surfaces may be approximated as blackbodies ( ε 1 = ε 2 = ε w = 1 ) . What is the duct wall temperature, Tw? By performing an energy balance on the gas in side 1, verify that Tg,1 is, in fact equal to 571 K.

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Fluid is flowing through a 20 mm inside diameter and 25 mm outside diameter brass tube at no leaking with temperature at 65℃ and length of 10 m. Surface conduction of hot fluid is 5.2W/(m^2℃) and thermal conductivity of brass is 12.84W/(m℃). Brass tube is covered by silica of 6 mm thickness with thermal conductivity of 13.84W/(m℃) . Outside of it, is a fluid with 45℃ with surface conductance of 3.2W/(m^2℃). Find the heat transfer from the hot fluid with temperature of 65℃ to fluid with temperature of 45℃.
Problem: Convection related   Water enters a tube at 27°C with a flow rate of 450 kg/h. The rate of heat transfer from the tube wall to the fluid is given as qs′(W/m)=ax, where the coefficient a is 20 W/m^2 and x(m) is the axial distance from the tube entrance.   (a)  Beginning with a properly defined differential control volume in the tube, derive an expression for the temperature distribution Tm(x) of the water. (b)  What is the outlet temperature of the water for a heated section 30 m long? (c)  Sketch the mean fluid temperature, Tm(x), and the tube wall temperature, Ts(x), as a function of distance along the tube for fully developed and developing flow conditions.
t = 30 + 0.9563 (62.2- 30) = 60.79°C (Ans.) Example 4.14. A very thin glass walled 3 mm diameter mercury thermometer is placed in a stream of air, where heat transfer coefficient is 55 W/m2°C, for measuring the unsteady temperature of air. Consider cylindrical thermometer bulb to consist of mercury only for which k and a = 0.0166 m2/h. Calculate the time required for the temperature change to reach half its final or, %3D 8.8 W/m C %3D value.

Chapter 13 Solutions

Fundamentals of Heat and Mass Transfer

Ch. 13 - Consider parallel planes of infinite extent normal...Ch. 13 - Consider the parallel planes of infinite extent...Ch. 13 - Consider two diffuse surfaces A1 and A2 on the...Ch. 13 - As shown in the sketch, consider the disk A1...Ch. 13 - A heat flux gage of 4mm diameter is positioned...Ch. 13 - A circular ice rink 25 m in diameter is enclosed...Ch. 13 - A drying oven consists of a long semicircular duct...Ch. 13 - Consider the arrangement of the three black...Ch. 13 - A long, Vshaped pan is heat treated by suspending...Ch. 13 - Consider coaxial, parallel, black disks separated...Ch. 13 - A tubular healer with a black inner surface of...Ch. 13 - A circular plate of 500-mm diameter is maintained...Ch. 13 - To enhance heat rejection from a spacecraft, an...Ch. 13 - Determine the temperatures of surfaces 1 through 4...Ch. 13 - A cylindrical cavity of diameter D and depth L is...Ch. 13 - In the arrangement shown, the tower disk has a...Ch. 13 - Two plane coaxial disks are separated by a...Ch. 13 - A radiometer views a small target (1) that is...Ch. 13 - A meter to measure the power of a laser beam is...Ch. 13 - The arrangement shown is to be used to calibrate a...Ch. 13 - A long, cylindrical heating element of 20-mm...Ch. 13 - Water flowing through a large number of long,...Ch. 13 - A row of regularly spaced, cylindrical heating...Ch. 13 - A manufacturing process calls for heating long...Ch. 13 - Consider the very long, inclined black surfaces...Ch. 13 - Many products are processed in a manner that...Ch. 13 - Consider two very large parallel plates with...Ch. 13 - A flat-bottomed hole 6 mm in diameter is bored to...Ch. 13 - In Problems 12.20 and 12.25, we estimated the...Ch. 13 - Consider the cavities formed by a cone, cylinder,...Ch. 13 - Consider the attic of a home located in a hot...Ch. 13 - A long, thin-walled horizontal tube 100 mm in...Ch. 13 - A t=5-mm -thick sheet of anodized aluminum is used...Ch. 13 - Consider the spacecraft heat rejection scheme of...Ch. 13 - A very long electrical conductor 10 mm in diameter...Ch. 13 - Liquid oxygen is stored in a thin-walled,...Ch. 13 - Two concentric spheres of diameter D1=0.8m and...Ch. 13 - Determine the steady-stale temperatures of two...Ch. 13 - Consider two large (infinite) parallel planes that...Ch. 13 - Consider two large, diffuse, gray, parallel...Ch. 13 - Heat transfer by radiation occurs between two...Ch. 13 - The end of a cylindrical liquid cryogenic...Ch. 13 - At the bottom of a very large vacuum chamber whose...Ch. 13 - A furnace is located next to a dense array of...Ch. 13 - A cryogenic fluid flows through a tube 20 mm in...Ch. 13 - A diffuse, gray radiation shield of 60mm diameter...Ch. 13 - Consider the three-surface enclosure shown. The...Ch. 13 - Two parallel, aligned disks, 0.4 m in diameter and...Ch. 13 - Coatings applied to long metallic strips are cured...Ch. 13 - A molten aluminum alloy at 900 K is poured into a...Ch. 13 - A long, hemicylindrical (1-m radius) shaped...Ch. 13 - The bottom of a steam-producing still of 200-mm...Ch. 13 - A long cylindrical healer element of diameter...Ch. 13 - A radiative heater consists of a bank of ceramic...Ch. 13 - Consider a long duct constructed with diffuse,...Ch. 13 - A solar collector consists of a long duct through...Ch. 13 - The cylindrical peephole in a furnace wall of...Ch. 13 - A composite wall is comprised of two large plates...Ch. 13 - A small disk of diameter D1=50mm and emissivity...Ch. 13 - Consider a cylindrical cavity of diameter D=100mm...Ch. 13 - Consider a circular furnace that is 0.3 m long and...Ch. 13 - Consider two very large metal parallel plates. The...Ch. 13 - Two convex objects are inside a large vacuum...Ch. 13 - the diffuse, gray, four-surface enclosure with all...Ch. 13 - A cylindrical furnace for heal-treating materials...Ch. 13 - A laboratory oven bas a cubical interior chamber 1...Ch. 13 - A small oven consists of a cubical box of...Ch. 13 - An opaque, diffuse, gray (200mm200mm) plate with...Ch. 13 - A tool for processing silicon waters is housed...Ch. 13 - Consider Problem 6.17. The stationary plate,...Ch. 13 - Most architects know that the ailing of an...Ch. 13 - Boiler tubes exposed to the products of coal...Ch. 13 - Consider two very large parallel plates. 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