Heat and Mass Transfer: Fundamentals and Applications
5th Edition
ISBN: 9780073398181
Author: Yunus A. Cengel Dr., Afshin J. Ghajar
Publisher: McGraw-Hill Education
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Chapter 4, Problem 17P
Metal plates
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4- Carbon steel balls 8 mm in diameter are annealed by heating them first to 900°C in a
furnace and then allowing them to cool slowly to 100°C in ambient air at 35°C. If the
average heat transfer coefficient is 75 W/m -°C, determine how long the annealing process
will take. If 2500 balls are to be annealed per hour
Given:
Carbon steel [k = 54 W/m.°C, p = 7833 kg/m, and C,= 0.465 kJ/kg. °C. and a= 1.474x 10* m²/s]
Air, 35°C
Fumace
Steel ball 100°C
900°C
During a picnic on a hot summer day, the only available drinks were those at the ambient temperature of 90°F. In an effort to cool a 12-fluid-oz drink in a can, which is 5 in high and has a diameter of 2.5 in, a person grabs the can and starts shaking it in the iced water of the chest at 32°F. The temperature of the drink can be assumed to be uniform at all times, and the heat transfer coefficient between the iced water and the aluminum can is 30 Btu/h·ft2·°F. Using the properties of water for the drink, estimate how long it will take for the canned drink to cool to 40°F.
A cylindrical rod with a diameter of 20
mm and a length of 300 mm is heated
to a temperature of 200°C. The rod is
then placed in a tank of water
maintained at a constant temperature
of 25°C. The convection heat transfer
coefficient for the water is 2000
W/m²K. Determine the time taken for
the temperature of the rod to reach
50°C.
Chapter 4 Solutions
Heat and Mass Transfer: Fundamentals and Applications
Ch. 4 - What is the physical significance of the Biot...Ch. 4 - What is lumped system analysis? When is it...Ch. 4 - In what medium is the lumped system analysis more...Ch. 4 - For which solid is the lumped system analysis more...Ch. 4 - For which kinds of bodies made of the same...Ch. 4 - Consider heat transfer between two identical hot...Ch. 4 - Consider heat transfer between two identical hot...Ch. 4 - Consider a hot baked potato on a plate. The...Ch. 4 - Consider a potato being baked in an oven that is...Ch. 4 - Consider two identical 4-kg pieces of roast beef....
Ch. 4 - Consider a sphere and a cylinder of equal volume...Ch. 4 - Obtain relations for the characteristic lengths of...Ch. 4 - Obtain a relation for the time required for a...Ch. 4 - A brick of 20310257mm in dimension is being burned...Ch. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Metal plates...Ch. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - A 6-mm-thick stainless steel strip...Ch. 4 - After heat treatment, the 2-cm-thick metal plates...Ch. 4 - A long copper rod of diameter 2.0 cm is initially...Ch. 4 - Prob. 23PCh. 4 - Steel rods...Ch. 4 - To warm up some milk for a baby, a mother pours...Ch. 4 - A person is found dead at 5 p.m. in a room whose...Ch. 4 - Prob. 27PCh. 4 - In an experiment, the temperature of a hot gas...Ch. 4 - Prob. 29PCh. 4 - Pulverized coal particles are used in oxy-fuel...Ch. 4 - Oxy-fuel combustion power plants use pulverized...Ch. 4 - Plasma spraying is a process used for coating a...Ch. 4 - Consider a spherical shell satellite with outer...Ch. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36EPCh. 4 - Consider a sphere of diameter 5 cm, a cube of side...Ch. 4 - Prob. 38PCh. 4 - An egg is to be cooked to a certain level of...Ch. 4 - What is an infinitely long cylinder? When is it...Ch. 4 - What is the physical significance of the Fourier...Ch. 4 - Prob. 42CPCh. 4 - Prob. 43CPCh. 4 - Prob. 44CPCh. 4 - The Biot number during a heat transfer process...Ch. 4 - A body at an initial temperature of Ti, is brought...Ch. 4 - Prob. 47PCh. 4 - In a meat processing plant, 2-cm-thick steaks...Ch. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Layers of 23-cm-thick meat slabs...Ch. 4 - Prob. 53PCh. 4 - Prob. 54PCh. 4 - Prob. 55EPCh. 4 - Prob. 56PCh. 4 - Prob. 57EPCh. 4 - Prob. 58PCh. 4 - A 30-cm-diameter, 4-m-high cylindrical column of a...Ch. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Prob. 62PCh. 4 - Prob. 63PCh. 4 - Prob. 64PCh. 4 - Prob. 65PCh. 4 - Prob. 66PCh. 4 - Prob. 67PCh. 4 - Prob. 68PCh. 4 - Prob. 69PCh. 4 - For heat transfer purposes, an egg can be...Ch. 4 - Citrus fruits are very susceptible to cold...Ch. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - A 9-cm-diameter potato...Ch. 4 - Chickens with an average mass of 1.7 kg...Ch. 4 - Prob. 76PCh. 4 - In Betty Crocker s Cookbook, it is stated that it...Ch. 4 - Prob. 78PCh. 4 - Prob. 79PCh. 4 - Oranges of 2.5-in-diameter...Ch. 4 - Prob. 81EPCh. 4 - Under what conditions can a plane wall be treated...Ch. 4 - What is a semi-infinite medium? Give examples of...Ch. 4 - Consider a hot semi-infinite solid at an initial...Ch. 4 - Prob. 85EPCh. 4 - Prob. 86PCh. 4 - In areas where the air temperature remains below...Ch. 4 - Prob. 88PCh. 4 - A highway made of asphalt is initially at a...Ch. 4 - A thick aluminum block initially at 20C is...Ch. 4 - Prob. 91PCh. 4 - A thick wall made of refractory bricks...Ch. 4 - Prob. 93PCh. 4 - Prob. 94PCh. 4 - A thick wood slab (k=0.17W/m.K,=1.2810-7m2/s) and...Ch. 4 - Prob. 96PCh. 4 - Prob. 97PCh. 4 - Prob. 98PCh. 4 - Prob. 99PCh. 4 - Prob. 100PCh. 4 - Prob. 101PCh. 4 - A barefooted person whose feet are at 32C steps on...Ch. 4 - What is the product solution method? How is it...Ch. 4 - How is the product solution used to determine the...Ch. 4 - Prob. 105CPCh. 4 - Consider a short cylinder whose top and bottom...Ch. 4 - Prob. 107PCh. 4 - Prob. 108PCh. 4 - A hot dog can be considered to be a cylinder 5 in...Ch. 4 - Prob. 110PCh. 4 - Prob. 111PCh. 4 - A 2-cm-high cylindrical ice block...Ch. 4 - Prob. 113PCh. 4 - Prob. 114PCh. 4 - Prob. 115PCh. 4 - Prob. 116PCh. 4 - Prob. 117PCh. 4 - Prob. 118PCh. 4 - Prob. 119CPCh. 4 - How does refrigeration prevent or delay the...Ch. 4 - What are the environmental factors that affect the...Ch. 4 - What is the effect of cooking on the...Ch. 4 - Prob. 123CPCh. 4 - Prob. 124CPCh. 4 - Prob. 125CPCh. 4 - Prob. 126CPCh. 4 - How does the rate of freezing affect the...Ch. 4 - Prob. 128CPCh. 4 - Prob. 129CPCh. 4 - Prob. 130CPCh. 4 - Prob. 131CPCh. 4 - Prob. 132CPCh. 4 - Prob. 133PCh. 4 - Prob. 134PCh. 4 - Chickens with an average mass of 2.2 kg and...Ch. 4 - Prob. 136EPCh. 4 - Prob. 137PCh. 4 - Prob. 138PCh. 4 - A long roll of 2-m-wide and 0.5-cm-thick 1-Mn...Ch. 4 - Prob. 140PCh. 4 - Prob. 141PCh. 4 - Prob. 142PCh. 4 - During a picnic on a hot summer day, the only...Ch. 4 - Two metal rods are being heated in an oven with...Ch. 4 - Stainless steel ball bearings...Ch. 4 - Prob. 146PCh. 4 - Prob. 147PCh. 4 - In Betty crockers Cookbook, it is stated that it...Ch. 4 - A watermelon initially at 35C is to be cooled by...Ch. 4 - Prob. 150PCh. 4 - Prob. 151PCh. 4 - Prob. 152PCh. 4 - Prob. 153PCh. 4 - Prob. 154PCh. 4 - Prob. 155PCh. 4 - Prob. 156PCh. 4 - Prob. 157PCh. 4 - Prob. 158PCh. 4 - Prob. 159PCh. 4 - Lumped system analysis of transient heat...Ch. 4 - Prob. 161PCh. 4 - Prob. 162PCh. 4 - An 18-cm-long, 16-cm-wide, and 12-cm-high hot iron...Ch. 4 - Prob. 164PCh. 4 - Prob. 165PCh. 4 - Prob. 166PCh. 4 - Prob. 167PCh. 4 - Prob. 168PCh. 4 - A long 18-cm-diameter bar made of hardwood...Ch. 4 - Consider a 7.6-cm-long and 3-cm-diameter...Ch. 4 - Consider a 7.6-cm-diameter cylindrical lamb meat...Ch. 4 - Prob. 172PCh. 4 - A small chicken (k=0.45W/m.K,=0.1510-6m2/s) and...Ch. 4 - A potato may be approximated as a 5.7-cm-diameter...Ch. 4 - When water, as in a pond or lake, is heated by...Ch. 4 - A large chunk of tissue at 35C with a thermal...Ch. 4 - Prob. 177PCh. 4 - Citrus trees are very susceptible to cold weather,...
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- water 4-26 Steel rods (p = 7832 kg/m³, c, = 434 J/kg-K, and k = 63.9 W/m-K) are heated in a furnace to 850°C and then quenched in a bath at 50°C for a period of 40 s as part of a hardening process. The convection heat transfer coefficient is 650 W/m²K. If the steel rods have diameter of 40 mm and length of 2 m, determine their average temperature when they are taken out of the water bath.arrow_forwardA long 35 cm diameter cylinder made of stainless steel 304 (k = 14.9 W/mo C, r = 7900 kg/m3 , Cp = 477 J/kgo C and a = 3.95´10-6 m2 /s) comes out of an oven at a uniform temperature of 400o C. The cylinder is then allowed to cool slowly in a chamber at 150o C with average convection heat transfer coefficient of h = 60 W/m2oC. Determine the temperature at the center of the cylinder 20 min after the start of the cooling process. Also, determine the heat transfer per unit length of the cylinder during this time period.arrow_forward3- Stainless steel ball bearings have a diameter of 1.2 cm are to be quenched in water. The balls leave the oven at a uniform temperature of 900°C and are exposed to air at 30°C for a while before they are dropped into the water. If the temperature of the balls is not to fall below 850°C prior to quenching and the heat transfer coefficient in the air is 125 W/m² - °C, determine how long they can stand in the air before being dropped into the water. Given: Stainless steel [ k= 15.1 W/m.°C, p= 8085 kg/m3, and Cp= 0.480 kJ/kg.°C. and a=3.95 × 106 m³/s]arrow_forward
- A cold aluminum-canned (ε=0.60) soda is initially at a uniform temperature of 6°C. The can is 12.27 cm high with diameter of 6.60 cm. If the convection heat transfer coefficient between the can and the surrounding air at 25°C is 4.85 W/(m²-ºC), determine how long it will take for the average temperature of the soda to rise to 10ºC. Solve this problem approximately by assuming a constant average temperature of the soda during the process. For the soda use the properties of water at room temperature, p 1000 kg/m³ and Cp = 4180 J/kg-°C. Consider both convective and radiative heat transfer. =arrow_forwardSteel rods (p = 7832 kg/m2, cn= 434 J/kg.K, and k = 63.9 W/m-K) are heated in a furnace to 850°C and then quenched in a water bath at 50°C for a period of 55 seconds as part of a hardening process. The convection heat transfer coefficient is 650 W/m2.K. If the steel rods have diameter of 40 mm and length of 2 m, determine their average temperature when they are taken out of the water bath. (Round off the answer to 1 decimal point.) °Carrow_forwardA slab of aluminium 10 cm thick is originally at a temperature of 500°C. It is suddenly immersed in a liquid at 100°C resulting it a heåt transfer coefficient of 1200. W/m2K. Determine the temperature at the center line and the surface 1 min after the immersion. Also the total thermal energy removal per unit area of slab during this period. The properties of aluminium for the given condition are, a = 8.4 x 10-5 m?/s, k =215 W/mK, p = 2700 kg/m3, C= 0.9.kJ/kgK.arrow_forward
- Take note that both sides of the plate are exposed to convection.arrow_forward4-38 Carbon steel balls (p = 7833 kg/m2, k = 54 W/m K, c = 0.465 kJ/kg°C, and a 1.474 - 10-6 m2/s) 8 mm in diameter are annealed by heating them first to 900°C in a furnace and then page 300 allowing them to cool slowly to 100°C in ambient air at 35°C. If the average heat transfer coefficient is 75 W/m2-K, determine how long the annealing process will take. If 2500 balls are to be annealed per hour, determine the total rate of heat transfer from the balls to the ambient air. FIGURE P4-38 Air, 35°C Furnace Steel ball 100C 900°Carrow_forwardA pipe in a manufacturing plant is transporting superheated vapor at a mass flow rate of 0.3 kg/s. The pipe is 10 m long, has an inner diameter of 5 cm and pipe wall thickness of 6 mm. The pipe has a thermal conductivity of 17 W/m.K, and the inner pipe surface is at a uniform temperature of 120 °C. The temperature drop between the inlet and the exit of the pipe is 7 °C, and the constant pressure specific heat of vapor is 2190 J/kg.°C. If the air temperature in the manufacturing plant is 25°C, determine the heat transfer coefficient as a result if convection between the outer pipe surface and the surrounding air. T(r) = 120°C Superheated Air, 25°C r2 vapor r1 0.3 kg/s L = 10 m Tin-Tout = 7°Carrow_forward
- Q4 A 3-m-internal-diameter spherical tank made of 5-cm thick stainless steel is used to store iced water at 0°C. The tank is located outdoors at 25°C. Assuming the entire steel tank to be at 0°C and thus the thermal resistance of the tank to be negligible, determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at 0°C that melts during a 24-hour period. The heat of fusion of water at atmospheric pressure is = 333.7 kJ/kg. The emissivity of the outer surface of the tank is 0.6, and the convection heat transfer coefficient on the outer surface can be taken to be 30 W/m2 · "C. Assume the average surrounding surface temperature for radiation exchange to be 15°C.arrow_forwardFor heat transfer purposes, an egg can be considered to be a 5.5-cm-diameter sphere having the properties of water. An egg that is initially at 8°C is dropped into the boiling water at 86°C. The heat transfer coefficient at the surface of the egg is estimated to be 800 W/m2-K. If the egg is considered cooked when its center temperature reaches 60°C, determine how long the egg should be kept in the boiling/water. Solve this problem using analytical one-term approximation method (not the Heisler charts). The length of/time for the egg to be kept in boiling water is determined to be min.arrow_forwardAn ordinary egg can be approximated as a 5.5-cm-diameter sphere whose properties are roughly k=0.6 W/m.oC and a=0.14 x 10-6 m2/s. The egg is initially at a uniform temperature of 8 oC and is dropped into boiling water at 97 oC. Taking the convection heat transfer coefficient to be h=1400 W/m2.oC, determine how long it will take for the center of the egg to reach 70oC.arrow_forward
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