HEAT+MASS TRANSFER:FUND.+APPL.
6th Edition
ISBN: 9780073398198
Author: CENGEL
Publisher: RENT MCG
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Chapter 4, Problem 67P
A 30-cm-diameter, 4-m-high cylindrical column of a house made of concrete
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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
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.
Humans are able to control their rates of heat production and heat loss to maintain a nearly constant core temperature of Tc = 37°C under a wide range of environmental conditions. This process is called thermoregulation. From the perspective of calculating heat transfer between a human body and its surroundings, we focus on a layer of skin and fat, with its outer surface exposed to the environment and its inner surface at a temperature slightly less than the core temperature, Ti = 35°C = 308 K. Consider a person with a skin/fat layer of thickness L = 2 mm and effective thermal conductivity k = 0.3 Wm ⋅ K. The person has a surface area A = 1.8 m2 and is dressed in a bathing suit. The emissivity of the skin is ε = 0.95.a). When the person is in still air at T∞ = 308 K, what is the skin surface temperature and rate of heat loss to the environment? Convection heat transfer to the air is characterized by a free convection coefficient of h = 2 W?2 ⋅ Kb). When the person is in water at T∞ =…
Chapter 4 Solutions
HEAT+MASS TRANSFER:FUND.+APPL.
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 - Prob. 17PCh. 4 - Metal plates...Ch. 4 - Prob. 19PCh. 4 - Prob. 20PCh. 4 - Prob. 21PCh. 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. 25PCh. 4 - Steel rods...Ch. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 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. 31PCh. 4 - In an experiment, the temperature of a hot gas...Ch. 4 - Prob. 33PCh. 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. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40EPCh. 4 - Consider a sphere of diameter 5 cm, a cube of side...Ch. 4 - Prob. 42PCh. 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. 46CPCh. 4 - Prob. 47CPCh. 4 - The Biot number during a heat transfer process...Ch. 4 - A body at an initial temperature of Ti, is brought...Ch. 4 - Prob. 50PCh. 4 - In a meat processing plant, 2-cm-thick steaks...Ch. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Layers of 23-cm-thick meat slabs...Ch. 4 - Prob. 57PCh. 4 - Prob. 58PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Prob. 62EPCh. 4 - Prob. 63PCh. 4 - Prob. 64PCh. 4 - Prob. 65PCh. 4 - Prob. 66PCh. 4 - A 30-cm-diameter, 4-m-high cylindrical column of a...Ch. 4 - Prob. 68PCh. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - For heat transfer purposes, an egg can be...Ch. 4 - Citrus fruits are very susceptible to cold...Ch. 4 - Chickens with an average mass of 1.7 kg...Ch. 4 - Prob. 74PCh. 4 - Prob. 75PCh. 4 - Prob. 76PCh. 4 - Oranges of 2.5-in-diameter...Ch. 4 - Prob. 78PCh. 4 - Prob. 79PCh. 4 - Prob. 80PCh. 4 - Prob. 81PCh. 4 - A 9-cm-diameter potato...Ch. 4 - In Betty Crocker s Cookbook, it is stated that it...Ch. 4 - Prob. 84PCh. 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. 88EPCh. 4 - Prob. 89PCh. 4 - In areas where the air temperature remains below...Ch. 4 - Prob. 91PCh. 4 - A highway made of asphalt is initially at a...Ch. 4 - A thick aluminum block initially at 20C is...Ch. 4 - Prob. 94PCh. 4 - A thick wall made of refractory bricks...Ch. 4 - Prob. 96PCh. 4 - Prob. 97PCh. 4 - A thick wood slab (k=0.17W/m.K,=1.2810-7m2/s) and...Ch. 4 - Prob. 99PCh. 4 - Prob. 100PCh. 4 - Prob. 101PCh. 4 - Prob. 102PCh. 4 - Prob. 103PCh. 4 - Prob. 104PCh. 4 - Prob. 105PCh. 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. 109CPCh. 4 - Consider a short cylinder whose top and bottom...Ch. 4 - Prob. 111PCh. 4 - Prob. 112PCh. 4 - Prob. 113PCh. 4 - A hot dog can be considered to be a cylinder 5 in...Ch. 4 - Prob. 115PCh. 4 - Prob. 116PCh. 4 - A 2-cm-high cylindrical ice block...Ch. 4 - Prob. 118PCh. 4 - Prob. 119PCh. 4 - Prob. 120PCh. 4 - Prob. 121PCh. 4 - Prob. 122PCh. 4 - Prob. 123PCh. 4 - Prob. 124CPCh. 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. 128CPCh. 4 - Prob. 129CPCh. 4 - Prob. 130CPCh. 4 - Prob. 131CPCh. 4 - How does the rate of freezing affect the...Ch. 4 - Prob. 133CPCh. 4 - Prob. 134CPCh. 4 - Prob. 135CPCh. 4 - Prob. 136CPCh. 4 - Prob. 137CPCh. 4 - Prob. 138PCh. 4 - Chickens with an average mass of 2.2 kg and...Ch. 4 - Prob. 140EPCh. 4 - Prob. 141PCh. 4 - Prob. 142PCh. 4 - A long roll of 2-m-wide and 0.5-cm-thick 1-Mn...Ch. 4 - Prob. 144PCh. 4 - Prob. 145PCh. 4 - Prob. 146PCh. 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. 150PCh. 4 - Prob. 151PCh. 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. 154PCh. 4 - Prob. 155PCh. 4 - Prob. 156PCh. 4 - Prob. 157PCh. 4 - Prob. 158PCh. 4 - Prob. 159PCh. 4 - Prob. 160PCh. 4 - Prob. 161PCh. 4 - Prob. 162PCh. 4 - Prob. 163PCh. 4 - Lumped system analysis of transient heat...Ch. 4 - Prob. 165PCh. 4 - Prob. 166PCh. 4 - An 18-cm-long, 16-cm-wide, and 12-cm-high hot iron...Ch. 4 - Prob. 168PCh. 4 - Prob. 169PCh. 4 - Prob. 170PCh. 4 - Prob. 171PCh. 4 - Prob. 172PCh. 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. 176PCh. 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. 181PCh. 4 - Citrus trees are very susceptible to cold weather,...
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- 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.arrow_forward1. For heat transfer purposes, an egg can be considered to be a 4-cm diameter sphere having the properties of water. An egg that is initially at 8°C is dropped into boiling water at 100°C. The heat transfer coefficient at the surface of the egg is estimated to be 400 W/m2°C. 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? Assume negligible internal resistance íarrow_forwardAn ice chest whose outer dimensions are 30 cm*40 cm*40 cm is made of 3 cm thick Styrofoam (k = 0.033 W/m°C). Initially, the chest is filled with 30 kg of ice at 0 °C, and the inner surface temperature of the ice chest can be taken to be 0 °C at all times. The heat of fusion of water at 0 °C is 333.7 kJ/kg, and the surrounding ambient air is at 20 °C. Disregarding any heat transfer from the 40 cm*40 cm base of the ice chest, determine how long it will take for the ice in the chest to melt completely if the ice chest is subjected to (a) calm air and (b) winds at 30 km/h (assume the heat transfer coefficient on the front, back and top surfaces to be the same as that on the side surfaces). Use the thermophysical properties of air as follows: k = 25.5×10-3 W/mK, ν = 15×10-6 m2/s, α = 21.1×10-6 m2/s, and β = 3.43×10-3 K-1.arrow_forward
- Steel 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_forwardLayers of 6-in-thick meat slabs (k = 0.26 Btu/h·ft·°F and a = 1.4 * 1026 ft2/s) initially at a uniform temperature of 50°F are cooled by refrigerated air at 23°F to a temperature of 36°F at their center in 12 h. Estimate the average heat transfer coefficient during this cooling process. Solve this problem using the Heisler charts.arrow_forwardA house is to be maintained at 21°C DBT and 50% RH, while the outdoor conditions are -30°C DBT and 100% RH. The inner and outer surface heat transfer coefficients are 8.3 W/m2.K and 34.4 W/m?.K, respectively. The exterior walls of the houses are chosen such that they have a thermal resistance of 0.45 m2.°C/W. Determine whether the walls are insulated sufficiently to prevent moisture condensation on the inner surfaces or not. If the selected wall construction may lead to condensation, what is the minimum thickness of insulation (kjns=0.036 W/m2 K) ?to be added to prevent condensationarrow_forward
- Ice water of 0°C is stored in a spherical container made of steel with an inner diameter of 3 m and a thickness of 1 cm. This container is located in a place where the external temperature is 25℃. The temperature of the entire container is assumed to be 0°C. If thermal resistance in the container is ignored, obtain (a) the heat transfer rate to ice water, and (b) the amount of ice that melts for 24 hours. The melting heat of ice at atmospheric pressure is 333.7 kJ/kg. The emissivity of the outer wall of the container is 0.75, and the convective thermoelectric transfer coefficient is 30 W/m2·K. The average temperature of the surrounding surface for radiation is 15℃. ***I would appreciate it if sir could write it in a way that I could read it well.**arrow_forward. A small dam, which can be idealized by a large slab 1.2-m thick, is to be completely poured in a short period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m3. Suatu pelat datar dari besi dari seterika listrik berdaya 1200-arrow_forwardA 30-cm-diameter, 4-m-high cylindrical column of a house made of concrete (k = 0.79 W/m·K, a 5 5.94 * 1027 m2/s, r = 1600 kg/m3, and cp = 0.84 kJ/kg·K) cooled to 14°C during a cold night is heated again during the day by being exposed to ambient air at an average temperature of 28°C with an average heat transfer coefficient of 14 W/m2?K. Using analytical one-term approximation method (not the Heisler charts), determine (a) how long it will take for the column surface temperature to rise to 27°C, (b) the amount of heat transfer until the center temperature reaches to 28°C, and (c) the amount of heat transfer until the surface temperature reaches to 27°C.arrow_forward
- Consider a curing kiln whose walls are made of 30-cm-thick concrete with a thermal diffusivity of a = 0.23 * 10-5 m2/s. Initially, the kiln and its walls are in equilibrium with the surroundings at 6°C. Then all the doors are closed and the kiln is heated by steam so that the temperature of the inner surface of the walls is raised to 42°C and the temperature is maintained at that level for 2.5 h. The curing kiln is then opened and exposed to the atmospheric air after the steam flow is turned off. If the outer surfaces of the walls of the kiln were insulated, would it save any energy that day during the period the kiln was used for curing for 2.5 h only, or would it make no difference? Base your answer on calculations.arrow_forwardQ2/ A 4-m-internal-diameter spherical tank made of 1.75-cm-thick stainless steel (k 15 W/m °C) is used to store iced water at 0°C. The tank is located in a room whose temperature is 35°C. The walls of the room are also at 35°C. The outer surface of the tank is black, and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are 80 W/m2 °C and 10 W/m2· °C, respectively. 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 l-h period. The heat of fusion of water at atmospheric pressure is hif 334 kJ/kg.arrow_forwardBrass plate of 6 cm thickness that are initially at 25 °C are heated by passing it through an oven that is maintained at 700 •C. The plate remains in the oven for a period of 10 minutes. Taking the heat transfer coefficient (h= 130 W/m2. °C). Determine the center temperature of the plate and the temperature at the distance of 2 cm from the center of the plate. Taking p=8530 kg/m3, Cp=380 J/kg. • * .C, a= 33.9*10-6 m2/sarrow_forward
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