Explanation Given Information: Length of the cubic block = 5 c m Height of the cylindrical block = 5 c m Diameter of the cylindrical block = 5 c m Initial temperature of the blocks, T i = 20 C 0 Thermal Conductivity, k = 2.5 W / m ⋅ C 0 Thermal Diffusivity, α = 1.15 × 10 − 6 m 2 / s Heat transfer coefficient, h = 40 W / m 2 ⋅ C 0 Concept: The equation for Biot number can be expressed as, B i = h L k Where, k - Thermal Conductivity h - Heat transfer coefficient L - Distance The equation for Fourier number can be expressed as, τ = α t L 2 Where, α - Thermal Diffusivity L - Distance t - Time The equation for product solution can be expressed as, θ ( 0 , 0 , 0 , t ) = [ θ ( 0 , t ) ] 3 T ( 0 , 0 , 0 , t ) − T ∞ T i − T ∞ = ( A i e − λ 1 2 τ ) 3 Calculation: The distance for cube block at the center is, L = 5 2 = 2.5 c m The distance for the cylinder at the center is, r = D 2 = 2.5 c m For Cubic Block, Biot number at the center temperature of a cubic block. B i = h L k B i = ( 40 ) ( 0.025 ) ( 2.5 ) B i = 0.400 for the Biot number B i = 0.4 , the values of λ 1 and A i are 0.5932 and 1.0580 respectively as per the table for cube block. Fourier number at center temperature of cubic block after 10 min , τ = α t L 2 = ( 1.15 × 10 − 6 ) ( 10 × 60 ) ( 0.025 ) 2 = 1.104 Here, Fourier number is greater than 0.2 Then, the product solution can be expressed as below to determine the temperature at the center. θ ( 0 , 0 , 0 , t ) b l o c k = [ θ ( 0 , t ) w a l l ] 3 T ( 0 , 0 , 0 , t ) − T ∞ T i − T ∞ = ( A i e − λ 1 2 τ ) 3 T ( 0 , 0 , 0 , t ) − 500 20 − 500 = [ ( 1.0580 ) e − ( 0.5932 ) 2 ( 1.104 ) ] 3 T ( 0 , 0 , 0 , t ) − 500 20 − 500 = 0.369 T ( 0 , 0 , 0 , t ) = 323 C 0 Fourier number at the center temperature of the cubic block after 20 min , τ = α t L 2 = ( 1.15 × 10 − 6 ) ( 20 × 60 ) ( 0.025 ) 2 = 2.208 Here, the Fourier number is greater than 0.2 . Then, the product solution can be expressed as below to determine the temperature at the center. T ( 0 , 0 , 0 , t ) − 500 20 − 500 = [ ( 1.0580 ) e − ( 0.5932 ) 2 ( 2.208 ) ] 3 T ( 0 , 0 , 0 , t ) − 500 20 − 500 = 0.115 T ( 0 , 0 , 0 , t ) = 445 C 0 Fourier number at the center temperature of the cubic block after 60 min , τ = α t L 2 = ( 1.15 × 10 − 6 ) ( 60 × 60 ) ( 0.025 ) 2 = 6.624 Here, Fourier number is greater than 0.2 . Then, the product solution can be expressed as below to determine the temperature at the center. T ( 0 , 0 , 0 , t ) − 500 20 − 500 = [ ( 1

HEAT&MASS TRANSF. (LL) W/CONNECT<CUSTOM>

6th Edition

ISBN: 9781266141652

Author: CENGEL

Publisher: MCG

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Chapter 4, Problem 111P

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The center temperature of each geometry using the analytical one-term approximation method.

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Chapter 4, Problem 110CP

Chapter 4, Problem 112P

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Chapter 4 Solutions

HEAT&MASS TRANSF. (LL) W/CONNECT<CUSTOM>

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. 15P Ch. 4 - Prob. 16P Ch. 4 - Prob. 17P Ch. 4 - Metal plates...Ch. 4 - Prob. 19P Ch. 4 - Prob. 20P Ch. 4 - Prob. 21P Ch. 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. 25P Ch. 4 - Steel rods...Ch. 4 - Prob. 27P Ch. 4 - Prob. 28P 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. 31P Ch. 4 - In an experiment, the temperature of a hot gas...Ch. 4 - Prob. 33P Ch. 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. 38P Ch. 4 - Prob. 39P Ch. 4 - Prob. 40EP Ch. 4 - Consider a sphere of diameter 5 cm, a cube of side...Ch. 4 - Prob. 42P Ch. 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. 46CP Ch. 4 - Prob. 47CP Ch. 4 - The Biot number during a heat transfer process...Ch. 4 - A body at an initial temperature of Ti, is brought...Ch. 4 - Prob. 50P Ch. 4 - In a meat processing plant, 2-cm-thick steaks...Ch. 4 - Prob. 52P Ch. 4 - Prob. 53P Ch. 4 - Prob. 54P Ch. 4 - Prob. 55P Ch. 4 - Layers of 23-cm-thick meat slabs...Ch. 4 - Prob. 57P Ch. 4 - Prob. 58P Ch. 4 - Prob. 59P Ch. 4 - Prob. 60P Ch. 4 - Prob. 61P Ch. 4 - Prob. 62EP Ch. 4 - Prob. 63P Ch. 4 - Prob. 64P Ch. 4 - Prob. 65P Ch. 4 - Prob. 66P Ch. 4 - A 30-cm-diameter, 4-m-high cylindrical column of a...Ch. 4 - Prob. 68P Ch. 4 - Prob. 69P Ch. 4 - Prob. 70P Ch. 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. 74P Ch. 4 - Prob. 75P Ch. 4 - Prob. 76P Ch. 4 - Oranges of 2.5-in-diameter...Ch. 4 - Prob. 78P Ch. 4 - Prob. 79P Ch. 4 - Prob. 80P Ch. 4 - Prob. 81P Ch. 4 - A 9-cm-diameter potato...Ch. 4 - In Betty Crocker s Cookbook, it is stated that it...Ch. 4 - Prob. 84P Ch. 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. 88EP Ch. 4 - Prob. 89P Ch. 4 - In areas where the air temperature remains below...Ch. 4 - Prob. 91P Ch. 4 - A highway made of asphalt is initially at a...Ch. 4 - A thick aluminum block initially at 20C is...Ch. 4 - Prob. 94P Ch. 4 - A thick wall made of refractory bricks...Ch. 4 - Prob. 96P Ch. 4 - Prob. 97P Ch. 4 - A thick wood slab (k=0.17W/m.K,=1.2810-7m2/s) and...Ch. 4 - Prob. 99P Ch. 4 - Prob. 100P Ch. 4 - Prob. 101P Ch. 4 - Prob. 102P Ch. 4 - Prob. 103P Ch. 4 - Prob. 104P Ch. 4 - Prob. 105P Ch. 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. 109CP Ch. 4 - Consider a short cylinder whose top and bottom...Ch. 4 - Prob. 111P Ch. 4 - Prob. 112P Ch. 4 - Prob. 113P Ch. 4 - A hot dog can be considered to be a cylinder 5 in...Ch. 4 - Prob. 115P Ch. 4 - Prob. 116P Ch. 4 - A 2-cm-high cylindrical ice block...Ch. 4 - Prob. 118P Ch. 4 - Prob. 119P Ch. 4 - Prob. 120P Ch. 4 - Prob. 121P Ch. 4 - Prob. 122P Ch. 4 - Prob. 123P Ch. 4 - Prob. 124CP Ch. 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. 128CP Ch. 4 - Prob. 129CP Ch. 4 - Prob. 130CP Ch. 4 - Prob. 131CP Ch. 4 - How does the rate of freezing affect the...Ch. 4 - Prob. 133CP Ch. 4 - Prob. 134CP Ch. 4 - Prob. 135CP Ch. 4 - Prob. 136CP Ch. 4 - Prob. 137CP Ch. 4 - Prob. 138P Ch. 4 - Chickens with an average mass of 2.2 kg and...Ch. 4 - Prob. 140EP Ch. 4 - Prob. 141P Ch. 4 - Prob. 142P Ch. 4 - A long roll of 2-m-wide and 0.5-cm-thick 1-Mn...Ch. 4 - Prob. 144P Ch. 4 - Prob. 145P Ch. 4 - Prob. 146P Ch. 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. 150P Ch. 4 - Prob. 151P Ch. 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. 154P Ch. 4 - Prob. 155P Ch. 4 - Prob. 156P Ch. 4 - Prob. 157P Ch. 4 - Prob. 158P Ch. 4 - Prob. 159P Ch. 4 - Prob. 160P Ch. 4 - Prob. 161P Ch. 4 - Prob. 162P Ch. 4 - Prob. 163P Ch. 4 - Lumped system analysis of transient heat...Ch. 4 - Prob. 165P Ch. 4 - Prob. 166P Ch. 4 - An 18-cm-long, 16-cm-wide, and 12-cm-high hot iron...Ch. 4 - Prob. 168P Ch. 4 - Prob. 169P Ch. 4 - Prob. 170P Ch. 4 - Prob. 171P Ch. 4 - Prob. 172P Ch. 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. 176P Ch. 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. 181P Ch. 4 - Citrus trees are very susceptible to cold weather,...

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