Explanation Given: The length of the cylindrical aluminum block is L = 30 cm . The diameter of the cylindrical aluminum block is D = 15 cm . The density of the cylindrical aluminum block is ρ = 2702 kg / m 3 . The specific heat of the cylindrical aluminum block is c p = 0.896 kJ / kg . The thermal conductivity of the cylindrical aluminum block is k = 236 W / m ⋅ K . The thermal diffusivity of the cylindrical aluminum block is α = 9.75 × 10 − 5 m 2 / s . The heat transfer coefficient of cylindrical aluminum block is h = 80 W / m 2 ⋅ K . The temperature of cylindrical aluminum block is T i = 20 ° C . The temperature of furnace is T ∞ = 1200 ° C . The temperature at the center is T o = 300 ° C . Formula used: The Biot number is given as, B i = h L k Here, L c is the characteristic length, h is the heat transfer coefficient and k is the thermal conductivity. The interpolation for the coefficient of Biot number is given as, y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) Here, y is the property that is to be calculated, x is the given value, x 1 is the nearest lower value to the given value, x 2 is the nearest highest value to the given value, y 1 is the property of lower value and y 2 is the property of the higher value. The Fourier number is given as, τ = α t L 2 Here, α is the thermal diffusivity, t is the characteristics time and L is the characteristic length. The one-term approximation for the cylindrical block is given as, θ ( 0 , 0 , t ) block = θ ( 0 , t ) wall θ ( 0 , t ) cyl = ( A 1 e − λ 2 τ ) wall ( A 1 e − λ 2 τ ) cyl T o − T ∞ T i − T ∞ = ( A e − λ 2 τ ) wall ( A e − λ 2 τ ) cyl The mass of cylinder block is given as, m = ρ π r o 2 L The maximum amount of heat transfer is given as, Q max = m c p ( T ∞ − T i ) The dimensionless heat transfer for the wall is given as, ( Q Q max ) wall = 1 − θ o,wall sin ( λ ) λ Calculation: The Biot number for long cylinder can be calculated as, B i = h L k = 80 W / m 2 ⋅ ° C × 0.3 m 236 W / m ⋅ ° C = 0.101 Refer table 4-2 “Coefficients used in the one term approximate solution” And obtain values at B i = 0.1 λ = 0.3111 A = 1.0161 The Biot number radial distance can be calculated as, B i r o = h r o k = 80 W / m 2 ⋅ ° C × 0.075 m 236 W / m 2 ⋅ ° C = 0.0254 Refer table 4-2 ‘coefficients used in the one term approximate solution’ And obtain values for B i 1 = 0.02 B i 2 = 0.04 λ 1 = 0.1995 λ 2 = 0.2814 Further, A 1 = 1.0050 A 2 = 1.0099 The interpolation for the coefficient of Biot number for cylinder length can be calculated as y = y 2 − y 1 x 2 − x 1 ( x − x 1 ) + y 1 λ = λ 2 − λ 1 B i 2 − B i 1 ( B i − B i 1 ) + λ 1 = 0.2814 − 0.1995 0.04 − 0.02 ( 0.0254 − 0.02 ) + 0.1995 = 0.2216 Solving for the constant A , A = A 2 − A 1 B i 2 − B i 1 ( B i − B i 1 ) + A 1 = 1

6th Edition

ISBN: 9780073398198

Author: CENGEL

Publisher: RENT MCG

See similar textbooks

Question

Chapter 4, Problem 122P

To determine

How long the block should be kept in the furnace.

The amount of heat transfer from the aluminum block.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 121P

Chapter 4, Problem 123P

Students have asked these similar questions

Q11. Determine the magnitude of the reaction force at C. 1.5 m a) 4 KN D b) 6.5 kN c) 8 kN d) e) 11.3 KN 20 kN -1.5 m- C 4 kN -1.5 m B Mechanical engineering, No Chatgpt.

please help with this practice problem(not a graded assignment, this is a practice exam), and please explain how to use sohcahtoa

Solve this problem and show all of the work

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. 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,...

Knowledge Booster

How long the block should be kept in the furnace. The amount of heat transfer from the aluminum block.

How long the block should be kept in the furnace. The amount of heat transfer from the aluminum block.

Want to see the full answer?

Chapter 4 Solutions

How long the block should be kept in the furnace.

The amount of heat transfer from the aluminum block.