Explanation Given information: The thermal conductivity of tree is 0.17 W / m ⋅ K , the thermal diffusivity of tree is 1.28 × 10 − 7 m 2 / s , the initial temperature of trees is 30 °C , the temperature of hot gases is 520°C , the time for exposure to hot gases is 5 h , the heat transfer coefficient is 65 W / m 2 ⋅ K , the ignition temperature of the trees is 410°C and the diameter of trunks of the trees is 20 cm . Write the expression for the outer radius of the rod. r o = d o 2 ...... (I) Here, the outer diameter is d o . Write the expression for the Biot number. B i = h r o k ...... (II) Here, the heat transfer coefficient is h , and the thermal conductivity is k . From the coefficient used in the one term approximation solution for transient heat conduction for cylinder.(Table-I) B i λ 1 A 1 30.0 2.3261 1.5973 38.2 ( λ 1 ) B i = 38.2 ( A 1 ) B i = 38.2 40.0 2.3455 1.5993 Write the expression for the Fourier number. τ = α t r o 2 ...... (III) Here, the thermal diffusivity is α , the time is t and the radius is r o . Write the expression for the dimensionless temperature equation to find the temperature after 5 hours. T − T ∞ T i − T ∞ = A 1 e − λ 1 2 τ J o ( λ 1 r r o ) ...... (IV) Here, the temperature after time t is T , the temperature of the surroundings is T ∞ , the initial temperature of the body is T i , the constants are λ 1 and A 1 , the zero order Bessel function is J o , the Fourier number is τ , the distance where the properties of body are to be determined is r and the outer radius is r o . From the Zeroth and first order Bessel function of the first kind.(Table-II) η J o ( η ) 2.3 0.0555 2.34 J o ( 2.34 ) 2.4 0.0025 Calculation: Substitute 20 cm for d o in Equation (I). r o = 20 cm 2 = 20 cm ( 1 m 100 cm ) 2 = 0.1 m Substitute 65 W / m 2 ⋅ K for h , 0 .1 m for r o and 0.17 W / m ⋅ K for k in Equation (II). B i = 65 W / m 2 ⋅ K × 0 .1 m 0.17 W / m ⋅ K = 38.2 The value of ( λ 1 ) B i = 38.2 by interpolating the values from Table-I. 38.2 − 30 40 − 30 = ( λ 1 ) B i = 38.2 − ( λ 1 ) B i = 30 ( λ 1 ) B i = 40 − ( λ 1 ) B i = 30 38

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 146P

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If the dry trees will ignite as the fire sweeps through them.

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Chapter 4, Problem 145P

Chapter 4, Problem 147P

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. 15P Ch. 4 - Prob. 16P Ch. 4 - Metal plates...Ch. 4 - Prob. 18P Ch. 4 - Prob. 19P 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. 23P Ch. 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. 27P Ch. 4 - In an experiment, the temperature of a hot gas...Ch. 4 - Prob. 29P 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. 34P Ch. 4 - Prob. 35P Ch. 4 - Prob. 36EP Ch. 4 - Consider a sphere of diameter 5 cm, a cube of side...Ch. 4 - Prob. 38P 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. 42CP Ch. 4 - Prob. 43CP Ch. 4 - Prob. 44CP 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. 47P Ch. 4 - In a meat processing plant, 2-cm-thick steaks...Ch. 4 - Prob. 49P Ch. 4 - Prob. 50P Ch. 4 - Prob. 51P Ch. 4 - Layers of 23-cm-thick meat slabs...Ch. 4 - Prob. 53P Ch. 4 - Prob. 54P Ch. 4 - Prob. 55EP Ch. 4 - Prob. 56P Ch. 4 - Prob. 57EP Ch. 4 - Prob. 58P Ch. 4 - A 30-cm-diameter, 4-m-high cylindrical column of a...Ch. 4 - Prob. 60P Ch. 4 - Prob. 61P Ch. 4 - Prob. 62P Ch. 4 - Prob. 63P Ch. 4 - Prob. 64P Ch. 4 - Prob. 65P Ch. 4 - Prob. 66P Ch. 4 - Prob. 67P Ch. 4 - Prob. 68P Ch. 4 - Prob. 69P Ch. 4 - For heat transfer purposes, an egg can be...Ch. 4 - Citrus fruits are very susceptible to cold...Ch. 4 - Prob. 72P Ch. 4 - Prob. 73P Ch. 4 - A 9-cm-diameter potato...Ch. 4 - Chickens with an average mass of 1.7 kg...Ch. 4 - Prob. 76P Ch. 4 - In Betty Crocker s Cookbook, it is stated that it...Ch. 4 - Prob. 78P Ch. 4 - Prob. 79P Ch. 4 - Oranges of 2.5-in-diameter...Ch. 4 - Prob. 81EP 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. 85EP Ch. 4 - Prob. 86P Ch. 4 - In areas where the air temperature remains below...Ch. 4 - Prob. 88P Ch. 4 - A highway made of asphalt is initially at a...Ch. 4 - A thick aluminum block initially at 20C is...Ch. 4 - Prob. 91P Ch. 4 - A thick wall made of refractory bricks...Ch. 4 - Prob. 93P Ch. 4 - Prob. 94P Ch. 4 - A thick wood slab (k=0.17W/m.K,=1.2810-7m2/s) and...Ch. 4 - Prob. 96P Ch. 4 - Prob. 97P Ch. 4 - Prob. 98P Ch. 4 - Prob. 99P Ch. 4 - Prob. 100P Ch. 4 - Prob. 101P 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. 105CP Ch. 4 - Consider a short cylinder whose top and bottom...Ch. 4 - Prob. 107P Ch. 4 - Prob. 108P Ch. 4 - A hot dog can be considered to be a cylinder 5 in...Ch. 4 - Prob. 110P Ch. 4 - Prob. 111P Ch. 4 - A 2-cm-high cylindrical ice block...Ch. 4 - Prob. 113P Ch. 4 - Prob. 114P Ch. 4 - Prob. 115P Ch. 4 - Prob. 116P Ch. 4 - Prob. 117P Ch. 4 - Prob. 118P Ch. 4 - Prob. 119CP 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. 123CP Ch. 4 - Prob. 124CP Ch. 4 - Prob. 125CP Ch. 4 - Prob. 126CP Ch. 4 - How does the rate of freezing affect the...Ch. 4 - Prob. 128CP Ch. 4 - Prob. 129CP Ch. 4 - Prob. 130CP Ch. 4 - Prob. 131CP Ch. 4 - Prob. 132CP Ch. 4 - Prob. 133P Ch. 4 - Prob. 134P Ch. 4 - Chickens with an average mass of 2.2 kg and...Ch. 4 - Prob. 136EP Ch. 4 - Prob. 137P Ch. 4 - Prob. 138P Ch. 4 - A long roll of 2-m-wide and 0.5-cm-thick 1-Mn...Ch. 4 - Prob. 140P Ch. 4 - Prob. 141P Ch. 4 - Prob. 142P 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. 146P Ch. 4 - Prob. 147P 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. 150P Ch. 4 - Prob. 151P Ch. 4 - Prob. 152P Ch. 4 - Prob. 153P 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 - Lumped system analysis of transient heat...Ch. 4 - Prob. 161P Ch. 4 - Prob. 162P Ch. 4 - An 18-cm-long, 16-cm-wide, and 12-cm-high hot iron...Ch. 4 - Prob. 164P Ch. 4 - Prob. 165P Ch. 4 - Prob. 166P Ch. 4 - Prob. 167P Ch. 4 - Prob. 168P 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. 172P 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. 177P Ch. 4 - Citrus trees are very susceptible to cold weather,...

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