Explanation Given information: The average diameter of the potato is 6 cm , the thermal conductivity of the potato is 0.50 W / m ⋅ K , the thermal diffusivity of the potato is 0.13 × 10 − 6 m 2 / s , the convective heat transfer coefficient is 19 W / m 2 ⋅ K , the flow velocity of air is 4 m / s , the air temperature is 2 ° C , the temperature of potato is 25 ° C , the temperature of the potato after cooling is 6 ° C . Write the expression for Biot number. Bi = h r k ....... (I) Here, the convective heat transfer coefficient is h , the radius of the spherical potato is r and the thermal conductivity of the block is k . Write the expression for Fourier number. τ = α t r 2 ....... (II) Here, the thermal diffusivity of the block is α and the time is t . Write the expression for the temperature distribution in the sphere for Lumped heat analysis. T ( t ) − T ∞ T i − T ∞ = ( A 1 e − λ 1 2 τ ) ....... (III) Here, the center temperature of potato after time t is T ( t ) , the surrounding temperature is T ∞ , the initial center temperature of potato is T i and A 1 and λ 1 are constants. Write the expression for radius of the potato. r = d 2 ....... (IV) Here, the diameter of potato is d . Write the expression for temperature distribution in the sphere when it experience chilling injury for lumped heat analysis. T ( t ) − T ∞ T i − T ∞ = ( A 1 e − λ 1 2 τ ) sin ( λ 1 r / r 0 ) λ 1 r / r 0 ....... (V) Here, r 0 is the actual radius of the sphere. Calculation: Substitute 6 cm for d in the Equation (IV). r = 6 cm × 10 − 2 m 1 cm 2 = 3 × 10 − 2 m Substitute, 19 W / m 2 ⋅ K for h , 0.50 W / m ⋅ K for k , and 3 × 10 − 2 m for r in the Equation (I). Bi = ( 19 W / m 2 ⋅ K ) ( 3 × 10 − 2 m ) 0.50 W / m ⋅ K = 1.14 Refer to the Table, "Coefficients used in the one-term approximate solution of transient onedimensional heat conduction in plane walls, cylinders, and spheres" to obtain the values of constants corresponding to the Biot number 1.14 using interpolation. For sphere, A 1 = ( 1.14 − 1 ) ( 1.4793 − 1.2732 ) 2 − 1 + 1.2732 = 1.302 λ 1 = ( 1.14 − 1 ) ( 2.0288 − 1.5708 ) 2 − 1 + 1.5708 = 1.635 Substitute, 2 ° C for T ∞ , 25 ° C for T i , 6 ° C for T ( t ) , 1.302 for A 1 , and 1.635 for λ 1 in the Equation (III). ( 6 ° C ) − ( 2 ° C ) ( 25 ° C ) − ( 2 ° C ) = ( 1

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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Question

Chapter 4, Problem 79P

To determine

The time required to reach the center temperature of potato to 6 °C and when the potato experiences the chilling injury during the process.

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Chapter 4, Problem 78P

Chapter 4, Problem 80EP

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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