Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 18, Problem 101RQ

a)

To determine

The average heat transfer coefficient at the surface of the turkey.

a)

Expert Solution
Check Mark

Explanation of Solution

Given:

Mass of the stuffed turkey (m) is 14lbm.

Initial temperature (Ti) is 40°F.

Temperature maintained at the oven (T) is 325°F.

Temperature at the meat (T(x,t)) is 185°F.

Time taken to roast the turkey (t) is 5h.

Calculation:

Write the given properties of the turkey.

  ρ=75lbm/ft3cp=0.98Btu/lbm°Fk=0.26Btu/hft°Fα=0.0035ft2/s

Calculate the radius of the roast (r0).

  m=ρVV=mρ43πr03=mρ

  r0=(3m4πρ)13=(3(14lbm)4π(75lbm/ft3))13=0.3545ft

Calculate the Fourier number (τ).

  τ=αtr02=(0.0035ft2/s)(5h)(0.3545ft)2=(0.0035ft2/s)(5×3600s)(0.3545ft)2=0.1392

The Fourier number is nearly close to 0.2(0.13920.2). Therefore, the one-term approximate solution can be applicable.

Calculate the dimensionless temperature of the roast (θ(x,t)sph).

  θ(x,t)sph=A1eλ12τsin(λ1rr0)λ1rr0T(x,t)TTiT=A1eλ12τsin(λ1rr0)λ1rr0185°F325°F40°F325°F=A1eλ12(0.1392)sin(0.333λ1)0.333λ10.491=A1eλ12(0.1392)sin(0.333λ1)0.333λ1        (I)

Solve Equation (I) by trial and error method using Table 18-2, Coefficients used in the one-term approximate solution of transient one-dimensional heat conduction in plane walls, cylinders, and spheres”.

Equation (I) is satisfied when the Biot number, Bi=20. It corresponds to the constants values given as follows:

  λ1=2.9857A1=1.9781

Calculate the average heat transfer coefficient at the surface of the turkey (h).

  Bi=hr0k

  h=k(Bi)r0=(0.26Btu/hft°F)(20)(0.3545ft)=14.7Btu/hft2°F

Thus, the average heat transfer coefficient at the surface of the turkey is 14.7Btu/hft2°F.

b)

To determine

The temperature of the skin of the turkey.

b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the temperature of the skin of the turkey (T(r0,t)).

  θ(r0,t)sph=A1eλ12τ[sin(λ1r0r0)(λ1r0r0)]T(r0,t)TTiT=A1eλ12τ[sin(λ1r0r0)(λ1r0r0)]

  T(r0,t)325°F40°F325°F=(1.9781)e(2.9857)2(0.1392)[sin(2.9857)(2.9857)]=0.02953

  T(r0,t)=317°F

Thus, the temperature of the skin of the turkey is 317°F.

c)

To determine

The amount of heat transferred to the turkey in the oven.

c)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the maximum amount of heat transferred to the turkey (Qmax).

  Qmax=mcp(TTi)=(14lbm)(0.98Btu/lbm°F)(325°F40°F)=3910Btu

Calculate the amount of heat transferred to the turkey in the oven (Q).

  (QQmax)cyl=13(θ0,sph)(sinλ1λ1cosλ1λ13)=13(0.495)(sin(2.9857)(2.9857)cos(2.9857)(2.9857)3)=0.828

  Q=(0.828)Qmax=(0.828)(3910Btu)=3240Btu

Thus, the amount of heat transferred to the rib is 3240Btu.

d)

To determine

The time taken to cook the medium-done rib.

d)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

It is given that the innermost temperature of the rib is 71°C.

  T0=71°C

Calculate the Fourier number (τ).

  θ0,sph=A1eλ12τT0TTiT=A1eλ12τ71°C163°C4.5°C163°C=(1.9898)e(3.0372)2ττ=0.1336

Calculate the time taken to cook the medium-done rib (t).

  t=τr02α=(0.1336)(0.08603m)20.91×107m2/s=10,866s

  =181min3hr

Thus, the time taken to cook the medium-done rib is 3hr.

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Chapter 18 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 18 - Prob. 11PCh. 18 - Prob. 12PCh. 18 - Prob. 13PCh. 18 - Prob. 14PCh. 18 - Consider a 1000-W iron whose base plate is made of...Ch. 18 - Metal plates (k = 180 W/m·K, ρ = 2800 kg/m3, and...Ch. 18 - A 5-mm-thick stainless steel strip (k = 21 W/m·K,...Ch. 18 - A long copper rod of diameter 2.0 cm is initially...Ch. 18 - Prob. 21PCh. 18 - Steel rods (ρ = 7832 kg/m3, cp = 434 J/kg·K, and k...Ch. 18 - Prob. 23PCh. 18 - The temperature of a gas stream is to be measured...Ch. 18 - Prob. 25PCh. 18 - A thermocouple, with a spherical junction diameter...Ch. 18 - Prob. 27PCh. 18 - Prob. 28PCh. 18 - Carbon steel balls (ρ = 7833 kg/m3, k = 54 W/m·K,...Ch. 18 - Prob. 31PCh. 18 - Prob. 32PCh. 18 - Prob. 33PCh. 18 - Prob. 34PCh. 18 - Prob. 35PCh. 18 - Prob. 36PCh. 18 - Prob. 37PCh. 18 - Prob. 38PCh. 18 - Prob. 39PCh. 18 - A body at an initial temperature of Ti is brought...Ch. 18 - In a meat processing plant, 2-cm-thick steaks (k =...Ch. 18 - Prob. 42PCh. 18 - Prob. 43PCh. 18 - Prob. 45PCh. 18 - Prob. 46PCh. 18 - Prob. 47PCh. 18 - Prob. 48PCh. 18 - Prob. 49PCh. 18 - A long iron rod (ρ = 7870 kg/m3, cp = 447 J/kg·K,...Ch. 18 - Prob. 51PCh. 18 - A long 35-cm-diameter cylindrical shaft made of...Ch. 18 - Prob. 54PCh. 18 - Prob. 55PCh. 18 - Prob. 56PCh. 18 - A father and son conducted the following simple...Ch. 18 - Prob. 58PCh. 18 - Prob. 59PCh. 18 - Citrus fruits are very susceptible to cold...Ch. 18 - Prob. 61PCh. 18 - Prob. 63PCh. 18 - Prob. 64PCh. 18 - Prob. 65PCh. 18 - White potatoes (k = 0.50 W/m·K and α = 0.13 × 10−6...Ch. 18 - Prob. 67PCh. 18 - Prob. 68PCh. 18 - Prob. 69PCh. 18 - Consider a hot semi-infinite solid at an initial...Ch. 18 - Prob. 71PCh. 18 - Prob. 72PCh. 18 - Prob. 73PCh. 18 - Prob. 74PCh. 18 - Prob. 75PCh. 18 - Prob. 76PCh. 18 - Prob. 77PCh. 18 - Prob. 78PCh. 18 - Prob. 79PCh. 18 - Prob. 81PCh. 18 - Prob. 82PCh. 18 - Prob. 83PCh. 18 - Prob. 84PCh. 18 - Prob. 85PCh. 18 - Prob. 86PCh. 18 - Prob. 88PCh. 18 - Prob. 89PCh. 18 - A 2-cm-high cylindrical ice block (k = 2.22 W/m·K...Ch. 18 - Prob. 91PCh. 18 - Prob. 93PCh. 18 - Prob. 94RQCh. 18 - Large steel plates 1.0-cm in thickness are...Ch. 18 - Prob. 96RQCh. 18 - Prob. 97RQCh. 18 - Prob. 98RQCh. 18 - Prob. 99RQCh. 18 - Prob. 100RQCh. 18 - Prob. 101RQCh. 18 - Prob. 102RQCh. 18 - The water main in the cities must be placed at...Ch. 18 - Prob. 104RQCh. 18 - Prob. 105RQCh. 18 - Prob. 106RQCh. 18 - Prob. 107RQ
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