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 17, Problem 119RQ
To determine

The fraction of heat lost from each person by respiration.

Expert Solution & Answer
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Explanation of Solution

Given:

Thermal conductivity of the first person (k1) is 0.159 W/mK.

Thermal conductivity of the second person (k2) is 0.13 W/mK.

Heat transfer coefficient (h) is 0.15 W/m2K.

Diameter of the cylinder (D) is 25 cm.

Length of the cylinder (L) is 1.7 m.

Calculation:

Determine the surface area of the first person’s body.

  A1=π2DL=π2(0.25 m)(1.7 m)=0.6675 m2

Determine the surface area of the second person’s body.

  A2=2A1=2×0.6675 m2=1.335 m2

Determine the thermal resistance from leather.

  Rleather =LkA=0.001 m(0.159 W/m°C)(0.6675 m2)=0.00942 °C/W

Determine the thermal resistance from convection.

  Rconv =1hA=1(15 W/m2°C)(0.6675 m2)=0.09988 °C/W

Determine the total thermal resistance from first person’s body.

  Rtotal =Rleather +Rconv =0.00942 °C/W+0.09988 °C/W=0.1093 °C/W

Determine the heat transfer through clothes.

  Q˙clothes =T1T2Rtotal =(32°C30°C)0.1093 °C/W=18.3 W

Determine heat transfer through skin.

  Q˙skin =T1T2Rconv =(32°C30°C)0.09988 °C/W=20 W

Determine the total sensible heat transfer.

  Q˙sensible =Q˙clothes +Q˙skin =18.3 W+20 W=38.3 W

Determine the fraction of heat lost by respiration.

  fQ˙respiration Q˙total =Q˙total Q˙sensible Q˙total =60 W38.3 W60 W=0.362

Thus, the fraction of heat lost by respiration is 0.362_.

Determine the thermal resistance from leather.

  Rsynthetic=LkA=0.001 m(0.13 W/m°C)(1.335 m2)=0.00576 °C/W

Determine the thermal resistance from convection.

  Rconv =1hA=1(15 W/m2°C)(1.335 m2)=0.04994 °C/W

Determine the total thermal resistance.

  Rtotal =Rsynthetic +Rconv =0.00576 °C/W+0.04994 °C/W=0.0557 °C/W

Determine the total sensible heat transfer.

  Q˙sensible =T1T2Rtotal =(32°C30°C)0.0557 °C/W=35.9 W

Determine the fraction of heat lost by respiration.

  fQ˙respiration Q˙total =Q˙total Q˙sensible Q˙total =60 W35.9 W60 W=0.402

Thus, the fraction of heat lost by respiration is 0.402_.

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Chapter 17 Solutions

Fundamentals of Thermal-Fluid Sciences

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