Thermodynamics HW Solutions 278

# Thermodynamics HW Solutions 278 - Chapter 3 Steady Heat...

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Unformatted text preview: Chapter 3 Steady Heat Conduction 3-167 Two persons are wearing different clothes made of different materials with different surface areas. The fractions of heat lost from each person’s body by respiration are to be determined. Assumptions 1 Heat transfer is steady. 2 Heat transfer is one-dimensional. 3 Thermal conductivities are constant. 4 Heat transfer by radiation is accounted for in the heat transfer coefficient. 5 The human body is assumed to be cylindrical in shape for heat transfer purposes. Properties The thermal conductivities of the leather and synthetic fabric are given to be k = 0.159 W/m⋅°C and k = 0.13 W/m⋅°C, respectively. Analysis The surface area of each body is first determined from A1 = πDL / 2 = π(0.25 m)(1.7 m)/2 = 0.6675 m 2 A2 = 2 A1 = 2 × 0.6675 = 1.335 m 2 The sensible heat lost from the first person’s body is Rleather 0.001 m L = = 0.00942 °C/W kA (0.159 W/m.°C)(0.6675 m 2 ) 1 1 = = = 0.09988 °C/W hA (15 W/m 2 .°C)(0.6675 m 2 ) Rleather = Rconv Rconv T1 T∞2 R total = Rleather + Rconv = 0.00942 + 0.09988 = 0.10930 °C/W The total sensible heat transfer is the sum of heat transferred through the clothes and the skin T −T (32 − 30)°C & Qclothes = 1 ∞ 2 = = 18.3 W R total 0.10930°C/W T −T (32 − 30)°C & Qskin = 1 ∞ 2 = = 20.0 W Rconv 0.09988°C/W & & & Qsensible = Qclothes + Qskin = 18.3 + 20 = 38.3 W Then the fraction of heat lost by respiration becomes f= & & & & Q respiration Q total − Qsensible 60 − 38.3 = = = 0.362 & & 60 Q total Q total Repeating similar calculations for the second person’s body L 0.001 m = = 0.00576 °C/W kA (0.13 W/m.°C)(1.335 m 2 ) 1 1 = = = 0.04994 °C/W 2 hA (15 W/m .°C)(1.335 m 2 ) Rsynthetic = Rconv R total = Rleather + Rconv = 0.00576 + 0.04994 = 0.05570 °C/W T − T∞ 2 (32 − 30)°C & = = 35.9 W Qsensible = 1 0.05570°C/W R total f= & & & & Q respiration Q total − Qsensible 60 − 35.9 = = = 0.402 & & 60 Q total Q total 3-121 T1 Rsynthetic Rconv T∞2 ...
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