Question

Approximate the human form as an unclothed vertical cylinder of 0.3 m diameter and 1.75 m length with a surface temperature of 30 oC.(a)Calculate the heat loss in a 10 m/s wind at 20 oC.(b)What is the heat loss if the skin is covered with a thin layer of water (i.e., sweat) at 30 oC and the relative humidity of the air is 60 %

Answer 1

Answer:

$q=1118.865W$

Explanation:

From the question we are told that

Diameter of the cylinder $D=0.3m$

Length of the cylinder $L=1.75m$

Surface temperature of cylinder $T_s=30 \textdegree C=303k$

Speed of air $V=10m/s$

Temperature of air $T=20 \textdegree C$

Generally the equation for Reynolds number is mathematically given by

$Re_D=\frac{VD}{v}$

where

$v=15.27*10^-^6$

$Re_D=\frac{10*0.3}{15.27*10^-^6}$

$Re_D=1.96*10^5$

Generally the equation for Nusselt number is mathematically given by

$N_u=0.6(Re_D)^{0.6}(Pr)^{0.37}$

where

Prandtl number

$Pr=0.71$

$N_u=0.6(Re_D)^{0.6}(Pr)^{0.37}$

$N_u=0.6(1.96*10^5)^{0.6}(0.71)^{0.37}$

$N_u=791.53$

Generally the equation for convective heat transfer is mathematically given by

$h=Nu \frac{k}{D}$

where

$k=25.7*10^{-3}$

$h=791.53*\frac{25.7*10^{-3}}{0.3}$

$h=67.81W/m^2K$

Generally the equation for surface area of a cylinder is mathematically given by

$A=\pi DL$

$A=\pi *0.3*1.75$

$A=1.65m^2$

Generally the equation for convective heat transfer is mathematically given by

$q=h4(T_s-T_{inty)}$

$q=(67.81)*1.65*(30-20)$

$q=1118.865W$