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

`q=1118.865W`

Step-by-step 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=(VD)/(v)`

where

`v=15.27*10^-^6`

`Re_D=(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 (k)/(D)`

where

`k=25.7*10^(-3)`

`h=791.53*(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`