Problem $1(35$ Points$)$

During the warmest week in Merced, a team of environmental researchers is interested in calculating the heat flux that occurs because of wind flowing parallel to the warm sidewalk. They need this calculation to prevent equipment damage. Upon consultation with a regional weather station, they find that wind flows parallel to the floor outside with a temperature $T_{}=37\mathrm{.}8C(100F).$ Upon cross$-$referencing the wind conditions with a table of fluid properties, they find that the convective heat transfer coefficient for the wind under these conditions is $h=25\frac{W}{m^2}*K.$

Assuming that radiative and conductive heat transfer are negligible, help the researchers calculate the heat flux, $q^{\text{'}\text{'}}$ between the hot floor and the wind. Assume that upon measurements with an infrared thermometer, the team found that the floor's surface temperature is $T_s=54C(130F).$ Convert all temperatures to Kelvin.

$U_{}37\mathrm{.}8c+273=310\mathrm{.}8K$

$T_{}$Longrightarrow$25\frac{w}{m^2}*K,+5$