Answer
$\dot{Q}=2096\ Btu/h=614\ W$
Work Step by Step
From the energy balance:
$\dot{Q}_w+\dot{m}h_1=\dot{m}h_2$
$\dot{Q}_w=\dot{m}c_p(T_2-T_1)$
$\dot{m}=\rho \frac{\pi}{4}D^2\mathcal{V}_1$
Given $\rho=62.11\ lbm/ft³,\ D=0.25\ in,\ \mathcal{V}_1=40\ ft/min$
$\dot{m}=50.9\ Btu/h$
Since $T_2=105°F,\ T_1=70°F,\ c_p=1.00\ Btu/lbm.°F$
$\dot{Q}_w=1781\ Btu/h$
With $0.85\dot{Q}=\dot{Q}_w$:
$\dot{Q}=2096\ Btu/h=614\ W$
