Heat Transfer Rate

300°C air flows across a surface that is 45°C. What is the heat transfer rate over 4 m^2 of surface if the heat transfer coefficient is 80 W/[m^2(°C)]?

Expand Hint
$$$\dot{Q}=hA(\Delta T)$$$
where $$h$$ is the convection heat transfer coefficient of the fluid, $$A$$ is the convection surface area, $$\Delta T$$ is the change in temperature.
Hint 2
You don’t need to convert to Kelvin units.
Convection is heat transfer from one location to another through the movement of fluid. In this scenario, the air flow acts as a fluid. Thus, Newton's Law of Cooling:
$$$\dot{Q}=hA(\Delta T)$$$
where $$h$$ is the convection heat transfer coefficient of the fluid, $$A$$ is the convection surface area, $$\Delta T$$ is the change in temperature.

Finally,
$$$\dot{Q}=80\frac{W}{m^2C}(4m^2)(300^{\circ}C-45^{\circ}C)=320(255)=81,600\:W$$$
81,600 W
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