## Heat Transfer Coefficient

Consider a square block with a surface area of 5 m^2 is made up of an unknown material. If the power required to heat the block from 20°C to 60°C is 10 kW, what is the heat-transfer coefficient in W/m^2∙K?

Expand Hint
The units for the heat-transfer coefficient in the problem statement provide some insights on the math operations needed.
Hint 2
$$\dot{Q}=hA\Delta T$$$where $$h$$ is the convection heat transfer coefficient of the fluid, $$A$$ is the convection surface area, $$\Delta T$$ is the change in temperature. 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.
$$10,000W=h(5m^2)[(60+273K)-(20+273K)]$$$$$h=\frac{10,000W}{(5m^2)(40K)}=50\:\frac{W}{m^2\cdot K}$$$
$$50\:\frac{W}{m^2\cdot K}$$\$
Similar Problems from FE Sub Section: Conduction

Similar Problems from FE Section: Basic Heat-Transfer Rate Equations