Step 1: Understanding the Concept:
Convective heat transfer is described by Newton's Law of Cooling, which relates the rate of heat transfer to the surface area and the temperature difference between the surface and the fluid.
Key Formula or Approach:
Newton's Law of Cooling is expressed as:
\[ q = h \cdot A \cdot \Delta T \]
where:
- $q$ is the heat transfer rate (Watts, $\text{W}$ or $\text{J/s}$).
- $h$ is the convective heat transfer coefficient.
- $A$ is the surface area ($\text{m}^2$).
- $\Delta T$ is the temperature difference between the surface and the fluid ($\text{K}$ or $^\circ\text{C}$).
To find the unit of $h$:
\[ h = \frac{q}{A \cdot \Delta T} \]
Step 2: Detailed Explanation:
Let us substitute the SI units into the equation:
- Unit of $q$ = Watts ($\text{W}$).
- Unit of $A$ = square meters ($\text{m}^2$).
- Unit of $\Delta T$ = degrees Celsius ($^\circ\text{C}$) or Kelvin ($\text{K}$).
This gives the SI unit of $h$ as:
\[ \text{Unit of } h = \frac{\text{W}}{\text{m}^2 \cdot ^\circ\text{C}} = \text{W/m}^2\text{}^\circ\text{C} \]
Let us review the other options:
- $\text{W/m}^\circ\text{C}$ (C) is the SI unit of thermal conductivity ($k$), used in conduction.
- $\text{Kcal/hr}$ (D) is a non-SI unit of heat flow rate.
Step 3: Final Answer:
The SI unit of the convective heat transfer coefficient is $\text{W/m}^2\text{}^\circ\text{C}$.