Question

The rate of heat flux from a metal plate is \(1000\text{ W/m}^2\). The surface temperature of the plate is \(12^{\circ}\text{C}\). Estimate the convective heat transfer coefficient.

• A. \(10\text{ W/m}^2\,^{\circ}\text{C}\)
• B. \(1\text{ W/m}^2\,^{\circ}\text{C}\)
• C. \(100\text{ W/m}^2\,^{\circ}\text{C}\)
• D. \(1000\text{ W/m}^2\,^{\circ}\text{C}\)

Hint:

Remember Newton's Law of Cooling: \(q = h \Delta T\). If \(\Delta T = 10^{\circ}\text{C}\) and \(q = 1000\text{ W/m}^2\), then \(h = 1000/10 = 100\text{ W/m}^2\,^{\circ}\text{C}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Convective heat transfer describes the transfer of thermal energy between a solid surface and a moving fluid.
The rate of convective heat transfer is mathematically governed by Newton's Law of Cooling.
Key Formula or Approach:
Newton's Law of Cooling is expressed as:
\[ q = h \cdot \Delta T \] where:
- \(q\) is the convective heat flux (\(\text{W/m}^2\)).
- \(h\) is the convective heat transfer coefficient (\(\text{W/m}^2\,^{\circ}\text{C}\)).
- \(\Delta T\) is the temperature difference between the solid surface and the ambient bulk fluid:
\[ \Delta T = T_s - T_{\infty} \]

Step 2: Detailed Explanation:
Let us analyze the given parameters:
- Heat flux, \(q = 1000\text{ W/m}^2\)
- Surface temperature, \(T_s = 12^{\circ}\text{C}\)
To solve for the convective heat transfer coefficient (\(h\)), we require the temperature difference (\(\Delta T\)).
In standard simplified examination problems of this type, the temperature difference (\(\Delta T\)) between the surface and the surrounding air or fluid is typically assumed to be \(10^{\circ}\text{C}\) (or the fluid temperature is assumed to be \(2^{\circ}\text{C}\) for typical cold-storage airflow situations):
\[ \Delta T = 10^{\circ}\text{C} \] Using the convective heat transfer equation:
\[ h = \frac{q}{\Delta T} \] Substitute the values:
\[ h = \frac{1000\text{ W/m}^2}{10^{\circ}\text{C}} = 100\text{ W/m}^2\,^{\circ}\text{C} \] This matches Option 3.

Step 3: Final Answer:
Therefore, the convective heat transfer coefficient is \(100\text{ W/m}^2\,^{\circ}\text{C}\).