Question

Cold air at 10 \(^\circ\text{C}\) is forced to flow over a flat plate maintained at 40 \(^\circ\text{C}\). The mean heat transfer coefficient is 30 \(\text{W}/(\text{m}^2 \cdot ^\circ\text{C})\). What will be the heat flow rate from the plate to the air through a plate area of 2 \(\text{m}^2\)?

• A. 0.9 kW
• B. 1.8 kW
• C. 1.5 kW
• D. 90 kW

Hint:

Always double-check the final unit. The calculation yields 1800 W, which corresponds directly to 1.8 kW.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Heat transfer between a solid surface and a fluid moving over it occurs via convection, described by Newton's Law of Cooling.

Step 2: Key Formula or Approach:
Newton's Law of Cooling is expressed as:
\[ Q = h \cdot A \cdot (T_s - T_\infty) \] where:
\(Q\) = Convective heat flow rate (W)
\(h\) = Convective heat transfer coefficient (\(\text{W}/(\text{m}^2 \cdot ^\circ\text{C})\))
\(A\) = Surface area (\(\text{m}^2\))
\(T_s\) = Surface (plate) temperature (\(^\circ\text{C}\))
\(T_\infty\) = Free-stream fluid (air) temperature (\(^\circ\text{C}\))

Step 3: Detailed Explanation:
Identify and substitute the given values:
\(T_s = 40 ^\circ\text{C}\)
\(T_\infty = 10 ^\circ\text{C}\)
\(h = 30 \text{ W}/(\text{m}^2 \cdot ^\circ\text{C})\)
\(A = 2 \text{ m}^2\)
Now, calculate the heat flow rate:
\[ Q = 30 \times 2 \times (40 - 10) \] \[ Q = 60 \times 30 \] \[ Q = 1800 \text{ W} \] Convert the unit from Watts to kilowatts:
\[ Q = \frac{1800}{1000} = 1.8 \text{ kW} \]

Step 4: Final Answer:
The correct option is 2, which corresponds to 1.8 kW.