Question

What will be the rate of heat loss from a red brick wall of length 5 m, height 4 m and thickness 0.25 m with temperature on inner surface as \(40\text{ }^\circ\text{C}\) and outer surface as \(110\text{ }^\circ\text{C}\). The thermal conductivity of red brick is k=0.70 W/mK.

• A. 2.19 kW
• B. 3.92 kW
• C. 4.52 kW
• D. 2.88 kW

Hint:

Always confirm that the units of temperature difference (\(\Delta T\)) match the units of thermal conductivity. A temperature interval of \(1\text{ }^\circ\text{C}\) is exactly equivalent to an interval of \(1\text{ K}\), so no unit conversion is required for \(\Delta T\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Heat transfer through a solid wall occurs primarily via conduction. Under steady-state conditions, this process is governed by Fourier's Law of Heat Conduction, which states that the rate of heat flow is proportional to the temperature gradient and the area perpendicular to the path of heat flow.
Key Formula or Approach:
The rate of heat transfer (\(Q\)) through a flat plane wall is given by: \[ Q = \frac{k \cdot A \cdot \Delta T}{L} \] where:
\(k\) = thermal conductivity of the wall material (\(\text{W/m}\cdot\text{K}\))

\(A\) = surface area of the wall perpendicular to heat flow (\(\text{m}^2\))

\(\Delta T = |T_1 - T_2|\) = temperature difference across the wall (\(\text{K}\) or \(^\circ\text{C}\))

\(L\) = thickness of the wall (\(\text{m}\))

Step 2: Detailed Explanation:
Let us identify the given values:
Thermal conductivity, \(k = 0.70 \text{ W/m}\cdot\text{K}\)

Length of the wall = \(5 \text{ m}\)

Height of the wall = \(4 \text{ m}\)

Surface area, \(A = \text{Length} \times \text{Height} = 5 \text{ m} \times 4 \text{ m} = 20 \text{ m}^2\)

Thickness, \(L = 0.25 \text{ m}\)

Temperature on the inner surface, \(T_{\text{inner}} = 40\text{ }^\circ\text{C}\)

Temperature on the outer surface, \(T_{\text{outer}} = 110\text{ }^\circ\text{C}\)

Temperature difference, \(\Delta T = |110 - 40| = 70\text{ }^\circ\text{C} = 70 \text{ K}\)
Now, substitute these values into Fourier's formula: \[ Q = \frac{0.70 \times 20 \times 70}{0.25} \] Simplify the numerator: \[ Q = \frac{980}{0.25} \] Dividing a number by \(0.25\) is equivalent to multiplying it by \(4\): \[ Q = 980 \times 4 = 3920 \text{ W} \] Convert the rate of heat transfer from Watts to kilowatts: \[ Q = \frac{3920}{1000} \text{ kW} = 3.92 \text{ kW} \] Thus, the rate of heat loss through the red brick wall is \(3.92 \text{ kW}\).

Step 3: Final Answer:
The rate of heat loss is \(3.92 \text{ kW}\), which corresponds to Option (B).