Question

A compound wall consists of parallel layers of two different materials, 10 cm of brick and 2 cm of wood. If the difference of temperature across the brick wall is 20° C calculate the temperature difference between the wooden wall and heat current per square metre of the wall. [Thermal conductivity of brick and wood are respectively 0.5Wm-K- and 0.125Wm-'K']

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Answer 1

The temperature difference between the wooden wall is 16⁰C, and the heat current per square metre of the wall is 7,325 W/m².

Temperature difference between the wooden wall

The temperature difference between the wooden wall is calculated as follows;

• Let the brick wall =  wall A
• Let the wooden wall = wall B
• Let the area of the walls = A

$\frac{dQ_A}{dt } = \frac{dQ_B}{dt} \\\\\frac{K_A \Delta T_A \times A}{L_A} = \frac{K_B \Delta T _B \times A}{L_B}\\\\\frac{K_A \Delta T_A }{L_A} = \frac{K_B \Delta T _B}{L_B}\\\\\frac{0.5 \times 20}{0.1} = \frac{0.125 \times \Delta T _B }{0.02} \\\\100 = 6.25\Delta T _B\\\\\Delta T _B = \frac{100}{6.25} \\\\\Delta T _B = 16 \ ^oC$

Heat flowing in the walls

Q = KL(ΔT)

Q = 0.5 x 0.1 x (20 + 273)

Q = 14.65 W

Heat current per square meter of the Walls

QA = W/A

QA = (14.65)/A

• Let the area of the wall = 10 cm x 2 cm = 0.1 m x 0.02 m = 0.002 m².

QA = 14.65/0.002

QA = 7,325 W/m²

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