A solid plate with a thickness of 15 cm and a thermal conductivity of 80 W/m·K is being cooled at the upper surface by air. The air temperature is 10°C, while the temperatures at the upper and lower surfaces of the plate are 50°C and 60°C, respectively. Determine the convection heat transfer coefficient of air at the upper surface.

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zainsubhani zainsubhani · Answer 1 · 2020-01-23T13:02:43+01:00

Answer:

[tex]h=133.333 W/m^2K[/tex]

Step-by-step explanation:

Heat transfer due to conduction:

[tex]Q_c=-KA\frac{T_s-T_b}{L}[/tex]

Where:

K is the thermal conductivity

A is the area of the Plate

T_s is the temperature at the upper surface

T_b is the temperature at the lower surface

L is the length of thickness of the plate

Heat Transfer due to convection:

[tex]Q_convection=hA(T_s-T_a)[/tex]

Where:

h is the convection heat transfer coefficient.

A is the area of the Plate.

T_s is the temperature at the upper surface.

T_a is the air temperature

Heat Transfer due to conduction=Heat Transfer due to convection

[tex]Q_c[/tex]=[tex]Q_convection[/tex]

[tex]-KA\frac{T_s-T_b}{L}[/tex]=[tex]hA(T_s-T_a)[/tex]

[tex]h=-K*\frac{T_s-T_b}{T_s-T_a}* \frac{1}{L} \\h=-80*\frac{50-60}{50-10}* \frac{1}{0.15m}\\h=133.333 W/m^2K[/tex]