Question

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.

Answer 1

Answer:

$h=133.333 W/m^2K$

Step-by-step explanation:

Heat transfer due to conduction:

$Q_c=-KA\frac{T_s-T_b}{L}$

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:

$Q_convection=hA(T_s-T_a)$

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

$Q_c$=$Q_convection$

$-KA\frac{T_s-T_b}{L}$=$hA(T_s-T_a)$

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