QQuestionPhysics
QuestionPhysics
**(3 points)** Q^1. Air at 30°C with a convection heat transfer coefficient of 28 W/m²·K blows over a horizontal steel hot plate (*k* = 50 W/m·K). The surface area of the plate is 0.68 m² with a thickness of 4 cm. The plate surface is maintained at a constant temperature of *Ts* = 310°C and the plate loses 420 W from its surface by radiation. Calculate the inside plate temperature (*Ti*).
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Answer
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Step 1:: Write down the formula for heat conduction through a plane wall.
- $A$ is the area (m²).
The heat conduction equation for a plane wall is given by: where
Step 2:: Find the temperature difference between the plate surface and the air.
T_s - T_a = \frac{420 \, \text{W}}{28 \, \frac{\text{W}}{\text{m}^2 \cdot \text{K}}} = 15 \, \text{K}
We are given that the convection heat transfer coefficient of the air is 28 W/m²·K and the surface area of the plate is 0.68 m². The heat transfer by convection is given by: where Since the plate loses 420 W from its surface by radiation, we have: Thus,
Step 3:: Calculate the inside plate temperature.
T_i = 15 \, \text{K} \cdot \frac{0.04 \, \text{m}}{50 \, \frac{\text{W}}{\text{m} \cdot \text{K}} \cdot 0.68 \, \text{m}^2} + 30 \, \text{°C} = 30.4 \, \text{°C}
Now, we can use the heat conduction equation to find the inside plate temperature. We are given that the thermal conductivity of the steel is 50 W/m·K and the thickness of the plate is 4 cm or 0.04 m. The heat transfer by conduction is given by: where Since the heat flux by convection and conduction are the same, we have:
Final Answer
The inside plate temperature is 30.4 °C.
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