Answer:
The inside temperature,
is approximately 248 °C.
Explanation:
The parameters given are;
Temperature of the air = 20°C
Carbon steel surface temperature 250°C
Area of surface = 50 cm × 75 cm = 0.5 × 0.75 = 0.375 m²
Convection heat transfer coefficient = 25 W/(m²·K)
Heat lost by radiation = 300 W
Assumption,
Air temperature = 20 °C
Hot plate temperature = 250 °C
Thermal conductivity K = 65.2 W/(m·K)
Steady state heat transfer process
One dimensional heat conduction
We have;
Newton's law of cooling;
q = h×A×(
-
) + Heat loss by radiation
= 25×0.325×(250 - 20) + 300
= 2456.25 W
The rate of energy transfer per second is given by the following relation;
![P = \dfrac{K \times A \times \Delta T}{L}](https://tex.z-dn.net/?f=P%20%3D%20%5Cdfrac%7BK%20%5Ctimes%20A%20%5Ctimes%20%5CDelta%20T%7D%7BL%7D)
Thermal conductivity K = 65.2 W/(m·K)
Therefore;
![2456.25 = \dfrac{65.2 \times 0.375 \times (250 - T_{in})}{0.02}](https://tex.z-dn.net/?f=2456.25%20%20%3D%20%5Cdfrac%7B65.2%20%5Ctimes%200.375%20%5Ctimes%20%28250%20-%20T_%7Bin%7D%29%7D%7B0.02%7D)
![T_{in} = 250 - \dfrac{2456.25 \times 0.02}{65.2 \times 0.375} = 247.99 ^{\circ}C](https://tex.z-dn.net/?f=T_%7Bin%7D%20%3D%20250%20-%20%5Cdfrac%7B2456.25%20%20%5Ctimes%200.02%7D%7B65.2%20%5Ctimes%200.375%7D%20%3D%20247.99%20%5E%7B%5Ccirc%7DC)
The inside temperature,
= 247.99 °C ≈ 248 °C.