Calculating Heat Transfer, Thermal Resistance, and Convection Coefficient

Question:

Given a surface area of 3m² at 200°C exchanging heat with another surface at 30°C by radiation with a factor of 0.69, how can we determine the rate of heat transfer, thermal resistance, and equivalent convection coefficient?

Answer:

To calculate the rate of heat transfer, we can use the Stefan-Boltzmann law, which states: Q = σ * A * ε * (T₁⁴ - T₂⁴). Here, Q represents the rate of heat transfer, σ is the Stefan-Boltzmann constant, A is the surface area, ε is the emissivity, T₁ is the temperature of the hot surface, and T₂ is the temperature of the cold surface.

Rate of Heat Transfer:

The rate of heat transfer can be calculated using the formula:

Q = 5.67 x 10^-8 W/(m²K⁴) * 3 m² * 0.69 * (473.15 K⁴ - 303.15 K⁴)

After calculation, we find that the rate of heat transfer is approximately 4885.6 W.

Thermal Resistance:

The thermal resistance (R) can be calculated as:

R = 1 / (h * A)

Given the rate of heat transfer, we can determine the thermal resistance to be 0.0348 °C/W.

Equivalent Convection Coefficient:

The equivalent convection coefficient (h) can be calculated as the reciprocal of the thermal resistance:

h = 1 / R

Therefore, the equivalent convection coefficient is 9.58 W/m² °C.