Find the heat flux due to radiation from a gasoline pool fire whose flame is 3 m tall with a 1 m diameter, and it is 3.5 m away from a target fuel. Assume e = 0.98 with a flame temperature of 1,300 K. Solve this problem by determining the configuration factor and assume a point source.
To find the heat flux due to radiation from a gasoline pool fire, we can use the concept of configuration factor and assume a point source. The configuration factor is a dimensionless quantity that represents the fraction of radiation leaving the source that is intercepted by the target.
Here's how you can solve this problem step by step:
Step 1: Calculate the area of the flame:
The base of the flame is a circle with a diameter of 1 m. Therefore, the area of the base can be calculated using the formula:
Area = π * (diameter/2)^2
Area = π * (1/2)^2 = 0.785 m^2
Step 2: Calculate the solid angle subtended by the target from the flame:
The solid angle is a measure of the extent of a cone-shaped region in space. With a point source assumption, the solid angle subtended by the target from the flame can be calculated using the formula:
Solid angle = 2π * (1 - cos(θ/2))
Here, θ is the angle subtended by the target from the flame. In this case, θ can be calculated by trigonometry.
θ = atan (height/distance)
θ = atan(3/3.5) = 42.26 degrees (converted to radians, π/180 * 42.26 = 0.74 radians)
Substituting the value of θ in the solid angle formula, we get:
Solid angle = 2π * (1 - cos(0.74/2))
Solid angle = 2π * (1 - cos(0.37))
Solid angle = 2π * (1 - 0.9297)
Solid angle = 0.514 steradians
Step 3: Calculate the configuration factor:
The configuration factor can be calculated using the formula:
Configuration factor = solid angle / (4π * distance^2)
Configuration factor = 0.514 / (4π * 3.5^2)
Configuration factor ≈ 0.0058
Step 4: Calculate the heat flux due to radiation:
The heat flux due to radiation can be calculated using the formula:
Heat flux = configuration factor * emissivity * Stefan-Boltzmann constant * (flame temperature)^4
In this case, we are given that the emissivity (e) is 0.98 and the flame temperature is 1300 K. The value of the Stefan-Boltzmann constant (σ) is 5.67 x 10^-8 W/(m^2*K^4).
Heat flux = 0.0058 * 0.98 * (5.67 x 10^-8) * (1300^4)
Heat flux ≈ 45,673 W/m^2
Therefore, the heat flux due to radiation from the gasoline pool fire is approximately 45,673 W/m^2.