Find the total normal radiation throughout the day received by a vertical south-west facing surface in January.

Steps to Solve

1. Determine Radiation Constant

Identify the solar radiation constant, which typically averages around $1367 , \text{W/m}^2$ (solar constant). This is the average amount of solar energy received outside the Earth's atmosphere.

2. Adjust for Time of Year

For January, we need to adjust the solar radiation for the time of year. The average daily solar radiation on a horizontal surface in winter can be approximated (for January) at about $3.5 , \text{kWh/m}^2/day$.

3. Calculate Effective Surface Area Orientation

Determine the orientation of the vertical surface. Since it is facing south-west, it will receive solar radiation differently than a surface facing south or west directly. The angle might generally be around $45°$ from the south.

4. Calculate Total Daily Radiation Received

Use the formula to calculate the total radiation received on the vertical surface:

$$ R = R_{horizontal} \times \cos(\theta) $$

Where:

• $R_{horizontal}$ is the solar radiation on a horizontal surface, given as $3.5 , \text{kWh/m}^2/day$.

• $\theta$ is the angle of incidence (in this case, let's assume $\theta = 45°$, then $\cos(45°) = \frac{1}{\sqrt{2}}$).

So,

$$ R = 3.5 , \text{kWh/m}^2/day \times \cos(45°) $$

5. Final Calculation

Calculate the total radiation received using the above values.

Performing the calculation yields:

$$ R = 3.5 , \text{kWh/m}^2/day \times \frac{1}{\sqrt{2}} \approx 2.47 , \text{kWh/m}^2/day $$

Therefore, the total normal radiation received by the vertical surface is roughly:

$$ R \approx 2.47 , \text{kWh/m}^2/day $$