Radiation solar flux on earth.xls



KNOWN: Solar flux at outer edge of earth's atmosphere, 1353 W/m2.

FIND: a) Emissive power of sun.

b) Surface temperature of sun.

c) Wavelength of maximum solar emission.

d) Earth equilibrium temperature.

ASSUMPTIONS: 1) Sun and earth act as blackbodies.

2) No attenuation of solar radiation en route to earth.

3) Earth atmosphere has no effect on earth energy balance.

ANALYSIS: Applying conservation of energy to the solar energy crossing two concentric spheres, one having the radius of the sun and the other having the radial distance from the edge of the earth's atmosphere to the centre of the sun.

Calculation Reference
Fundamentals of Heat and Mass Transfer - Frank P. Incropera

To find the surface temperature of a spherical interplanetary probe, considering the diameter, emissivity, and power dissipation within the probe, you can follow these steps:

  1. Calculate the surface area: The surface area of a sphere can be calculated using the formula:

    Surface Area = 4πr^2

    Where r is the radius of the sphere. Since the diameter (D) is known, you can calculate the radius (r) as r = D/2.

  2. Calculate the power radiated by the probe: The power radiated by the probe can be calculated using the Stefan-Boltzmann Law:

    Power Radiated = ε * σ * Surface Area * T^4

    Where ε is the emissivity of the probe, σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/(m^2·K^4)), Surface Area is the surface area of the probe, and T is the surface temperature of the probe.

  3. Set up the energy balance equation: For steady-state conditions, the power dissipated within the probe must equal the power radiated by the probe:

    Power Dissipated = Power Radiated

    Substitute the known power dissipation within the probe into the equation.

  4. Solve for the surface temperature: Rearrange the energy balance equation to solve for the surface temperature (T):

    T = ((Power Dissipated) / (ε * σ * Surface Area))^0.25

    Substitute the known values of power dissipation, emissivity, Stefan-Boltzmann constant, and surface area into the equation and solve for the surface temperature.

By following these steps and applying the principle of energy conservation, you can determine the surface temperature of the spherical interplanetary probe, considering its diameter, emissivity, and power dissipation. This calculation accounts for the balance between energy generation within the probe and radiation emission from its surface.

24 Jan 2007
Last Modified
18 Jul 2023
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