This section focuses on the fundamentals of the radiation heat transfer, the nature of solar energy as electromagnetic radiation, and interactions of solar radiation with various materials. Radiation heat transfer is often addressed only briefly in any heat transfer course. However, In solar energy conversion systems, where the total energy flux is often orders of magnitude smaller than in conventional heat transfer systems, the contribution of the radiation heat transfer mechanism is significant. Conduction and convection also play a significant role in the performance of certain solar energy conversion systems.

#### Reading Assignment

To become introduced to the theory of the heat transfer as it applies to solar thermal systems, please read the following text:

Duffie, J.A., and Beckman, W.A., Solar Engineering of Thermal Processes, Wiley and Sons, 2013, Chapter 3, Sections 3.1-3.10.

Radiation heat transfer is dependent on the specific wavelength of the radiation. The distribution of wavelengths from a blackbody radiation source, such as the sun, is described by Planck’s Law (Equation 3.4.1 Duffie & Beckman, 2013). This equation can be integrated for a wavelength range of interest to find the total energy for different scenarios. The results of this integration are given in various simplified forms, which are convenient for practical use. Two important expressions derived from the Planck's law are Wien's displacement law (Equation 3.4.2 Duffie & Beckman, 2013) and Stefan-Boltzmann equation (Equation 3.5.1 Duffie & Beckman, 2013). Take a closer look at those expressions and understand what they are used for.

Another way Planck's law intergration data are often presented is Radiation Tables. Those become handy when the total emount of energy emitted by a blackbody source needs to be estimated for a specific wavelength interval. The example video (6:45) below specifically illustrates how such data are made useful to answer some practical questions.

Many solar thermal energy conversion systems use flat plate collectors, which are essentially two parallel plates (one transparent and the other absorptive) exchanging radiation. Calculating the radiation heat exchange between the two surfaces is a necessary aspect of understanding the energy balance of a system. Example 3.10.1 (Duffie & Beckman, 2013) is given below in a brief (6:19) video.

#### Self Check:

**1. What is the purpose of the following equations? **(click on the name to see the answer)

*Planck's Law*

ANSWER: Planck's equation describes the distribution of the radiation emitted by a blackbody over the range of wavelengths.

*Wien's Displacement Law*

ANSWER: Wien's equation determines the wave length at which a blackbody of a certain temperature emits the maximum radiation.

*Stefan-Boltzmann Equation*

ANSWER: Stefan-Boltzmann equation is used to found the total energy flux emitted by a blackbody at a certain temperature T.

**2. What is the purpose of the radiation tables?**

*Click here for answer*

ANSWER: Radiation tables (Table 3.6.1a in Duffie & Beckman, 2013) are a simplified result of the integration of the Planck's equation - they allow determining the fraction of radiative energy emitted by a black body within a certain wave length range.