In the the Stefan-Boltzmann law , only one variable parameter is epsilon. This will come under heat exchange between surface. You need to feed the both the emissivity of surfaces which are considered.

Hi Franklin Uriel Parás Hernández ,

I think you need to provide a more detailed explanation of your question in order that the RG members can help you. For example, are you interested only in the heat transfer from the hot body (a perfect blackbody?) to a real surface? Does the real surface have some transparency (obviously, it cannot be completely transparent as you stated that it has a finite absorptivity)? Do you have plots for the reflectivity, absorptivity, and transmissivity versus wavelength for the real surface? Note, for the incident radiation, there is a relation amongst the reflectivity, absorptivity, and transmissivity: 1=R+A+T. Note, the absorptivity and emissivity are equal by Kirchhoff's law, which yields the following relation E=A, although, this relation usually assumes equilibrium, which you do not have.

Regards,

Tom Cuff

I agree with Thomas Cuff . More information is needed. You can study CHAPTER 8. RADIATION HEAT TRANSFER. from the book TRANSFERENCIA DE CALOR by J. P. Holman (8th edition)

If I understand your question, I think you need to link the heat transfer equation that takes into consideration the conduction and stefan-Boltzman relation (radiation) to Lambert-Beer equation (external energy). The absorption and other optical and energetic factors are considered into this last equation.

Dear Franklin,

I understand the optical materials surface with some additional developments can be used to solve the problem of heat radiation transfer absorptivity, emissivity and some transmissivity.

Metamaterials are artificial structures (products of human ingenuity), may be designed to obtain controllable electromagnetic or optical properties. Multilayer insulation (also called superinsulation or multi-layer insulation are thermal irradiation or radiative emission barriers can be used in systems where insulation is needed in a vacuum environment. A high reflectivity and zero transmissivity implies a low emissivity according to the energy balance, resulting in equation

ρλ + λ + τλ = 1

Optical properties are a function of wavelength, directionality, and temperature. In the case of emission, it’s the temperature of the object. In the case of absorption, the temperature is that of the irradiating object. So the real, total, hemispherical emissivity is just the ratio of real emission to ideal blackbody emission at the temperature of the object’s surface. Optical properties may be directionally dependent so need to obtain directional emissivity curve for a dielectric with an index of refraction (In my opinion directional emissivity and specular, mirrorlike reflections should not be ignored). Modeling super insulation and floating shield model (some time it may suffer from heat sink but most of the time with good model it can work) may be helpful here. I must say optical property that refers to an optically thick layer can be aluminized so that absorptivity and transmission loss not occur.

Ashish

In the the Stefan-Boltzmann law , only one variable parameter is epsilon. This will come under heat exchange between surface. You need to feed the both the emissivity of surfaces which are considered.

Yes, please pay attention to the answer of Thomas Cuff .

Regards.

I agree with Dhinakaran answer