Numerical-experimental evaluation of FRESNEL lens heating dynamics

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ORIGINAL

Numerical-experimental evaluation of FRESNEL lens heating dynamics Dayana D’Arc de Fátima Palhares 1 & Bruna Sene Alves Araújo 1 & Érica Victor de Faria 1 & Luiz Gustavo Martins Vieira 1 Received: 6 April 2020 / Accepted: 16 July 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract Fresnel lenses allow the concentration of sunlight that can be employed in different thermal unitary operations or endothermic chemical transformations. A system with Fresnel lenses should also take into account vessel or reactor surface thermal losses (reflection, convection and emission), as well as the thermal energy required to keep the vessel or reactor structure warm. In this paper, a numerical and experimental analysis indicated that the solar radiation incident on the lens, the Fresnel lens area and the specimen mass can be represented by a grouping called Heating Factor (31 ≤ Ψ (W/kg) ≤ 3347). The Heating Factor (Ψ) was strongly correlated with the maximum temperature conductive specimens could reach when inserted at the focal point of a Fresnel Lens. Equilibrium Temperatures were predicted by a physical-mathematical model and validated by experimental tests. The Fresnel lens system has been shown to be able of providing Equilibrium Temperatures from 345 to 1600 K for specimens with Heating Times between 3 and 85 min and Initial Thermal Rates from 1.16 to 312.00 K/min. Numerical-experimental analyses also showed that the heating dynamic was strongly influenced by the nature of the materials that constituted the specimens (specific mass and the specific heat). Nomenclature a parameter adjusted for Equilibrium Temperature Eq. (K kgm/Wm). ac gravitational acceleration (m/s2). ai linear effects (i = 1..3) of variables on Equilibrium Temperature (K). Aij nonlinear effects (i,j = 1..3) of variables on Equilibrium Temperature (K). aS surface area of specimen (m2). AL Fresnel lens useful area (m2). b parameter adjusted for Heating Time Equation (min). bi linear effects (i = 1..3) of variables on Heating Time (min).

Bij ci Cij cPF cPS D f FS → ∞ g G

* Luiz Gustavo Martins Vieira [email protected] Dayana D’Arc de Fátima Palhares [email protected] Bruna Sene Alves Araújo [email protected] Érica Victor de Faria [email protected] 1

Faculty of Chemical Engineering, Federal University of Uberlândia, Uberlândia, MG, Brazil

h H kF kS ℓ L m n M

nonlinear effects (i, j = 1..3) of variables on Heating Time (min). linear effects (i = 1..3) of variables on the Initial Thermal Rate (K/min). nonlinear effects (i, j = 1..3) of variables on the Initial Thermal Rate (K/min). specific heat of the fluid (J/kg K). specific heat of the specimen (J/kg K). sphere diameter (m). parameter adjusted for Initial Thermal Rate Eq. (K kgg/min Wg). form factor between specimen and environment (−). parameter adjusted for Initial Thermal Rate Equation (−). incident solar radiation on the top of the Fresnel lens (W/m2). convective heat transfer coefficients (W/m2K). height of the aluminum frame experimental unit (m). flu