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Effects of nonlinear optical parameters on the thermal performance of an indirect solar dryer under natural convection regime

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Abstract

Numerical analyses have been performed in order to understand the thermal behavior of an indirect solar dryer. However, not much attention has been given to the nonlinear optical properties influence on its dynamic. This paper studies the effect of nonlinear absorption and transmission parameters on the thermal performance of an indirect solar dryer. The main goal was to improve the output energy of collector and drying chamber. The nonlinear absorption and transmission coefficients are established as quadratic functions of the temperature. Theoretical investigations are conducted for the proposed nonlinear model. On the basis of these investigations, the established mathematical equations describing the solar drying system are solved numerically using a developed MATLAB program. A specific application is first made for constant absorption coefficient distribution and the predictions are in excellent agreement with the experimental results from the literature. Predictions of nonlinear optical absorption and transmission coefficients variation are then performed. A comparison of the results with constant and nonlinear absorptivity and transmissivity shows a significant 10% enhancement of the collector thermal performance by using nonlinear parameters.

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Abbreviations

\({c}_{pi}\) :

Specific heat of the element \(\left\{i\right\}\) (J/Kg °C)

\({h}_{di\_j}\) :

Sonduction heat transfer coefficient between the surface \(\left\{i\right\}\) and the surface \(\left\{j\right\}\) (W/m2 °C)

\({h}_{ci\_j}\) :

Convection heat transfer coefficient between element \(\left\{i\right\}\) and element \(\left\{j\right\}\) (W/m2 °C)

\({h}_{ri\_j}\) :

Radiation heat transfer coefficient between the surface \(\left\{i\right\}\) and the surface \(\left\{j\right\}\) (W/m2 °C)

i:

Space node along the collector length

j:

Space node along the drying unit height

k:

Time node

\(L\) :

Length (m)

\(l\) :

Width (m)

\({m}_{i}\) :

Masse of element \(\left\{i\right\}\) (Kg)

\(n\) :

Degree of the quadratic nonlinear property

\({N}_{u}\) :

Nusselt number (dimensionless)

\(Q\) :

Air flowing rate (Kg/s)

\({S}_{i}\) :

Surface of element \(\left\{i\right\}\) (m2)

\({T}_{S}\) :

Temperature of the sun (°C)

\({T}_{0}\) :

Temperature of the soil surface (°C)

\({T}_{1}\) :

Temperature of the sky (°C)

\({T}_{2}\) :

Ambient air temperature (°C)

\({T}_{3}\) :

Temperature of the first glass cover (°C)

\({T}_{4}\) :

Temperature of the second glass cover (°C)

\({T}_{5}\) :

Temperature of the outlet air (°C)

\({T}_{6}\) :

Temperature of the first absorber plate (°C)

\({T}_{7}\) :

Temperature of the second absorber plate (°C)

\({T}_{8}\) :

Temperature of the inlet air (°C)

\({T}_{9}\) :

Temperature of the aluminium plate (°C)

\({T}_{10}\) :

Temperature of insulating material (°C)

\({T}_{11}\) :

Temperature of bottom surface of the collector (°C)

\({T}_{12}\) :

Drying air temperature (°C)

\({T}_{13}\) :

Internal dryer wall temperature (°C)

\({T}_{14}\) :

Drying unit insulator material temperature (°C)

\({T}_{15}\) :

External dryer wall temperature (°C)

\({T}_{16}\) :

Top dryer outer wall temperature (°C)

\({T}_{17}\) :

Top dryer inner plate temperature (°C)

\({T}_{18}\) :

Bottom dryer inner plate temperature (°C)

\({T}_{19}\) :

Bottom dryer outer plate temperature (°C)

\(t\) :

Time (s)

\(V\) :

Air speed (m/s)

x, y:

Space coordinate (m

\(\alpha\) :

Absorptivity

\(\gamma\) :

Constant parameter (1/°C)

\(\beta\) :

Constant parameter (1/ °C 2)

\(\delta\) :

Thickness (m)

\(\Theta\) :

Inclination of the glass cover (°)

\(\varepsilon\) :

Emissivity

\(\eta\) :

Efficiency

\(\rho\) :

Density (kg/m3)

\(\lambda\) :

Conductivity (W/m °C)

\(\sigma\) :

Stephan Boltzman constant (W/m2 K4)

\(\tau\) :

Transmissivity

\(avr\) :

Average

\(max\) :

Maximum

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Authors and Affiliations

  1. Department of Physics, University of Dschang, Dschang, Cameroon

    Carine Pamela Aghogue Donchi, Ernest Léontin Lemoubou & Hervé Thierry Tagne Kamdem

  2. Institute of Technology Fotso-Victor Bandjoun, Department of Physics, Bandjoun, Cameroon

    René Tchinda

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  1. Carine Pamela Aghogue Donchi
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  2. Ernest Léontin Lemoubou
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  3. Hervé Thierry Tagne Kamdem
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Correspondence to Carine Pamela Aghogue Donchi.

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Donchi, C.P.A., Lemoubou, E.L., Kamdem, H.T.T. et al. Effects of nonlinear optical parameters on the thermal performance of an indirect solar dryer under natural convection regime. Heat Mass Transfer 58, 1723–1737 (2022). https://doi.org/10.1007/s00231-022-03198-y

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