Numerical modelling of study the effect of the entrainment velocity, the number of Nusselt and the thickness of the non-convective zone on the stability of the pond solar

Year 2021, Volume: 50 Issue: 4, 918 - 933, 06.08.2021

Sabrina Gheraibia , Amar Guesmıa

https://doi.org/10.15672/hujms.816059

Abstract

In this paper, the effect of the entrainment velocity, the Nusselt number, and the thickness of the salinity gradient zone $(NCZ)$ on the stability of the solar pond are studied. The modelling equations of thermal energy and mass transfer in a salt gradient solar pond are discretized by finite difference methods in the transient regime. A new border condition applicable near the equilibrium of interface between the $(NCZ)$ and the $(LCZ)$ region is proposed. We take account of the effects of both turbulent entrainment and diffusion on the growth or erosion of the gradient zone $(NCZ)$. The obtained numerical results show an additional condition of solar pond's stability which links between the salinity gradient $\left( \Delta C\right) \ $ and the temperature gradient $\left( \Delta T\right)$ in the $(NCZ)$ region.

Keywords

Solar pond , Entrainment velocity , Finite difference method

References

• [1] Z. Ayati and J. Biazar, On the convergence of the homotopy perturbation method, J. Egyptian Math. Soc. 23 (2), 424–428, 2015.
• [2] P.K. Bansal and N.D. Kaushika, Salt gradient stabilized solar pond collector, Energy Convers. Manag. 21, 81–95, 1981.
• [3] R.S. Beniwal and R. Singh, Calculation of thermal efficiency of salt-gradient solar ponds, Heat Recov. Syst. CHP, 7 (6), 497–516, 1987.
• [4] T.L. Bergman, F.P. Incropera and R. Viskanta. A multi-layer model for mixing layer development in a double diffusive thermohaline system heated from below, Int. J. Heat Mass Transf. 25, 1411–1418, 1982.
• [5] F. Bernad, S. Casas, O. Gibert, A. Akbarzadeh, J.L. Cortina and C. Valderrama, Salinity gradient solar pond: Validation and simulation model, Sol. Energy 98, 366– 374, 2013.
• [6] R. Boudhiaf, A.B. Moussa and M. Baccar, A two-dimensional numerical study of hydrodynamic, heat and mass transfer and stability in a salt gradient solar pond, Energies 5 (12), 3986-4007, 2012.
• [7] G. Boyle, Renewable Energy: Power for a Sustainable Future, 2nd ed., Oxford, UK: Oxford University Press, 2004.
• [8] M.M. Dah, Etude numerique et experimentale de la stabilité des etangs solaires a gradient de sel, PhD. Thesis, University of Tunisia El Manar, 2010.
• [9] A. Defant, Physical Oceanography, Pergamon Press, Oxford, UK, 1961.
• [10] D. Gonzalez, J. Amigo, S. Lorente, A. Bejan and F.Suarez, Constructal design of salt gradient solar pond fields, Int. J. Energy Res. 10, 1428–1446, 2016.
• [11] A. Guesmia and N. Daili, Finite volume approximation of stationary Burgers equation, J. Anal. Appl. 6 (3), 179–193, 2008.
• [12] A. Guesmia and N. Daili, Approche numérique de la solution entropique de l’équation d’évolution de Bürgers par la méthode des lignes, Gen. Math. Sci. 17 (2), 99–111, 2009.
• [13] A. Guesmia and N. Daili, Numerical approximation of fractional Burgers equation, Commun. Math. Appl. 1 (3), 1–16, 2010.
• [14] J.R. Hull, C.E. Nielsen and P. Golding, Salinity-gradient solar ponds, CRC Press, Boca Raton, FL, 1989.
• [15] P.D. Lax and R.D. Richtmyer, Survey of the stability of linear finite difference equations, Comm. Pure Appl. Math. 9, 267–293, 1956.
• [16] M.M. Ould Dah, M.Ouni, A. Guizani and A. Belghith, The influence of the heat extraction mode on the performance and stability of a mini solar pond, Appl. Energy 87, 3005–3010, 2010.
• [17] A. Rabl and C.E. Nielson, Solar ponds for space heating, Sol. Energy 17, 1-12, 1975.
• [18] K.R. Sreenivas, J.H. Arakeri and J. Srinivasan, Modeling of the dynamics of the mixed layer in solar ponds, Sol. Energy 54 (3), 193–202, 1995.
• [19] M. Turkyilmazoglu, An effective approach for approximate analytical solutions of the damped Duffing equation, Phys. Scr. 86, 015301, 2012.
• [20] M. Turkyilmazoglu, Is homotopy perturbation method the traditional Taylor series expansion, Hacet. J. Math. Stat. 44 (3), 651–657, 2015.
• [21] M. Turkyilmazoglu, Convergence accelerating in the homotopy analysis method: a new approach, Adv. Appl. Math. Mech. 10 (4), 925–947, 2018.
• [22] M. Turkyilmazoglu, A simple algorithm for high order Newton iteration formulae and some new variants, Hacet. J. Math. Stat. 49 (1), 425–438, 2020.
• [23] Y.F. Wang and A.A. Akbarzadeh, A parametric study on solar ponds, Sol. Energy 30, 555–562, 1983.
• [24] H. Wang, M. Xie and W. Sun, Nonlinear dynamic behavior of non-convective zone in salt gradient solar pond, Sol. Energy 85, 1745–1757, 2011.
• [25] H. Xu, Laboratory studies on dynamical process in salinity gradient solar pond, Ph.D. Thesis, Ohio State University, 1990.
• [26] F. Zangrando and H.J.S. Femando, A predictive model for migration of doublediffusive interfaces, Sol. Energy 113, 59–65, 1991.