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APPLICATION OF THE CONTINUOUS (NON-DISCRETE) LAPLACE TRANSFORM FOR SOLVING A MATHEMATICAL MODEL IN SOLAR ENERGY
Keywords:
non-discrete Laplace transform, analytic solution, solar energy.DOI:
https://doi.org/10.17654/0974165823005Abstract
The discrete (noncontinuous) and the continuous (non-discrete) Laplace transforms are effective tools to solve linear difference equations and differential equations (ordinary or partial) with constant coefficients, respectively. The present work applies the continuous (non-discrete) Laplace transform on a system of linear partial differential equations (PDEs) describing a solar collector. The analytic solution is determined in explicit form in terms of some entire special functions. Numerical calculations are accomplished and illustrated through graphs and tables.
Received: November 12, 2022;
Revised: December 10, 2022;
Accepted: December 24, 2022;
References
S. U. S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, FED231/MD 66, 1995, pp. 99-105.
J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Transfer 128 (2006), 240-250.
R. K. Tiwari and M. K. Das, Heat transfer augmentation in a two sided lid driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer 50 (2007), 2002-2018.
A. Ebaid, F. Al Mutairi and S. M. Khaled, Effect of velocity slip boundary condition on the flow and heat transfer of Cu-water and -water nanofluids in the presence of a magnetic field, Adv. Math. Phys. 2014, Article ID 538950, 9 pp. http://dx.doi.org/10.1155/2014/538950.
Fahd Almutairi, S. M. Khaled and Abdelhalim Ebaid, MHD flow of nanofluid with homogeneous-heterogeneous reactions in a porous medium under the influence of second-order velocity slip, Mathematics 7(3) (2019), 220.
doi:10.3390/math7030220.
E. R. El-Zahar, A. F. Aljohani, W. Alharbi and A. Ebaid, Exact solution of non-Newtonian blood flow with nanoparticles through porous arteries: a comparative study, Computers, Materials & Continua 63(3) (2020), 1143-1157.
Y. R. Sekhar, K. V. Sharma and S. Kamal, Nanofluid heat transfer under mixed convection flow in a tube for solar thermal energy applications, Environ. Sci. Pollut. Res. 23 (2016), 9411-9417. https://doi.org/10.1007/s11356-015-5715-9.
N. A. Sheikh, F. Ali, I. Khan and M. Gohar, A theoretical study on the performance of a solar collector using and water based nanofluids with inclined plate: Atangana-Baleanu fractional model, Chaos Solitons Fractals 115 (2018), 135-142.
R. Mehmood, Rabil Tabassum, S. Kuharat, O. Anwar Bég and M. Babaie, Thermal slip in oblique radiative nano-polymer gel transport with temperature-dependent viscosity: solar collector nanomaterial coating manufacturing simulation, Arabian Journal for Science and Engineering 44 (2019), 1525-1541. https://doi.org/10.1007/s13369-018-3599-y.
A. M. Norouzi, M. Siavashi and M. Khaliji Oskouei, Efficiency enhancement of the parabolic trough solar collector using the rotating absorber tube and nanoparticles, Renew. Energy 145 (2020), 569-584.
http://dx.doi.org/10.1016/j.renene.2019.06.027.
S. E. Ghasemi and M. Hatami, Solar radiation effects on MHD stagnation point flow and heat transfer of a nanofluid over a stretching sheet, Case Studies in Thermal Engineering 25 (2021), 100898.
https://doi.org/10.1016/j.csite.2021.100898.
E. A. C. Panduro, F. Finotti, G. Largiller and K. Y. Lervåg, A review of the use of nanofluids as heat-transfer fluids in parabolic-trough collectors, Applied Thermal Engineering 211 (2022), 118346.
G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Acad., Boston, MA, USA, 1994.
A. M. Wazwaz, Adomian decomposition method for a reliable treatment of the Bratu-type equations, Appl. Math. Comput. 166 (2005), 652-663.
A. Ebaid, Approximate analytical solution of a nonlinear boundary value problem and its application in fluid mechanics, Z. Naturforschung A 66 (2011), 423-426.
J. S. Duan and R. Rach, A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations, Appl. Math. Comput. 218 (2011), 4090-4118.
A. Ebaid, A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method, J. Comput. Appl. Math. 235 (2011), 1914-1924.
J. Diblík and M. Kúdelcíková, Two classes of positive solutions of first order functional differential equations of delayed type, Nonlinear Anal. 75 (2012), 4807-4820.
A. Ebaid, M. D. Aljoufi and A.-M. Wazwaz, An advanced study on the solution of nanofluid flow problems via Adomian’s method, Appl. Math. Lett. 46 (2015), 117-122.
S. Bhalekar and J. Patade, An analytical solution of Fisher’s equation using decomposition method, Am. J. Comput. Appl. Math. 6 (2016), 123-127.
A. Alshaery and A. Ebaid, Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method, Acta Astronautica 140 (2017), 27-33.
H. O. Bakodah and A. Ebaid, The Adomian decomposition method for the slip flow and heat transfer of nanofluids over a stretching/shrinking sheet, Rom. Rep. Phys. 70 (2018), 115.
H. O. Bakodah and A. Ebaid, Exact solution of Ambartsumian delay differential equation and comparison with Daftardar-Gejji and Jafari approximate method, Mathematics 6 (2018), 331.
A. Ebaid, A. Al-Enazi, B. Z. Albalawi and M. D. Aljoufi, Accurate approximate solution of Ambartsumian delay differential equation via decomposition method, Math. Comput. Appl. 24(1) (2019), 7.
A. Patra and S. Saha Ray, Homotopy perturbation Sumudu transform method for solving convective radial fins with temperature-dependent thermal conductivity of fractional order energy balance equation, Int. J. Heat and Mass Transfer 76 (2014), 162-170.
A. Ebaid, Remarks on the homotopy perturbation method for the peristaltic flow of Jeffrey fluid with nano-particles in an asymmetric channel, Comput. Math. Appl. 68(3) (2014), 77-85.
Z. Ayati and J. Biazar, On the convergence of homotopy perturbation method, J. Egypt. Math. Soc. 23 (2015), 424-428.
A. A. Alatawi, M. Aljoufi, F. M. Alharbi and A. Ebaid, Investigation of the surface brightness model in the milky way via homotopy perturbation method, J. Appl. Math. Phys. 8(3) (2020), 434-442.
S. M. Khaled, E. R. El-Zahar and A. Ebaid, Solution of Ambartsumian delay differential equation with conformable derivative, Mathematics 7 (2019), 425.
S. M. Khaled, A. Ebaid and F. Al Mutairi, The exact endoscopic effect on the peristaltic flow of a nanofluid, J. Appl. Math. Volume 2014, Article ID 367526, 11 pages. http://dx.doi.org/10.1155/2014/367526.
A. Ebaid and M. Al Sharif, Application of Laplace transform for the exact effect of a magnetic field on heat transfer of carbon-nanotubes suspended nanofluids, Z. Nature. A 70(6) (2015), 471-475.
A. Ebaid, A. M. Wazwaz, E. Alali and B. Masaedeh, Hypergeometric series solution to a class of second-order boundary value problems via Laplace transform with applications to nanofluids, Commun. Theor. Phys. 67 (2017), 231.
H. Saleh, E. Alali and A. Ebaid, Medical applications for the flow of carbon-nanotubes suspended nanofluids in the presence of convective condition using Laplace transform, J. Assoc. Arab Univ. Basic Appl. Sci. 24 (2017), 206-212.
A. Ebaid, E. Alali and H. Saleh, The exact solution of a class of boundary value problems with polynomial coefficients and its applications on nanofluids, J. Assoc. Arab Univ. Basic Appl. Sci. 24 (2017), 156-159.
S. M. Khaled, The exact effects of radiation and Joule heating on magnetohydrodynamic Marangoni convection over a flat surface, Therm. Sci. 22 (2018), 63-72.
H. S. Ali, E. Alali, A. Ebaid and F. M. Alharbi, Analytic solution of a class of singular second-order boundary value problems with applications, Mathematics 7 (2019), 172. https://doi.org/10.3390/math7020172.
A. Ebaid, W. Alharbi, M. D. Aljoufi and E. R. El-Zahar, The exact solution of the falling body problem in three-dimensions: comparative study, Mathematics 8(10) (2020), 1726. https://doi.org/10.3390/math8101726.
A. F. Aljohani, A. Ebaid, E. A. Algehyne, Y. M. Mahrous, P. Agarwal, M. Areshi and H. K. Al-Jeaid, On solving the chlorine transport model via Laplace transform, Scientific Reports 12 (2022), 12154.
https://doi.org/10.1038/s41598-022-14655-3.
M. R. Spiegel, Laplace Transforms, McGraw-Hill Inc., 1965.
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