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A mathematical model for thermography on viscous fluid based on damped thermal flux

  • Qasim Ali , Samia Riaz , Aziz Ullah Awan und Kashif Ali Abro EMAIL logo
Veröffentlicht/Copyright: 25. Januar 2021
Zeitschrift für Naturforschung A
Aus der Zeitschrift Zeitschrift für Naturforschung A Band 76 Heft 3

Abstract

Thermography is a fully noninvasive technique that discerns the thermal profiles of highly viable rheological parameters in heat and mass transference. In this paper, the free convection flow of viscous fluid among two vertical and parallel plates in the existence of a transverse magnetic field is investigated. The Caputo time-fractional derivative is manipulated for introducing a thermal transport equation along with a weak memory. The analytical and closed-form fractional solution for the temperature and velocity profiles are obtained through Laplace paired in conjunction with the finite Sine-Fourier transforms technique. The solution to the classical model is concluded as a special case for the solutions to the fractional modeled problem when the memory factor (the order of fractional derivative) approaches 1. Also, the solutions are stated in connection with the Mittag–Leffler function. The influences of variations of fractional and material parameters are depicted through MathCad15.

Keywords: Caputo time-fractional derivative; damped thermal flux; free convective flow; magnetic field; viscous fluid
Corresponding author: Kashif Ali Abro, Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan; and Institute of Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] M. Narahari, “Natural convection in unsteady Couette flow between two vertical parallel plates in the presence of constant heat flux and radiation,” in MACMESE’09 Proceedings of the 11th WSEAS international conference on mathematical and computational methods in science and engineering, 2009, pp. 73–78.Suche in Google Scholar

[2] N. Ahmed and M. Dutta, “Transient mass transfer flow past an impulsively started infinite vertical plate with ramped plate velocity and ramped temperature,” Int. J. Phys. Sci., vol. 8, no. 7, pp. 254–263, 2013.10.12988/ams.2013.13228Suche in Google Scholar

[3] C. Fetecau, N. A. Shah, and D. Vieru, “General solutions for hydromagnetic free convection flow over an infinite plate with Newtonian heating, mass diffusion and chemical reaction,” Commun. Theor. Phys., vol. 68, no. 6, p. 768, 2017.10.1088/0253-6102/68/6/768Suche in Google Scholar

[4] N. A. Shah, A. A. Zafar, and S. Akhtar, “General solution for MHD-free convection flow over a vertical plate with ramped wall temperature and chemical reaction,” Arab. J. Math., vol. 7, no. 1, pp. 49–60, 2018.10.1007/s40065-017-0187-zSuche in Google Scholar

[5] C. Fetecau, R. Ellahi, M. Khan, and N. A. Shah, “Combined porous and magnetic effects on some fundamental motions of Newtonian fluids over an infinite plate,” J. Porous Media, vol. 21, no. 7, pp. 589–605, 2018.10.1615/JPorMedia.v21.i7.20Suche in Google Scholar

[6] I. Khan, S. T. Saeed, M. B. Riaz, K. A. Abro, S. M. Husnine, and K. S. Nisar, “Influence in a Darcy’s medium with heat production and radiation on MHD convection flow via modern fractional approach,” J. Mater. Res. Technol., vol. 9, no. 5, pp. 10016–10030, 2020.10.1016/j.jmrt.2020.06.059Suche in Google Scholar

[7] Q. Ali, S. Riaz, and A. U. Awan, “Free convection MHD flow of viscous fluid by means of damped shear and thermal flux in a vertical circular tube,” Phys. Scripta, vol. 95, no. 9, p. 095212, 2020.10.1088/1402-4896/abab39Suche in Google Scholar

[8] C. Bernardi, B. Mtivet, and B. Pernaud-Thomas, “Pairing Navier–Stokes equations and heat: the model and its approximation by finite elements,” ESAIM Math. Model. Numer. Anal. Math. Model. Digit. Anal., vol. 29, no. 7, pp. 871–921, 1995.10.1051/m2an/1995290708711Suche in Google Scholar

[9] E. Maruic-Paloka and I. Paanin, “Non-isothermal fluid flow through a thin pipe with cooling,” Hist. Anthropol., vol. 88, no. 4, pp. 495–515, 2009.10.1080/00036810902889542Suche in Google Scholar

[10] E. Maruic-Paloka and I. Paanin, “On the effects of curved geometry on heat conduction through a distorted pipe,” Nonlinear Anal. R. World Appl., vol. 11, no. 6, pp. 4554–4564, 2010.10.1016/j.nonrwa.2008.09.016Suche in Google Scholar

[11] G. S. Seth, B. Kumbhakar, and R. Sharma, “Unsteady hydromagnetic natural convection flow of a heat absorbing fluid within a rotating vertical channel in porous medium with Hall effects,” J. Appl. Fluid Mech., vol. 8, no. 4, pp. 767–779, 2015.10.18869/acadpub.jafm.67.223.22918Suche in Google Scholar

[12] G. S. Seth, S. Sarkar, and O. D. Makinde, “Combined free and forced convection Couette–Hartmann flow in a rotating channel with arbitrary conducting walls and Hall effects,” J. Mech., vol. 32, no. 5, pp. 613–629, 2016.10.1017/jmech.2016.70Suche in Google Scholar

[13] G. Seth, R. Sharma, and B. Kumbhakar, “Effects of Hall current on unsteady MHD convective Couette flow of heat absorbing fluid due to accelerated movement of one of the plates of the channel in a porous medium,” J. Porous Media, vol. 19, no. 1, pp. 13–30, 2016.10.1615/JPorMedia.v19.i1.20Suche in Google Scholar

[14] G. S. Seth and J. K. Singh, “Mixed convection hydromagnetic flow in a rotating channel with Hall and wall conductance effects,” Appl. Math. Model., vol. 40, no. 4, pp. 2783–2803, 2016.10.1016/j.apm.2015.10.015Suche in Google Scholar

[15] M. Narahari, “Transient free convection flow between long vertical parallel plates with ramped wall temperature at one boundary in the presence of thermal radiation and constant mass diffusion,” Meccanica, vol. 47, no. 8, pp. 1961–1976, 2012.10.1007/s11012-012-9567-9Suche in Google Scholar

[16] B. K. Jha, A. K. Singh, and H. S. Takhar, “Transient free-convective flow in a vertical channel due to symmetric heating,” Int. J. Appl. Mech. Eng., vol. 8, no. 3, pp. 497–502, 2003.Suche in Google Scholar

[17] K. Boulama and N. Galanis, “Analytical solution for fully developed mixed convection between parallel vertical plates with heat and mass transfer,” J. Heat Tran., vol. 126, no. 3, pp. 381–388, 2004.10.1115/1.1737774Suche in Google Scholar

[18] A. K. Singh and T. Paul, “Transient natural convection between two vertical walls heated/cooled asymmetrically,” Int. J. Appl. Mech. Eng., vol. 11, no. 1, pp. 143–154, 2006.Suche in Google Scholar

[19] A. Pantokratoras, “Fully developed laminar free convection with variable thermophysical properties between two open-ended vertical parallel plates heated asymmetrically with large temperature differences,” J. Heat Tran., vol. 128, no. 4, pp. 405–408, 2006.10.1115/1.2175154Suche in Google Scholar

[20] M. Narahari, “Oscillatory plate temperature effects of free convection flow of dissipative fluid between long vertical parallel plates,” Int. J. Appl. Math. Mech., vol. 5, no. 3, pp. 30–46, 2009.Suche in Google Scholar

[21] Schlichting, H., Gersten, K., Boundary-Layer Theory, 9th ed., Springer-Verlag, Berlin Heidelberg, 2016, https://doi.org/10.1007/978-3-662-52919-5.Suche in Google Scholar

[22] A. Atangana, “On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation,” Appl. Math. Comput., vol. 273, pp. 948–956, 2016.10.1016/j.amc.2015.10.021Suche in Google Scholar

[23] B. Ahmad, S. I. A. Shah, S. U. Haq, and N. A. Shah, “Analysis of unsteady natural convective radiating gas flow in a vertical channel by employing the Caputo time-fractional derivative,” Eur. Phys. J. Plus, vol. 132, no. 9, p. 380, 2017.10.1140/epjp/i2017-11651-1Suche in Google Scholar

[24] M. I. Asjad, N. A. Shah, M. Aleem, and I. Khan, “Heat transfer analysis of fractional second-grade fluid subject to Newtonian heating with Caputo and Caputo–Fabrizio fractional derivatives: a comparison,” Eur. Phys. J. Plus, vol. 132, no. 8, p. 340, 2017.10.1140/epjp/i2017-11606-6Suche in Google Scholar

[25] J. Hristov, “A transient flow of a non-Newtonian fluid modelled by a mixed time-space derivative: an improved integral-balance approach,” in Mathematical Methods in Engineering, Cham, Springer, 2018, pp. 153–174.10.1007/978-3-319-90972-1_11Suche in Google Scholar

[26] N. Ahmed, N. A. Shah, and D. Vieru, “Natural convection with damped thermal flux in a vertical circular cylinder,” Chin. J. Phys., vol. 56, no. 2, pp. 630–644, 2018.10.1016/j.cjph.2018.02.007Suche in Google Scholar

[27] N. Ahmed, D. Vieru, C. Fetecau, and N. A. Shah, “Convective flows of generalized time-nonlocal nanofluids through a vertical rectangular channel,” Phys. Fluids, vol. 30, no. 5, p. 052002, 2018.10.1063/1.5032165Suche in Google Scholar

[28] N. A. Shah, N. Ahmed, D. Vieru, and C. Fetecau, “Effects of double stratification and heat flux damping on convective flows over a vertical cylinder,” Chin. J. Phys., vol. 60, pp. 290–306, 2019.10.1016/j.cjph.2019.05.008Suche in Google Scholar

[29] A. Jajarmi, D. Baleanu, S. S. Sajjadi, and J. H. Asad, “A new feature of the fractional Euler-Lagrange equations for a coupled oscillator using a nonsingular operator approach,” Front. Phys., vol. 7, p. 196, 2019.10.3389/fphy.2019.00196Suche in Google Scholar

[30] D. Baleanu, S. S. Sajjadi, A. Jajarmi, and J. H. Asad, “New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator,” Eur. Phys. J. Plus, vol. 134, no. 4, p. 181, 2019.10.1140/epjp/i2019-12561-xSuche in Google Scholar

[31] A. U. Awan, N. A. Shah, N. Ahmed, Q. Ali, and S. Riaz, “Analysis of free convection flow of viscous fluid with damped thermal and mass fluxes,” Chin. J. Phys., vol. 60, pp. 98–106, 2019.10.1016/j.cjph.2019.05.006Suche in Google Scholar

[32] Q. Ali, S. Riaz, and A. U. Awan, “Thermal investigation for electrified convection flow of Newtonian fluid subjected to damped thermal flux on a permeable medium,” Phys. Scripta, vol. 95, p. 115003, 2020.10.1088/1402-4896/abbc2eSuche in Google Scholar

[33] N. Ullah, S. Nadeem, and A. U. Khan, “Finite element simulations for natural convective flow of nanofluid in a rectangular cavity having corrugated heated rods,” J. Therm. Anal. Calorim., pp. 1–13, 2020.10.1007/s10973-020-09378-4Suche in Google Scholar

[34] S. Ahmad and S. Nadeem, “Flow analysis by Cattaneo–Christov heat flux in the presence of Thomson and Troian slip condition,” Appl. Nanosci., vol. 10, pp. 4673–4687, 2020.10.1007/s13204-020-01267-4Suche in Google Scholar

[35] S. T. Saeed, M. B. Riaz, D. Baleanu, and K. A. Abro, “A mathematical study of natural convection flow through a channel with non-singular kernels: an application to transport phenomena,” Alex. Eng. J., vol. 59, no. 4, pp. 2269–2281, 2020.10.1016/j.aej.2020.02.012Suche in Google Scholar

[36] M. B. Riaz and N. Iftikhar, “A comparative study of heat transfer analysis of MHD Maxwell fluid in view of local and nonlocal differential operators,” Chaos Solit. Fractals, vol. 132, p. 109556, 2020.10.1016/j.chaos.2019.109556Suche in Google Scholar

[37] M. B. Riaz, A. Atangana, and N. Iftikhar, “Heat and mass transfer in Maxwell fluid in view of local and non-local differential operators,” J. Therm. Anal. Calorim., pp. 1–17, 2020.10.1007/s10973-020-09383-7Suche in Google Scholar

[38] D. Baleanu, A. Fernandez, and A. Akgul, “On a fractional operator combining proportional and classical differintegrals,” Mathematics, vol. 8, no. 3, p. 360, 2020.10.3390/math8030360Suche in Google Scholar

[39] K. A. Abro, “A fractional and analytic investigation of thermo-diffusion process on free convection flow: an application to surface modification technology,” Eur. Phys. J. Plus, vol. 135, no. 1, p. 31, 2020.10.1140/epjp/s13360-019-00046-7Suche in Google Scholar

[40] K. A. Abro and A. Atangana, “Role of non-integer and integer order differentiations on the relaxation phenomena of viscoelastic fluid,” Phys. Scripta, vol. 95, no. 3, p. 035228, 2020.10.1088/1402-4896/ab560cSuche in Google Scholar

[41] X. Wang, H. Xu, and H. Qi, “Transient magnetohydrodynamic flow and heat transfer of fractional Oldroyd-B fluids in microchannel with slip boundary condition,” Phys. Fluids, vol. 32, no. 10, p. 103104, 2020.10.1063/5.0025195Suche in Google Scholar

[42] X. Wang, H. Xu, and H. Qi, “Numerical analysis for rotating electro-osmotic flow of fractional Maxwell fluids,” Appl. Math. Lett., vol. 103, p. 106179, 2020.10.1016/j.aml.2019.106179Suche in Google Scholar

[43] J. Boussinesq, Théorie Analytique de la Chaleur, vol. II, Paris, Gauthier-Villars, Ed., 1903, p. 172.Suche in Google Scholar

[44] Y. Z. Povstenko, “Fractional heat conduction equation and associated thermal stress,” J. Therm. Stresses, vol. 28, no. 1, pp. 83–102, 2004.10.1080/014957390523741Suche in Google Scholar

[45] H. J. Haubold, A. M. Mathai, and R. K. Saxena, “Mittag-Leffler functions and their applications,” J. Appl. Math., vol. 2011, p. 298628, 2011.10.1155/2011/298628Suche in Google Scholar

[46] I. Q. Memon, K. A. Abro, M. A. Solangi, and A. A. Shaikh, “Functional shape effects of nanoparticles on nanofluid suspended in ethylene glycol through Mittage-Leffler approach,” Phys. Scripta, vol. 96, no. 2, p. 025005, 2020. https://doi.org/10.1088/1402-4896/abd1b3.Suche in Google Scholar

[47] K. A. Abro, A. Siyal, B. Souayeh, and A. Atangana, “Application of statistical method on thermal resistance and conductance during magnetization of fractionalized free convection flow,” Int. Commun. Heat Mass Tran., vol. 119, p. 104971, 2020. https://doi.org/10.1016/j.icheatmasstransfer.2020.104971.Suche in Google Scholar

[48] K. A. Abro, M. Soomro, A. Atangana, J. Francisco, and G. Aguilar, “Thermophysical properties of Maxwell nanofluids via fractional derivatives with regular kernel,” J. Therm. Anal. Calorim., 2020. https://doi.org/10.1007/s10973-020-10287-9.Suche in Google Scholar

[49] A. A. Kashif and A. Atangana, “Numerical and mathematical analysis of induction motor by means of AB-fractal–fractional differentiation actuated by drilling system,” Numer. Methods Part. Differ. Equ., pp. 1–15, 2020. https://doi.org/10.1002/num.22618.Suche in Google Scholar

[50] A. A. Kashif and B. Das, “A scientific report of non-singular techniques on microring resonators: an application to optical technology,” Optik Int. J. Light Electron Opt., vol. 224, p. 165696, 2020. https://doi.org/10.1016/j.ijleo.2020.165696.Suche in Google Scholar

[51] A. Yoku¸ H. Durur, K. Ali Abro, and D. Kaya, “Role of Gilson–Pickering equation for the different types of soliton solutions: a nonlinear analysis,” Eur. Phys. J. Plus, vol. 135, p. 657, 2020, https://doi.org/10.1140/epjp/s13360-020-00646-.Suche in Google Scholar

[52] K. Ali Abro, “A fractional and analytic investigation of thermo-diffusion process on free convection flow: an application to surface modification technology,” Eur. Phys. J. Plus, vol. 135, no. 1, pp. 31–45, 2020. https://doi.org/10.1140/epjp/s13360-019-00046-7.Suche in Google Scholar

[53] K. A. Abro and A. Atangana, “A comparative study of convective fluid motion in rotating cavity via Atangana–Baleanu and Caputo–Fabrizio fractal–fractional differentiations,” Eur. Phys. J. Plus, vol. 135, pp. 226–242, 2020. https://doi.org/10.1140/epjp/s13360-020-00136-x.Suche in Google Scholar

[54] K. A. Abro, A. Siyal, and A. Atangana, “Thermal stratification of rotational second-grade fluid through fractional differential operators,” J. Therm. Anal. Calorim., 2020. https://doi.org/10.1007/s10973-020-09312-8.Suche in Google Scholar

[55] A. A. Kashif and A. Atangana, “Role of non-integer and integer order differentiations on the relaxation phenomena of viscoelastic fluid,” Phys. Scripta, vol. 95, p. 035228, 2020. https://doi.org/10.1088/1402-4896/ab560c.Suche in Google Scholar

[56] K. A. Ali and A. Atangana, “Mathematical analysis of memristor through fractal?fractional differential operators: a numerical study,” Math. Methods Appl. Sci., pp. 1–18, 2020. https://doi.org/10.1002/mma.6378.Suche in Google Scholar

[57] K. A. Ali and A. Atangana, “Numerical study and chaotic analysis of meminductor and memcapacitor through fractal–fractional differential operator,” Arabian J. Sci. Eng., 2020. https://doi.org/10.1007/s13369-020-04780-4.Suche in Google Scholar

[58] A. A. Kashif and A. Abdon, “A comparative analysis of electromechanical model of piezoelectric actuator through Caputo–Fabrizio and Atangana–Baleanu fractional derivatives,” Math. Methods Appl. Sci., pp. 1–11, 2020. https://doi.org/10.1002/mma.6638.Suche in Google Scholar

[59] Q. Ali, S. Riaz, A. Ullah Awan, and K. Ali Abro, “Thermal investigation for electrified convection flow of Newtonian fluid subjected to damped thermal flux on a permeable medium,” Phys. Scripta, 2020. https://doi.org/10.1088/1402-4896/abbc2e.Suche in Google Scholar

[60] A. A. Kashif, “Role of fractal–fractional derivative on ferromagnetic fluid via fractal Laplace transform: a first problem via fractal–fractional differential operator,” Eur. J. Mech. B Fluid, vol. 85, pp. 76–81, 2021. https://doi.org/10.1016/j.euromechflu.2020.09.002.Suche in Google Scholar

[61] K. A. Abro, “Fractional characterization of fluid and synergistic effects of free convective flow in circular pipe through Hankel transform,” Phys. Fluids, vol. 32, p. 123102, 2020. https://doi.org/10.1063/5.0029386.Suche in Google Scholar

[62] K. A. Abro, M. Imran Qasim, and S. Ambreen, “Thermal transmittance and thermo-magnetization of unsteady free convection viscous fluid through non-singular differentiations,” Phys. Scripta, 2020. https://doi.org/10.1088/1402-4896/abc981.Suche in Google Scholar

Received: 2020-11-17
Accepted: 2021-01-04
Published Online: 2021-01-25
Published in Print: 2021-03-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. General
  3. Remarks on axion-electrodynamics
  4. Dynamical Systems & Nonlinear Phenomena
  5. Interaction of waves in one-dimensional dusty gas flow
  6. On the ferrofluid lubricated exponential squeeze film-bearings
  7. Modeling and simulation of capillary ridges on the free surface dynamics of third-grade fluid
  8. Hydrodynamics
  9. Ternary-hybrid nanofluids: significance of suction and dual-stretching on three-dimensional flow of water conveying nanoparticles with various shapes and densities
  10. Solid State Physics & Materials Science
  11. Electronic and magnetic properties of Fe-doped GaN: first-principle calculations
  12. Genetic evolutionary approach for surface roughness prediction of laser sintered Ti–6Al–4V in EDM
  13. Thermodynamics & Statistical Physics
  14. Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field
  15. A mathematical model for thermography on viscous fluid based on damped thermal flux
https://doi.org/10.1515/zna-2020-0322
Schlagwörter für diesen Artikel
Caputo time-fractional derivative; damped thermal flux; free convective flow; magnetic field; viscous fluid

Artikel in diesem Heft

  1. Frontmatter
  2. General
  3. Remarks on axion-electrodynamics
  4. Dynamical Systems & Nonlinear Phenomena
  5. Interaction of waves in one-dimensional dusty gas flow
  6. On the ferrofluid lubricated exponential squeeze film-bearings
  7. Modeling and simulation of capillary ridges on the free surface dynamics of third-grade fluid
  8. Hydrodynamics
  9. Ternary-hybrid nanofluids: significance of suction and dual-stretching on three-dimensional flow of water conveying nanoparticles with various shapes and densities
  10. Solid State Physics & Materials Science
  11. Electronic and magnetic properties of Fe-doped GaN: first-principle calculations
  12. Genetic evolutionary approach for surface roughness prediction of laser sintered Ti–6Al–4V in EDM
  13. Thermodynamics & Statistical Physics
  14. Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field
  15. A mathematical model for thermography on viscous fluid based on damped thermal flux
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