International Journal of Applied Mathematics and Theoretical Physics

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Thermophoresis and Viscous Dissipation Effect of Free Convective Boundary Layer Flow over a Porous Medium: Spectral Homotopy Analysis

Received: Mar. 10, 2022    Accepted: Jul. 11, 2022    Published: Aug. 17, 2022
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Abstract

In this study, an investigation is made into the effects of thermophoresis and viscous dissipation on chemically steady hydromagnetic free convective boundary layer flow in a porous media. A mathematical model was designed to govern the flow used in the study of the effects of chemical reaction, magnetic field, viscous dissipation, and thermophoresis on free convective boundary layer flow of an incompressible, electrically conducting fluid past a heated vertical permeable flat plate embedded in a uniform porous medium. This flow is observed as it moves past the plate, which is embedded in a uniform porous medium. The governing equations and their related boundary conditions have been converted into dimensionless equations by using the similarity transformations. These dimensionless equations are a boundary valued problem of coupled ordinary differential equations, and they have been solved by employing the Spectral Homotopy Analysis Method, which is a numerical approach of the traditional Homotopy Approximate Method (HAM). The Chebyshev-Gauss-Lobatto points are used to discretize the spatial domains, and numerical computation is used to determine the non-dimensional properties of the physical parameters. The SHAM solution series converges to the numerical solution with an accuracy of up to six decimal places, as demonstrated by our simulations. A parametric investigation of some of the parameters that are available is carried out, and the results for velocity, temperature, and concentration are graphically displayed, in addition to the discussion of the physical components of the issue. When the computational results from SHAM and those from the literature are compared to one another, they show a good degree of agreement with one another. It has been determined that the flow parameters have a significant impact on the flow profiles, and this connection has been investigated in depth. Findings that are really significant.

DOI 10.11648/j.ijamtp.20220802.11
Published in International Journal of Applied Mathematics and Theoretical Physics ( Volume 8, Issue 2, June 2022 )
Page(s) 30-42
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Thermophoresis, Viscous Dissipation, Porous Medium, Magnetic Effect, Chemical Reaction, Spectral Homotopy Analysis Method (SHAM)

References
[1] S. L. Goren: Thermophoresis of Aerosol Particles in the Laminar Boundary Layer on a Flat Plate. J. Colloid Interface Sci. Vol. (61), 77-85, (1977).
[2] B. Chandra and M. Kumar: The Combined Effect of Chemical Reaction, Radiation on Heat and Mass Transfer along a Continuously Moving Surface in Presence of Thermophoresis. Journal of Applied Fluid Mechanics Vol. (6) 3, 351-356, (2013).
[3] M. S. Alam, M. M. Rahman and M. A. Sattar: Transient Magnetohydrodynamic Free Convective Heat and Mass Transfer Flow with Thermophoresis past a Radiate Inclined Permeable Plate in the Presence of Variable Chemical Reaction and Temperature Dependent Viscosity Nonlinear Analysis: Modelling and Control Vol. (14) 1, 3-20, (2009).
[4] U. N. Das, R. K. Deka and V. M. Soundalgekar: Effects of Mass Transfer on Flow Past an Impulsively started Infinite Vertical Plate with Constant Heat Flux and Chemical reaction. Forschung in Inge-Engg Research Vol. (60), 284-287, (1994).
[5] S. P. Anjali devi and R. Kandasamy: Effects of a chemical reaction heat and mass transfer on MHD flow past a semi-infinite plate. Z. Angew. Math. Mech. Vol. (80), 697-701, (2000).
[6] R. Kandasamy, K. Periasamy and K. K. S. Prabhu: Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects. International Journal Heat and Mass Transfer Vol. (48) 21-22, 4557- 4561, (2005).
[7] M. Q. Al-Odat and Al-Azab: Influence of chemical reaction on transient MHD free convection over a moving vertical plate. Emirates Journal of Engineering Research Vol. (12) 3, 15-21, (2007).
[8] S. Ahmed: Influence of chemical reaction on transient MHD free Convective flow over a vertical plate in slipflow Regime. Emirates Journal for Engineering Research Vol. (15) 1, 25-34, (2010).
[9] R. N. Jat and S. Chaudhary: Hydromagnetic Flow and heat transfer on a continuously moving surface. Applied Mathematical Sciences Vol. (4) 2, 65-78, (2010).
[10] B. Gebhart B: Effects of viscous dissipation in natural convection. Journal of Fluid Mechanics Vol. (14), 225- 232, (1962).
[11] H. G. Takhar and O. A. Beg: Effects of transverse magnetic field, Prandtl number and Reynolds number on non-Darcy mixed convective flow of an incompressible viscous fluid past a porous vertical flat plate in a saturated porous medium. International Journal of Energy Research. Vol. (21), 87-100, (1997).
[12] P. V. S. N. Murthy and P. Singh: Effect of viscous dissipation on a non-Darcy natural convection regime. International Journal of Heat and Mass Transfer Vol. (40), 1251-1260, (1997).
[13] D. A. S. Rees, E. Magyari, and B. Keller: The development of the asymptotic viscous dissipation profile in a vertical free convective boundary layer flow in a porous medium. Transport in Porous Media Vol (53), 347-355, (2003).
[14] D. A. Nield: The modeling of viscous dissipation in a saturated porous medium. Journal of Heat Transfer Vol. (129) 1459, (2007).
[15] P. Loganathan, Arasu P. Puvi: Thermophoresis effects on non-darcy mhd mixed convective heat and mass transfer past a porous wedge in the presence of suction/ injection. Theoret. Appl. Mech., 37 (3), 203-227, (2010).
[16] A. Mahdy: Thermophoresis particle deposition and variable viscosity effects on non-darcy free convection in a fluid saturated porous media with uniform suction/injection. Latin America Applied Research Vol. (43), 113-119, (2013).
[17] Felix Ilesanmi Alao, Chika Uchechukwu Boneze, Adeyemi Isaiah Fagbade. Soret and Dufour Effects on Heat and Mass Transfer of Boundary Layer Flow over Porous Wedge with Thermal Radiation: Bivariate Spectral Relaxation Method. American Journal of Chemical Engineering. Vol. 7, No. 1, 2019, pp. 7-21. doi: 10.11648/j.ajche.20190701.12.
[18] Muhaimin I., Kandasamy R. and Kamis A. B.: Thermophoresis and chemical reaction effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of suction. Latin America Applied Research 40 (2), ISSN 1851-8796, (2008).
[19] N. Kishan and S. Maripala: Thermophoresis and viscous dissipation effects on darcy-forcheimer MHD mixed convection in a fluid saturated porous media. Advances in Applied Science Research Vol. (3), 60-74, (2012).
[20] A. I. Fagbade, B. O Falodun and C. U. Boneze: The influence of magnetic field, viscous dissipation, and thermophoresis on darcy-forcheimer mixed convection flow in fluid saturated porous media. American Journal of Computational Mathematics Vol. (5), 18-40. http://dx.doi.org/10.4236/ajcm.2015.51002, (2015).
[21] Talbot, L., Cheng, R. K., Scheffer, R. W. and Wills, D. R.: Thermophoresis of Particles in a Heated Boundary Layer. Journal of Fluid Mechanics Vol. (101), 737-758, (1980). http://dx.doi.org/10.1017/S0022112080001905.
[22] Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A.: Spectral Methods in Fluid Dynamics. SpringerVerlag, Berlin, (1988). http://dx.doi.org/10.1007/978-3-642-84108-8.
[23] Trefethen, L. N.: Spectral Methods in MATLAB. SIAM, Philadelphia, (2000), http://dx.doi.org/10.1137/1.9780898719598.
[24] Liao, S. J.: Beyond Perturbation: Introduction to the Homotopy Analysis Method. Chapman and Hall/CRC Press, Boca Raton, (2003). http://dx.doi.org/10.1201/9780203491164.
[25] Liao, S. J.: Homotopy Analysis Method in Nonlinear Differential Equations. Springer and Higher Education Press, Berlin Beijing, (2012). http://dx.doi.org/10.1007/978-3-642-25132-0.
[26] Motsa, S. S., Sibanda, P. and Shateyi, S.: A New Spectral-Homotopy Analysis Method for Solving a Nonlinear Second Order BVP. Communications in Nonlinear Science and Numerical Simulation, Vol. (15), 2293-2302, (2010). http://dx.doi.org/10.1016/j.cnsns.2009.09.019.
[27] Motsa, S. S., Sibanda, P., Awad, F. G. and Shateyi, S. A New Spectral-Homotopy Analysis Method for the MHD Jeffery-Hamel Problem. Computers and Fluids Vol. (39), 1219-1225, (2010).
[28] S. Y. Ibrahim and O. D. Makinde: Chemically reacting MHD boundary layer flow of heat and mass transfer over a moving vertical plate with suction. Scientific Research and Essays, 5 (19), 2875-2882, (2010).
[29] K. Gangadhar and N. Bhaskar Reddy: Chemically Reacting MHD Boundary Layer Flow of Heat and Mass Transfer over a Moving Vertical Plate in a Porous Medium with Suction. Journal of Applied Fluid Mechanics, Vol. 6, No. 1, pp. 107-114, (2013).
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    Chika Uchechukwu Boneze, Adeolu John Omowaye, Adeyemi Isaiah Fagbade, Ayodele Adedeji Ashefon. (2022). Thermophoresis and Viscous Dissipation Effect of Free Convective Boundary Layer Flow over a Porous Medium: Spectral Homotopy Analysis. International Journal of Applied Mathematics and Theoretical Physics, 8(2), 30-42. https://doi.org/10.11648/j.ijamtp.20220802.11

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    ACS Style

    Chika Uchechukwu Boneze; Adeolu John Omowaye; Adeyemi Isaiah Fagbade; Ayodele Adedeji Ashefon. Thermophoresis and Viscous Dissipation Effect of Free Convective Boundary Layer Flow over a Porous Medium: Spectral Homotopy Analysis. Int. J. Appl. Math. Theor. Phys. 2022, 8(2), 30-42. doi: 10.11648/j.ijamtp.20220802.11

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    AMA Style

    Chika Uchechukwu Boneze, Adeolu John Omowaye, Adeyemi Isaiah Fagbade, Ayodele Adedeji Ashefon. Thermophoresis and Viscous Dissipation Effect of Free Convective Boundary Layer Flow over a Porous Medium: Spectral Homotopy Analysis. Int J Appl Math Theor Phys. 2022;8(2):30-42. doi: 10.11648/j.ijamtp.20220802.11

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  • @article{10.11648/j.ijamtp.20220802.11,
      author = {Chika Uchechukwu Boneze and Adeolu John Omowaye and Adeyemi Isaiah Fagbade and Ayodele Adedeji Ashefon},
      title = {Thermophoresis and Viscous Dissipation Effect of Free Convective Boundary Layer Flow over a Porous Medium: Spectral Homotopy Analysis},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {8},
      number = {2},
      pages = {30-42},
      doi = {10.11648/j.ijamtp.20220802.11},
      url = {https://doi.org/10.11648/j.ijamtp.20220802.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijamtp.20220802.11},
      abstract = {In this study, an investigation is made into the effects of thermophoresis and viscous dissipation on chemically steady hydromagnetic free convective boundary layer flow in a porous media. A mathematical model was designed to govern the flow used in the study of the effects of chemical reaction, magnetic field, viscous dissipation, and thermophoresis on free convective boundary layer flow of an incompressible, electrically conducting fluid past a heated vertical permeable flat plate embedded in a uniform porous medium. This flow is observed as it moves past the plate, which is embedded in a uniform porous medium. The governing equations and their related boundary conditions have been converted into dimensionless equations by using the similarity transformations. These dimensionless equations are a boundary valued problem of coupled ordinary differential equations, and they have been solved by employing the Spectral Homotopy Analysis Method, which is a numerical approach of the traditional Homotopy Approximate Method (HAM). The Chebyshev-Gauss-Lobatto points are used to discretize the spatial domains, and numerical computation is used to determine the non-dimensional properties of the physical parameters. The SHAM solution series converges to the numerical solution with an accuracy of up to six decimal places, as demonstrated by our simulations. A parametric investigation of some of the parameters that are available is carried out, and the results for velocity, temperature, and concentration are graphically displayed, in addition to the discussion of the physical components of the issue. When the computational results from SHAM and those from the literature are compared to one another, they show a good degree of agreement with one another. It has been determined that the flow parameters have a significant impact on the flow profiles, and this connection has been investigated in depth. Findings that are really significant.},
     year = {2022}
    }
    

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    T1  - Thermophoresis and Viscous Dissipation Effect of Free Convective Boundary Layer Flow over a Porous Medium: Spectral Homotopy Analysis
    AU  - Chika Uchechukwu Boneze
    AU  - Adeolu John Omowaye
    AU  - Adeyemi Isaiah Fagbade
    AU  - Ayodele Adedeji Ashefon
    Y1  - 2022/08/17
    PY  - 2022
    N1  - https://doi.org/10.11648/j.ijamtp.20220802.11
    DO  - 10.11648/j.ijamtp.20220802.11
    T2  - International Journal of Applied Mathematics and Theoretical Physics
    JF  - International Journal of Applied Mathematics and Theoretical Physics
    JO  - International Journal of Applied Mathematics and Theoretical Physics
    SP  - 30
    EP  - 42
    PB  - Science Publishing Group
    SN  - 2575-5927
    UR  - https://doi.org/10.11648/j.ijamtp.20220802.11
    AB  - In this study, an investigation is made into the effects of thermophoresis and viscous dissipation on chemically steady hydromagnetic free convective boundary layer flow in a porous media. A mathematical model was designed to govern the flow used in the study of the effects of chemical reaction, magnetic field, viscous dissipation, and thermophoresis on free convective boundary layer flow of an incompressible, electrically conducting fluid past a heated vertical permeable flat plate embedded in a uniform porous medium. This flow is observed as it moves past the plate, which is embedded in a uniform porous medium. The governing equations and their related boundary conditions have been converted into dimensionless equations by using the similarity transformations. These dimensionless equations are a boundary valued problem of coupled ordinary differential equations, and they have been solved by employing the Spectral Homotopy Analysis Method, which is a numerical approach of the traditional Homotopy Approximate Method (HAM). The Chebyshev-Gauss-Lobatto points are used to discretize the spatial domains, and numerical computation is used to determine the non-dimensional properties of the physical parameters. The SHAM solution series converges to the numerical solution with an accuracy of up to six decimal places, as demonstrated by our simulations. A parametric investigation of some of the parameters that are available is carried out, and the results for velocity, temperature, and concentration are graphically displayed, in addition to the discussion of the physical components of the issue. When the computational results from SHAM and those from the literature are compared to one another, they show a good degree of agreement with one another. It has been determined that the flow parameters have a significant impact on the flow profiles, and this connection has been investigated in depth. Findings that are really significant.
    VL  - 8
    IS  - 2
    ER  - 

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Author Information
  • Department of Mathematics, University of Louisiana, Lafayette, U.S.A

  • Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria

  • Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria

  • Department of Mathematics, University of Louisiana, Lafayette, U.S.A

  • Section