Analysis of the magnetohydrodynamic flow in a porous medium

E. Arul Vijayalakshmi; S. S. Santra; T. Botmart; H. Alotaibi; G. B. Loganathan; M. Kannan; J. Visuvasam; V. Govindan; E. Arul Vijayalakshmi; S. S. Santra; T. Botmart; H. Alotaibi; G. B. Loganathan; M. Kannan; J. Visuvasam; V. Govindan

doi:10.3934/math.2022832

AIMS Mathematics

2022, Volume 7, Issue 8: 15182-15194. doi: 10.3934/math.2022832

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Research article

Analysis of the magnetohydrodynamic flow in a porous medium

1.
Department of Mathematics, Government Arts College, Ariyalur, Affiliated to Bharathidhasan University, Thiruchirappalli,Tamil Nadu, India
2.
Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal-741235, India
3.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
4.
Department of Mathematics and Statistics, College of Science, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia
5.
Department of Mechatronics Engineering, Tishk International University, Erbil, KRG, Iraq
6.
Department of Mathematics, Rathanavel Subramaniam College of Arts and Science, Sulur, Coimbatore-641402, Tamil Nadu, India
7.
Department of Mathematics, Dmi St John The Baptist University, Mangochi, Central Africa, Malawi-409

Received: 26 February 2022 Revised: 19 May 2022 Accepted: 06 June 2022 Published: 16 June 2022
MSC : 76W05, 76S05

This paper develops the combined effects of free convection magnetohydrodynamic (MHD) flow past a vertical plate embedded in a porous medium. The dimensionless coupled non-linear equations are solved to get the approximate analytical expression for the concentration by using the homotopy perturbation method. For all possible values of parameters, skin lubrication, Nusselt number and Sherwood number are derived.

Keywords:

Citation: E. Arul Vijayalakshmi, S. S. Santra, T. Botmart, H. Alotaibi, G. B. Loganathan, M. Kannan, J. Visuvasam, V. Govindan. Analysis of the magnetohydrodynamic flow in a porous medium[J]. AIMS Mathematics, 2022, 7(8): 15182-15194. doi: 10.3934/math.2022832

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Abstract

1. Introduction

The study on flow of fluids which are electrically conducting is known as magnetohydrodynamics (MHD). The magnetohydrodynamics have important applications in the polymer industry and engineering fields (Garnier ^[1]). Heat transfer caused by hydromagnetism was discussed by Chakrabarthi and Gupta ^[2]. Using an exponentially shrinking sheet, Nadeem et al. ^[3] investigated the MHD flow of a Casson fluid. Krishnendu Bhattacharyya ^[4] examined the effect of thermal radiation on MHD stagnation-point Flow over a Stretching Sheet.

Mixed convection magnetohydrodynamics flow is described by Ishak on a vertical and on a linearly stretching sheet ^[5,6,7]. Hayat et al. ^[10] examine a mixed convection flow within a stretched sheet of Casson nanofluid. Subhas Abel and Monayya Mareppa, examine magnetohydrodynamics flow on a vertical plate ^[11]. Shen et al. ^[12], examined a vertical stretching sheet which was non-linear. Ishikin Abu Bakar ^[13] investigates how boundary layer flow is affected by slip and convective boundary conditions over a stretching sheet. A vertical plate oscillates with the influence of slip on a free convection flow of a Casson fluid ^[14].

Nasir Uddin et al. ^[15] used a Runge-Kutta sixth-order integration method. Barik et al. ^[16] implicit finite distinction methodology of Crank Sir Harold George Nicolson sort Raman and Kumar ^[17] utilized an exact finite distinction theme of DuFort–Frankel. Mondal et al. ^[18] used a numerical theme over the whole vary of physical parameters. With the laplace transform method, we can determine the magnetohydrodynamic flow of a viscous fluid ^[19]. Thamizh Suganya et al. ^[20] obtained that the MHD for the free convective flow of fluid is based on coupled non-linear differential equations. In this study, the analytical approximation of concentration profiles in velocity, temperature and concentration using homotopy perturbation method (HPM).

2. Mathematical construction of the problem

The governing differential equations in dimensionless form ^[19] as follows:

$\begin{align} \frac{d^2 u}{dy^2} - Hu + Gr \theta + Gm \phi = 0, \end{align}$

(2.1)

$\begin{align} \frac{1}{F} \frac{d^2 \theta}{dy^2} = 0, \end{align}$

(2.2)

$\begin{align} \frac{1}{Sc} \frac{d^2 \phi}{dy^2} - Sr \frac{\partial^2 \phi}{\partial y^2} - \gamma \phi = 0. \end{align}$

(2.3)

The dimensionless boundary conditions given by:

$\begin{equation} u = 0, \ \theta = 1, \phi = 0 \ \ at \ \ y = 0 \end{equation}$

(2.4)

and

$\begin{equation} u = 0, \ \theta = 0, \phi = 0 \ \ at \ \ y \to \infty. \end{equation}$

(2.5)

3. Solutions of steady-state concentration profile using the Homotopy Perturbation Method

He ^[21,22] established the homotopy perturbation method, which waives the requirement of small parameters. Many researchers have used HPM to obtain approximate analytical solutions for many non-linear engineering dynamical systems ^[23,24]. The basic concept of the HPM as follows:

$\begin{align} \frac{d^2 u}{dy^2} - Hu + Gr \theta + Gm \phi = 0 \end{align}$

(3.1)

$\begin{align} \frac{1}{F} \frac{d^2 \theta}{dy^2} = 0 \end{align}$

(3.2)

$\begin{align} \frac{1}{Sc} \frac{d^2 \phi}{dy^2} - Sr \frac{\partial^2 \phi}{\partial y^2} - \gamma \phi = 0 \end{align}$

(3.3)

with initial and boundary conditions given by:

$\begin{align} y = 0 \ \ &at \ u = 0, \ \theta = 1, C = 1 \\ y \to \infty \ \ &as \ u = 0, \ \theta = 1, \phi = 0. \end{align}$

(3.4)

Homotopy for the above Eqs (3.1) to (3.4) can be constructed as follows:

$\begin{align} (1 - p) \left[\frac{d^2 u}{dy^2} - Hu + Gr \theta + Gm \phi\right] + p \left[\frac{d^2 u}{dy^2} - Hu + Gr \theta + Gm \phi\right] = 0 \end{align}$

(3.5)

$\begin{align} (1 - p) \left[\frac{1}{F} \frac{d^2 \theta}{dy^2} - \theta\right] + p \left[\frac{1}{F} \frac{d^2 \theta}{dy^2} - \theta + \theta\right] = 0 \end{align}$

(3.6)

$\begin{align} (1 - p) \left[\frac{1}{Sc} \frac{d^2 \phi}{dy^2} - \gamma \phi \right] + p \left[\frac{1}{Sc} \frac{d^2 \phi}{dy^2} - Sr \frac{\partial^2 \theta}{\partial y^2} - \gamma \phi \right] = 0 \end{align}$

(3.7)

The approximate solution of the Eqs (3.5) to (3.7) are

$\begin{align} u & = u_0 + pu_1 + p^2 u_2 + p^3 u_3 + ... \end{align}$

(3.8)

$\begin{align} \theta & = \theta_0 + p \theta_1 + p^2 \theta_2 + p^3 \theta_3 + ... \end{align}$

(3.9)

$\begin{align} \phi & = \phi_0 + p \phi_1 + p^2 \phi_2 + p^3 \phi_3 + ... \end{align}$

(3.10)

Substitution Eqs (3.5) to (3.7) in Eqs (3.8) to (3.10) respectively. We obtain the following equations

$\begin{align} (1 - p) &\left[\frac{d^2 (u_0 + pu_1 + p^2 u_2 + p^3 u_3 + ...)}{dy^2} - H(u_0 + pu_1 + p^2 u_2 + p^3 u_3 + ...) \right. \\ &\left.+ Gr (\theta_0 + p \theta_1 + p^2 \theta_2 + p^3 \theta_3 + ...) + Gm (\phi_0 + p \phi_1 + p^2 \phi_2 + p^3 \phi_3 + ...)\right] \\ &+ p\left[\frac{d^2 (u_0 + pu_1 + p^2 u_2 + p^3 u_3 + ...)}{dy^2} - H(u_0 + pu_1 + p^2 u_2 + p^3 u_3 + ...)\right. \\ &\left.+ Gr (\theta_0 + p \theta_1 + p^2 \theta_2 + p^3 \theta_3 + ...) + Gm (\phi_0 + p \phi_1 + p^2 \phi_2 + p^3 \phi_3 + ...)\right] = 0 \end{align}$

(3.11)

and

$\begin{align} (1 - p) &\left[\frac{1}{F} \frac{d^2 (\theta_0 + p \theta_1 + p^2 \theta_2 + p^3 \theta_3 + ...)}{dy^2} - (\theta_0 + p \theta_1 + p^2 \theta_2 + p^3 \theta_3 + ...)\right] \\ &+ p \left[\frac{1}{F} \frac{d^2 (\theta_0 + p \theta_1 + p^2 \theta_2 + p^3 \theta_3 + ...)}{dy^2} - (\theta_0 + p \theta_1 + p^2 \theta_2 + p^3 \theta_3 + ...) \right. \\ &\left.+ (\theta_0 + p \theta_1 + p^2 \theta_2 + p^3 \theta_3 + ...)\right] = 0, \end{align}$

(3.12)

and

$\begin{align} (1 - p) &\left[\frac{1}{Sc} \frac{d^2 (\phi_0 + p \phi_1 + p^2 \phi_2 + p^3 \phi_3 + ...)}{dy^2} - \gamma (\phi_0 + p \phi_1 + p^2 \phi_2 + p^3 \phi_3 + ...)\right] \\ &+ p \left[\frac{1}{Sc} \frac{d^2 (\phi_0 + p \phi_1 + p^2 \phi_2 + p^3 \phi_3 + ...)}{dy^2} - Sr \frac{\partial^2 (\theta_0 + p \theta_1 + p^2 \theta_2 + p^3 \theta_3 + ...)}{\partial y^2} \right. \\ &\left.- \gamma (\phi_0 + p \phi_1 + p^2 \phi_2 + p^3 \phi_3 + ...) \right] = 0. \end{align}$

(3.13)

Equating the coefficient of $p$ on both sides, we get the following equations

$\begin{align} P^0 &: \frac{d^2 u_0}{dy^2} - Hu_0 + Gr \theta_0 + Gm \phi_0 = 0; \end{align}$

(3.14)

$\begin{align} p^0 &: \frac{1}{F} \frac{d^2 \theta_0}{dy^2} - \theta_0 = 0; \end{align}$

(3.15)

$\begin{align} P^1 &: \frac{1}{F} \frac{d^2 \theta_0}{dy^2} - \theta_0 + \theta_1 = 0; \end{align}$

(3.16)

$\begin{align} P^1 &: \frac{1}{Sc} \frac{d^2 \phi_0}{dy^2} - \gamma \phi_0 = 0; \end{align}$

(3.17)

$\begin{align} P^1 &: \frac{1}{Sc} \frac{d^2 \phi_0}{dy^2} - Sr \frac{\partial^2 \theta_0}{\partial y^2} - \gamma \phi_0 = 0. \end{align}$

(3.18)

The boundary conditions are

$\begin{align} u_0 = 0, \ \theta_0 = 1, \phi_0 = 1 \ \ at \ \ y = 0 \\ u_0 = 0, \ \theta_0 = 1, \phi_0 = 1 \ \ at \ \ y \to \infty. \end{align}$

(3.19)

and

$\begin{align} u_1 = 0, \ \theta_1 = 0, \phi_1 = 0 \ \ at \ \ y = 0 \\ u_1 = 0, \ \theta_1 = 0, \phi_1 = 0 \ \ at \ \ y \to \infty. \end{align}$

(3.20)

Solving the Eqs (3.9)–(3.14), we obtain

$\begin{align} u_0(t) & = \frac{Gr}{\sqrt{\frac{1}{F}} + H} \left[e^{-y \sqrt{\frac{1}{F}}} - e^{-y \sqrt{H}}\right] + \frac{Gm}{\sqrt{\gamma Sc + H}} \left[e^{-y \sqrt{\gamma Sc}} - e^{-y \sqrt{H}}\right]; \end{align}$

(3.21)

$\begin{align} \theta_0(y) & = e^{-y \sqrt{\frac{1}{F}}}; \end{align}$

(3.22)

$\begin{align} \phi_0(y) & = e^{-y \sqrt{\gamma Sc}}; \end{align}$

(3.23)

$\begin{align} \phi_1(y) & = \frac{Sc Sr}{\sqrt{F} + F \gamma Sc} \left[e^{-y \sqrt{\frac{1}{F}}} - e^{-y \sqrt{\gamma Sc}}\right]. \end{align}$

(3.24)

Considering the iteration, we get,

$\begin{align} u(t) & = \frac{Gr}{\sqrt{\frac{1}{F}} + H} \left[e^{-y \sqrt{\frac{1}{F}}} - e^{-y \sqrt{H}}\right] + \frac{Gm}{\sqrt{\gamma Sc + H}} \left[e^{-y \sqrt{\gamma Sc}} - e^{-y \sqrt{H}}\right]; \end{align}$

(3.25)

$\begin{align} \theta(y) & = e^{-y \sqrt{F}}; \end{align}$

(3.26)

$\begin{align} \phi(y) & = e^{-y \sqrt{\gamma Sc}} + \frac{Sc Sr}{\sqrt{F} + F \gamma Sc} \left[e^{-y \sqrt{\frac{1}{F}}} - e^{-y \sqrt{\gamma Sc}}\right]. \end{align}$

(3.27)

4. Approximate analytical solutions for the skiin friction, Nusselt and Sherwood numbers

From the Eqs (3.25)–(3.27), we obtain

$\begin{array}{l} C_f = - \left(\frac{\partial u}{\partial y}\right)_{y = 0} \\ = \frac{\left(Gm \sqrt{\gamma Sc} - Gm \sqrt{H} + Gr(\gamma Sc + H) \sqrt{1 + \frac{R}{Pr}} + Gm H \sqrt{\gamma Sc} + (-Gm - Gr) H^{\frac{3}{2}} - \gamma Gr \sqrt{H} Sc\right)}{\left(\sqrt{1 + \frac{R}{Pr} + H} (\gamma Sc + H)\right)}; \end{array}$

(4.1)

$\begin{align} N_u & = - \left(\frac{\partial \theta}{\partial y}\right)_{y = 0} = \sqrt{\frac{1 + R}{Pr}}; \end{align}$

(4.2)

$\begin{array}{l} S_h = - \left(\frac{\partial \phi}{\partial y}\right)_{y = 0} \\= \frac{Sc Sr (1 + R) \sqrt{1 + \frac{R}{Pr}} - \sqrt{\gamma Sc} \left((-R - 1) \sqrt{1 + \frac{R}{Pr}} + ((1 + R)Sc - Pr \gamma) Sc \right)}{(1 + R) \sqrt{1 + \frac{R}{Pr}} Pr \gamma Sc} \end{array}$

(4.3)

5. Results and discussion

The combined impacts of transient MHD free convective flows of an incompressible viscous fluid through a vertical plate moving with uniform motion and immersed in a porous media are examined using an exact approach. The approximate analytical expressions for the velocity $u$ , temperature $\theta$ , and concentration profile $\phi$ are solved by using the homotopy perturbation method for fixed values of parameters is graphically presented.

Velocity takes time at first, and for high values of y, it takes longer, and the velocity approaches zero as time increases. The velocity of fluid rises with Gr increasing, as exposed in Figure 1.

Figure 1. An illustration of velocity profiles for different values of Gr.

[1]	M. Garnier, Magneto hydrodynamics in materials processing, Philos. Trans. R. Soc. Phys. Sci. Eng., 344 (1962), 249–263.
[2]	A. Chakrabarti, A. S. Gupta, Hydromagnetic flow and heat transfer over a stretching sheet, Quart Appl. Math., 37 (1979), 13–78. https://doi.org/10.1090/qam/99636 doi: 10.1090/qam/99636
[3]	S. Nadeem, U. I. HaqRizwana, C. Lee, MHD flow of a casson fluid over an exponentially shrinking sheet, Sci. Iran., 19 (2012), 1550–1553. https://doi.org/10.1016/j.scient.2012.10.021 doi: 10.1016/j.scient.2012.10.021
[4]	K. Bhattacharya, MHD stagnation point flow of casson fluid and heat transfer over a stretching sheet with thermal radiation, J. Thermody., 2013 (2013), Article ID 169674. https://doi.org/10.1155/2013/169674 doi: 10.1155/2013/169674
[5]	A. Ishak, R. Nazar, I. Pop, Mixed convection on the stagnation pit flow toward a vertical, continuously stretching sheet, J. Heat Transfer, 129 (2007), 1087–1090. https://doi.org/10.1115/1.2737482 doi: 10.1115/1.2737482
[6]	A. Ishak, R. Nazar, I. Pop, Post stagnation point boundary layer flow and mixed convection heat transfer over a vertical, linearly stretching sheet, Arch. Mech., 60 (2008), 303–322.
[7]	A. Ishak, K. Jafar, R. Nazar, Pop, MHD stagnation point flow towards a stretching sheet, Physics A, 388 (2009), 3377–3383. https://doi.org/10.1016/j.physa.2009.05.026 doi: 10.1016/j.physa.2009.05.026
[8]	S. Gala, M. A. Ragusa, Y. Sawano, H. Tanaka, Uniqueness criterion of weak solutions for the dissipative quasi-geostrophic equations in Orlicz–Morrey spaces, Appl. Anal., 93 (2014), 356–368. https://doi.org/10.1080/00036811.2013.772582 doi: 10.1080/00036811.2013.772582
[9]	R. P. Agarwal, O. Bazighifan, M. A. Ragusa, Nonlinear neutral delay differential equations of fourth-Order: Oscillation of solutions, Entropy, 23 (2021), 129. https://doi.org/10.3390/e23020129 doi: 10.3390/e23020129
[10]	T. Hayat, M. Bilal Ashraf, S. A. Shehzad, A. Alsaedi, Mixed convection flow of Cassonnanofluid over a stretching sheet with convectively heated chemical reaction and heat source/sink, J. Appl. Fluid Mech., 8 (2015), 803–813. https://doi.org/10.18869/acadpub.jafm.67.223.22995 doi: 10.18869/acadpub.jafm.67.223.22995
[11]	M. S. Abel, M. Mareppa, MHD flow and heat transfer of the mixed hydrodynamic/thermal slip over a linear vertically stretching sheet, Int. J. Math. Archive, 4 (2013), 156–163.
[12]	M. Shen, F. Wang, H. Chen, MHD mixed convection slip flow near a stagnation point on a non-linearly vertical stretching sheet, Boundary Value Probl., 2015 (2015), 78. https://doi.org/10.1186/s13661-015-0340-6 doi: 10.1186/s13661-015-0340-6
[13]	N. Ashikin, A. Bakar, W. MohdKhairy, A. W. Zaimi, R. A. Hamid, B. Bidin, et al., Boundary layer flow over a stretching sheet with a convective boundary condition and slip effect, World Appl. Sci. J., 17 (2012), 49–53.
[14]	M. A. Imran, S. Sarwar, M. Imran, Effects of slip on free convection flow of Casson fluid over an oscillating vertical plate, Boundary Value Probl., 2016 (2016), 30. https://doi.org/10.1186/s13661-016-0538-2 doi: 10.1186/s13661-016-0538-2
[15]	N. Uddin Md, A. MA, MMK. Chowdhury, Effects of mass transfer on MHD mixed convective flow along inclined porous plate, Procedia Eng., 90 (2014), 491–496. https://doi.org/10.1016/j.proeng.2014.11.762 doi: 10.1016/j.proeng.2014.11.762
[16]	R. N. Barik, G. C. Dash, Thermal radiation effect on an unsteady magnetohydrodynamic flow past inclined porous heated plate in the presence of chemical reaction and viscous dissipation, Appl. Math. Comput., 226 (2014), 423–434. https://doi.org/10.1016/j.amc.2013.09.077 doi: 10.1016/j.amc.2013.09.077
[17]	R. M. Ramana, J. G. Kumar, Chemical reaction effects on MHD free convective flow past an inclined plate, Asian J. Current Eng. Math., 3 (2014), 66–71.
[18]	H. Mondal, D. Pal, S. Chatterjee, P. Sibanda, Thermophoresis and Soret-Dufour on MHD mixed convection mass transfer over an inclined plate with non-uniform heat source/sink and chemical reaction, Ain Shams Eng. J., 9 (2018), 2111–2121. https://doi.org/10.1016/j.asej.2016.10.015 doi: 10.1016/j.asej.2016.10.015
[19]	F. Ali, I. Khan, S. Shafie, N. Musthapa, Heat and mass transfer with free convection MHD flow past a vertical plate embedded in a porous medium, Math. Probl. Eng., 2013 (2013), Art. ID 346281, 13 pp. https://doi.org/10.1155/2013/346281 doi: 10.1155/2013/346281
[20]	S. Thamizh, P. Suganya, L. Balaganesan, M. A. Rajendran, Analytical discussion and sensitivity analysis of parameters of magnetohydrodynamic free convective flow in an inclined plate, Eur. J. Pure Appl. Math., 13 (2020), 631–644. https://doi.org/10.29020/nybg.ejpam.v13i3.3730 doi: 10.29020/nybg.ejpam.v13i3.3730
[21]	H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 178 (1999), 257–262. https://doi.org/10.1016/S0045-7825(99)00018-3 doi: 10.1016/S0045-7825(99)00018-3
[22]	J. H. He, Application of homotopy perturbation method to non-linear wave equations, Chaos Soliton. Fract., 26 (2005), 695–700. https://doi.org/10.1016/j.chaos.2005.03.006 doi: 10.1016/j.chaos.2005.03.006
[23]	A. Meena, L. Rajendran, Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations Homotopy perturbation approach, J. Electroanal. Chem., 644 (2010), 50–59. https://doi.org/10.1016/j.jelechem.2010.03.027 doi: 10.1016/j.jelechem.2010.03.027
[24]	S. T. Suganya, P. Balaganesan, J. Visuvasam, L. Rajendran, An analytical expression of Non-Nernstian catalytic mechanism at Micro and Macro electroduces at voltammetry, Asia Mathematika, 5 (2021), 1–10.

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AIMS Mathematics

Analysis of the magnetohydrodynamic flow in a porous medium

Related Papers:

Abstract

1. Introduction

2. Mathematical construction of the problem

3. Solutions of steady-state concentration profile using the Homotopy Perturbation Method

4. Approximate analytical solutions for the skiin friction, Nusselt and Sherwood numbers

5. Results and discussion

6. Conclusions

Conflict of interest

Acknowledgement

References

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