doi: 10.3934/dcdss.2020059

MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination

Department of Mathematics, GC University Lahore, Lahore, 54000, Pakistan

* Corresponding author: Khurram Shabbir

Received  August 2018 Revised  October 2018 Published  March 2019

The aim of this article is to study the natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination. Existing solutions of similar models can be recovered as the limiting cases of horizontal and vertical plates from our generalized problem. Moreover, porous effects and the influence of transverse magnetic field; fixed to the fluid or the plate are accounted. The dimensionless velocity, in conjunction with the corresponding skin friction, have been presented as the sum of mechanical, thermal and concentration components. Furthermore, the contribution of the system parameters to the fluid motion in question has been depicted graphically. The novelty of the present study is to analyze the effect of angle of inclination of the plate and the case when the magnetic field is fixed relative to the fluid or to the plate on the fluid motion.

Citation: Azhar Ali Zafar, Khurram Shabbir, Asim Naseem, Muhammad Waqas Ashraf. MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020059
References:
[1]

H. AbidZ. IsmailI. KhanA. G. Hussein and S. Shafie, Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating, The European Physical Journal Plus, 129 (2014), 1-16.

[2]

R. N. BarikG. C. Dash and P. K. Rath, Thermal Radiation effect on an unsteady MHD flow past inclined porous heated plate in the presence of chemical reaction and viscous-dissipation, Appl Math Comput, 226 (2014), 423-434. doi: 10.1016/j.amc.2013.09.077.

[3]

C. H. Chen, Heat and mass transfer in MHD flow by natural convection from a permeable inclined surface with variable wall temperature and concentration, Acta Mech, 172 (2004), 219-235. doi: 10.1007/s00707-004-0155-5.

[4]

C. FetecauM. Rana and C. Fetecau, Radiative and porous effects on free convection flow near a vertical plate that applies shear stress to the fluid, Zeitschrift fur Naturforschung, 68 (2013), 130-138.

[5]

C. Fetecau, A. Shahraz, I. Pop and C. Fetecau, Unsteady general solutions for MHD natural convection flow with radiative effects, heat source and shear stress on the boundary, International Journal of Numerical Methods for Heat & Fluid Flow, 27 2016. doi: 10.1108/HFF-02-2016-0069.

[6]

C. Fetecau, D. Vieru, C. Fetecau and I. Pop, Slip effects on the unsteady radiative MHD free convection flow over a moving plate with mass diffusion and heat source, The European Physical Journal Plus, 130 (2015), 6. doi: 10.1140/epjp/i2015-15006-8.

[7]

A. Khan, I. Khan, F. Ali and S. Shafie, Effects of wall shear stress on MHD conjugate flow over an inclined plate in a porous medium with ramped wall temperature, Mathematical Problems in Engineering, 2014 (2014), Article ID 861708, 15 pages. doi: 10.1155/2014/861708.

[8]

E. Magyari and A. Pantokratoras, Note on the effect of thermal radiation in the linearized Rosseland approximation on the heat transfer characteristics of various boundary layer flows, International Communications in Heat and Mass Transfer, 38 (2011), 554-556. doi: 10.1016/j.icheatmasstransfer.2011.03.006.

[9]

M. Narahari and L. Debnath, Unsteady magnetohydrodynamic free convection flow past an accelerated vertical plate with constant heat flux and heat generation or absorption, Zeitschrift fr Angewandte Mathematik und Mechanik, 93 (2013), 38-49. doi: 10.1002/zamm.201200008.

[10]

N. Narahari and B. K. Dutta, Effects of thermal radiation and mass diffusion on free convection flow near a vertical plate with Newtonian heating, Chemical Engineering Communications, 199 (2012), 628-643.

[11]

M. NarahariSowmya TippaRajashekhar Pendyala and M. Y. Nayan, Ramped temperature effect on unsteady MHD natural convection flow past an infinite inclined plate in the presence of radiation, heat source and chemical reaction, Recent Advances in Applied and Theoretical Mechanics, 7 (2013), 126-137.

[12]

G. Palani, Convection effects on flow past an inclined plate with variable surface temperatures in water at 4 C, Ann. Faculty Eng. Hunedora VI, 1 (2008), 75-82.

[13]

B. P. Reddy, Effects of thermal diffusion and viscous dissipation on unsteady MHD free convection flow past a vertical porous plate under oscillatory suction velocity with heat sink, International Journal of Applied Mechanics and Engineering, 19 (2014), 303-320.

[14]

Q. Rubbab, D. Vieru, C. Fetecau and C. Fetecau, Natural convection flow near a vertical plate that applies a shear stress to a viscous fluid, PLoS ONE, 8 (2013), e78352. doi: 10.1371/journal.pone.0078352.

[15]

G. S. SethMd. S. Ansari and R. Nandkeolyar, MHD natural convection flow with radiative heat transfer past an impulsively moving plate with ramped wall temperature, Heat Mass Transfer, 47 (2011), 555-561. doi: 10.1007/s00231-010-0740-1.

[16]

G. S. SethS. M. Hussain and S. Sarkar, Hydromagnetic natural convection flow with heat and mass transfer of a chemically reacting and heat absorbing fluid past an accelerated moving vertical plate with ramped temperature and ramped surface concentration through a porous medium, Journal of the Egyptian Mathematical Society, 23 (2015), 197-207. doi: 10.1016/j.joems.2014.03.006.

[17]

N. A. ShahA. 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., 7 (2018), 49-60. doi: 10.1007/s40065-017-0187-z.

[18]

N. A. Shah, A. A. Zafar, C. Fetecau and A. Naseem, Effects of exponential heating on double-diffuse free convection flows on a moving vertical plate, Mathematical Reports, to be appear (2018).

[19]

G. Singh and O. D. Makinde, Computational dynamics of MHD free convection flow along an inclined plate with Newtonian heating in the presence of volumetric heat generation, Chem Eng Commun., 199 (2012), 1144-1154. doi: 10.1080/00986445.2011.651184.

[20]

L. Sreekala and E. K. Reddy, Steady MHD Couette flow of an incompressible viscous fluid through a porous medium between two infinite parallel plates under effect of inclined magnetic field, The International Journal of Engineering and Science, 3 (2014), 18-37.

[21]

J. N. Tokis, A class of exact solutions of the unsteady magnetohydrodynamic free-convection flows, Astrophys. Space Sci., 112 (1985), 413-422. doi: 10.1007/BF00653524.

[22]

Z. Uddin and M. Kumar, Unsteady free convection in a fluid past an inclined plate immersed in a porous medium, Comput. Model New Tech, 14 (2010), 41-47.

[23]

A. Umemura and C. K. Law, Natural convection boundary layer flow over a heated plate with arbitrary inclination, J. Fluid Mech, 219 (1990), 571-584. doi: 10.1017/S0022112090003081.

[24]

D. VieruC. FetecauC. Fetecau and N. Nigar, Magnetohydrodynamic natural convection flow with Newtonian heating and mass diffusion over an infinite plate that applies shear stress to a viscous fluid, Zeitschrift fur Naturforschung A, 69 (2014), 714-724. doi: 10.5560/zna.2014-0068.

[25]

C. ZhangL. ZhengX. Zhang and G. Chen, MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction, Applied Mathematical Modelling, 39 (2015), 165-181. doi: 10.1016/j.apm.2014.05.023.

show all references

References:
[1]

H. AbidZ. IsmailI. KhanA. G. Hussein and S. Shafie, Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating, The European Physical Journal Plus, 129 (2014), 1-16.

[2]

R. N. BarikG. C. Dash and P. K. Rath, Thermal Radiation effect on an unsteady MHD flow past inclined porous heated plate in the presence of chemical reaction and viscous-dissipation, Appl Math Comput, 226 (2014), 423-434. doi: 10.1016/j.amc.2013.09.077.

[3]

C. H. Chen, Heat and mass transfer in MHD flow by natural convection from a permeable inclined surface with variable wall temperature and concentration, Acta Mech, 172 (2004), 219-235. doi: 10.1007/s00707-004-0155-5.

[4]

C. FetecauM. Rana and C. Fetecau, Radiative and porous effects on free convection flow near a vertical plate that applies shear stress to the fluid, Zeitschrift fur Naturforschung, 68 (2013), 130-138.

[5]

C. Fetecau, A. Shahraz, I. Pop and C. Fetecau, Unsteady general solutions for MHD natural convection flow with radiative effects, heat source and shear stress on the boundary, International Journal of Numerical Methods for Heat & Fluid Flow, 27 2016. doi: 10.1108/HFF-02-2016-0069.

[6]

C. Fetecau, D. Vieru, C. Fetecau and I. Pop, Slip effects on the unsteady radiative MHD free convection flow over a moving plate with mass diffusion and heat source, The European Physical Journal Plus, 130 (2015), 6. doi: 10.1140/epjp/i2015-15006-8.

[7]

A. Khan, I. Khan, F. Ali and S. Shafie, Effects of wall shear stress on MHD conjugate flow over an inclined plate in a porous medium with ramped wall temperature, Mathematical Problems in Engineering, 2014 (2014), Article ID 861708, 15 pages. doi: 10.1155/2014/861708.

[8]

E. Magyari and A. Pantokratoras, Note on the effect of thermal radiation in the linearized Rosseland approximation on the heat transfer characteristics of various boundary layer flows, International Communications in Heat and Mass Transfer, 38 (2011), 554-556. doi: 10.1016/j.icheatmasstransfer.2011.03.006.

[9]

M. Narahari and L. Debnath, Unsteady magnetohydrodynamic free convection flow past an accelerated vertical plate with constant heat flux and heat generation or absorption, Zeitschrift fr Angewandte Mathematik und Mechanik, 93 (2013), 38-49. doi: 10.1002/zamm.201200008.

[10]

N. Narahari and B. K. Dutta, Effects of thermal radiation and mass diffusion on free convection flow near a vertical plate with Newtonian heating, Chemical Engineering Communications, 199 (2012), 628-643.

[11]

M. NarahariSowmya TippaRajashekhar Pendyala and M. Y. Nayan, Ramped temperature effect on unsteady MHD natural convection flow past an infinite inclined plate in the presence of radiation, heat source and chemical reaction, Recent Advances in Applied and Theoretical Mechanics, 7 (2013), 126-137.

[12]

G. Palani, Convection effects on flow past an inclined plate with variable surface temperatures in water at 4 C, Ann. Faculty Eng. Hunedora VI, 1 (2008), 75-82.

[13]

B. P. Reddy, Effects of thermal diffusion and viscous dissipation on unsteady MHD free convection flow past a vertical porous plate under oscillatory suction velocity with heat sink, International Journal of Applied Mechanics and Engineering, 19 (2014), 303-320.

[14]

Q. Rubbab, D. Vieru, C. Fetecau and C. Fetecau, Natural convection flow near a vertical plate that applies a shear stress to a viscous fluid, PLoS ONE, 8 (2013), e78352. doi: 10.1371/journal.pone.0078352.

[15]

G. S. SethMd. S. Ansari and R. Nandkeolyar, MHD natural convection flow with radiative heat transfer past an impulsively moving plate with ramped wall temperature, Heat Mass Transfer, 47 (2011), 555-561. doi: 10.1007/s00231-010-0740-1.

[16]

G. S. SethS. M. Hussain and S. Sarkar, Hydromagnetic natural convection flow with heat and mass transfer of a chemically reacting and heat absorbing fluid past an accelerated moving vertical plate with ramped temperature and ramped surface concentration through a porous medium, Journal of the Egyptian Mathematical Society, 23 (2015), 197-207. doi: 10.1016/j.joems.2014.03.006.

[17]

N. A. ShahA. 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., 7 (2018), 49-60. doi: 10.1007/s40065-017-0187-z.

[18]

N. A. Shah, A. A. Zafar, C. Fetecau and A. Naseem, Effects of exponential heating on double-diffuse free convection flows on a moving vertical plate, Mathematical Reports, to be appear (2018).

[19]

G. Singh and O. D. Makinde, Computational dynamics of MHD free convection flow along an inclined plate with Newtonian heating in the presence of volumetric heat generation, Chem Eng Commun., 199 (2012), 1144-1154. doi: 10.1080/00986445.2011.651184.

[20]

L. Sreekala and E. K. Reddy, Steady MHD Couette flow of an incompressible viscous fluid through a porous medium between two infinite parallel plates under effect of inclined magnetic field, The International Journal of Engineering and Science, 3 (2014), 18-37.

[21]

J. N. Tokis, A class of exact solutions of the unsteady magnetohydrodynamic free-convection flows, Astrophys. Space Sci., 112 (1985), 413-422. doi: 10.1007/BF00653524.

[22]

Z. Uddin and M. Kumar, Unsteady free convection in a fluid past an inclined plate immersed in a porous medium, Comput. Model New Tech, 14 (2010), 41-47.

[23]

A. Umemura and C. K. Law, Natural convection boundary layer flow over a heated plate with arbitrary inclination, J. Fluid Mech, 219 (1990), 571-584. doi: 10.1017/S0022112090003081.

[24]

D. VieruC. FetecauC. Fetecau and N. Nigar, Magnetohydrodynamic natural convection flow with Newtonian heating and mass diffusion over an infinite plate that applies shear stress to a viscous fluid, Zeitschrift fur Naturforschung A, 69 (2014), 714-724. doi: 10.5560/zna.2014-0068.

[25]

C. ZhangL. ZhengX. Zhang and G. Chen, MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction, Applied Mathematical Modelling, 39 (2015), 165-181. doi: 10.1016/j.apm.2014.05.023.

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