Modeling Non-Darcy Natural Convection Flow of a Micropolar Dusty Fluid with Convective Boundary Condition
A numerical approach of the effectiveness of numerous
parameters on magnetohydrodynamic (MHD) natural convection
heat and mass transfer problem of a dusty micropolar fluid in
a non-Darcy porous regime is prepared in the current paper.
In addition, a convective boundary condition is scrutinized into
the micropolar dusty fluid model. The governing boundary layer
equations are converted utilizing similarity transformations to a
system of dimensionless equations to be convenient for numerical
treatment. The resulting equations for fluid phase and dust phases
of momentum, angular momentum, energy, and concentration with
the appropriate boundary conditions are solved numerically applying
the Runge-Kutta method of fourth-order. In accordance with the
numerical study, it is obtained that the magnitude of the velocity
of both fluid phase and particle phase reduces with an increasing
magnetic parameter, the mass concentration of the dust particles, and
Forchheimer number. While rises due to an increment in convective
parameter and Darcy number. Also, the results refer that high values
of the magnetic parameter, convective parameter, and Forchheimer
number support the temperature distributions. However, deterioration
occurs as the mass concentration of the dust particles and Darcy
number increases. The angular velocity behavior is described by
progress when studying the effect of the magnetic parameter and
microrotation parameter.
[1] A. C. Eringen, “Theory of thermomicropolar fluids”, J. Math. Appl. voI.
38, PP. 480-495, 1972.
[2] A. C. Eringen, “Theory of micropolar fluids”, J. Math. Mech. voI. 16,
pp. 1-18, 1966.
[3] T. Ariman, M. A. Turk, N. D. Sylvester, “Microcontinuum fluid
mechanicsa review”, Int. J. Eng. Sci. voI. 11, PP. 905-929, 1973.
[4] T. Ariman, M. A. Turk, N. D. Sylvester, “Applications of
microcontinuum fluid mechanics”, Int. J. Eng. Sci. voI. 12, PP. 273-293,
1974.
[5] H. P. Rani, C. N. Kim, “A transient natural convection of micropolar
fluids over a vertical cylinder”, Heat Mass Transfer voI. 46, PP.
1277-1285, 2010.
[6] C. Y. Cheng, “Natural convection of a micropolar fluid from a vertical
truncated cone with power-law variation in surface temperature”, Int.
Commun. Heat Mass Transfer voI. 35, PP. 39-46, 2008.
[7] R. A. Damseh, T. A. Al-Azab, B. A. Shannak, M. Al Husein, “Unsteady
natural convection heat transfer of micropolar fluid over a vertical surface
with constant heat flux”, Turk. J. Eng. Environ. Sci. voI. 31, PP. 225-233,
2007.
[8] I .A. Hassanien, A. H. Essawy, N .M. Moursy, Natural convection flow
of micropolar fluid from a permeable uniform heat flux surface in porous
medium, Appl. Math. Comput. voI. 152, PP. 323-335, 2004.
[9] M. Ferdows, D. Liu, “Natural convective flow of a magneto-micropolar
fluid along a vertical plate”, Propul. Power. Rese. voI. 7, PP. 43-51, 2018.
[10] N. V. K. Rao, C. Srinivasulu, C. S. K. Raju, B. Devika, “Thermal natural
convection of magneto hydrodynamics micropolar unsteady fluid over a
radiated stretching sheet with viscous dissipation”, J. Nanofluids voI. 8,
PP. 550-555, 2019.
[11] L. Rundora, O. D. Makinde, “Unsteady MHD flow of non-Newtonian
fluid in a channel filled with a saturated porous medium with asymmetric
navier slip and convective heating”, Appl. Math. Inform. Sci. Int. J. voI.
12, PP. 483-493, 2018.
[12] A. Mahdy, “Unsteady MHD slip flow of a non-Newtonian Casson fluid
due to stretching sheet with suction or blowing effect”, J. Appl. Fluid
Mech. voI. 9, PP. 785- 793, 2016.
[13] A. Mahdy, S. A. Ahmed, “Unsteady MHD convective flow of
non-Newtonian Casson fluid in the stagnation region of an impulsively
rotating sphere”, J. Aero. Eng. voI. 30, PP. 04017036 (8 pages), 2017.
[14] F. M. Hady, A. Mahdy, R. A. Mohamed, Omima A. Abo Zaid, “Effects
of viscous dissipation on unsteady MHD thermo bioconvection boundary
layer flow of a nanofluid containing gyrotactic microorganisms along a
stretching sheet”, World J. Mech. voI. 6, PP. 505-526, 2016.
[15] S. A. Ahmed, A. Mahdy, “Unsteady MHD double diffusive convection
in the stagnation region of an impulsively rotating sphere in the presence
of thermal radiation effect”, J. Taiwan Institu. Chemical Eng. voI. 58,
PP. 173-180, 2016.
[16] S. R. Sheri, “Heat and mass transfer on the MHD flow of micro polar
fluid in the presence of viscous dissipation and chemical reaction”,
Procedia Eng. voI. 127, PP. 885-892, 2015.
[17] S. A. Shehzad, T. Hayat, A. Alsaedi, “MHD flow of Jeffrey nanofluid
with convective boundary conditions”, J. Braz. Soc. Mech. Sci. Eng. voI.
37, PP. 873-883, 2015.
[18] S. L. Lee, J. H. Yang, “Modeling of Darcy-Forchheimer drag for fluid
flow across a bank of circular cylinders”, Int. J. Heat Mass Transfer voI.
40, PP. 3149-3155, 1997.
[19] V. Prasad, N. Kladias, “Non-Darcy natural convection in saturated
porous media, In: S Kaka, B Kilkis, FA Kulacki and F Arin (eds)”,
Convective Heat Mass Transfer Porous Media. voI. 196, PP. 173-224,
1991.
[20] A. L. Dye, J. E.McClure, C. T. Miller, W. G. Gray, “Description of
non-Darcy flows in porous medium systems”, Phys. Rev. E voI. 87, PP.
033012 (14 pages), 2013.
[21] J. S. R. Prasad, K. Hemalatha, “A study on mixed convective, MHD
flow from a vertical plate embedded in non-Newtonian fluid saturated
non- Darcy porous medium with melting effect”, J. Appl. Fluid Mech.
voI. 9, PP. 293-302, 2016.
[22] P. Nithiarasu, K. N. Seetharamu, T. Sundararajan, “Non-Darcy
double-diffusive natural convection in axisymmetric fluid saturated
porous cavities”, Heat Mass Transfer voI. 32, PP. 427-433, 1997.
[23] A. Y. Bakier, “Natural convection heat and mass transfer in a
micropolar fluid- saturated non-Darcy porous regime with radiation and
thermophoresis effects”, Therm. Sci. voI. 15, PP. S317-S326, 2011.
[24] F. M. Hady, R. A. Mohamed, A. Mahdy, “Non-Darcy natural convection
flow along a vertical wavy plate embedded in a non-Newtonian fluid
saturated porous medium”, Int. J. Appl. Mech. Eng. voI. 13, PP. 91-100,
2008.
[25] F. M. Hady, R. A. Mohamed, A. Mahdy, Omima A. Abo-Zaid,
“Non-Darcy natural convection boundary layer flow over a vertical
cone in porous media saturated with a nanofluid containing gyrotactic
microorganisms with a convective boundary condition”, J. Nanofluids
voI. 5, PP. 765-773, 2016.
[26] R. A. Mohamed, A. Mahdy, S. Abo-Dahab, “Effects of thermophoresis,
heat source/sink, variable viscosity and chemical reaction on non-Darcian
mixed convective heat and mass transfer flow over a semi-infinite porous
inclined plate in the presence of thermal radiation”, J. Computational
Theoretical Nanoscie. voI. 10, PP. 1366-1375, 2013.
[27] S. Siddiqa, N. Begum, Md. A. Hossain, R. S. R. Gorla, “Natural
convection flow of a two-phase dusty non-Newtonian fluid along a
vertical surface”, Int. J. Heat Mass Transfer voI. 113, PP. 482-489, 2017.
[28] S. Siddiqa, N. Begum, M. A. Hossain, R. S. R. Gorla, “Numerical
solutions of natural convection flow of a dusty nanofluid about a vertical
wavy truncated cone”, J. Heat Transfer voI. 139, PP. 022503 (11 pages),
2017.
[29] S. Siddiqa, N. Begum, M. A. Hossain, R. S. R. Gorla, “Two-phase
natural convection flow of a dusty fluid”, Int. J. Numer. Meth. Heat
Fluid Flow voI. 25, PP. 1542-1556, 2015.
[30] D. C. Dalal, N. Datta, S. K. Mukherjea, “Unsteady natural convection
of a dusty fluid in an infinite rectangular channel”, Int. J. Heat Mass
Transfer voI. 41, PP. 547-562, 1998.
[31] S. M. Silu, M. Wainaina, M. Kimathi, “Effects of magnetic induction
on MHD boundary Layer flow of dusty fluid over a stretching sheet”,
Global J. Pure Appl. Math. voI. 14, PP. 1197-1215, 2018.
[32] B. J. Gireesha, R. S. R. Gorla, M. R. Krishnamurthy, B. C.
Prasannakumara, “Biot number effect on MHD flow and heat transfer
of nanofluid with suspended dust particles in the presence of
nonlinear thermal radiation and non-uniform heat source/sink”, Acta Et
Commentationes Universitatis Tartuensis De Mathematica voI. 22, PP.
91-114, 2018.
[33] B. J. Gireesha, R. S. R. Gorla, M. R. Krishnamurthy, B. C.
Prasannakumara, “MHD flow and radiative heat transfer of micropolar
dusty fluid suspended with alumina nanoparticles over a stretching sheet
embedded in a porous medium”, JNNCE J. Eng. Manag. voI. 2, PP.
30-45, 2018.
[1] A. C. Eringen, “Theory of thermomicropolar fluids”, J. Math. Appl. voI.
38, PP. 480-495, 1972.
[2] A. C. Eringen, “Theory of micropolar fluids”, J. Math. Mech. voI. 16,
pp. 1-18, 1966.
[3] T. Ariman, M. A. Turk, N. D. Sylvester, “Microcontinuum fluid
mechanicsa review”, Int. J. Eng. Sci. voI. 11, PP. 905-929, 1973.
[4] T. Ariman, M. A. Turk, N. D. Sylvester, “Applications of
microcontinuum fluid mechanics”, Int. J. Eng. Sci. voI. 12, PP. 273-293,
1974.
[5] H. P. Rani, C. N. Kim, “A transient natural convection of micropolar
fluids over a vertical cylinder”, Heat Mass Transfer voI. 46, PP.
1277-1285, 2010.
[6] C. Y. Cheng, “Natural convection of a micropolar fluid from a vertical
truncated cone with power-law variation in surface temperature”, Int.
Commun. Heat Mass Transfer voI. 35, PP. 39-46, 2008.
[7] R. A. Damseh, T. A. Al-Azab, B. A. Shannak, M. Al Husein, “Unsteady
natural convection heat transfer of micropolar fluid over a vertical surface
with constant heat flux”, Turk. J. Eng. Environ. Sci. voI. 31, PP. 225-233,
2007.
[8] I .A. Hassanien, A. H. Essawy, N .M. Moursy, Natural convection flow
of micropolar fluid from a permeable uniform heat flux surface in porous
medium, Appl. Math. Comput. voI. 152, PP. 323-335, 2004.
[9] M. Ferdows, D. Liu, “Natural convective flow of a magneto-micropolar
fluid along a vertical plate”, Propul. Power. Rese. voI. 7, PP. 43-51, 2018.
[10] N. V. K. Rao, C. Srinivasulu, C. S. K. Raju, B. Devika, “Thermal natural
convection of magneto hydrodynamics micropolar unsteady fluid over a
radiated stretching sheet with viscous dissipation”, J. Nanofluids voI. 8,
PP. 550-555, 2019.
[11] L. Rundora, O. D. Makinde, “Unsteady MHD flow of non-Newtonian
fluid in a channel filled with a saturated porous medium with asymmetric
navier slip and convective heating”, Appl. Math. Inform. Sci. Int. J. voI.
12, PP. 483-493, 2018.
[12] A. Mahdy, “Unsteady MHD slip flow of a non-Newtonian Casson fluid
due to stretching sheet with suction or blowing effect”, J. Appl. Fluid
Mech. voI. 9, PP. 785- 793, 2016.
[13] A. Mahdy, S. A. Ahmed, “Unsteady MHD convective flow of
non-Newtonian Casson fluid in the stagnation region of an impulsively
rotating sphere”, J. Aero. Eng. voI. 30, PP. 04017036 (8 pages), 2017.
[14] F. M. Hady, A. Mahdy, R. A. Mohamed, Omima A. Abo Zaid, “Effects
of viscous dissipation on unsteady MHD thermo bioconvection boundary
layer flow of a nanofluid containing gyrotactic microorganisms along a
stretching sheet”, World J. Mech. voI. 6, PP. 505-526, 2016.
[15] S. A. Ahmed, A. Mahdy, “Unsteady MHD double diffusive convection
in the stagnation region of an impulsively rotating sphere in the presence
of thermal radiation effect”, J. Taiwan Institu. Chemical Eng. voI. 58,
PP. 173-180, 2016.
[16] S. R. Sheri, “Heat and mass transfer on the MHD flow of micro polar
fluid in the presence of viscous dissipation and chemical reaction”,
Procedia Eng. voI. 127, PP. 885-892, 2015.
[17] S. A. Shehzad, T. Hayat, A. Alsaedi, “MHD flow of Jeffrey nanofluid
with convective boundary conditions”, J. Braz. Soc. Mech. Sci. Eng. voI.
37, PP. 873-883, 2015.
[18] S. L. Lee, J. H. Yang, “Modeling of Darcy-Forchheimer drag for fluid
flow across a bank of circular cylinders”, Int. J. Heat Mass Transfer voI.
40, PP. 3149-3155, 1997.
[19] V. Prasad, N. Kladias, “Non-Darcy natural convection in saturated
porous media, In: S Kaka, B Kilkis, FA Kulacki and F Arin (eds)”,
Convective Heat Mass Transfer Porous Media. voI. 196, PP. 173-224,
1991.
[20] A. L. Dye, J. E.McClure, C. T. Miller, W. G. Gray, “Description of
non-Darcy flows in porous medium systems”, Phys. Rev. E voI. 87, PP.
033012 (14 pages), 2013.
[21] J. S. R. Prasad, K. Hemalatha, “A study on mixed convective, MHD
flow from a vertical plate embedded in non-Newtonian fluid saturated
non- Darcy porous medium with melting effect”, J. Appl. Fluid Mech.
voI. 9, PP. 293-302, 2016.
[22] P. Nithiarasu, K. N. Seetharamu, T. Sundararajan, “Non-Darcy
double-diffusive natural convection in axisymmetric fluid saturated
porous cavities”, Heat Mass Transfer voI. 32, PP. 427-433, 1997.
[23] A. Y. Bakier, “Natural convection heat and mass transfer in a
micropolar fluid- saturated non-Darcy porous regime with radiation and
thermophoresis effects”, Therm. Sci. voI. 15, PP. S317-S326, 2011.
[24] F. M. Hady, R. A. Mohamed, A. Mahdy, “Non-Darcy natural convection
flow along a vertical wavy plate embedded in a non-Newtonian fluid
saturated porous medium”, Int. J. Appl. Mech. Eng. voI. 13, PP. 91-100,
2008.
[25] F. M. Hady, R. A. Mohamed, A. Mahdy, Omima A. Abo-Zaid,
“Non-Darcy natural convection boundary layer flow over a vertical
cone in porous media saturated with a nanofluid containing gyrotactic
microorganisms with a convective boundary condition”, J. Nanofluids
voI. 5, PP. 765-773, 2016.
[26] R. A. Mohamed, A. Mahdy, S. Abo-Dahab, “Effects of thermophoresis,
heat source/sink, variable viscosity and chemical reaction on non-Darcian
mixed convective heat and mass transfer flow over a semi-infinite porous
inclined plate in the presence of thermal radiation”, J. Computational
Theoretical Nanoscie. voI. 10, PP. 1366-1375, 2013.
[27] S. Siddiqa, N. Begum, Md. A. Hossain, R. S. R. Gorla, “Natural
convection flow of a two-phase dusty non-Newtonian fluid along a
vertical surface”, Int. J. Heat Mass Transfer voI. 113, PP. 482-489, 2017.
[28] S. Siddiqa, N. Begum, M. A. Hossain, R. S. R. Gorla, “Numerical
solutions of natural convection flow of a dusty nanofluid about a vertical
wavy truncated cone”, J. Heat Transfer voI. 139, PP. 022503 (11 pages),
2017.
[29] S. Siddiqa, N. Begum, M. A. Hossain, R. S. R. Gorla, “Two-phase
natural convection flow of a dusty fluid”, Int. J. Numer. Meth. Heat
Fluid Flow voI. 25, PP. 1542-1556, 2015.
[30] D. C. Dalal, N. Datta, S. K. Mukherjea, “Unsteady natural convection
of a dusty fluid in an infinite rectangular channel”, Int. J. Heat Mass
Transfer voI. 41, PP. 547-562, 1998.
[31] S. M. Silu, M. Wainaina, M. Kimathi, “Effects of magnetic induction
on MHD boundary Layer flow of dusty fluid over a stretching sheet”,
Global J. Pure Appl. Math. voI. 14, PP. 1197-1215, 2018.
[32] B. J. Gireesha, R. S. R. Gorla, M. R. Krishnamurthy, B. C.
Prasannakumara, “Biot number effect on MHD flow and heat transfer
of nanofluid with suspended dust particles in the presence of
nonlinear thermal radiation and non-uniform heat source/sink”, Acta Et
Commentationes Universitatis Tartuensis De Mathematica voI. 22, PP.
91-114, 2018.
[33] B. J. Gireesha, R. S. R. Gorla, M. R. Krishnamurthy, B. C.
Prasannakumara, “MHD flow and radiative heat transfer of micropolar
dusty fluid suspended with alumina nanoparticles over a stretching sheet
embedded in a porous medium”, JNNCE J. Eng. Manag. voI. 2, PP.
30-45, 2018.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:79446", author = "F. M. Hady and A. Mahdy and R. A. Mohamed and Omima A. Abo Zaid", title = "Modeling Non-Darcy Natural Convection Flow of a Micropolar Dusty Fluid with Convective Boundary Condition", abstract = "A numerical approach of the effectiveness of numerous
parameters on magnetohydrodynamic (MHD) natural convection
heat and mass transfer problem of a dusty micropolar fluid in
a non-Darcy porous regime is prepared in the current paper.
In addition, a convective boundary condition is scrutinized into
the micropolar dusty fluid model. The governing boundary layer
equations are converted utilizing similarity transformations to a
system of dimensionless equations to be convenient for numerical
treatment. The resulting equations for fluid phase and dust phases
of momentum, angular momentum, energy, and concentration with
the appropriate boundary conditions are solved numerically applying
the Runge-Kutta method of fourth-order. In accordance with the
numerical study, it is obtained that the magnitude of the velocity
of both fluid phase and particle phase reduces with an increasing
magnetic parameter, the mass concentration of the dust particles, and
Forchheimer number. While rises due to an increment in convective
parameter and Darcy number. Also, the results refer that high values
of the magnetic parameter, convective parameter, and Forchheimer
number support the temperature distributions. However, deterioration
occurs as the mass concentration of the dust particles and Darcy
number increases. The angular velocity behavior is described by
progress when studying the effect of the magnetic parameter and
microrotation parameter.", keywords = "Micropolar dusty fluid, convective heating, natural
convection, MHD, porous media.", volume = "14", number = "2", pages = "53-7", }
