Effect of Variable viscosity on Convective Heat Transfer along an Inclined Plate Embedded in Porous Medium with an Applied Magnetic Field
The flow and heat transfer characteristics for natural
convection along an inclined plate in a saturated porous medium with
an applied magnetic field have been studied. The fluid viscosity has
been assumed to be an inverse function of temperature. Assuming
temperature vary as a power function of distance. The transformed
ordinary differential equations have solved by numerical integration
using Runge-Kutta method. The velocity and temperature profile
components on the plate are computed and discussed in detail for
various values of the variable viscosity parameter, inclination angle,
magnetic field parameter, and real constant (λ). The results have also
been interpreted with the aid of tables and graphs. The numerical
values of Nusselt number have been calculated for the mentioned
parameters.
[1] A. Bejan, and K.R. Khair , Heat and mass transfer by natural convection
in a porous medium, International J. Heat Mass Transfer, Vol. 28, no.
5, pp 909-918, 1985.
[2] S. Abel, K.V. Prasad, and A. Mahaboob, Buoyancy force and thermal
radiation effects in MHD boundary layer visco-elastic fluid flow over
continuously moving stretching surface. Int. J. thermal Sciences, Vol. 44
pp. 465-476, 2005.
[3] Cheng Ching-Yang, An integral approach for hydro-magnetic natural
convection heat and mass transfer from vertical surfaces with power law
variation in wall temperature and concentration in porous medium,
International Communications in Heat and Mass Transfer, Vol. 32, pp
204-213, 2005.
[4] K.C. Sarangi, and C.B. Jose, "Unsteady free convective MHD flow and
Mass Transfer past a vertical porous plate with variable temperature",
Bull. Cal. Math. Soc., Vol. 97, no. 2, pp 137-146, 2005.
[5] S. M. M. EL-Kabeir, M.A. El-Hakiem and A. M. Rashad, "Natural
Convection from a Permeable Sphere Embedded in a Variable Porosity
Porous Medium Due to Thermal Dispersion", Nonlinear Analysis:
Modelling and Control, Vol. 12, No. 3, pp 345-357, 2007.
[6] Anuar Ishak, Roslinda Nazar, Norihan M. Arifin and Ioan Pop, "Dual
Solutions in Mixed Convection Flow Near a Stagnation Point on a
Vertical Porous Plate", International Journal of Thermal Sciences, Vol.
47, pp 417-422, 2008.
[7] A.M. Rashad and A.Y. Bakier, "MHD Effects on Non-Darcy Forced
Convection Boundary Layer Flow Past a Permeable Wedge in Porous
Medium with Uniform Heat Flux", Nonlinear Analysis: Modelling and
Control, Vol. 14, No. 2, pp 249-261, 2009.
[8] M.S. Abel, N. Mahesha and J. Tawade, "Heat transfer in a liquid film
over an unsteady stretching surface with viscous dissipation in presence
of external magnetic field", Applied Mathematical Modelling, Vol. 33,
pp 3430-3441, 2009.
[9] M.A. El-Aziz, "Radiation effect on the flow and heat transfer over an
unsteady stretching sheet", International Communications in Heat and
Mass Transfer, Vol. 36, pp 521-524, 2009.
[10] P. Singh, N.S. Tomer and D. Sinha, "Numerical study of heat transfer
over stretching surface in porous media with transverse magnetic field",
Proceeding of International Conference on Challenges and application
of Mathematics in Sciences and Technology 2010, ISBN 023- 032-875-
X, pp 422-430.
[11] P. Singh, N.S. Tomer, S. Kumar and D. Sinha, "MHD oblique
stagnation-point flow towards a stretching sheet with heat transfer",
International Journal of Applied Mathematics and Mechanics, Vol. 6,
no. 13, pp 94-111, 2010.
[12] P. Singh, A. Jangid, N.S. Tomer, S. Kumar and D. Sinha, "Effects of
Thermal Radiation and Magnetic Field on Unsteady Stretching
Permeable Sheet in Presence of Free Stream Velocity", International
Journal of Information and Mathematical Sciences, Vol.6, no.3, pp-63-
69, 2010.
[13] E. M. A. Elbashbeshy, D. M. Yassmin and A. A. Dalia, "Heat Transfer
Over an Unsteady Porous Stretching Surface Embedded in a Porous
Medium with Variable Heat Flux in the Presence of Heat Source or
Sink", African Journal of Mathematics and Computer Science Research
Vol. 3, no.5, pp 68-73, 2010.
[14] A. Ishak, "Unsteady MHD flow and heat transfer over a stretching
plate", Journal of Applied Sciences, vol. 10, No. 18, pp 2127-2131,
2010.
[15] M.A. El-Aziz, "Flow and heat transfer over an unsteady stretching
surface with Hall effect", Meccanica, vol. 45, pp 97-109, 2010.
[16] Adrian Postelnicu, "Heat and Mass Transfer by Natural Convection at a
Stagnation Point in a Porous Medium Considering Soret and Dufour
Effects", Heat Mass Transfer, vol. 46, pp 831-840, 2010.
[1] A. Bejan, and K.R. Khair , Heat and mass transfer by natural convection
in a porous medium, International J. Heat Mass Transfer, Vol. 28, no.
5, pp 909-918, 1985.
[2] S. Abel, K.V. Prasad, and A. Mahaboob, Buoyancy force and thermal
radiation effects in MHD boundary layer visco-elastic fluid flow over
continuously moving stretching surface. Int. J. thermal Sciences, Vol. 44
pp. 465-476, 2005.
[3] Cheng Ching-Yang, An integral approach for hydro-magnetic natural
convection heat and mass transfer from vertical surfaces with power law
variation in wall temperature and concentration in porous medium,
International Communications in Heat and Mass Transfer, Vol. 32, pp
204-213, 2005.
[4] K.C. Sarangi, and C.B. Jose, "Unsteady free convective MHD flow and
Mass Transfer past a vertical porous plate with variable temperature",
Bull. Cal. Math. Soc., Vol. 97, no. 2, pp 137-146, 2005.
[5] S. M. M. EL-Kabeir, M.A. El-Hakiem and A. M. Rashad, "Natural
Convection from a Permeable Sphere Embedded in a Variable Porosity
Porous Medium Due to Thermal Dispersion", Nonlinear Analysis:
Modelling and Control, Vol. 12, No. 3, pp 345-357, 2007.
[6] Anuar Ishak, Roslinda Nazar, Norihan M. Arifin and Ioan Pop, "Dual
Solutions in Mixed Convection Flow Near a Stagnation Point on a
Vertical Porous Plate", International Journal of Thermal Sciences, Vol.
47, pp 417-422, 2008.
[7] A.M. Rashad and A.Y. Bakier, "MHD Effects on Non-Darcy Forced
Convection Boundary Layer Flow Past a Permeable Wedge in Porous
Medium with Uniform Heat Flux", Nonlinear Analysis: Modelling and
Control, Vol. 14, No. 2, pp 249-261, 2009.
[8] M.S. Abel, N. Mahesha and J. Tawade, "Heat transfer in a liquid film
over an unsteady stretching surface with viscous dissipation in presence
of external magnetic field", Applied Mathematical Modelling, Vol. 33,
pp 3430-3441, 2009.
[9] M.A. El-Aziz, "Radiation effect on the flow and heat transfer over an
unsteady stretching sheet", International Communications in Heat and
Mass Transfer, Vol. 36, pp 521-524, 2009.
[10] P. Singh, N.S. Tomer and D. Sinha, "Numerical study of heat transfer
over stretching surface in porous media with transverse magnetic field",
Proceeding of International Conference on Challenges and application
of Mathematics in Sciences and Technology 2010, ISBN 023- 032-875-
X, pp 422-430.
[11] P. Singh, N.S. Tomer, S. Kumar and D. Sinha, "MHD oblique
stagnation-point flow towards a stretching sheet with heat transfer",
International Journal of Applied Mathematics and Mechanics, Vol. 6,
no. 13, pp 94-111, 2010.
[12] P. Singh, A. Jangid, N.S. Tomer, S. Kumar and D. Sinha, "Effects of
Thermal Radiation and Magnetic Field on Unsteady Stretching
Permeable Sheet in Presence of Free Stream Velocity", International
Journal of Information and Mathematical Sciences, Vol.6, no.3, pp-63-
69, 2010.
[13] E. M. A. Elbashbeshy, D. M. Yassmin and A. A. Dalia, "Heat Transfer
Over an Unsteady Porous Stretching Surface Embedded in a Porous
Medium with Variable Heat Flux in the Presence of Heat Source or
Sink", African Journal of Mathematics and Computer Science Research
Vol. 3, no.5, pp 68-73, 2010.
[14] A. Ishak, "Unsteady MHD flow and heat transfer over a stretching
plate", Journal of Applied Sciences, vol. 10, No. 18, pp 2127-2131,
2010.
[15] M.A. El-Aziz, "Flow and heat transfer over an unsteady stretching
surface with Hall effect", Meccanica, vol. 45, pp 97-109, 2010.
[16] Adrian Postelnicu, "Heat and Mass Transfer by Natural Convection at a
Stagnation Point in a Porous Medium Considering Soret and Dufour
Effects", Heat Mass Transfer, vol. 46, pp 831-840, 2010.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50338", author = "N.S. Tomer and Phool Singh and Manoj Kumar", title = "Effect of Variable viscosity on Convective Heat Transfer along an Inclined Plate Embedded in Porous Medium with an Applied Magnetic Field", abstract = "The flow and heat transfer characteristics for natural
convection along an inclined plate in a saturated porous medium with
an applied magnetic field have been studied. The fluid viscosity has
been assumed to be an inverse function of temperature. Assuming
temperature vary as a power function of distance. The transformed
ordinary differential equations have solved by numerical integration
using Runge-Kutta method. The velocity and temperature profile
components on the plate are computed and discussed in detail for
various values of the variable viscosity parameter, inclination angle,
magnetic field parameter, and real constant (λ). The results have also
been interpreted with the aid of tables and graphs. The numerical
values of Nusselt number have been calculated for the mentioned
parameters.", keywords = "Heat Transfer, Magnetic Field, Porosity, Viscosity", volume = "5", number = "3", pages = "237-5", }
