Influence of Magnetic Field and Thermal Radiation by Natural Convection Past a Vertical Cone Subjected to a Variable Surface Heat Flux

G.Palani<; Kwang Yong Kim

doi:10.3879/j.issn.1000-0887.2012.05.006

Volume 33 Issue 5

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2012 > 33(5): 574-587

G.Palanidoi: 10.3879/j.issn.1000-0887.2012.05.006

Citation:

G.Palani<, Kwang Yong Kim. Influence of Magnetic Field and Thermal Radiation by Natural Convection Past a Vertical Cone Subjected to a Variable Surface Heat Flux[J]. Applied Mathematics and Mechanics, 2012, 33(5): 574-587. doi: 10.3879/j.issn.1000-0887.2012.05.006

G.Palanidoi: 10.3879/j.issn.1000-0887.2012.05.006

Citation:

PDF( 1948 KB)

Influence of Magnetic Field and Thermal Radiation by Natural Convection Past a Vertical Cone Subjected to a Variable Surface Heat Flux

doi: 10.3879/j.issn.1000-0887.2012.05.006

G.Palani<¹,
Kwang Yong Kim²

¹Department of Mathematics, Dr Ambedkar Govt Arts College, Chennai 600-039, Tamil Nadu, India;²Department of Mechanical Engineering, Inha University, Incheon 402-751, Republic of Korea

Received Date: 2010-12-15
Rev Recd Date: 2012-01-04
Publish Date: 2012-05-15

Abstract

Abstract

A numerical study was performed to examine the heat transfer characteristics of natural convection past a vertical cone under the combined effects of magnetic field and thermal radiation. The surface of the cone was subjected to a variable surface heat flux. The fluid considered was a gray, absorbing-emitting radiation but a non-scattering medium, with approximate transformations the boundary layer equations governing the flow were reduced to a non-dimensional equations valid in the free convection regime. The dimensionless governing equations were solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent, more accurate and unconditionally stable. Numerical results are obtained and presented for velocity, temperature, local and average wall shear stress, local and average Nusselt number in air and water. The present results are compared with the previously published work and are found to be in an excellent agreement.
- apex,
- magnetohydrodynamics,
- radiation,
- finite difference,
- skin friction,
- vertical cone

FullText(HTML)

References(32)

References

[1]	Merk H J, Prins J A. Thermal convection laminar boundary layer Ⅰ[J]. Appl Sci Res, 1954, 4(1):11-24.
[2]	Merk H J, Prins J A. Thermal convection laminar boundary layer Ⅱ[J]. Appl Sci Res, 1954, 4(3): 195-206.
[3]	Alamgir M. Overall heat transfer from vertical cones in laminar free convection: an approximate method[J]. ASME Journal of Heat Transfer, 1989, 101: 174-176.
[4]	Pop I, Takhar H S. Compressibility effects in laminar free convection from a vertical cone[J]. Appl Sci Res, 1991, 48(1): 71-82.
[5]	Pop I, Grosan T, Kumar M. Mixed convection along a vertical cone for fluids of any Prandtl number case of constant wall temperature[J]. Int J Numerical Methods Heat Fluid Flow, 2003, 13(7): 815-829.
[6]	Takhar H S, Chamkha A J, Nath G. Effect of thermo-physical quantities on the natural convection flow of gases over a vertical cone[J]. Int J Engg Sci, 2004, 42: 243-256.
[7]	Lin F N. Laminar convection from a vertical cone with uniform surface heat flux[J]. Letters Heat Mass Transfer, 1976, 3(1/2): 49-58.
[8]	Na T Y, Chiou J P. Laminar natural convection over a frustum of a cone[J]. Appl Sci Res, 1979, 35(5/6): 409-421.
[9]	Gorla R S R, Krishnan V, Pop I. Natural convection flow of a power-law fluid over a vertical frustum of a cone under uniform heat flux conditions[J]. Mech Res Comm, 1994, 21: 139-146.
[10]	Kumari M, Pop I. Free convection over a vertical rotating cone with constant wall heat flux[J]. J Appl Mech Engg, 1998, 3(3): 451-464.
[11]	Hossain M A, Paul S C, Mandal A C. Natural convection flow along a vertical circular cone with uniform surface temperature and surface heat flux in a thermally stratified medium[J]. Int J Numer Methods Heat Fluid Flow, 2002, 12(3): 290-305.
[12]	Bapuji P J, Ekambavannan K, Pop I. Transient laminar free convection from a vertical cone with non-uniform surface heat flux[J]. Studia Univ,Mathematica, 2008, 53(1): 75-99.
[13]	Sparrow E M, Cess R D. The effect of a magnetic field on free convection heat transfer[J]. International Journal of Heat and Mass Transfer, 1961, 3(4):267-274.
[14]	Cess R D. The interaction of thermal radiation with free convection heat transfer[J]. International Journal of Heat and Mass Transfer, 1966, 9(11):1269-1277.
[15]	Kumari M, Nath G. Development of two dimensional boundary layer with an applied magnetic field due to an impulsive motion[J]. Indian J Pure Appl Math, 1999, 30: 695-708.
[16]	Takhar H S, Chamkha A J, Nath G. Unsteady mixed convection flow from a rotating vertical cone with magnetic field[J]. Heat and Mass Transfer, 2003, 39(4): 297-304.
[17]	Ozturk A. Unsteady laminar mixed convection about a spinning sphere with a magnetic field[J]. Heat and Mass Transfer, 2005, 41(10): 864-874.
[18]	Chamkha A J, Al-Mudaf A. Unsteady heat and mass transfer from a rotating vertical cone with a magnetic field and heat generation or absorption effects[J]. Int J Thermal Sci, 2005, 44(3): 267-276.
[19]	Ece M C. Free convection flow about a vertical spinning cone under a magnetic field[J]. Applied Mathematics and Computation, 2006, 179(1): 231-242.
[20]	Soundalgekar V M, Takhar H S. Radiation effects on free convection flow past a semi-infinite vertical plate[J]. Modelling Measurement and Control, B, 1993, 51: 31-40.
[21]	Hossain M A, Takhar H S. Radiation effects on mixed convection along a vertical plate with uniform surface temperature[J]. Heat and Mass Transfer, 1996, 31(4): 243-248.
[22]	Raptis A, Perdikis C. Radiation and free convection flow past a moving plate[J]. Appl Mech and Engg, 1999, 4(4): 817-821.
[23]	Muthucumaraswamy R, Ganesan P. Radiation effects on flow past an impulsively started infinite vertical plate with variable temperature[J]. Int J Appl Mech Engg, 2003, 8(1): 125-129.
[24]	Raptis A, Massalas C V. Magnetohydrodynamic flow past a plate by the presence of radiation[J]. Heat and Mass Transfer, 1998, 34(2/3): 107-109.
[25]	Yih K A. Radiation effects on mixed convection over an isothermal cone in porous media[J]. Heat and Mass Transfer, 2001, 37(1): 53-57.
[26]	Takhar H S, Beg O A, Chamkha A J, Filip D, Pop I. Mixed radiation-convection boundary layer flow of an optically dense fluid along a vertical flat plate in a non-Darcy porous medium[J]. Int J Applied Mechanics and Engineering, 2003, 8(3): 483-496.
[27]	Afify A A. The effect of radiation on free convective flow and mass transfer past a vertical isothermal cone surface with chemical reaction in the presence of a transverse magnetic field[J]. Can J Physics, 2004, 82(6): 447-458.
[28]	Bég O A, Zueco J, Takhar H S, Bég T A. Network numerical simulation of impulsively-started transient radiation-convection heat and mass transfer in a saturated Darcy-Forchheimer porous medium[J]. Nonlinear Analysis: Modelling and Control, 2008, 13(3): 281-303.
[29]	Abd El-Naby M A, Elbarbary M E, AbdElazem N Y. Finite difference solution of radiation on MHD unsteady free-convection flow over vertical porous plate[J]. Applied Mathematics and Computation, 2004, 151(2): 327-346.
[30]	Roming M F. The influence of electric and magnetic fields on heat transfer to electrically conducting fluid[C]Advances in Heat Transfer. New York: Academic Press, 1964: 286-354.
[31]	Brewester M Q. Thermal Radiative Transfer and Properties[M]. New York: John Wiley and Sons, Inc, 1992.
[32]	Carnahan B, Luther H A, Wilkes J O. Applied Numerical Methods[M]. New York: John Wiley and Sons, 1969.