Skip to main content
SpringerLink
Log in

Natural Convection Between Vertical Walls Due To Point/Line Heat Source/Sink

  • Original paper
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

In the present paper, we have investigated the influence of constant point/line heat source on fully developed free convective laminar flow between two infinite vertical walls of an electrically conducting and viscous incompressible fluid. The Heaviside step function is used to model the constant heat source/sink and further this function can be converted into line heat source/sink. The compact solution has been obtained by using Laplace transform method. The effects of physical parameters such as constant point/line heat source parameter and Hartmann number on the velocity and temperature fields are shown graphically while on skin friction, mass flow rate and Nusselt number of the fluid are presented in tabular form. It is found that the velocity and temperature field of the fluid increases when the point heat source changes into a line heat source. Also, we have observed that the velocity and temperature profiles increase as the value of constant point/line heat source parameter increases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Abbreviations

B 0 :

Constant magnetic field

C p :

Specific heat at constant pressure

d :

Distance between two walls

g :

Gravitational acceleration

Ha :

Hartmann number

Nu 0 :

Nusselt number at left wall

Nu 1 :

Nusselt number at right wall

Q 0 :

Volumetric rate of heat generation/absorption

S :

Constant heat source parameter

T c :

Temperature of both walls

T :

Temperature of the fluid

T*:

Dimensionless temperature of the fluid

u :

Velocity of the fluid in x-direction

u 0 :

Characteristic velocity of the fluid

u*:

Dimensionless velocity

β :

Coefficient of thermal expansion

κ :

Thermal conductivity

μ :

Coefficient of viscosity

μ e :

Magnetic permeability

υ:

Kinematic viscosity of the fluid

ρ :

Fluid density

σ:

Electrical conductivity

τ 0 :

Skin friction coefficient at the left wall

τ 1 :

Skin friction coefficient at the right wall

References

  1. Hartmann, J.: Hg-dynamics I: theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field. Math. Fys. Medd. 15(6), 1–28 (1937)

    MathSciNet  Google Scholar 

  2. Poots, G.: Laminar natural convection flow in magneto-hydrodynamics. Int. J. Heat Mass Transf. 3, 1–25 (1961)

    Article  Google Scholar 

  3. Sparrow, E.M., Cess, R.D.: Temperature-dependent heat sources or sinks in a stagnation point flow. Appl. Sci. Res. 10, 185–197 (1961)

    Article  MATH  Google Scholar 

  4. Katagiri, M.: Flow formation in coquette motion in magnetohydrodynamic. J. Phys. Soc. Jpn. 17, 393–396 (1962)

    Article  MATH  Google Scholar 

  5. Singer, R.M.: Transient magnetohydrodynamics flow and heat transfer. J. Appl. Math. Phys. 16(4), 483–494 (1965)

    MathSciNet  Google Scholar 

  6. Cramer, K.R., Pai, S.I.: Magnetofluiddynamics for Engineering and Applied Physicists. McGraw-Hill, New York (1973)

    Google Scholar 

  7. Georgantopoulos, G.A., Nanousis, N.D.: Effect of mass transfer on the hydromagnetic free convective flow in the Stokes’ problems. Astrophys. Space Sci. 67, 229–236 (1980)

    Article  MathSciNet  Google Scholar 

  8. Raptis, A., Singh, A.K.: MHD free convection flow past an accelerated vertical plate. Int. Commun. Heat Mass Transf. 10, 313–321 (1983)

    Article  Google Scholar 

  9. Sacheti, N.C., Chandran, P., Singh, A.K.: An exact solution for unsteady magnetohydrodynamic free convection flow with constant heat flux. Int. Commun. Heat Mass Transf. 21(1), 131–142 (1994)

    Article  Google Scholar 

  10. Chamkha, A.J.: Hydromagnetic natural convection from an isothermal inclined surface adjacent to a thermally stratified porous medium. Int. J. Eng. Sci. 35, 975–986 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ghosh, S.K., Nandi, D.K.: Magnetohydrodynamic fully developed combined convection flow between vertical plates heated asymmetrically. J. Tech. Phys. 41, 173–185 (2000)

    MATH  Google Scholar 

  12. Chamkha, A.J., Takhar, H.S., Nath, G.: Mixed convection flow over a vertical plate with localized heating (cooling), magnetic field and suction (injection). Heat Mass Transf. 40(11), 835–841 (2004)

    Article  Google Scholar 

  13. Singh, A.K., Paul, T.: Transient natural convection between two vertical walls heated/cooled asymmetrically. Int. J. Appl. Mech. Eng. 11, 143–154 (2006)

    MATH  Google Scholar 

  14. Hamza, M.M., Usman, I.G., Sule, A.: Unsteady/Steady Hydromagnetic convective flow between two vertical walls in the presence of variable thermal conductivity. J. Fluids, Article ID 358053, 1–9 (2015)

    Article  Google Scholar 

  15. Jha, B.K.: MHD free and forced convection flow past an infinite vertical plate with heat source. Astrophys. Space Sci. 183, 169–175 (1991)

    Article  MATH  Google Scholar 

  16. Sharma, P.R., Singh, G.: Effect of variable thermal conductivity and heat source/sink on MHD flow near a stagnation point on a linearly stretching sheet. J. Appl. Fluid Mech. 2(1), 13–21 (2009)

    Google Scholar 

  17. Bhattacharyya, K.: Effects of radiation and heat source/sink on unsteady MHD boundary layer flow and heat transfer over a shrinking sheet with suction/injection. Front. Chem. Sci. Eng. 5(3), 376–384 (2011)

    Article  Google Scholar 

  18. Umavathi, J.C., Liu, I.C.: Magnetoconvection in a vertical channel with heat source or sink. Meccanica 48(9), 2221–2232 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ramandevi, B., Reddy, J.V.R., Sugunamma, V., Sandeep, N.: Combined influence of viscous dissipation and non-uniform heat source/sink on MHD non-Newtonian fluid flow with Cattaneo-Christov heat flux. Alex. Eng. J. 57(2), 1009–1018 (2018)

    Article  Google Scholar 

  20. Seth, G.S., Nandkeolyar, R., Ansari, MdS: Unsteady MHD convection flow within a parallel plate rotating channel with thermal source/sink in a porous medium under slip boundary conditions. Int. J. Eng. Sci. Technol. 2(11), 1–16 (2010)

    Google Scholar 

  21. Seth, G.S., Sarkar, S., Mahato, G.K.: Effect of Hall current on hydromagnetic free convection flow with heat and mass transfer of a heat absorbing fluid past an impulsively moving vertical plate with ramped temperature. Int. J. Heat Technol. 31(1), 85–96 (2013)

    Google Scholar 

  22. Seth, G.S., Sharma, R., Hussain, S.M., Sarkar, S.: Hall effect on unsteady MHD natural convection flow of a heat absorbing and radiating fluid past an accelerated moving vertical plate with ramped temperature. Int. J. Energy Technol. 6(12), 1–13 (2014)

    Google Scholar 

  23. Seth, G.S., Sharma, R., Sarkar, S.: Natural convention heat and mass transfer flow with Hall current, rotation, radiation and heat absorption past an accelerated moving vertical plate with ramped temperature. J. Appl. Fluid Mech. 8(1), 7–20 (2015)

    Google Scholar 

  24. Seth, G.S., Kumbhakar, B., Sharma, R.: Unsteady hydromagnetic natural convection flow of a heat absorbing fluid within a rotating vertical channel in porous medium with Hall effects. J. Appl. Fluid Mech. 8(4), 767–779 (2015)

    Article  Google Scholar 

  25. Seth, G.S., Sharma, R., Kumbhakar, B.: Effect of Hall current on unsteady MHD convective Couette flow of heat absorbing fluid due to accelerated movement of one of the plates of the channel in a porous medium. J. Porous Media 19(1), 13–30 (2016)

    Article  Google Scholar 

  26. Sarkar, S., Seth, G.S.: Unsteady hydromagnetic natural convection flow past a vertical plate with time-dependent free stream through a porous medium in the presence of Hall current, rotation and heat absorption. J. Aerospace Eng. 30(1), 04016081 (2016)

    Article  Google Scholar 

  27. Seth, G.S., Bhattacharyya, A., Tripathi, R.: Effect of Hall current on MHD natural convection heat and mass transfer flow of rotating fluid past a vertical plate with ramped wall temperature. Front. Heat Mass Transf. 9, 21 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

The author (Naveen Dwivedi) expresses special thanks to the UGC, New Delhi, India, for providing financial support in the form of a Junior Research Fellowship to accomplish this work (UGC Ref. No. 1274 (PWD)).

Author information

Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India

    Naveen Dwivedi & A. K. Singh

  2. Department of Mathematics, Central University of Rajasthan, Ajmer, India

    Anand Kumar

Authors
  1. Naveen Dwivedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. K. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anand Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anand Kumar.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dwivedi, N., Singh, A.K. & Kumar, A. Natural Convection Between Vertical Walls Due To Point/Line Heat Source/Sink. Int. J. Appl. Comput. Math 5, 75 (2019). https://doi.org/10.1007/s40819-019-0659-2

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s40819-019-0659-2

Keywords

Search

Navigation