Skip to main content
SpringerLink
Log in

Magnetohydrodynamic Free Convection Flow and Heat Transfer of Non-Newtonian Tangent Hyperbolic Fluid from Horizontal Circular Cylinder with Biot Number Effects

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

Abstract

This article presents the nonlinear, steady boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic non-Newtonian fluid from a Horizontal Circular Cylinder in the presence of magnetic field and Biot number effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), power law index (n), Prandtl number (Pr), Biot number \((\upgamma )\), the magnetic parameter (M) and dimensionless tangential coordinate (\(\xi \)) on velocity and temperature evolution on the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that the velocity, skin friction and heat transfer rate reduce with increasing We. Whereas, there is slight increase in temperature. Increasing n is observed to increase the velocity and heat transfer rate but decreases temperature and skin friction. An increasing \(\upgamma \) is seen to increase velocity, temperature, local skin friction and heat transfer rate. And an increasing M is found to decrease velocity, skin friction and heat transfer rate but increases the temperature. The study is relevant to chemical materials processing applications.

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
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

a:

radius of the cylinder

\(B_{0 }\) :

externally imposed radial magnetic field

\(C_{f}\) :

Skin friction coefficient

f :

Non-dimensional steam function

Gr :

Grashof number

g :

Acceleration due to gravity

k:

Thermal conductivity of fluid

M :

Magnetic parameter

n :

Power law index

Nu :

Heat transfer rate (Local Nusselt number)

Pr :

Prandtl number

T :

Temperature of the fluid

u, v :

Non-dimensional velocity components along the x and y directions, respectively

V :

Velocity vector

We :

Weissenberg number

x :

Stream wise coordinate

y :

Transverse coordinate

\(\alpha \) :

Thermal diffusivity

\(\beta \) :

The coefficient of thermal expansion

\(\varPhi \) :

Azimuthal coordinate

\(\phi \) :

Non-dimensional concentration

\(\eta \) :

The dimensionless radial coordinate

\(\mu \) :

Dynamic viscosity

\(\nu \) :

Kinematic viscosity

\(\theta \) :

Non-dimensional temperature

\(\rho \) :

Density of non-Newtonian fluid

\(\xi \) :

The dimensionless tangential coordinate

\(\psi \) :

Dimensionless stream function

\(\gamma \) :

Biot number

\(\Gamma \) :

Time dependent material constant

\(\Pi \) :

Second invariant strain tensor

w :

Conditions at the wall (cylinder surface)

\(\infty \) :

Free stream conditions

References

  1. Ramachandra Prasad, V., Subba Rao, A., Bhaskar Reddy, N., Vasu, B., Anwar Bég, O.: Modelling laminar transport phenomena in a Cassonrheological fluid from a horizontal circular cylinder with partialslip. Proc. IMechE Part E: J Process Mech. Eng. 227(4), 309–326 (2013). doi:10.1177/0954408912466350

    Google Scholar 

  2. Norouzi, M., Davoodi, M., Bég, O.A., Joneidi, A.A.: Analysis of the effect of normal stress differences on heat transfer in creeping viscoelastic Dean flow. Int. J. Therm. Sci. 69, 61–69 (2013)

    Article  Google Scholar 

  3. Uddin, M.J., Yusoff, N.H.M., Bég, O.A., Ismail, A.I.: Lie group analysis and numerical solutions for non-Newtonian nanofluid flow in a porous medium with internal heat generation. Physica Scripta 87(2), 025401(e) (2013)

    Article  MATH  Google Scholar 

  4. Rashidi, M.M., Keimanesh, M., Bég, O.A., Hung, T.K.: Magneto-hydrodynamic biorheological transport phenomena in a porous medium: A simulation of magnetic blood flow control. Int. J. Numer. Meth. Biomed. Eng. 27, 805–821 (2011)

    Article  MATH  Google Scholar 

  5. Tripathi, D., Pandey, S.K., Bég, O.A.: Mathematical modelling of heat transfer effects on swallowing dynamics of viscoelastic food bolus through the human oesophagus. Int. J. Therm. Sci. 70, 41–53 (2013)

    Article  Google Scholar 

  6. Ishak, A.: Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition. Appl. Math. Comput. 217(2), 837–842 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Aziz, A.: A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Comm. Non. Sci. Num. Sim. 14(14), 1064–1068 (2009)

    Article  Google Scholar 

  8. Aziz, A.: Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition. Comm. Non. Sci. Num. Sim. 15(3), 573–580 (2010)

    Article  Google Scholar 

  9. Makinde, O.D., Olanrewaju, P.O.: Buoyancy effects on thermal boundary layer over a vertical plate with a convective surface boundary condition. ASME Int. J. Fluids Eng 132(4), 044502 (2010)

    Article  Google Scholar 

  10. Makinde, O.D., Aziz, A.: MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition. Int. J. Therm. Sci 49(9), 1813–1820 (2010)

    Article  Google Scholar 

  11. Makinde, O.D., Zimba, K., Bég, O.A.: Numerical study of chemically-reacting hydromagnetic boundary layer flow with Soret/Dufour effects and a convective surface boundary condition. Int. J. Therm. Environ. Eng. 4(1), 89–98 (2012)

    Article  Google Scholar 

  12. Bég, O.A., Uddin, M.J., Rashidi, M.M., Kavyani, N.: Double-diffusive radiative magnetic mixed convective slip flow with Biot number and Richardson number effects. J. Eng. Thermophys. 23(2), 79–97 (2014)

    Article  Google Scholar 

  13. Eijkel, J.C.T., Dalton, C., Hayden, C.J., Burt, J.P.H., Manz, A.: A circular ac magnetohydrodynamic micropump for chromatographic applications. Sens. Actuators B Chem. 92(1–2), 215–221 (2003)

    Article  Google Scholar 

  14. Liuta, I., Larachi, F.: Magnetohydrodynamics of trickle bed reactors: mechanistic model, experimental validation and simulations. Chem. Eng. Sci. 58(2), 297–307 (2003)

    Article  Google Scholar 

  15. Chang, T.-B., Bég, O.A., Kahya, E.: Numerical study of laminar incompressible velocity and magnetic boundary layers along a flat plate with wall effects. Int. J. Appl. Math. Mech. 6(6), 99–118 (2010)

    Google Scholar 

  16. Bég, O.A., Bakier, A.Y., Prasad, V.R.: Numerical study of free convection magnetohydrodynamic heat and mass transfer from a stretching surface to a saturated porous medium with Soret and Dufour effects. Comput. Mater. Sci. 46(1), 57–65 (2009)

    Article  Google Scholar 

  17. Makinde, O.D., Bég, O.A.: On inherent irreversibility in a reactive hydromagnetic channel flow. J. Therm. Sci. 19(1), 72–79 (2010)

  18. Bég, O.A., Bakier, A.Y., Prasad, V.R., Ghosh, S.K.: Nonsimilar, laminar, steady, electrically-conducting forced convection liquid metal boundary layer flow with induced magnetic field effects. Int. J. Therm. Sci. 48(8), 1596–1606 (2009)

    Article  Google Scholar 

  19. Lioubashevski, O., Katz, E., Willner, I.: Magnetic force effects on electrochemical processes: a theoretical hydrodynamic model. J. Phys. Chem. B 108, 5778–5784 (2004)

    Article  Google Scholar 

  20. Pop, I., Ingham, D.B.: Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media. Pergamon, Amsterdam (2001)

    Google Scholar 

  21. Nadeem, S., Akram, S.: Peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel. ZNA 64a(9–10), 559–567 (2009)

    Google Scholar 

  22. Nadeem, S., Akram, S.: Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer. Acta Mech. Sin. 27(2), 237–250 (2013). doi:10.1007/s10409-011-0423-2

    Article  MathSciNet  MATH  Google Scholar 

  23. Akram, S., Nadeem, S.: Simulation of heat and mass transfer on peristaltic flow of hyperbolic tangent fluid in an asymmetric channel. Int. J. Numer. Meth. In Fluids 70(12), 1475–1493 (2012). doi:10.1002/fld.2751

    Article  MathSciNet  Google Scholar 

  24. Akbar, N.S., Nadeem, S., Haq, R.U., Khan, Z.H.: Numerical solution of Magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet. Indian J. Phys 87(11), 112–1124 (2013). doi:10.1007/s12648-013-0339-8

    Article  Google Scholar 

  25. Eswara, A.T., Nath, G.: Unsteady forced convection laminar boundary layer flow over a moving longitudinal cylinder. Acta Mech. 93(1), 13–28 (1992)

    Article  MATH  Google Scholar 

  26. Zueco, J., Bég, O.A., Bég, T.A., Takhar, H.S.: Numerical study of chemically-reactive buoyancy-driven heat and mass transfer across a horizontal cylinder in a high-porosity non-Darcian regime. J. Porous Media 12(6), 519–535 (2009)

    Article  Google Scholar 

  27. Chang, C.L.: Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder. Int. J. Heat Mass Transf. 49, 4932–4942 (2006)

    Article  MATH  Google Scholar 

  28. Anwar, I., Amin, N., Pop, I.: Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder. Int. J. Non-Linear Mech. 43(9), 814–821 (2008)

    Article  MATH  Google Scholar 

  29. Rehman, M.A., Nadeem, S.: Mixed convection heat transfer in micropolar nanofluid over a vertical slender cylinder. Chin. Phys. Lett. 29(12), 124701 (2012)

    Article  Google Scholar 

  30. Prasad, V.R., Vasu, B., Bég, O.Anwar, Parshad, D.R.: Thermal radiation effects on magnetohydrodynamic free convection heat and mass transfer from a sphere in a variable porosity regime, Comm. Nonlinear Science Numerical. Simulation 17(2), 654–671 (2012)

    MathSciNet  Google Scholar 

  31. Makinde, O.D., Bég, O.A., Takhar, H.S.: Magnetohydrodynamic viscous flow in a rotating porous medium cylindrical annulus with an applied radial magnetic field. Int. J. Appl. Math. Mech. 5(6), 68–81 (2009)

    Google Scholar 

  32. Ishak, A., Nazar, R., Pop, I.: Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder. Energy Convers. Manag. 49(11), 3265–3269 (2008)

    Article  MATH  Google Scholar 

  33. EL-Hakiem, M.A.: Radiation effects on hydromagnetic free convective and mass transfer flow of a gas past a circular cylinder with uniform heat and mass flux. Int. J. Numer. Method Heat Fluid Flow 19(3/4), 445–458 (2009)

    Article  Google Scholar 

  34. Yih, K.A.: Viscous and Joule Heating effects on non-Darcy MHD natural convection flow over a permeable sphere in porous media with internal heat generation. Int. Commun. Heat Mass Transf. 27(4), 591–600 (2000)

    Article  Google Scholar 

  35. Keller, H.B.: Numerical methods in boundary-layer theory. Ann. Rev. Fluid Mech. 10, 417–433 (1978)

    Article  MathSciNet  Google Scholar 

  36. Subhas Abel, M., Datti, P.S., Mahesha, N.: Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source. Int. J. Heat Mass Transf. 52(11), 2902–2913 (2009)

    Article  MATH  Google Scholar 

  37. Chen, C.-H.: Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption. Int. J. Non-Linear Mech. 44(6), 596–603 (2009)

    Article  MATH  Google Scholar 

  38. Zhang, Y.L., Vairavamoorthy, K.: Analysis of transient flow in pipelines with fluid-structure interaction using method of lines. Int. J. Num. Meth. Eng. 63(10), 1446–1460 (2005)

    Article  MATH  Google Scholar 

  39. Kumari, M., Nath, G.: Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field. Int. J. Nonlinear Mech. 44(10), 1048–1055 (2009)

    Article  MATH  Google Scholar 

  40. Nazar, R., Amin, N., Pop, I.: Free convection boundary layer on an isothermal horizontal circular cylinder in a micropolar fluid, Heat transfer. In Proceeding of the 12th international conference (2002)

  41. Prhashanna, A., Chhabra, R.P.: Free convection in power-law fluids from a heated sphere. Chem. Eng. Sci. 65(23), 6190–6205 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jawaharlal Nehru Technological University Anantapur, Anantapuramu, 515002, India

    S. Abdul Gaffar & E. Keshava Reddy

  2. Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, 517325, India

    V. Ramachandra Prasad

Authors
  1. S. Abdul Gaffar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Ramachandra Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Keshava Reddy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Abdul Gaffar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gaffar, S.A., Prasad, V.R. & Reddy, E.K. Magnetohydrodynamic Free Convection Flow and Heat Transfer of Non-Newtonian Tangent Hyperbolic Fluid from Horizontal Circular Cylinder with Biot Number Effects. Int. J. Appl. Comput. Math 3, 721–743 (2017). https://doi.org/10.1007/s40819-015-0130-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40819-015-0130-y

Keywords

Search

Navigation