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MHD flow and heat transfer of a viscous fluid over a radially stretching power-law sheet with suction/injection in a porous medium


A steady boundary layer flow and heat transfer over a radially stretching isothermal porous sheet is analyzed. Stretching is assumed to follow a radial power law, and the fluid is electrically conducting in the presence of a transverse magnetic field with a very small magnetic Reynolds number. The governing nonlinear partial differential equations are reduced to a system of nonlinear ordinary differential equations by using appropriate similarity transformations, which are solved analytically by the homotopy analysis method (HAM) and numerically by employing the shooting method with the adaptive Runge-Kutta method and Broyden’s method in the domain [0,∞). Analytical expressions for the velocity and temperature fields are derived. The influence of pertinent parameters on the velocity and temperature profiles is discussed in detail. The skin friction coefficient and the local Nusselt number are calculated as functions of several influential parameters. The results predicted by both methods are demonstrated to be in excellent agreement. Moreover, HAM results for a particular problem are also compared with exact solutions.

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  1. L. J. Crane, “Flow Past a Stretching Plate,” Z. Angew. Math. Phys. 21, 645–655 (1970).

    Article  Google Scholar 

  2. P. Carragher and L. J. Crane, “Heat Transfer on a Continuous Stretching Sheet,” Z. Angew. Math. Mech. 62, 564–573 (1982).

    Article  Google Scholar 

  3. E. Magyari and B. Keller, “Heat and Mass Transfer in the Boundary Layers on an Exponentially Stretching Continuous Surface,” J. Phys. D. Appl. Phys. 32, 577–585 (1999).

    ADS  Article  Google Scholar 

  4. M. K. Partha, P. V. S. N. Murthy, and R. Rajasekhar, “Effect of Viscous Dissipation on the Mixed Convection Heat Transfer from an Exponentially Stretching Surface,” Heat Mass Transfer 41, 360–366 (2005).

    ADS  Article  Google Scholar 

  5. M. Sajid and T. Hayat, “Influence of Thermal Radiation on the Boundary Layer Flow due to an Exponentially Stretching Sheet,” Int. Comm. Heat Mass Transfer 35, 347–356 (2008).

    Article  Google Scholar 

  6. B. Bidin and R. Nazar, “Numerical Solution of the Boundary Layer Flow over an Exponentially Stretching Sheet with Thermal Radiation,” Eur. J. Sci. Res. 33, 710–717 (2009).

    Google Scholar 

  7. J. Alinejad and S. Samarbakhsh, “Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation,” J. Appl. Math. 2012. 587834 (2012). DOI: 10.1155/2012/587834.

    MathSciNet  Article  Google Scholar 

  8. M. Misra, N. Ahmad, and Z. U. Siddiqui, “Unsteady Boundary Layer Flow Past a Stretching Plate and Heat Transfer with Variable Thermal Conductivity,” World J. Mech. 2, 35–41 (2012).

    Article  Google Scholar 

  9. M. S. Abel, S. K. Khan, and K. Prasad, “Convective Heat and Mass Transfer in a Viscoelastic Fluid Flow through a Porous Medium over a Stretching Sheet,” Int. J. Numer. Methods Heat Fluid Flow 11, 779–793 (1991).

    Article  Google Scholar 

  10. R. Bhargava, L. Kumar, and H. S. Takhar, “Finite Element Solution of Mixed Convection Micropolar Flow Driven by a Porous Stretching Sheet,” Int. J. Eng. Sci. 41, 2161–2178 (2003).

    MATH  Article  Google Scholar 

  11. A. M. Rashad, “Radiative Effect on Heat Transfer from a Stretching Surface in a Porous Medium,” Int. J. Appl. Math. Mech. 3, 14–23 (2007).

    Google Scholar 

  12. S. Shafie, N. Amin, and I. Pop, “Unsteady Boundary Layer due to a Stretching Sheet in a Porous Medium using Brinkman Equation Model,” Int. J. Heat Tech. 24, 111–117 (2006).

    Google Scholar 

  13. P. Ganesan and G. Palani, “Finite Difference Analysis of Unsteady Natural Convection MHD Past an Inclined Plate with Variable Surface Heat and Mass Flux,” Int. J. Heat Mass Transfer 47, 4449–4457 (2004).

    MATH  Article  Google Scholar 

  14. G. K. Ramesh, B. J. Gireesha, and C. S. Bagewadi, “Heat Transfer in MHD Dusty Boundary Layer Flow over an Inclined Stretching Sheet with Non-Uniform Heat Source/Sink,” Adv. Math. Phys. 2012, 657805 (2012). DOI: 10.1155/2012/657805.

    Article  Google Scholar 

  15. A. Shahzad, R. Ali, and M. Khan, “On the Exact Solution for Axisymmetric Flow and Heat Transfer over a Nonlinear Radially Stretching Sheet,” Chinese Phys. Lett. 29, 084705 (2012).

    Article  Google Scholar 

  16. P. S. Gupta and A. S. Gupta, “Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing,” Canad. J. Chem. Eng. 55, 744–746 (1977).

    Article  Google Scholar 

  17. R. Bhargava, S. Sharma, H. S. Takhar, et al., “Numerical Solutions for Micropolar Transport Phenomena over a Nonlinear Stretching Sheet,” Nonlinear Anal. Model. Control 12, 45–63 (2007).

    MATH  Google Scholar 

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Correspondence to M. Khan.

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Original Russian Text © M. Khan, A. Munir, A. Shahzad, A. Shah.


Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 2, pp. 76–86, March–April, 2015.

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Khan, M., Munir, A., Shahzad, A. et al. MHD flow and heat transfer of a viscous fluid over a radially stretching power-law sheet with suction/injection in a porous medium. J Appl Mech Tech Phy 56, 231–240 (2015).

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  • axisymmetric flow
  • heat transfer
  • suction/injection