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Heat transfer characteristics for the Maxwell fluid flow past an unsteady stretching permeable surface embedded in a porous medium with thermal radiation

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Abstract

An unsteady boundary layer flow of a non-Newtonian fluid over a continuously stretching permeable surface in the presence of thermal radiation is investigated. The Maxwell fluid model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained. The transformed boundary layer equations are then solved numerically by the shooting method. The flow features and heat transfer characteristics for different values of the governing parameters (unsteadiness parameter, Maxwell parameter, permeability parameter, suction/blowing parameter, thermal radiation parameter, and Prandtl number) are analyzed and discussed in detail.

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References

  1. A. Ishak, R. Nazar, and I. Pop, “Hydromagnetic Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet,” Heat Mass Transfer 44, 921–927 (2008).

    Article  ADS  Google Scholar 

  2. 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 

  3. J. Vleggaar, “Laminar Boundary-Layer Behavior on Continuous Accelerating Surfaces,” Chem. Eng. Sci. 32, 1517–1525 (1977).

    Article  Google Scholar 

  4. B. K. Dutta, P. Roy, and A. S. Gupta, “Temperature Field in Flow over a Stretching Sheet with Uniform Heat Flux,” Int. Commun. Heat Mass Transfer 12, 89–94 (1985).

    Article  Google Scholar 

  5. L. J. Crane, “Flow Past a Stretching Plate,” Z. Angew. Math. Phys. 21, 645–647 (1970).

    Article  Google Scholar 

  6. I. C. Liu and H. I. Andersson, “Heat Transfer in a Liquid Film on an Unsteady Stretching Sheet,” Int. J. Thermal Sci. 47, 766–772 (2008).

    Article  Google Scholar 

  7. H. I. Andersson, K. H. Bech, and B. S. Dandapat, “Magnetohydrodynamic Flow of a Power Law Fluid over a Stretching Sheet,” Int. J. Non-Linear Mech. 27, 929–936 (1992).

    Article  MATH  Google Scholar 

  8. I. A. Hassanien, “Flow and Heat Transfer on a Continuous Flat Surface Moving in a Parallel Free Stream of Power-Law Fluid,” Appl. Model. 20, 779–784 (1996).

    Article  MATH  Google Scholar 

  9. K. Sadeghy and M. Sharifi, “Local Similarity Solution for the Flow of a ‘Second-Grade’ Viscoelastic Fluid above a Moving Plate,” Int. J. Non-Linear Mech. 39, 1265–1273 (2004).

    Article  ADS  MATH  Google Scholar 

  10. B. Serdar and M. SalihDokuz, “Three-Dimensional Stagnation Point Flow of a Second Grade Fluid Towards a Moving Plate,” Int. J. Eng. Sci. 44, 49–58 (2006).

    Article  Google Scholar 

  11. M. H. Haroun, “Effect of Deborah Number and Phase Difference on Peristaltic Transport of a Third-Order Fluid in an Asymmetric Channel,” Commun. Nonlinear Sci. Numer. Simulat. 12, 1464–1480 (2007).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. A. M. Siddiqui, A. Zeb, Q. K. Ghori, and A. M. Benharbit, “Homotopy Perturbation Method for Heat Transfer Flow of a Third Grade Fluid between Parallel Plates.” Chaos Solitons Fractals 36, 182–192 (2008).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. M. Sajid, I. Ahmad, T. Hayat, and M. Ayub, “Unsteady Flow and Heat Transfer of a Second Grade Fluid over a Stretching Sheet,” Commun. Nonlinear Sci. Numer. Simulat. 14, 96–108 (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. M. M. Heyhat and N. Khabazi, “Non-Isothermal Flow of Maxwell Fluids above Fixed Flat Plates under the Influence of a Transverse Magnetic Field,” Proc. Inst. Mech. Eng., C: J. Mech. Eng. Sci. 225, 909–916 (2010).

    Article  Google Scholar 

  15. C. H. Johnson and P. Cheng, “Possible Similarity Solutions for Free Convection Boundary Layers Adjacent to Flat Plates in Porous Media,” Int. J. Heat Mass Transfer 21, 709–718 (1978).

    Article  ADS  MATH  Google Scholar 

  16. I. Pop and D. B. Ingham, Convective Heat Transfer. Mathematical and Computational Modeling of Viscous Fluids and Porous Media (Pergamon, Oxford, 2001).

    Google Scholar 

  17. Transport Phenomena in Porous Media, Ed. by D. B. Ingham and I. Pop (Elsevier, Oxford, 2002), Vol. 2.

    MATH  Google Scholar 

  18. A. Bejan, I. Dincer, S. Lorente, A. F. Miguel, A. H. Reis, Porous and Complex Flow Structures in Modern Technologies (Springer, New York, 2004).

    Book  Google Scholar 

  19. D. B. Ingham, A. Bejan, E. Mamut, I. Pop, Emerging Technologies and Techniques in Porous Media (Kluwer, Dordrecht, 2004).

    Book  MATH  Google Scholar 

  20. D. B. Ingham, I. Pop, Transport Phenomena in Porous Media (Elsevier, Oxford, 2005), Vol. 3.

    Google Scholar 

  21. K. Vafai, Handbook of Porous Media (Taylor and Francis, New York, 2005.

    Book  Google Scholar 

  22. H. I. Andersson, J. B. Aarseth, and B. S. Dandapat, “Heat Transfer in a Liquid Film on an Unsteady Stretching Surface,” Int. J. Heat Mass Transfer 43, 69–74 (2000).

    Article  MATH  Google Scholar 

  23. E. M. A. Elbashbeshy, and M. A. A. Bazid, “Heat Transfer over an Unsteady Stretching Surface,” Heat Mass Transfer 41, 1–4 (2004).

    Article  ADS  Google Scholar 

  24. S. Sharidan, T. Mahmood, and I. Pop, “Similarity Solutions for the Unsteady Boundary Layer Flow and Heat Transfer due to a Stretching Sheet,” Int. J. Appl. Mech. Eng. 11, 647–654 (2006).

    MATH  Google Scholar 

  25. M. E. Ali and E. Magyari, “Unsteady Fluid and Heat Flow Induced by a Submerged Stretching Surface While Its Steady Motion is Slowed Down Gradually,” Int. J. Heat Mass Transfer 50(1/2), 188–195 (2007).

    Article  MATH  Google Scholar 

  26. B. S. Dandapat, B. Santra, and K. Vajravelu, “The Effects of Variable Fluid Properties and Thermocapillarity on the Flow of a Thin Film on an Unsteady Stretching Sheet,” Int. J. Heat Mass Transfer 50(5/6), 991–996 (2007).

    Article  MATH  Google Scholar 

  27. R. Tsai, K. H. Huang, and J. S. Huang, “Flow and Heat Transfer over an Unsteady Stretching Surface with a Non-Uniform Heat Source,” Int. Commun. Heat Mass Transfer 35, 1340–1343 (2008).

    Article  Google Scholar 

  28. S. Mukhopadhyay, “Effect of Thermal Radiation on Unsteady Mixed Convection Flow and Heat Transfer over a Porous Stretching Surface in Porous Medium,” Int. J. Heat Mass Transfer 52, 3261–3265 (2009).

    Article  MATH  Google Scholar 

  29. S. Mukhopadhyay, “Effects of Slip on Unsteady Mixed Convective Flow and Heat Transfer Past a Stretching Surface,” Chinese Phys. Lett. 27(12), 124401 (2010).

    Article  ADS  Google Scholar 

  30. S. Mukhopadhyay, “Heat Transfer Analysis for Unsteady MHD Flow Past a Non-Isothermal Stretching Surface,” Nuclear Eng. Design 241, 4835–4839 (2011).

    Article  Google Scholar 

  31. S. Mukhopadhyay, “Heat Transfer Analysis for Unsteady Flow of a Maxwell Fluid over a Stretching Surface in the Presence of a Heat Source/Sink,” Chinese Phys. Lett. 29(5), 054703 (2012).

    Article  Google Scholar 

  32. A. J. Chamkha, A. M. Aly, and M. A. Mansour, “Similarity Solution for Unsteady Heat and Mass Transfer from a Stretching Surface Embedded in a Porous Medium with Suction/Injection and Chemical Reaction Effects,” Chem. Eng Commun. 197, 846–858 (2010).

    Article  Google Scholar 

  33. K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “Slip Effects on an Unsteady Boundary Layer Stagnation-Point Flow and Heat Transfer Towards a Stretching Sheet,” Chinese Phys. Lett. 28(9), 094702 (2011).

    Article  Google Scholar 

  34. V. Kumaran, A. K. Banerjee, A. V. Kumar, and K. Vajravelu, “MHD Flow Past a Stretching Permeable Sheet,” Appl. Math. Comput. 210(1), 26–32 (2008).

    Article  Google Scholar 

  35. A. Ishak, R. Nazar, and I. Pop, “The Effects of Transpiration on the Flow and Heat Transfer over a Moving Permeable Surface in a Parallel Stream,” Chem. Eng J. 148, 63–67 (2009).

    Article  Google Scholar 

  36. M. A. Chaudhary and J. H. Merkin, “The Effects of Blowing and Suction on Free Convection Boundary Layers on Vertical Surfaces with Prescribed Heat Flux,” J. Eng. Math. 27(3), 265–292 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  37. S. Mukhopadhyay and G. C. Layek, “Effect of Thermal Radiation and Variable Fluid Viscosity on Free Convective and Heat Transfer Past a Porous Stretching Surface,” Int. J. Heat Mass Transfer 51, 2167–2178 (2008).

    Article  MATH  Google Scholar 

  38. K. Bhattacharyya, S. Mukhopadhyay, G. C. Layek, and I. Pop, “Effects of Thermal Radiation on Micropolar Fluid Flow and Heat Transfer over a Porous Shrinking Sheet,” Int. J. Heat Mass Transfer 55, 2945–2952 (2012).

    Article  Google Scholar 

  39. K. Vafai and C. L. Tien, “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media,” Int. J. Heat Mass Transfer 24, 195–204 (1981).

    Article  MATH  Google Scholar 

  40. H. S. Takhar, R. Bhargava, S. Rawat, et al., “Finite Element Modeling of Laminar Flow of a Third Grade Fluid in a Darcy-Forcheimer Porous Medium with Suction Effects,” Int. J. Appl. Mech. Eng. 12(1), 215–233 (2007).

    Google Scholar 

  41. M. Q. Brewster, Thermal Radiative Transfer Properties (John Wiley and Sons, New York, 1992).

    Google Scholar 

  42. S. Mukhopadhyay and K. Vajravelu, “Effects of Transpiration and Internal Heat Generation/Absorption on the Unsteady Flow of a Maxwell Fluid at a Stretching Surface,” Trans. ASME, J. Appl. Mech. 79(4), 044508 (2012).

    Article  ADS  Google Scholar 

  43. A. Alizadeh-Pahlavan and K. Sadeghy, “On the use of Homotopy Analysis Method for Solving Unsteady MHD Flow of Maxwellian Fluids above Impulsively Stretching Sheets,” Commun. Nonlinear Sci. Numer. Simulat. 14, 1355–1365 (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. K. V. Prasad, A. Sujatha, K. Vajravelu, and I. Pop, “MHD Flow and Heat Transfer of a UCM Fluid over a Stretching Surface with Variable Thermophysical Properties,” Meccanica 47(6), 1425–1439 (2012).

    Article  MathSciNet  Google Scholar 

  45. L. J. Grubka and K. M. Bobba, “Heat Transfer Characteristics of a Continuous Stretching Surface with Variable Temperature,” Trans. ASME, J. Heat Transfer 107, 248–250 (1985).

    Article  Google Scholar 

  46. C. H. Chen, “Laminar Mixed Convection Adjacent to Vertical, Continuously Stretching Sheets,” Heat Mass Transfer 33, 471–476 (1998).

    Article  ADS  Google Scholar 

  47. K. Sadeghy, H. Hajibeygi, and S. M. Taghavi, “Stagnation Point Flow of Upper-Convected Maxwell Fluids,” Int. J. Non-Linear Mech. 41, 1242–1247 (2006).

    Article  ADS  Google Scholar 

  48. M. S. Abel, J. V. Tawade, and M. M. Nandeppanavar, “MHD Flow and Heat Transfer for the Upper-Convected Maxwell Fluid over a Stretching Sheet,” Meccanica 47(2), 385–393

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Authors and Affiliations

  1. The University of Burdwan, Burdwan, 713104, India

    S. Mukhopadhyay, P. Ranjan De & G. C. Layek

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  1. S. Mukhopadhyay
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  2. P. Ranjan De
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  3. G. C. Layek
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Correspondence to S. Mukhopadhyay.

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Original Russian Text © S. Mukhopadhyay, P. Ranjan De, G.C. Layek.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 54, No. 3, pp. 51–64, May–June, 2013.

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Mukhopadhyay, S., Ranjan De, P. & Layek, G.C. Heat transfer characteristics for the Maxwell fluid flow past an unsteady stretching permeable surface embedded in a porous medium with thermal radiation. J Appl Mech Tech Phy 54, 385–396 (2013). https://doi.org/10.1134/S0021894413030061

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  • DOI: https://doi.org/10.1134/S0021894413030061

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