Unsteady and velocity-slip effects on laminar boundary layer flow and forced convective heat transfer over a moving wedge

Document Type : Research Paper

Authors

1 Regional Research Centre, VTU, Belagavi-590018, India.

2 Department of Mathematics, KLE Technological University, Hubballli-580 031, India.

3 Department of Mathematics, S. S. Government First Grade College and P. G. Studies Centre, Nargund-582 207, India.

4 Department of Mathematics, KLE Technological University, Dr. M. S. Sheshgiri Campus, Belagavi-590008, India.

Abstract

The focus of this study is to examine the effects of velocity-slip on the surface of the moving wedge on the laminar boundary layer flow of a viscous fluid, in addition to the heat transfer across the moving wedge. When fluid and solid interact, velocity-slip effects may have a major impact on most industrial applications. It is considered that the mainstream and wedge velocities and the shape of the velocity-slip depend on the distance along the boundary layer wall. These equations offer the essence of a set of ordinary differential equations for the momentum and thermal boundary layer systems. The numerical solutions reveal that when the velocity-slip and unstable parameters increase, the thermal and momentum boundary layers narrow. The momentum boundary layer domain also appears to be reduced due to pressure gradient effects. There is also little variation in the thermal boundary layers as the wall shear stress (skin friction) and temperature gradient curves grow flat with increasing velocity-slip parameter. The physical mechanisms underlying these remarkable results are further discussed.

Keywords

Main Subjects


  • [1] T. A. Abdelhafez, Skin friction and heat transfer on a continuous flat surface moving in a parallel free stream, International Journal of Heat and Mass Transfer, 28 (1985), 1234-1237.
  • [2] N. Afzal, A. Badaruddin, and A. A. Elgarvi, Momentum and heat transport on a continuous flat surface moving in a parallel stream, International Journal of Heat and Mass Transfer, 36 (1993), 3399-3403.
  • [3] M. T. Akolade, Thermo-physical impact on the squeezing motion of non-Newtonian fluid with quadratic convection, velocity slip, and convective surface conditions between parallel disks, Partial Differential Equations in Applied Mathematics, 4 (2021), 100056.
  • [4] P. D. Ariel, T. Hayat, and S. Asghar, The flow of an elastico-viscous fluid past a stretching sheet with partial slips, Acta Mechanics, 187 (2006), 29-35.
  • [5] N. Bachok, A. Ishak, and I. Pop, Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet, Physics Letters A, 374 (2010), 4075-4079.
  • [6] G. K. Batchelor, An introduction to fluid dynamics, first ed., Cambridge University Press, (1967).
  • [7] K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, MHD boundary layer slip flow and heat transfer over a flat plate, Chinese Physics Letters, 28 (2011), 024701-024704.
  • [8] K. Cebeci and P. Bradshaw, Momentum transfer in boundary layers, Mc-Graw Hill, New York, (1977).
  • [9] N. V. Churaev, V. D. Sobolev, and N. Somov, Slippage of liquids over lyophobic solid surfaces, Journal of Colloidal and Interface Science, 97 (1984), 574-581.
  • [10] V. S. J. Craig, C. Neto, and D. R. M. Williams, Shear-dependent boundary slip in an aqueous Newtonian liquid, Physical Review Letters, 87 (2001), 054504/1-4.
  • [11] L. J. Crane, Flow past a stretching plate, Journal of Applied Mathematics and Physics, 21 (1970), 645-647.
  • [12] P. W. Duck and S. L. Dry, On a class of unsteady, nonparallel, three-dimensional disturbances to boundary-layer flows, Journal of Fluid Mechanics, 441 (2001), 31-65.
  • [13] P. W. Duck, S. R. Stow, and M. R. Dhanak, Boundary-layer flow along a ridge: alternatives to the Falkner-Skan solutions, Philosophical Transactions of the Royal Society A, 358 (2000), 3075-3090.
  • [14] R. Ellahi, S. Z. Alamri, A. Basit, and A. Majeed, Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation, Journal of Taibah University for Science, 12 (2016), 476-482.
  • [15] T. Grosan and I. Pop, Forced convection boundary layer flow past non-isothermal thin needles in nanofluids, ASME-Journal of Heat Transfer, 133 (2011), 054503.
  • [16] S. P. Hastings and W. C. Troy, Oscillating solutions of the Falkner-Skan equation for negative β, SIAM Journal on Mathematical Analysis, 18 (1987), 422-429.
  • [17] W. Ibrahim and B. Shanker, Magnetohydrodynamic boundary layer flow and heat transfer of a nanofluid over non-isothermal stretching sheet, ASME-Journal of Heat Transfer, 136 (2014), 051701.
  • [18] K. Kaladhar, K. Madhusudhan Reddy, and D. Srinivasacharya, Inclined magnetic field and Soret effects on mixed convection flow between vertical parallel plates, Journal of Applied Analysis and Computation, 9(6) (2019), 2111- 2123.
  • [19] H. B. Keller, Numerical methods in boundary layer theory, Annual Review of Fluid Mechanics, 10 (1978), 417-428.
  • [20] W. A. Khan and I. Pop, Free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with a nanofluid, ASME-Journal of Heat Transfer, 133 (2011), 094501.
  • [21] R. B. Kudenatti, N. E. Misbah, and M. C. Bharathi, Linear Stability of Momentum Boundary Layer Flow and Heat Transfer Over a Moving Wedge, Journal of Heat Transfer-Transactions of the ASME, 142(6) (2020), 061804.
  • [22] M. K. Mishra, G. S. Seth, and R. Sharma, Navier’s slip effect on mixed convection flow of non-Newtonian nanofluid: Buongiorno’s model with passive control approach, International Journal of Applied and Computational Mathematics, 5 (2019), 107.
  • [23] S. Mukhopadhyay and R. S. R. Gorla, Effects of partial slip on boundary layer flow past a permeable exponential stretching sheet in presence of thermal radiation, Heat and Mass Transfer, 48 (2012), 1773-1781.
  • [24] S. Mukhopadhyay, Slip effects on MHD boundary layer flow over an exponentially stretching sheet with suction/blowing and thermal radiation, Ain Shams Engineering Journal, 4 (2013), 485-491.
  • [25] A. Nakayama, Kokudai, and H. Koyama, Non-Darcian boundary layer flow and forced convective heat transfer over a flat plate in a fluid-saturated porous medium, ASME-Journal of Heat Transfer, 112 (1990), 157-162.
  • [26] C. L. Navier and M. H. Memoire, Sur les lois du mouvement des fluids, Mem. Academic Science Institute of France, 6 (1823), 389–440.
  • [27] B. Oskam and A. E. P. Veldman, Branching of the Falkner-Skan solutions for λ < 0, Journal of Engineering Mathematics, 16 (1982), 295-308.
  • [28] A. Parmar and S. Jain, Exploration of heat and mass transfer in the convective slip flow of non-Newtonian Casson fluid, International Journal of Applied and Computational Mathematics, 4 (2018), 67.
  • [29] J. Rao and K. R. Rajagopal, The effect of the slip boundary condition on the flow of fluids in a channel, Acta Mechanica, 135 (1999), 113–126.
  • [30] P. L. Sachdev, R. B. Kudenatti, and N. M. Bujurke, Exact analytic solution of boundary value problem for the Falkner-Skan equation, Studies in Applied Mathematics, 120 (2008), 1-16.
  • [31] B. C. Sakiadis, Boundary-layer behavior on continuous solid surfaces, Journal of AICHE, 7 (1961), 26-28.
  • [32] M. Z. Salleh, R. Nazar, and I. Pop, Forced convection boundary layer flow at a forward stagnation point with Newtonian heating, Chemical Engineering Communications, 196 (2009), 987-996.
  • [33] S. R. Sayyed, B. B. Singh, and B. Nasreen, Analytical solution of MHD slip flow past a constant wedge within a porous medium using DTM-Pade, Applied Mathematics and Computation, 321 (2018), 472-482.
  • [34] H. Schlichting and K. Gersten, Boundary Layer Theory, 8th ed., Springer, New York, 2004.
  • [35] M. Sheikholeslami and A. J. Chamkha, Influence of Lorentz forces on nanofluid forced convection considering Marangoni convection, Journal of Molecular Liquids, 225 (2017), 750-757.
  • [36] M. Sheikholeslami, H. R. Kataria, and A. S. Mittal, Effect of thermal diffusion and heat-generation on MHD nanofluid flow past an oscillating vertical plate through porous medium, Journal of Molecular Liquids, 257 (2018), 12-25.
  • [37] C. Y. Wang, Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear Analysis: Real World Applications, 10 (2009), 375-380.
  • [38] H. T. Yang and L. C. Chien, Analytic solutions of the Falkner-Skan equation when β = -1 and γ = 0, SIAM Journal on Applied Mathematics, 29 (1975), 558-569.