THERMAL SCIENCE

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Numerical and analytical approach for Sakiadis rheology of generalized polymeric material with magnetic field and heat source/sink

ABSTRACT
In this analysis, Sakiadis rheology of the generalized polymeric material has been presented with magnetic field and heat source/sink. Convective heating process with thermal radiations have been incorporated. Mathematical modelling has been performed for the conversion of physical problem into set of nonlinear equations. Suitable transformations have been employed in order to convert the derived PDEs into set of nonlinear ODEs. Analytical as well as finite difference method based numerical solutions for the velocity and temperature profiles are computed. Graphical and numerical illustrations have been presented in order to analyze the behavior of involved physical quantities. Error analysis for the nonlinear system has been presented in order to show the validity of the obtained results. Bar charts have been plotted to present the heat flux analysis. Tabular values of local Nusselt number are computed for the involved key parameters. Heat transfer rates against magnetic and porosity effects found to be decreased since magnetic field and porosity retard the molecular movement of the fluid particles. This controlling property of magnetic field and porosity effects have application in MHD power generation, electromagnetic casting of metals, MHD ion propulsion etc. Moreover internal heat generation and absorption effects have opposite effects on the fluid temperature.
KEYWORDS
PAPER SUBMITTED: 2018-04-26
PAPER REVISED: 2018-09-13
PAPER ACCEPTED: 2018-09-15
PUBLISHED ONLINE: 2018-10-06
DOI REFERENCE: https://doi.org/10.2298/TSCI180426284A
REFERENCES
  1. Jie, P et al., Characteristics of electrorheological fluid flow between two concentric cylinders. Chinese Physics Letters, 17 (2000), 4, pp.298.
  2. Daniel, Y.S., et al., Effects of thermal radiation, viscous and Joule heating on electrical MHD nanofluid with double stratification. Chinese Journal of Physics, 55 (2017) ,3, pp.630-651.
  3. Gireesha, B.J., et al.,. Nonlinear convective heat and mass transfer of Oldroyd-B nanofluid over a stretching sheet in the presence of uniform heat source/sink. Results in Physics, 9(2018), pp.1555-1563.
  4. Kumar, G., et al.,. Thermal analysis of generalized Burgers nanofluid over a stretching sheet with nonlinear radiation and non uniform heat source/sink. Archives of Thermodynamics.(2018)
  5. Ramesh, G.K. and Gireesha, B.J.,Influence of heat source/sink on a Maxwell fluid over a stretching surface with convective boundary condition in the presence of nanoparticles. Ain Shams Engineering Journal, 5(2014), 3,pp.991-998.
  6. Colangelo, G., et al., 2017. Cooling of electronic devices: Nanofluids contribution. Applied Thermal Engineering, 127, pp.421-435.
  7. Gusain, R. and Khatri, O.P., Ultrasound assisted shape regulation of CuO nanorods in ionic liquids and their use as energy efficient lubricant additives. Journal of Materials Chemistry A, 1(2013), 18, pp.5612-5619.
  8. B. C. Sakiadis, Boundary layer behavior on continuous solid surface I: Boundary layer equations for two dimensional and axisymmetric flow, AIChE J., 7 (1961) 26-28.
  9. B. C. Sakiadis, Boundary layer behavior on continuous solid surface II: Boundary layer on a continuous flat surface, AIChE J., 7 (1962) 221-225.
  10. J. Zierep and C. Fetecau, Energetic balance for the Rayleigh--Stokes problem of a Maxwell fluid, Int. J. Engng. Sci., 45 (2007) 617-627.
  11. M. Jamil, et al.,, Unsteady helical flows of Oldroyd-B fluids, Comm. Nonlinear Sci. Numer. Simulat., 16 (2011) 1378-1386.
  12. W. Tan and T. Masuoka, Stability analysis of a Maxwell fluid in a porous medium heated from below, Phys. Letters A, 360 (2007) 454-460.
  13. S. Nadeem, et al., HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet, Comm. Nonlinear Sci. Numer. Simulat., 15 (2010) 475-481.
  14. T. Hayat, A. Alsaedi, On thermal radiation and Joule heating effects on MHD flow of an Oldroyd-B fluid with thermophoresis. Arb. J. Sci. Eng. 36(2011) 1113-1124.
  15. M. Y. Malik, et al.,, Magnetohydrodynamic three-dimensional Maxwell fluid flow towards a horizontal stretched surface with convective wall, Int. J. BioEngng. Life Sci., 2 (2015).
  16. T. Hayat, et al.,, Mixed convection three-dimensional flow of an upper-convected Maxwell (UCM) Fluid under magnetic field, thermal-diffusion and diffuion-thermo effects, ASME, J. Heat Transfer, 134 (2012) 044503.
  17. Mehmood, Z., et al.,, 2017. Numerical investigation of micropolar Casson fluid over a stretching sheet with internal heating. Communications in Theoretical Physics, 67(2017),4, p.443.
  18. Ramesh, G.K. and Gireesha, B.J.,Influence of heat source/sink on a Maxwell fluid over a stretching surface with convective boundary condition in the presence of nanoparticles. Ain Shams Engineering Journal, 5(2014), 3,pp.991-998.
  19. Mehmood, R., et al.,Flow and heat transfer analysis of Jeffery nano fluid impinging obliquely over a stretched plate. Journal of the Taiwan Institute of Chemical Engineers, 74(2017) , pp.49-58.
  20. Kumar, K.G., et al.,. Characteristics of Joule heating and viscous dissipation on three-dimensional flow of Oldroyd B nanofluid with thermal radiation. Alexandria Engineering Journal.(2017)
  21. Rana, S., et al.,.Free convective nonaligned non-Newtonian flow with non-linear thermal radiation. Communications in Theoretical Physics, 66(2016), 6, p.687.
  22. Awais, M., et al.,. Generalized magnetic effects in a Sakiadis flow of polymeric nano-liquids: Analytic and numerical solutions. Journal of Molecular Liquids. 241 (2017), pp 570-576.
  23. Ahmed, N., et al., 2018. A theoretical investigation of unsteady thermally stratified flow of γAl2O3− H2O and γAl2O3− C2H6O2 nanofluids through a thin slit. Journal of Physics and Chemistry of Solids (2018).
  24. Phule, A.D., et al.,Negative optical absorption and up-energy conversion in dendrites of nanostructured silver grafted with α/β-poly (vinylidene fluoride) in small hierarchical structures. Journal of Physics and Chemistry of Solids, 115 (2018), pp.254-264.
  25. Rana, S., et al.,. Mixed convective oblique flow of a Casson fluid with partial slip, internal heating and homogeneous-heterogeneous reactions. Journal of Molecular liquids, 222(2016), pp.1010-1019.
  26. Iqbal, Z et al.,. Impact of inclined magnetic field on micropolar Casson fluid using Keller box algorithm. The European Physical Journal Plus, 132(2017), 4,p.175.
  27. Tabassum, et al.,. Impact of viscosity variation and micro rotation on oblique transport of Cu-water fluid. Journal of colloid and interface science, 501(2017), pp.304-310.
  28. Awais, M., et al.,. Hydromagnetic mixed convective flow over a wall with variable thickness and Cattaneo-Christov heat flux model: OHAM analysis. Results Physics, 8 (2018), pp 621-627
  29. Mehmood, R., et al.,. Effects of transverse magnetic field on a rotating micropolar fluid between parallel plates with heat transfer. Journal of Magnetism and Magnetic Materials, 401(2016), pp.1006-1014.
  30. Rehman, A.U et al.,. Entropy analysis of radioactive rotating nanofluid with thermal slip. Applied Thermal Engineering, 112(2017), pp.832-840.
  31. Ramesh, G.K., et al., MHD mixed convection flow of a viscoelastic fluid over an inclined surface with a nonuniform heat source/sink. Canadian Journal of Physics, 91(2013),12, pp.1074-1080.
  32. T. Hayat, et al.,, Similar solution for three-dimensional flow in an Oldroyd-B fluid over a stretching Surface, International Journal for Numerical Methods in Fluids, 70 (2012) 851-859.
  33. Awais, et al., Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material. Results in Physics, 8(2018), pp.1038-1045.
  34. Awan, S.E., et al., 2018. Dynamical analysis for nanofluid slip rheology with thermal radiation, heat generation/absorption and convective wall properties. AIP Advances, 8(2018),7, p.075122.
  35. Siddiqa, S., et al., 2018. Thermal radiation therapy of biomagnetic fluid flow in the presence of localized magnetic field. International Journal of Thermal Sciences, 132, pp.457-465.
  36. Awan, S.E., et al.,Numerical Treatment for Hydro-magnetic Unsteady Channel Flow of Nanofluid with Heat Transfer. Results in Physics. 9(2018) ,pp. 1543-1554.
  37. Mehmood, A., et al., Intelligent computing to analyze the dynamics of Magnetohydrodynamic flow over stretchable rotating disk model. Applied Soft Computing, 6(2018) 7, pp.8-28.
  38. Raja, M.A.Z., et al.,. Intelligent computing strategy to analyze the dynamics of convective heat transfer in MHD slip flow over stretching surface involving carbon nanotubes. Journal of the Taiwan Institute of Chemical Engineers, 8(2017) , pp.935-953.
  39. Raja, M.A.Z., et al.,. Bio-inspired computational heuristics to study the boundary layer flow of the Falkner-Scan system with mass transfer and wall stretching. Applied Soft Computing, 57(2017), pp.293-314.
  40. Raja, M.A.Z., et al.,. Design of bio-inspired computing technique for nanofluidics based on nonlinear Jeffery-Hamel flow equations. Canadian Journal of Physics, 94(2016), 5, pp.474-489.
  41. Raja, M.A.Z., Manzar, M.A., Shah, F.H. and Shah, F.H., 2018. Intelligent computing for Mathieu's systems for parameter excitation, vertically driven pendulum and dusty plasma models. Applied Soft Computing, 62, pp.359-372.