Investigation into thermophoresis and Brownian motion effects of nanoparticles on radiative heat transfer in Hiemenz flow using spectral method

Document Type : Article

Authors

1 Department of Mathematics Islamabad College for Boys G-6/3, Islamabad 44000, Pakistan.

2 Department of Mathematics, University of Education, Lahore (Attock Campus 43600), Pakistan

3 Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan

Abstract

A study based on the theoretical investigation of Thermophoresis and Brownian motion effects on radiative heat transfer in the neighborhood of stagnation point. Thermophoresis and Brownian motion play an important role in thermal and mass concentration analyses. These analyses help to comprehend the core ideas to carry out in the discipline of science and technology. An electrically conducting nanofluid is considered which is described by the Buongiorno transport model. The power-law form of the stretching wall velocity allows the similarity solution, the transformed system of the ordinary differential equations is computed numerically with the efficient rapid convergent spectral scheme. The obtained results for velocity, temperature, concentration, shear strain, mass and heat transfer rates are presented graphically for various values of the pertinent parameters. The outcomes divulge that with the increase of power-law exponent, mass and heat transfer rates enhance. The information for the volume and high-temperature transfer rate is provided in the form of Tables. The obtained results are matched with the existing results and are shown to be a good agreement.

Keywords

Main Subjects


1. Hiemenz, K. Die Grenzschicht an einem in den Gleichformingen Flussigkeitsstrom eingetauchten Graden Kreiszylinder", Dinglers Polytech. J., 326, pp. 321-324 (1911). 2. Homann, F. Der Einuss grosser Zahigkeit bei der Stromung um den Zylinder und um die Kugel", Z. Angew Math. Mech., 16, pp. 153-164 (1936). 3914 M.S. Iqbal et al./Scientia Iranica, Transactions F: Nanotechnology 26 (2019) 3905{3916 3. Howarth, L. On the solution of the laminar boundary layer equations", Proc. R. Soc. A, 164(919), pp. 547- 579 (1938). 4. Chiam, T.C. Stagnation-point ow towards a stretching plate", J. Phys. Soc. Jpn, 63(6), pp. 2443-2444 (1994). 5. Layek, G.C., Mukhopadhyay, S., and Samad, S.A. Heat and mass transfer analysis for boundary layer stagnation point ow towards a heated porous stretching sheet with heat absorption/generation and suction/ blowing", Int. Commun. Heat Mass Transfer, 34(3), pp. 347-356 (2007). 6. Ishak, A., Nazar, R., and Pop, I. Mixed convection stagnation point ow of a micropolar uid towards a stretching sheet", Meccanica, 43(4), pp. 411-418 (2008). 7. Bhattacharyya, K., Mukhopadhyay, S., and Layek, G.C. Reactive solute transfer in magneto hydrodynamic boundary layer stagnation-point ow over a stretching sheet with suction/ blowing", Chem. Eng. Commun., 199(3), pp. 368-383 (2012). 8. Mabood, F., Khan, W.A., and Ismail, A.M. MHD stagnation point ow and heat transfer impinging on stretching sheet with chemical reaction and transpiration", Chem. Eng., 273, pp. 430-437 (2015). 9. Hayat, T., Anwar, M.S., Farooq, M., and Alsaedi, A. MHD stagnation point ow of second grade uid over a stretching cylinder with heat and mass transfer", Int. J. Non. Sci. Num. Sim., 15(6), pp. 365-376 (2014). 10. Rashidi, M.M. and Erfani, E. A new analytical study of MHD stagnation-point ow in porous media with heat transfer", Comp. Fluids, 40(1), pp. 172-178 (2011). 11. Pop, S.R., Grosan, T., and Pop, I. Radiation e_ects on the ow near the stagnation point of a stretching sheet", Technische Mechanik, 25(2), pp. 100-106 (2004). 12. Hayat, T., Javed, T., and Abbas, Z. MHD ow of a micropolar uid near a stagnation point towards a non-linear stretching surface", Non-Linear Anal. Real World Appl., 10, pp. 1514-1526 (2009). 13. Shateyi, S. and Makinde, O.D. Hydromagnetic stagnation-point ow towards a radially stretching convectively heated disk", Math. Prob. Eng., 2013, ID 616947 (2013). 14. Miklavcic, M. and Wang, C.Y. Viscous ow due to a shrinking sheet", Appl. Math., 64, pp. 283-290 (2006). 15. Mahapatra, T.R. and Gupta, A.G. Heat transfer in stagnation point ow towards a stretching sheet", Heat Mass Transfer, 38, pp. 517-521 (2002). 16. Mahmoud, M.A. Hydromagnetic stagnation point ow towards a porous stretching sheet with variable surface heat ux in the presence of heat generation", Chem. Eng. Commun., 198(7), pp. 837-846 (2011). 17. Chen, H. Mixed convection unsteady stagnation point ow towards a stretching sheet with slip e_ects and noticed that the reverse ow occurs near the sheet", Math. Prob. Eng., 2014, ID 435697 (2014). 18. Makinde, O.D. Heat and mass transfer by MHD mixed convection stagnation point ow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation", Meccanica, 47(5), pp. 1173-1184 (2012). 19. Boutros, Y.Z., Abd-el-Malek, M.B., Badran, N.A., and Hassan, H.S. Lie-group method of solution for steady two-dimensional boundary-layer stagnation-point ow towards a heated stretching sheet placed in a porous medium", Meccanica, 41, pp. 681-691 (2006). 20. Nazar, R., Amin, N., Filip, D., and Pop, I. Stagnation point ow of a micropolar uid towards a stretching sheet", Int. J. Non-Linear Mech., 39, pp. 1227-1235 (2004). 21. Hayat, T., Waqas, M., Shehzad, S.A., and Alsaedi, A. Mixed convection radiative ow of Maxwell uid near stagnation point with convective condition", J. Mech., 29, pp. 403-409 (2013). 22. Mehmood, A. and Ali, A. An explicit analytic solution of steady three-dimensional stagnation point ow of second grade uid toward a heated plate", J. App. Mech. Trans. ASME., 75(6), p. 061003 (2008). 23. Anwar, M.I., Khan, I., Hussnan, A., Salleh, M.Z., and Sharidan, S. Stagnation point ow of a nanouid over a nonlinear stretching sheet", W. App. Sci. J., 23(8), pp. 998-1006 (2013). 24. Wakif, A., Boulahia, Z., Animasaun, I.L., Afridi, M.I., Qasimd, M., and Sehaqui, R. Magneto- convection of alumina-water nanouid within thin horizontal layers using the revised generalized Buonjiorno's model", Frontiers Heat Mass Transfer, 12(3), pp. 1-15 (2019). 25. Wakif, A., Boulahia, Z., Ali, F., Eid, M.R., and Sehaqui, R. Numerical analysis of the unsteady natural convection MHD couette nanouid ow in the presence of thermal radiation using single and twophase nanouid models for Cu-water nanouids", Int. J. Appl. Comp. Math., 4(3), p. 81 (2018). 26. Wakif, A., Boulahia, Z., and Sehaqui, R. A semianalytical analysis of electro-thermo-hydrodynamic stability in dielectric nanouids using Buongiorno's mathematical model together with more realistic boundary conditions", Results Phys., 9, pp. 1438-1454 (2018). 27. Wakif, A., Boulahia, Z., Mishra, S.R., Rashidi, M.M., and Sehaqui, R. Inuence of a uniform transverse magnetic _eld on the thermo-hydrodynamic stability in water-based nanouids with metallic nanoparticles using the generalized Buongiorno's mathematical model", Eur. Phys. J. Plus, 133(5), pp. 181 (2018). 28. Wakif, A., Boulahia, Z., and Sehaqui, R. Numerical study of the onset of convection in a Newtonian nanouid layer with spatially uniform and non-uniform internal heating", J. Nanouids, 6(1), pp. 136-148 (2017). M.S. Iqbal et al./Scientia Iranica, Transactions F: Nanotechnology 26 (2019) 3905{3916 3915 29. Wakif, A., Boulahia, Z., and Sehaqui, R. Numerical analysis of the onset of longitudinal convective rolls in a porous medium saturated by an electrically conducting nanouid in the presence of an external magnetic _eld", Results Phys., 7, pp. 2134-2152 (2017). 30. Boulahia, Z., Wakif, A., and Sehaqui, R. Heat transfer and Cu-water nanouid ow in a ventilated cavity having central cooling cylinder and heated from the below considering three di_erent outlet port locations", Frontiers Heat Mass Transfer, 11, p. 11 (2018). 31. Boulahia, Z., Wakif, A., and Sehaqui, R. Modeling of free convection heat transfer utilizing nanouid inside a wavy enclosure with a pair of hot and cold cylinders", Frontiers Heat Mass Transfer, 8(14), pp. 1-10 (2017). 32. Boulahia, Z., Wakif, A., Chamkha, A.J., and Sehaqui, R. Numerical study of natural and mixed convection in a square cavity _lled by a Cu-water nanouid with circular heating and cooling cylinders", Mech. Ind., 18(5), p. 502 (2017). 33. Tayebi, T., Chamkha, A.J., and Djezzar, M. Natural convection of CNT-water nanouid in an annular space between confocal elliptic cylinders with constant heat ux on inner wall", Sci. Iran, 26(5), pp. 2770-2783 (2018). 34. Abbasi, A.S. and Ghayen, M. Vapor solidi_cation of saturated air in two-dimensional stagnation ow", Sci. Iran (2018) DOI: 10.24200/SCI.2018.4956.1007. 35. Rana, S., Nawaza, M., and Qureshi, I.H. Numerical study of hydrothermal characteristics in nanouid using KKL model with Brownian motion", Sci. Iran, 26(3), pp. 1931-1943 (2019). 36. Ramly, N.A., Sivasankaran, S., and Noor, N.F.F. Zero and nonzero normal uxes of thermal radiative boundary layer ow of nanouid over a radially stretched surface", Sci. Iran, 24(6), pp. 2895-2903 (2017). 37. Karbasi, S., Zarei, M., and Foroughi, M.R. E_ects of Multi-Wall carbon Nano-Tubes (MWNTs) on structural and mechanical properties of electrospun poly (3- hydroxybutyrate) sca_old for tissue engineering applications", Sci. Iran, Transactions F, Nanotechnology, 23(6), p. 3145 (2016). 38. Hakeem, A.A., Govindaraju, M., Ganga, B., and Kayalvizhi, M. Second law analysis for radiative MHD slip ow of a nanouid over a stretching sheet with nonuniform heat source e_ect", Sci. Iran, Transactions F, Nanotechnology, 23(3), p. 1524 (2016). 39. Wanga, X. and Dai, W. Numerical investigation on natural convection of nanouids in an inclined square enclosure with non-uniform heated walls", Sci. Iran, 26(4), pp. 2311-2328 (2019). 40. Kasmani, R.M., Sivasankaran, S., Bhuvaneswari, M., Alshomrani, A.S., and Siri, Z. Soret and Dufour e_ects on doubly di_usive convection of nanouid over a wedge in the presence of thermal radiation and suction", Sci. Iran, 26(5), pp. 2817-2826 (2019). 41. Ganji, D.D., Sheikholeslami, M., Zhixiong, L., and Hosseinnejad, R. Numerical simulation of thermal radiative heat transfer e_ects on Fe3O4-Ethylene glycol nanouid EHD ow in a porous enclosure", Sci. Iran, 26(3), pp. 1405-1414 (2019). 42. Ibrahim, W., Shankar, B., Mahantesh, M., and Nandeppanavar, M. MHD stagnation point ow and heat transfer due to nanouid towards a stretching sheet", Int. J. Heat Mass Transfer, 56, pp. 1-9 (2013). 43. Hamad, M.A.A. and Ferdows, M. Similarity solution of boundary layer stagnation-point ow towards a heated porous stretching sheet saturated with a nanouid with heat absorption/generation and injection/ blowing: a lie group analysis", Comp. Nonlinear Sci. and Num. Simul., 17, pp. 132-140 (2011). 44. Alsaedi, A., Awais, M., and Hayat, T. E_ects of heat generation/absorption on stagnation-point ow of nanouid over a surface with convective boundary conditions", Comp. Nonlinear Sci. Numer. Simul., 17, pp. 4210-4223 (2012). 45. Khan, Z.H., Khan, W.A., Qasim, M., and Shah, I.A. MHD stagnation point ferrouid ow and heat transfer toward a stretching sheet", IEEE Transactions on Nanotechnology, 13(1), pp. 35-40 (2014). 46. Hamad, M. and Pop, I. Scaling transformations for boundary layer ow near the stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanouid and heat generation/ absorption e_ects", Transp. Porous Med., 87, pp. 25-39 (2011). 47. Mustafa, M., Hayat, T., Pop, I., Asghar, S., and Obaidat, S. Stagnation-point ow of a nanouid towards a stretching sheet", Int. J Heat Mass Transfer, 54, pp. 5588-5594 (2011). 48. Ibrahim, W., Shankar, B., and Nandeppanavar, M.M. MHD stagnation point ow and heat transfer due to nanouid towards a stretching sheet", Int. J. Heat Mass Transfer, 56(1), pp. 1-9 (2013). 49. Hakeem, A.A., Ganesh, N.V., and Ganga, B. Heat transfer of non-Darcy MHD ow of nanouid over a stretching/shrinking surface in a thermally strati_ed medium with second order slip model", Sci. Iran, Transactions F, Nanotechnology, 22(6), pp. 2766-2784 (2015). 50. Hakeem, A.A., Govindaraju, M., Ganga, B., and Kayalvizhi, M. Second law analysis for radiative MHD slip ow of a nanouid over a stretching sheet with nonuniform heat source e_ect", Sci. Iran, Transactions F, Nanotechnology, 23(3), pp. 1524-1538 (2016). 51. Akram, S. Nanouid e_ects on peristaltic transport of a fourth grade uid in the occurrence of inclined magnetic _eld", Scientia Iran, Transactions F, Nanotechnology, 23(3), pp. 1502-1516 (2016). 3916 M.S. Iqbal et al./Scientia Iranica, Transactions F: Nanotechnology 26 (2019) 3905{3916 52. Gha_arpasand, O. and Fazeli, D. Numerical analysis of MHD mixed convection ow in a parallelogramic porous enclosure _lled with nanouid and in the presence of magnetic _eld induction", Sci. Iran, Transactions F, Nanotechnology, 25(3), pp. 1789-1807 (2018). 53. Golshokooh, S., Ramazani, S.A., and Hekmatzadeh, M. Investigating the e_ect of hybrid silica nanoparticles-copolymer on increasing oil recovery in a three dimensional porous media", Sci. Iran, Transactions F, Nanotechnology, 24(6), pp. 3466-3475 (2017). 54. Buongiorno, J. Convective transport in nanouids", J. Heat Transfer, 128, pp. 240-250 (2006). 55. Buongiorno, J., Venerus, D., Prabhat, N., McKrell, T., and Townsend, J. A benchmark study on the thermal conductivity of nanouids", J. Appl. Phys., 106(9), p. 094312 (2009). 56. Majeed, A., Javed, T., Gha_ari, A., and Rashidi, M.M. Analysis of heat transfer due to stretching cylinder with partial slip and prescribed heat ux: A Chebyshev spectral Newton iterative scheme", Alex. Eng. J., 54(4), pp. 1029-1036 (2015). 57. Gha_ari, A., Javed, T., and Labropulu, F. Oblique stagnation point ow of a non-Newtonian nanouid over stretching surface with radiation: a numerical study", Therm. Sci., 21(5), pp. 2139-2153 (2017). 58. Mahmood, A., Chen, B., and Gha_ari, A. Hydromagnetic Hiemenz ow of micropolar uid over a nonlinearly stretching/shrinking sheet: Dual solutions by using Chebyshev spectral Newton iterative scheme", J. Magn. Magn. Mater., 416, pp. 329-334 (2016). 59. Uddin, M.J., Khan, W.A., and Ismail, A.I. MHD forced convective laminar boundary layer ow of convectively heated moving vertical plate with radiation and transpiration e_ect", Plos One, 8(5), p. 62664 (2013). 60. Bianco, V., Manca, O., and Vafai, K., Heat Transfer Enhancement with Nanouids, CRC Press, London, New York (2015). 61. Yih, K.A. MHD forced convection ow adjacent to a non-isothermal wedge", Int. Commun. Heat Mass Transfer, 26(6), pp. 819-827 (1999). 62. Cebeci, T. and Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer, New York (1988).