Document Type : Research Paper

Authors

1 Government First Grade College, Koppa, Chikkamagaluru-577126, Karnataka, INDIA

2 Government First Grade College, Koppa, Chikkamagaluru-577126, Karnataka, INDIA.

Abstract

The steady three-dimensional boundary layer flow and heat transfer of a dusty fluid towards a stretching sheet with convective boundary conditions is investigated by using similarity solution approach. The free stream along z-direction impinges on the stretching sheet to produce a flow with different velocity components. The governing equations are reduced into ordinary differential equations by using appropriate similarity variables. Reduced nonlinear ordinary differential equations subjected to the associated boundary conditions are solved numerically by using Runge–Kutta fourth-fifth order method along with Shooting technique. The effects of the physical parameters like magnetic parameter, velocity ratio, fluid and thermal particle interaction parameter, Prandtl number, Eckert number and Biot number on flow and heat characteristics are examined, illustrated graphically, and discussed in detail. The results indicate that the fluid phase velocity is always greater than that of the particle phase and temperature profiles of fluid and dust phases increases with the increase of the Eckert number.

Graphical Abstract

Three-Dimensional Boundary Layer Flow and Heat Transfer of a Dusty Fluid Towards a Stretching Sheet with Convective Boundary Conditions

Keywords

Main Subjects

[1]           B. C. Sakiadis, “Boundary layer behaviour on continuous solid surface”, American Institute of Chemical Engineering Journal, Vol. 7, No. 1, pp. 26-28, (1961).
[2]           L. J. Crane, “Flow past a stretching sheet”, Zeitschrift für angewandte Mathematik und Physik (ZAMP), Vol. 21, No. 4, pp. 645-647, (1970).
[3]           I. C. Liu, H. H. Wanga and Y. F. Peng,  “Flow and heat transfer for three-dimensional flow over an exponentially stretching surface”, Chemical Engineering Communications, Vol. 200, No. 2, pp. 253-268, (2013).
[4]           T. Hayat, B. Ashraf, S. A. Shehzad, and E. Abouelmagd, “Three-dimensional flow of Eyring Powell nanofluid over an exponentially stretching sheet”, International Journal of Numerical Methods for Heat and  Fluid Flow, Vol. 25, No. 3, pp. 593-616, (2014).
[5]           S. Nadeem, R. U. Haq, and N. S. Akbar, “MHD three-dimensional boundary layer flow of Casson nanofluid past a linearly stretching sheet with convective boundary condition”, IEEE Transactions on Nanotechnology, Vol. 13, No. 1, pp. 109-115, (2014).
[6]           M. H. Abolbashari, N. Freidoonimehr, F. Nazari, and M. M. Rashidi, “Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid”, Powder Technology, Vol. 267, pp. 256-267, (2014).
[7]           N. Freidoonimehr, M. M. Rashidi, and S.Mahmud, “Unsteady MHD free convective flow past a permeable stretching vertical surface in a nano-fluid”, International Journal of Thermal Sciences, Vol. 87, pp.136-145, (2014).
[8]           A. S. Butt, A. Ali, and A. Mehmood, “Study of flow and heat transfer on a stretching surface in a rotating Casson fluid”, Proceedings of the National Academy of Science (Springer), Vol. 85, No. 3, pp. 421-426, (2015).
[9]          J. A. Khan, M.  Mustafa, T. Hayat, and A. Alsaedi, “Three-dimensional flow of nanofluid over a non-linearly stretching sheet: An application to solar energy”, International Journal of Heat and Mass Transfer, Vol. 86, pp.158-164, (2015).
[10]       S. A. Shehzad, Z. Abdullah, F. M.  Abbasi, T. Hayat, and A. Alsaedi, “Magnetic field effect in three-dimensional flow of an Oldroyd-B nanofluid over a radiative surface”, Journal of Magnetism and Magnetic Materials, Vol. 399, pp.97-108, (2016).
[11]       L. Kolsi, H. F. Oztop, A. Alghamdi, N. Abu-Hamdeh, A.  Borjini, and H. B. A. Aissia, “Computational work on a three dimensional analysis of natural convection and entropy generation in nanofluid filled enclosures with triangular solid insert at the corners”, Journal of Molecular Liquids, Vol. 218, pp. 260-274, (2016).
[12]      T. Hayat, T. Muhammad, S. A. Shehzad, and A. Alsaedi, “On three-dimensional boundary layer flow of Sisko nanofluid with magnetic field effects”, Advanced Powder Technology, Vol. 27, No. 2, pp. 504-512, (2016).
[13]       T. Hayat, M. Mumtaz, A. Shafiq, and A. Alsaedi, “Thermal stratified three‑ dimensional flow with inclined magnetic field and Joule heating”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 39, No. 5, pp. 1607-1621, (2017).
[14]      P. G. Saffman, “On the stability of laminar flow of a dusty gas”, Journal of Fluid Mechanics, Vol. 13, No. 1, pp. 120-128, (1962).
[15]       K. M. Chakrabarti, “Note on boundary layer in a dusty gas”, American Institute of Aeronautics and Astronautics Journal, Vol. 12, No. 8, pp. 1136-1137, (1974).
[16]       N. Datta,  and S. K. Mishra, “Boundary layer flow of a dusty fluid over a semi-infinite flat plate”, Acta Mechanica, Vol. 42, No. 1-2, pp. 71-82, (1982).
[17]      S. Mosayebidorcheh, M. Hatami, D. D. Ganji, T. Mosayebidorcheh, and  S. M. Mirmohammadsadeghi, “Investigation of transient MHD couette flow and heat transfer of dusty fluid with temperature-dependent properties”, Journal of Fluid Mechanics, Vol. 8, No. 4, pp. 921-929, (2015).
[18]       O. M. Prakash, O. D. Makinde, D. Kumar,  and Y. K. Dwivedi, “Heat transfer to MHD oscillatory dusty fluid flow in a channel filled with a porous medium”, Sadhana, Vol. 40, No. 4, pp. 1273-1282, (2015).
[19]      H. A. Attia, W. Abbas, A. E. D. Abdin, and  M. A. M. Abdeen,  “Effects of ion slip and hall current on unsteady couette flow of a dusty fluid through porous media with heat transfer”, High Temperature,  Vol. 53, No. 6, pp. 891-898, (2015).
[20]      R. Muthuraj, K. Nirmala, and S. Srinivas, “Influences of chemical reaction and wall properties on MHD peristaltic transport of a dusty fluid with heat and mass transfer”,  Alexandria Engineering Journal, Vol. 55, No. 1, pp. 597-611, (2016).
[21]      S. Manjunatha, and B. J. Gireesha, “Effects of variable viscosity and thermal conductivity on MHD flow and heat transfer of a dusty fluid”, Ain Shams Engineering Journal, Vol. 7, No. 1, pp. 505-515, (2016).
[22]       M. R. Mohaghegh, and A. B. Rahimi,  “Three–dimensional stagnation–point flow and heat transfer of a dusty fluid toward a stretching sheet”, Journal of Heat Transfer, Vol. 138, No. 1, pp. 112001 (12 pages), (2016).
[23]      V. W. J. Anand, S. Ganesh, A. M.  Ismail, and C. K. Kirubhashankar, “Unsteady MHD dusty fluid flow of an exponentially stretching sheet with heat source through porous medium”, Applied Mathematical Sciences, Vol. 9, No. 42, pp. 2083-2090, (2015).
[24]      P. T. Manjunatha, B. J. Gireesha, and  B. C. Prasannakumara, “Effect of radiation on flow and heat transfer of MHD dusty fluid over a stretching cylinder embedded in a porous medium in presence of heat source”, International Journal of Applied and Computational Mathematics, Vol. 3, No. 1, pp. 293-310, (2017).
[25]       B. C. Prasannakumara, B. J. Gireesha, and P. T. Manjunatha, “Melting phenomenon in MHD stagnation point flow of dusty fluid over a stretching sheet in the presence of thermal radiation and non-uniform heat source/sink”, International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 16, No. 5, pp. 265-274, (2015).
[26]     M. M. Bhatti, A. Zeeshan, and R. Ellahi, “Study of heat transfer with nonlinear thermal radiation on sinusoidal motion of magnetic solid particles in a dusty fluid”, Journal of Theoretical and Applied Mechanics, Vol. 46, No. 3, pp. 75-94, (2016).
[27]     B. J. Gireesha, P. Venkatesh, N. S. Shashikumar, and B. C. Prasannakumara, “Boundary layer flow of dusty fluid over a permeable radiating stretching surface embedded in a thermally stratified porous medium in the presence of uniform heat source”, Nonlinear Engineering, Vol. 6, No. 1, pp. 31-41, (2017).
[28]     R. C. Bataller, “Radiation effects for the Blassius and Sakiadis flows with a convective surface boundary condition”, Applied Mathematics and Computation, Vol. 206, No. 2, pp. 832-840, (2008).
[29]     A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 4, pp. 1064-1068, (2009).
[30]     O. D. Makinde, “Similarity solution of hydromagnetic heat and mass transfer over a vertical plate with a convective surface boundary condition”, International Journal of Physical Sciences, Vol. 5, No. 6, pp. 700-710, (2010).
[31]     J. H. Merkin, and I. Pop, “The forced convection flow of a uniform stream over a flat surface with a convective surface boundary condition”, Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 9, pp. 3602-3609, (2011).
[32]     G. K. Ramesh, B. J. Gireesha, and R. S. R. Gorla, “Boundary layer flow past a stretching sheet with fluid‑particle suspension and convective boundary condition”, Heat Mass Transfer, Vol. 51, No. 8, pp.1061-1066, (2015).
[33]     M. H. Abolbashari, N. Freidoonimehr, F. Nazari, and M. M. Rashidi, “Analytical modeling of entropy generation for Casson nano-fluid flow induced by a stretching surface”, Advanced Powder Technology, Vol. 26, No. 2, pp. 542-552, (2015).
[34]     R. Kandasamy, C. Jeyabalan, and K. K.S. Prabhu, “Nanoparticle volume fraction with heat and mass transfer on MHD mixed convection flow in a nanofluid in the presence of thermo-diffusion under convective boundary condition”, Applied Nanoscience, Vol. 6, No. 2, pp. 287-300, (2016).
[35]     M. R. Krishnamurthy, B. C. Prasannakumara, R. S. R. Gorla, and B. J. Gireesha, “Non-linear thermal radiation and slip effect on boundary layer flow and heat transfer of suspended nanoparticles over a stretching sheet embedded in porous medium with convective boundary conditions”, Journal of Nanofluids, Vol. 5, No. 4, pp. 522-530, (2016).
[36]       T. Hayat, S. Makhdoom, M. Awais, S. Saleem, and M. M. Rashidi,  “Axisymmetric Powell-Eyring fluid flow with convective boundary condition: optimal analysis”, Applied Mathematics and Mechanics, Vol. 37, No. 7, pp. 919-928, (2016).
[37]      N. Freidoonimehr, and M. M. Rashidi,  “Analytical approximation of heat and mass transfer in MHD non-Newtonian nanofluid flow over a stretching sheet with convective surface boundary conditions”, International Journal of Biomathematics, Vol. 10, No. 1, pp. 1750008 (25 pages), (2017).
CAPTCHA Image