A mathematical model of MHD nanofluid flow having gyrotactic microorganisms with thermal radiation and chemical reaction effects

In this article, we have examined three-dimensional unsteady MHD boundary layer flow of viscous nanofluid having gyrotactic microorganisms through a stretching porous cylinder. Simultaneous effects of nonlinear thermal radiation and chemical reaction are taken into account. Moreover, the effects of velocity slip and thermal slip are also considered. The governing flow problem is modelled by means of similarity transformation variables with their relevant boundary conditions. The obtained reduced highly nonlinear coupled ordinary differential equations are solved numerically by means of nonlinear shooting technique. The effects of all the governing parameters are discussed for velocity profile, temperature profile, nanoparticle concentration profile and motile microorganisms’ density function presented with the help of tables and graphs. The numerical comparison is also presented with the existing published results as a special case of our study. It is found that velocity of the fluid diminishes for large values of magnetic parameter and porosity parameter. Radiation effects show an increment in the temperature profile, whereas thermal slip parameter shows converse effect. Furthermore, it is also observed that chemical reaction parameter significantly enhances the nanoparticle concentration profile. The present study is also applicable in bio-nano-polymer process and in different industrial process.

[1]  Mohammad Mehdi Rashidi,et al.  Ferrofluid flow and heat transfer in a semi annulus enclosure in the presence of magnetic source considering thermal radiation , 2015 .

[2]  Sabu Thomas,et al.  Advances in polymer processing , 2009 .

[3]  L. Crane.  Flow past a stretching plate , 1970 .

[4]  E. Mureithi,et al.  Natural Convection Flow past an Impermeable Vertical Plate Embedded In Nanofluid Saturated Porous Medium with Temperature Dependent Viscosity , 2014 .

[5]  Cha'o-Kuang Chen,et al.  Heat transfer of a continuous, stretching surface with suction or blowing , 1988 .

[6]  I. Pop,et al.  Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder , 2008 .

[7]  I. Hamley,et al.  Effect of Stretching on the Structure of Cylinder- and Sphere-Forming Styrene―Isoprene―Styrene Block Copolymers , 2009 .

[8]  M. Subhas Abel,et al.  Visco-elastic MHD flow, heat and mass transfer over a porous stretching sheet with dissipation of energy and stress work , 2003 .

[9]  Wenhua Yu,et al.  Nanofluids: Science and Technology , 2007 .

[10]  Shijun Liao,et al.  Unsteady mixed nano-bioconvection flow in a horizontal channel with its upper plate expanding or contracting , 2015 .

[11]  Kannan M. Munisamy,et al.  Review of convection heat transfer and fluid flow in porous media with nanofluid , 2015 .

[12]  Mohammad Mehdi Rashidi,et al.  Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet , 2016 .

[13]  Mohammad Mehdi Rashidi,et al.  Numerical simulation of Fluid flow over a shrinking porous sheet by Successive linearization method , 2016 .

[14]  Swati Mukhopadhyay,et al.  MHD boundary layer slip flow along a stretching cylinder , 2013 .

[15]  J. Oh,et al.  Biopolymer-based microgels/nanogels for drug delivery applications , 2009 .

[16]  Sarit K. Das,et al.  Effect of particle size on the convective heat transfer in nanofluid in the developing region , 2009 .

[17]  T. Hayat,et al.  Similarity solution to three dimensional boundary layer flow of second grade nanofluid past a stretching surface with thermal radiation and heat source/sink , 2015 .

[18]  Emad M. Abo-Eldahab,et al.  Radiation effect on heat transfer in an electrically conducting fluid at a stretching surface with a uniform free stream , 2000 .

[19]  Faisal Md Basir,et al.  Nanofluid slip flow over a stretching cylinder with Schmidt and Péclet number effects , 2016 .

[20]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow , 1961 .

[21]  Mohammad Mehdi Rashidi,et al.  Effect of space dependent magnetic field on free convection of Fe3O4–water nanofluid , 2015 .

[22]  Mohammad Mehdi Rashidi,et al.  Numerical Simulation of Entropy Generation with Thermal Radiation on MHD Carreau Nanofluid towards a Shrinking Sheet , 2016, Entropy.

[23]  R. Cortell.  Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet , 2006 .

[24]  Ioan Pop,et al.  Mixed convection flow over a solid sphere embedded in a porous medium filled by a nanofluid containing gyrotactic microorganisms , 2013 .

[25]  Ioan Pop,et al.  Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms , 2014 .

[26]  Raed Abed Mahdi,et al.  Improvement of convection heat transfer by using porous media and nanofluid: review , 2013 .

[27]  M. Subhas Abel,et al.  Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a non-uniform heat source , 2009 .

[28]  B. K. Dutta,et al.  Temperature field in flow over a stretching sheet with uniform heat flux , 1985 .

[29]  I. Pop,et al.  A note on MHD flow over a stretching permeable surface , 1998 .

[30]  R. Cortell.  Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet , 2008 .

[31]  S. Saranya,et al.  Review of Nanobiopolymers for Controlled Drug Delivery , 2014 .

[32]  Anuar Ishak.  Unsteady MHD Flow and Heat Transfer over a Stretching Plate , 2010 .

[33]  Kaufui V. Wong,et al.  Applications of Nanofluids: Current and Future , 2010 .

[34]  M. M. Rashidi,et al.  Entropy Generation with Nonlinear Thermal Radiation in MHD Boundary Layer Flow Over a Permeable Shrinking/Stretching Sheet: Numerical Solution , 2016 .

[35]  Rahman Saidur,et al.  A REVIEW ON APPLICATIONS AND CHALLENGES OF NANOFLUIDS , 2011 .

[36]  C. Wang,et al.  Slip flow due to a stretching cylinder , 1988 .

[37]  Mohsen Sheikholeslami Kandelousi.  Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition , 2014 .

[38]  R. Kandasamy,et al.  Effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate , 1999 .

[39]  T. Pedley.  Instability of uniform micro-organism suspensions revisited , 2010, Journal of Fluid Mechanics.

[40]  Mohammad Mehdi Rashidi,et al.  A New Numerical Simulation of MHD Stagnation-Point Flow Over a Permeable Stretching/Shrinking Sheet in Porous Media with Heat Transfer , 2017 .

[41]  Norfifah Bachok,et al.  Flow and Heat Transfer over a Stretching Cylinder with Prescribed Surface Heat Flux , 2010 .

[42]  Ioan Pop,et al.  Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms , 2012 .

[43]  Wei Yu,et al.  A review on nanofluids: preparation, stability mechanisms, and applications , 2012 .