Unsteady flow and heat transfer of power-law nanofluid thin film over a stretching sheet with variable magnetic field and power-law velocity slip effect

Abstract This paper studies the flow and heat transfer of the power-law nanofluid thin film due to a stretching sheet with magnetic field and velocity slip effects. Unlike classical work, Fourier's law is modified by assuming that the thermal conductivity is power-law-dependent on the velocity gradient. Meanwhile, the power law wall temperature and the power law velocity slip effects are taken into account. Three different types of nanoparticles, Al 2 O 3 , TiO 2 and CuO are considered with ethylene vinyl acetate copolymer (EVA) used as a base fluid. The governing equations are solved by using DTM–NIM which is combined the differential transform method (DTM) with Newton Iteration method (NIM). The results show that for the specific physical parameters, the two different velocity profiles have always an intersection which goes from a far-field region to the stretching sheet as increasing velocity slip parameter. Furthermore, CuO–EVA nanofluid has better enhancement on heat transfer than TiO 2 /Al 2 O 3 –EVA.

[1]  Liancun Zheng,et al.  Unsteady flow and heat transfer of pseudo-plastic nanoliquid in a finite thin film on a stretching surface with variable thermal conductivity and viscous dissipation , 2015 .

[2]  Liancun Zheng,et al.  Laminar film condensation of pseudo-plastic non-Newtonian fluid with variable thermal conductivity on an isothermal vertical plate , 2016 .

[3]  S. K. Nandy,et al.  Unsteady flow of Maxwell fluid in the presence of nanoparticles toward a permeable shrinking surface with Navier slip , 2015 .

[4]  Sohail Nadeem,et al.  Heat transfer analysis of water-based nanofluid over an exponentially stretching sheet , 2014 .

[5]  Liancun Zheng,et al.  MHD thermosolutal marangoni convection heat and mass transport of power law fluid driven by temperature and concentration gradient , 2015 .

[6]  Helge I. Andersson,et al.  Heat transfer in a liquid film on an unsteady stretching sheet , 2008 .

[7]  Ishak Hashim,et al.  Thermocapillarity and magnetic field effects in a thin liquid film on an unsteady stretching surface , 2010 .

[8]  O. Abdulaziz,et al.  MHD flow and heat transfer in a thin liquid film on an unsteady stretching sheet by the homotopy analysis method , 2010 .

[9]  J. Yeh,et al.  Morphology, mechanical, and rheological behavior of microcellular injection molded EVA–clay nanocomposites ☆ , 2012 .

[10]  S. Tanpichai,et al.  Enhancement of thermal, mechanical and barrier properties of EVA solar cell encapsulating films by reinforcing with esterified cellulose nanofibres , 2015 .

[11]  I. Pop,et al.  Mixed Convection to Power-Law Type Non-Newtonian Fluids from a Vertical Wall , 1991 .

[12]  Mohammad Mehdi Rashidi,et al.  Buoyancy effect on MHD flow of nanofluid over a stretching sheet in the presence of thermal radiation , 2014 .

[13]  Liancun Zheng,et al.  MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction , 2015 .

[14]  Sohail Nadeem,et al.  Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet , 2015 .

[15]  Chaoyang Wang.  Liquid film on an unsteady stretching surface , 1990 .

[16]  Liancun Zheng,et al.  MHD mixed convective heat transfer over a permeable stretching wedge with thermal radiation and ohmic heating , 2012 .

[17]  Analysis of Marangoni convection of non-Newtonian power law fluids with linear temperature distribution , 2011 .

[18]  I. Pop,et al.  Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method , 2006 .

[19]  Yasir Khan,et al.  The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet , 2011, Comput. Math. Appl..

[20]  Liancun Zheng,et al.  MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation , 2015 .

[21]  I. Pop,et al.  Flow and heat transfer in a nano-liquid film over an unsteady stretching surface , 2013 .

[22]  K. Naikoti,et al.  Effects of heat source/sink on magnetohydrodynamic flow and heat transfer of a non-Newtonian power-law fluid on a stretching surface , 2016 .

[23]  Xinxin Zhang,et al.  Marangoni convection of power law fluids driven by power-law temperature gradient , 2012, J. Frankl. Inst..

[24]  Chun Wang.  Analytic solutions for a liquid film on an unsteady stretching surface , 2006 .

[25]  T. Aziz,et al.  Heat Transfer Analysis for Stationary Boundary Layer Slip Flow of a Power-Law Fluid in a Darcy Porous Medium with Plate Suction/Injection , 2015, PloS one.

[26]  Chien-Hsin Chen.  Heat transfer in a power-law fluid film over a unsteady stretching sheet , 2003 .

[27]  Min Zhang,et al.  Flow and heat transfer of an Oldroyd-B nanofluid thin film over an unsteady stretching sheet , 2016 .

[28]  Liancun Zheng,et al.  DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip , 2012 .

[29]  A. Alsaedi,et al.  Three-dimensional boundary layer flow of Maxwell nanofluid: mathematical model , 2015 .

[30]  Mostafa A. A. Mahmoud,et al.  Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation , 2011, Math. Comput. Model..

[31]  M. D. Lemos,et al.  Mathematical modeling and numerical results of power-law fluid flow over a finite porous medium , 2016 .

[32]  E. Aly,et al.  Analysis of fluid motion and heat transport on magnetohydrodynamic boundary layer past a vertical power law stretching sheet with hydrodynamic and thermal slip effects , 2015 .

[33]  Liancun Zheng,et al.  Analysis of MHD thermosolutal Marangoni convection with the heat generation and a first-order chemical reaction , 2012 .

[34]  P. Rana,et al.  Critical values in slip flow and heat transfer analysis of non-Newtonian nanofluid utilizing heat source/sink and variable magnetic field: Multiple solutions , 2016 .

[35]  Liancun Zheng,et al.  A new diffusion for laminar boundary layer flow of power law fluids past a flat surface with magnetic effect and suction or injection , 2015 .

[36]  B. S. Dandapat,et al.  Flow of a power-law fluid film on an unsteady stretching surface , 1996 .

[37]  Hai Lin,et al.  Lessons Learned from Whole Exome Sequencing in Multiplex Families Affected by a Complex Genetic Disorder, Intracranial Aneurysm , 2015, PloS one.

[38]  M. Jaunich,et al.  Investigation of the crosslinking behaviour of ethylene vinyl acetate (EVA) for solar cell encapsulation by rheology and ultrasound , 2012 .

[39]  Mohammad Mehdi Rashidi,et al.  The modified differential transform method for investigating nano boundary‐layers over stretching surfaces , 2011 .

[40]  Azeem Shahzad,et al.  Axisymmetric flow and heat transfer over an unsteady stretching sheet in power law fluid , 2016 .

[41]  K. Naikoti,et al.  Effects of heat source/sink on MHD flow and heat transfer of a non-Newtonian power-law fluid on a stretching surface with thermal radiation and slip-conditions , 2014 .

[42]  H. Andersson,et al.  Heat transfer over a bidirectional stretching sheet with variable thermal conditions , 2008 .

[43]  Pushpanjali G. Metri,et al.  Fluid flow and radiative nonlinear heat transfer in a liquid film over an unsteady stretching sheet , 2012, 2016 7th International Conference on Mechanical and Aerospace Engineering (ICMAE).

[44]  Stephen U. S. Choi.  Enhancing thermal conductivity of fluids with nano-particles , 1995 .