Heat transfer analysis on peristaltically induced motion of particle-fluid suspension with variable viscosity: Clot blood model

In this article, heat transfer analysis on clot blood model of the particle-fluid suspension through a non-uniform annulus has been investigated. The blood propagating along the whole length of the annulus was induced by peristaltic motion. The effects of variable viscosity and slip condition are also taken into account. The governing flow problem is modeled using lubrication approach by taking the assumption of long wavelength and creeping flow regime. The resulting equation for fluid phase and particle phase is solved analytically and closed form solutions are obtained. The physical impact of all the emerging parameters is discussed mathematically and graphically. Particularly, we considered the effects of particle volume fraction, slip parameter, the maximum height of clot, viscosity parameter, average volume flow rate, Prandtl number, Eckert number and fluid parameter on temperature profile, pressure rise and friction forces for outer and inner tube. Numerical computations have been used to determine the behavior of pressure rise and friction along the whole length of the annulus. The present study is also presented for an endoscope as a special case of our study. It is observed that greater influence of clot tends to rise the pressure rise significantly. It is also found that temperature profile increases due to the enhancement in Prandtl number, Eckert number, and fluid parameter. The present study reveals that friction forces for outer tube have higher magnitude as compared to the friction forces for an inner tube. In fact, the results for present study can also be reduced to the Newtonian fluid by taking ζ → ∞.

[1]  Kambiz Vafai,et al.  The effect of the slip condition on Stokes and Couette flows due to an oscillating wall: exact solutions , 2004 .

[2]  K. Mekheimer,et al.  Peristaltic transport of a particle--fluid suspension through a uniform and non-uniform annulus , 2008 .

[3]  Y. Abd Elmaboud,et al.  Peristaltic Flow through a Porous Medium in an Annulus: Application of an Endoscope , 2008 .

[4]  A. Abd-Alla,et al.  Effect of an endoscope and rotation on the peristaltic flow involving a Jeffrey fluid with magnetic field , 2015 .

[5]  Muhammad Mubashir Bhatti,et al.  Slip effects and endoscopy analysis on blood flow of particle-fluid suspension induced by peristaltic wave , 2016 .

[6]  Noreen Sher Akbar,et al.  Simulation of peristaltic flow of chyme in small intestine for couple stress fluid , 2014 .

[7]  Rahmat Ellahi,et al.  Study of Heat Transfer with Nonlinear Thermal Radiation on Sinusoidal Motion of Magnetic Solid Particles in a Dusty Fluid , 2016 .

[8]  Abd El Hakeem Abd El Naby,et al.  Effects of a Fluid with Variable Viscosity and an Endoscope on Peristaltic Motion , 2003 .

[9]  L M Srivastava,et al.  Peristaltic transport of a particle-fluid suspension. , 1989, Journal of biomechanical engineering.

[10]  Tasawar Hayat,et al.  Effect of heat transfer on the peristaltic flow of an electrically conducting fluid in a porous space , 2009 .

[11]  E. F. Elshehawey,et al.  Peristaltic transport of three-layered flow with variable viscosity , 2004, Appl. Math. Comput..

[12]  K. Vafai,et al.  Peristaltic Transport of a Jeffrey Fluid with Variable Viscosity through a Porous Medium in an Asymmetric Channel , 2012 .

[13]  Sohail Nadeem,et al.  Influence of induced magnetic field and heat transfer on the peristaltic motion of a Jeffrey fluid in an asymmetric channel: Closed form solutions , 2013 .

[14]  Abd El Hakeem Abd El Naby,et al.  Effects of an endoscope and fluid with variable viscosity on peristaltic motion , 2004, Appl. Math. Comput..

[15]  Tasawar Hayat,et al.  Effects of slip and heat transfer on the peristaltic flow of a third order fluid in an inclined asymmetric channel , 2011 .

[16]  Rahmat Ellahi,et al.  The Effects of Variable Viscosity on the Peristaltic Flow of Non-Newtonian Fluid through a Porous Medium in an Inclined Channel with Slip Boundary Conditions , 2013 .

[17]  Rahmat Ellahi,et al.  Effects of heat and mass transfer on peristaltic flow in a non-uniform rectangular duct , 2014 .

[18]  L. M. Srivastava,et al.  Influence of wall elasticity and poiseuille flow on peristaltic induced flow of a particle-fluid mixture , 1997 .

[19]  N. Akbar,et al.  Characteristics of heating scheme and mass transfer on the peristaltic flow for an Eyring–Powell fluid in an endoscope , 2012 .

[20]  M. M. Bhatti,et al.  Analytic study of heat transfer with variable viscosity on solid particle motion in dusty Jeffery fluid , 2016 .

[21]  B. Martin.  Some analytical solutions for viscometric flows of power-law fluids with heat generation and temperature dependent viscosity , 1967 .

[22]  R. Haynes.  Physical basis of the dependence of blood viscosity on tube radius. , 1960, The American journal of physiology.

[23]  D. Tripathi,et al.  Mathematical modelling of heat transfer effects on swallowing dynamics of viscoelastic food bolus through the human oesophagus , 2013 .

[24]  K. Ramesh,et al.  THE INFLUENCE OF HEAT TRANSFER ON PERISTALTIC TRANSPORT OF MHD SECOND GRADE FLUID THROUGH POROUS MEDIUM IN A VERTICAL ASYMMETRIC CHANNEL , 2015 .

[25]  Sohail Nadeem,et al.  Peristaltic Flow of a Jeffrey Fluid with Variable Viscosity in an Asymmetric Channel , 2009, Zeitschrift für Naturforschung A.

[26]  Tasawar Hayat,et al.  Peristaltic flow of a Williamson fluid in an inclined asymmetric channel with partial slip and heat transfer , 2012 .

[27]  Mohammad Mehdi Rashidi,et al.  Three dimensional peristaltic flow of hyperbolic tangent fluid in non-uniform channel having flexible walls , 2016 .

[28]  A. M. Abd-Alla,et al.  Effects of rotation and initial stress on peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field , 2014 .

[29]  N. Akbar,et al.  Exact solution of peristaltic flow of biviscosity fluid in an endoscope: A note , 2014 .

[30]  S Nadeem,et al.  Peristaltic flow of a Jeffrey fluid in a rectangular duct , 2010 .

[31]  Dharmendra Tripathi,et al.  A mathematical model for swallowing of food bolus through the oesophagus under the influence of heat transfer , 2012 .

[32]  Kh. S. Mekheimer,et al.  Peristaltic Motion of a Particle-Fluid Suspension in a Planar Channel , 1998 .

[33]  G. Vinogradov,et al.  Wall slippage and elastic turbulence of polymers in the rubbery state , 1968 .

[34]  Rahmat Ellahi,et al.  Effects of heat transfer on peristaltic motion of Oldroyd fluid in the presence of inclined magnetic field , 2014 .

[35]  V. P. Srivastava,et al.  A two-fluid model of non-Newtonian blood flow induced by peristaltic waves , 1995 .

[36]  G. C. Shit,et al.  Hydromagnetic effect on inclined peristaltic flow of a couple stress fluid , 2014 .

[37]  Giles R Cokelet,et al.  The rheology of human blood , 1963 .

[38]  G. Moatimid,et al.  Electrohydrodynamic peristaltic flow of a viscoelastic Oldroyd fluid with a mild stenosis: Application of an endoscope , 2016 .

[39]  Mohammad Mehdi Rashidi,et al.  APPLICATION OF DRUG DELIVERY IN MAGNETOHYDRODYNAMICS PERISTALTIC BLOOD FLOW OF NANOFLUID IN A NON-UNIFORM CHANNEL , 2016 .

[40]  M. M. Bhatti,et al.  Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls , 2016 .

[41]  M. M. Bhatti,et al.  HEAT AND MASS TRANSFER ANALYSIS ON PERISTALTIC FLOW OF PARTICLE–FLUID SUSPENSION WITH SLIP EFFECTS , 2017 .

[42]  K. Migler,et al.  Slip transition of a polymer melt under shear stress. , 1993, Physical review letters.