scholarly journals Influence of slip condition on peristaltic transport of a viscoelastic fluid with fractional Burger’s model

2011 ◽  
Vol 15 (2) ◽  
pp. 501-515 ◽  
Author(s):  
Dharmendra Tripathi ◽  
Praveen Gupta ◽  
Subir Das
Keyword(s):  
Viscoelastic Fluid ◽  
Approximate Analytical Solution ◽  
Volume Flow Rate ◽  
Wall Slip ◽  
Volume Flow ◽  
Slip Condition ◽  
Slip Parameter ◽  
Analysis Method ◽  
Long Wavelength ◽  
Homotopy Analysis

The investigation is to explore the transportation of a viscoelastic fluid with fractional Burgers? model by peristalsis through a channel under the influence of wall slip condition. This analysis has been carried out under the assumption of long wavelength and low Reynolds number. An approximate analytical solution of the problem is obtained by using Homotopy Analysis method (HAM). It is assumed that the cross-section of the channel varies sinusoidally along the length of channel. The expressions for axial velocity, volume flow rate and pressure gradient are obtained. The effects of fractional parameters ? and ?, material constants ?1,?2,?3, slip parameter k and amplitude ? on the pressure difference and friction force across one wavelength are discussed numerically and with the help of illustrations.

Slip And Hall Effects On The Flow Of A Hyperbolic Tangent Fluid Through Porous Medium In A Planar Channel With Peristalsis

GIS Business ◽  
2020 ◽  
Vol 15 (1) ◽  
pp. 383-394
Author(s):  
K. Shalini ◽  
K.Rajasekhar
Keyword(s):  
Porous Medium ◽  
Pressure Gradient ◽  
Volume Flow Rate ◽  
Perturbation Technique ◽  
Volume Flow ◽  
Planar Channel ◽  
Hyperbolic Tangent ◽  
Closed Form Solutions ◽  
Long Wavelength ◽  
Hall Effects

In this paper, the effect of Slip and Hall effects on the flow of Hyperbolic tangent fluid through a porous medium in a planar channel with peristalsis under the assumption of long wavelength is investigated. A Closed form solutions are obtained for axial velocity and pressure gradient by employing perturbation technique. The effects of various emerging parameters on the pressure gradient, time averaged volume flow rate and frictional force are discussed with the aid of graphs.

PERISTALTIC TRANSPORT OF MAXWELL VISCOELASTIC FLUIDS WITH A SLIP CONDITION: HOMOTOPY ANALYSIS OF GASTRIC TRANSPORT

2015 ◽  
Vol 15 (03) ◽  
pp. 1550021 ◽  
Author(s):  
D. TRIPATHI ◽  
O. ANWAR BÉG
Keyword(s):  
Relaxation Time ◽  
Frictional Force ◽  
Viscoelastic Fluids ◽  
Transport Processes ◽  
Peristaltic Transport ◽  
Slip Condition ◽  
Slip Parameter ◽  
Analytical Technique ◽  
Approximate Analytical Solutions ◽  
Homotopy Analysis

Viscoelastic fluids arise frequently in numerous biophysical transport processes including gastric flow, embryology, haemo-dynamics and synovial lubrication. In the present article, we examine the effect of slip condition on peristaltic transport of viscoelastic fluids with the fractional Maxwell model through a two-dimensional deformable channel under the long wavelength and low Reynolds number assumptions, as a simulation of gastric flow. The channel is subjected to sinusoidal waves traveling along the walls. A versatile semi-analytical technique, the homotopy analysis method (HAM) is used to obtain approximate analytical solutions for the non-dimensionalized flow problem. The convergence of the HAM which depends on ℏ-curves is illustrated for relevant parameters. The effects of fractional parameters, relaxation time and slip parameter on the pressure difference and frictional force across one wavelength against time and averaged flow rate are illustrated graphically. It is found that effect of both fractional parameters on pressure is opposite to each other. The relaxation time and slip parameter are found to assist the peristaltic transportation. The behavior of frictional force is found to be similar to pressure in a magnitude sense whereas it is opposite in direction.

scholarly journals On the Solution of Burgers’ Equation with the New Fractional Derivative

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Ali Kurt ◽  
Yücel Çenesiz ◽  
Orkun Tasbozan
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Fractional Derivative ◽  
Burgers Equation ◽  
Approximate Analytical Solution ◽  
Initial Conditions ◽  
Conformable Fractional Derivative ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Homotopy Analysis

AbstractFirstly in this article, the exact solution of a time fractional Burgers’ equation, where the derivative is conformable fractional derivative, with dirichlet and initial conditions is found byHopf-Cole transform. Thereafter the approximate analytical solution of the time conformable fractional Burger’s equation is determined by using a Homotopy Analysis Method(HAM). This solution involves an auxiliary parameter ~ which we also determine. The numerical solution of Burgers’ equation with the analytical solution obtained by using the Hopf-Cole transform is compared.

Unsteady Unidirectional Flow of Bingham Fluid Through the Parallel Microgap Plates with Wall Slip and Given Inlet Volume Flow Rate Variations

2013 ◽  
Vol 29 (2) ◽  
pp. 355-362
Author(s):  
Y.W. Lin ◽  
C.-I. Chen ◽  
C.-K. Chen
Keyword(s):  
Flow Rate ◽  
Volume Flow Rate ◽  
Flow Behavior ◽  
Linear Acceleration ◽  
Wall Slip ◽  
Transformation Method ◽  
Bingham Fluid ◽  
Volume Flow ◽  
Unidirectional Flow ◽  
Flow Motion

AbstractIn this paper, Laplace transformation method is used to solve the velocity profile and pressure gradient of the unsteady unidirectional flow of Bingham fluid. Between the parallel microgap plates, the flow motion is induced by a prescribed arbitrary inlet volume flow rate which varies with time. Due to the rarefaction, the wall slip condition is existed; therefore, the complexity of solution is also increased. In order to understand the flow behavior of Bingham fluid, there are two basic flow situations are solved. One is a suddenly started flow and the other is constant acceleration flow. Furthermore, linear acceleration and oscillatory flow are also considered. The result indicates when the yield stress τ0 is zero; the solution of the problem reduces to Newtonian fluid.

scholarly journals Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
M. M. Rashidi ◽  
E. Momoniat ◽  
B. Rostami
Keyword(s):  
Boundary Layer ◽  
Viscoelastic Fluid ◽  
Homotopy Analysis Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Stretching Surface ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Homotopy Analysis ◽  
Energy Equations

In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM) with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid). It is clear that by the use of second auxiliary parameter, the straight line region inℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a) prescribed surface temperature (PST) and (b) prescribed heat flux (PHF). The effect of involved parameters on velocity and temperature is investigated.

EFFECTS OF TRANSVERSE MAGNETIC FIELD ON THE PERISTALTIC TRANSPORT OF VISCOELASTIC FLUID WITH JEFFREY MODEL IN A FINITE LENGTH CHANNEL

2011 ◽  
Vol 25 (26) ◽  
pp. 3455-3471 ◽  
Author(s):  
D. TRIPATHI ◽  
T. HAYAT ◽  
N. ALI ◽  
S. K. PANDEY
Keyword(s):  
Magnetic Field ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Viscoelastic Fluid ◽  
Transverse Magnetic Field ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Transverse Magnetic ◽  
Volume Flow ◽  
Wall Shear

This paper investigates the peristaltic flow of viscoelastic fluid represented by Jeffrey model in presence of transverse magnetic field under long wavelength and low Reynolds number assumptions. The expressions of pressure gradient, volume flow rate, average volume flow rate and local wall shear stress are obtained. The effects of transverse magnetic field, electrical conductivity (i.e., Hartman number M), relaxation time and retardation time on pressure difference, local wall shear stress, and mechanical efficiency of peristaltic pump are discussed. Reflux limit for viscoelastic fluid is also found and the effects of all parameters on reflux phenomena are discussed. Comparative study of integral and nonintegral number of waves propagate in a train is presented.

scholarly journals Approximate Analytical Solutions to Conformable Modified Burgers Equation Using Homotopy Analysis Method

2019 ◽  
Vol 33 (1) ◽  
pp. 159-167 ◽  
Author(s):  
Ali Kurt ◽  
Orkun Tasbozan
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Homotopy Analysis Method ◽  
Burgers Equation ◽  
Approximate Analytical Solution ◽  
Analysis Method ◽  
Conformable Derivative ◽  
Modified Burgers Equation ◽  
Approximate Analytical Solutions ◽  
Homotopy Analysis

AbstractIn this paper the authors aspire to obtain the approximate analytical solution of Modified Burgers Equation with newly defined conformable derivative by employing homotopy analysis method (HAM).

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