Effects of Transpiration and Internal Heat Generation/Absorption on the Unsteady Flow of a Maxwell Fluid at a Stretching Surface

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Swati Mukhopadhyay ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Differential Equations ◽  
Newtonian Fluid ◽  
Fluid Model ◽  
Fluid Velocity ◽  
Internal Heat ◽  
Maxwell Fluid ◽  
Shear Thinning ◽  
Stretching Surface ◽  
Flow Features ◽  
Two Dimensional Flow

The effect of transpiration on unsteady two-dimensional flow of an MHD non-Newtonian Maxwell fluid over a stretching surface in the presence of a heat source/sink is investigated. The upper convected Maxwell fluid model is used to characterize the non-Newtonian fluid behavior. Using a similarity transformation the governing partial differential equations of the problem are reduced to a system of ordinary differential equations (ODEs), and the ODEs are solved numerically by a shooting method. The flow features and the heat transfer characteristics are analyzed and discussed in detail for several sets of values of the governing parameters. Though the velocity of the fluid initially decreases with increasing unsteady parameter but it increases finally. Quite the opposite is true with the temperature. Furthermore, the velocity of the fluid decreases with an increasing magnetic or Maxwell parameter. But the temperature is enhanced with an increasing Maxwell parameter. It is observed that the effect of the transpiration is to decrease the fluid velocity as well as the temperature. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

scholarly journals Unsteady MHD boundary layer flow of an upper convected Maxwell fluid past a stretching sheet with first order constructive/destructive chemical reaction

2012 ◽  
Vol 9 (2) ◽  
pp. 123-133 ◽  
Author(s):  
Swati Mukhopadhyay ◽  
Rama S. R. Gorla
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Fluid Model ◽  
Fluid Velocity ◽  
Maxwell Fluid ◽  
Similarity Solutions ◽  
First Order ◽  
Two Dimensional Flow ◽  
Layer Flow

The mass transfer of unsteady two-dimensional flow of MHD non-Newtonian Maxwell fluid over a stretching surface in the presence of first order constructive/destructive chemical reaction is presented. Upper convected Maxwell (UCM) fluid model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions the governing partial differential equations are transformed to ordinary differential equations and are then solved numerically by shooting method. The flow field and mass transfer are significantly influenced by the governing parameters. The results show that fluid velocity initially decreases with increasing unsteadiness parameter (0 to 0.3) and concentration decreases significantly due to unsteadiness. The effect of increasing values of the Maxwell parameter (0 to 0.4) is to suppress the velocity field. The concentration is enhanced with increasing Maxwell parameter. The fluid velocity decreases with increasing magnetic parameter (0 to 0.3). DOI: http://dx.doi.org/10.3329/jname.v9i2.12541 Journal of Naval Architecture and Marine Engineering 9(2012) 123-133

Upper-Convected Maxwell Fluid Flow over an Unsteady Stretching Surface Embedded in Porous Medium Subjected to Suction/Blowing

2012 ◽  
Vol 67 (10-11) ◽  
pp. 641-646 ◽  
Author(s):  
Swati Mukhopadhyay
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Fluid Model ◽  
Fluid Velocity ◽  
Boundary Layer Equation ◽  
Flow Characteristics ◽  
Maxwell Fluid ◽  
Momentum Equation ◽  
Stretching Surface ◽  
Similarity Transformations

Unsteady two-dimensional flow of a Maxwell fluid over a stretching surface in a porous medium subjected to suction/blowing is investigated. The upper-convected Maxwell fluid model is used to characterize the non-Newtonian fluid behaviour. With the help of similarity transformations, the boundary layer equation corresponding to the momentum equation is transformed to an ordinary one and then solved numerically by the shooting method. The flow characteristics for different values of the governing parameters are analyzed and discussed in detail. The fluid velocity initially decreases with increasing unsteadiness parameter. Also, it is found that the fluid velocity decreases with increasing permeability parameter. The effect of increasing values of the Maxwell parameter is to suppress the velocity field. Due to suction, the fluid velocity is found to decrease in the boundary layer region.

Convection heat transfer in a Maxwell fluid at a non-isothermal surface

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Kuppalapalle Vajravelu ◽  
Kerehalli Prasad ◽  
Ashwatha Sujatha
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Variable Temperature ◽  
Nonlinear Partial Differential Equations ◽  
Convection Heat Transfer ◽  
Maxwell Fluid ◽  
Convection Heat ◽  
Stretching Surface ◽  
Coupled Equations ◽  
Wide Range

AbstractAnalysis is carried out to study the convection heat transfer in an upper convected Maxwell fluid at a non-isothermal stretching surface. This is a generalization of the paper by Sadeghy et al. [21] to study the effects of free convection currents, variable thermal conductivity and the variable temperature at the stretching surface. Unlike in Sadeghy et al., here the governing nonlinear partial differential equations are coupled. These coupled equations are transformed in to a system of nonlinear ordinary differential equations and are solved numerically by a finite difference scheme (known as the Keller-Box method) and the numerical results are presented through graphs and tables for a wide range of governing parameters. The results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study of nonlinear convection heat transfer.

scholarly journals Numerical study of chemically reacting unsteady Casson fluid flow past a stretching surface with cross diffusion and thermal radiation

2017 ◽  
Vol 7 (1) ◽  
pp. 69-76 ◽  
Author(s):  
K. Pushpalatha ◽  
J.V. Ramana Reddy ◽  
V. Sugunamma ◽  
N. Sandeep
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Casson Fluid ◽  
Stretching Surface ◽  
Cross Diffusion ◽  
Similarity Transformations ◽  
Chemically Reacting ◽  
Fourth Order Method

AbstractThe problem of an unsteady MHD Casson fluid flow towards a stretching surface with cross diffusion effects is considered. The governing partial differential equations are converted into a set of nonlinear coupled ordinary differential equations with the help of suitable similarity transformations. Further, these equations have been solved numerically by using Runge-Kutta fourth order method along with shooting technique. Finally, we studied the influence of various non-dimensional governing parameters on the flow field through graphs and tables. Results indicate that Dufour and Soret numbers have tendency to enhance the fluid velocity. It is also found that Soret number enhances the heat transfer rate where as an opposite result is observed with Casson parameter. A comparison of the present results with the previous literature is also tabulated to show the accuracy of the results.

scholarly journals Hydrodynamics Interactions of Metachronal Waves on Particulate-Liquid Motion through a Ciliated Annulus: Application of Bio-Engineering in Blood Clotting and Endoscopy

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 532 ◽  
Author(s):  
Muhammad Mubashir Bhatti ◽  
Asmaa F. Elelamy ◽  
Sadiq M. Sait ◽  
Rahmat Ellahi
Keyword(s):  
Newtonian Fluid ◽  
Volume Fraction ◽  
Fluid Model ◽  
Flow Behavior ◽  
Blood Clot ◽  
Fluid Velocity ◽  
Particle Volume Fraction ◽  
Particle Volume ◽  
Entire Cross Section ◽  
Bio Engineering

This study deals with the mass transport phenomena on the particle-fluid motion through an annulus. The non-Newtonian fluid propagates through a ciliated annulus in the presence of two phenomenon, namely (i) endoscopy, and (ii) blood clot. The outer tube is ciliated. To examine the flow behavior we consider the bi-viscosity fluid model. The mathematical modeling has been formulated for small Reynolds number to examine the inertia free flow. The purpose of this assumption is that wavelength-to-diameter is maximal, and the pressure could be considerably uniform throughout the entire cross-section. The resulting equations are analytically solved, and exact solutions are given for particle- and fluid-phase profiles. Computational software Mathematica has been used to evaluate both the closed-form and numerical results. The graphical behavior across each parameter has been discussed in detail and presented with graphs. The trapping mechanism is also shown across each parameter. It is noticed clearly that particle volume fraction and the blood clot reveal converse behavior on fluid velocity; however, the velocity of the fluid reduced significantly when the fluid behaves as a Newtonian fluid. Schmidt and Soret numbers enhance the concentration mechanism. Furthermore, more pressure is required to pass the fluid when the blood clot appears.

Non-isothermal flow of Maxwell fluids above fixed flat plates under the influence of a transverse magnetic field

2011 ◽  
Vol 225 (4) ◽  
pp. 909-916 ◽  
Author(s):  
M M Heyhat ◽  
N Khabazi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Velocity ◽  
Maxwell Fluid ◽  
Transverse Magnetic ◽  
Deborah Number ◽  
Flat Plates ◽  
Two Dimensional Flow ◽  
Energy Equations

In this article, the magnetohydrodynamic flow and heat transfer of an upper-convected Maxwell fluid is studied theoretically above a flat rigid surface with constant temperature. It is assumed that the Reynolds number of the flow is high enough for boundary layer approximation to be valid. Assuming a laminar, two-dimensional flow above the plate, the concept of stream function coupled with the concept of similarity solution is utilized to reduce the governing equations, which are continuity, momentum, and energy equations, into two ordinary differential equations. The spectral method is used for solving the equations numerically. The effects of magnetic field, and Deborah, Prandtl, and Eckert numbers on the fluid velocity field and heat transfer behaviour are shown in several plots. Obtained results show that fluid velocity can be decreased by increasing the magnetic number while it increases by increasing the Deborah number. Moreover, the thickness of the thermal boundary layer is decreased by increasing the Deborah and Prandtl numbers. It is increased by an increase in the Eckert number.

scholarly journals UNSTEADY TWO-LAYERED BLOOD FLOW THROUGH A -SHAPED STENOSED ARTERY USING THE GENERALIZED OLDROYD-B FLUID MODEL

2016 ◽  
Vol 58 (1) ◽  
pp. 96-118 ◽  
Author(s):  
AKBAR ZAMAN ◽  
NASIR ALI ◽  
O. ANWAR BEG ◽  
M. SAJID
Keyword(s):  
Blood Flow ◽  
Differential Equations ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Initial Boundary ◽  
Momentum Conservation ◽  
Rheological Parameters ◽  
Stenosed Artery ◽  
Flow Through

A theoretical study of an unsteady two-layered blood flow through a stenosed artery is presented in this article. The geometry of a rigid stenosed artery is assumed to be$w$-shaped. The flow regime is assumed to be laminar, unsteady and uni-directional. The characteristics of blood are modelled by the generalized Oldroyd-B non-Newtonian fluid model in the core region and a Newtonian fluid model in the periphery region. The governing partial differential equations are derived for each region by using mass and momentum conservation equations. In order to facilitate numerical solutions, the derived differential equations are nondimensionalized. A well-tested explicit finite-difference method (FDM) which is forward in time and central in space is employed for the solution of a nonlinear initial boundary value problem corresponding to each region. Validation of the FDM computations is achieved with a variational finite element method algorithm. The influences of the emerging geometric and rheological parameters on axial velocity, resistance impedance and wall shear stress are displayed graphically. The instantaneous patterns of streamlines are also presented to illustrate the global behaviour of the blood flow. The simulations are relevant to haemodynamics of small blood vessels and capillary transport, wherein rheological effects are dominant.

Analytical Treatment for the Dynamics of Second Law Analysis of Jeffery Nanofluid with Convective Heat and Mass Conditions

2021 ◽  
Vol 16 (1) ◽  
pp. 89-96
Author(s):  
Rizwan Akhtar ◽  
Muhammad Awais ◽  
Muhammad Asif Zahoor Raja ◽  
M. N. Abrar ◽  
Sayyar Ali Shah ◽  
...  
Keyword(s):  
Viscous Dissipation ◽  
Newtonian Fluid ◽  
Entropy Generation ◽  
Fluid Model ◽  
Second Law ◽  
Jeffrey Fluid ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Second Law Analysis ◽  
Jeffery Nanofluid

This study has been managed for the investigation of entropy generation of inclined magnetic field (MG) on the Jeffery nanofluid flow on a stretching surface containing viscous dissipation. Heat generation or absorption effects are likewise considered on the magnetohydromagnetic flow problem and electric field is considered negligible. The boundary layer approach is incorporated for simplification of the proposed governing equations in which the target of analysis is focused near the surface of the fluidic problem. The concept of dimensionless parameters are used for simplification of the proposed system which overcomes the complexity of the problem. The relaxation and retardation times are also considered for the non-Newtonian Jeffrey fluid model for better analysis of the entropy generation of inclined MG on the Jeffery nanofluid flow on a stretching surface containing viscous dissipation. The strength of analytical homotopy analysis approach is employed for finding the solutions of the proposed fluidic system in terms of energy, momentum and concentration which is effective in the spatial domain. Graphical explanation for flow parameters have been incorporated. The tabular description is given for the convergence analysis and comparison of velocity gradient at the sheet surface f″ (0) for analytical solution (HAM) computed in this manuscript along with the numerical solution. The aim of second law analysis can be achieved by increasing the magnitude of the finite different temperature parameter. The current study is also described for Newtonian fluid as a special case of our study. Stream lines patterns are also provided for both Newtonian and non-Newtonian fluid models.

scholarly journals Novel numerical analysis of multi-term time fractional viscoelastic non-newtonian fluid models for simulating unsteady MHD Couette flow of a generalized Oldroyd-B fluid

2018 ◽  
Vol 21 (4) ◽  
pp. 1073-1103 ◽  
Author(s):  
Libo Feng ◽  
Fawang Liu ◽  
Ian Turner ◽  
Liancun Zheng
Keyword(s):  
Finite Difference ◽  
Couette Flow ◽  
Newtonian Fluid ◽  
Fluid Model ◽  
Time Derivative ◽  
Maxwell Fluid ◽  
Stability And Convergence ◽  
Finite Difference Schemes ◽  
Fluid Models ◽  
Mhd Couette Flow

Abstract In this paper, we consider the application of the finite difference method for a class of novel multi-term time fractional viscoelastic non-Newtonian fluid models. An important contribution of the work is that the new model not only has a multi-term time derivative, of which the fractional order indices range from 0 to 2, but also possesses a special time fractional operator on the spatial derivative that is challenging to approximate. There appears to be no literature reported on the numerical solution of this type of equation. We derive two new different finite difference schemes to approximate the model. Then we establish the stability and convergence analysis of these schemes based on the discrete H1 norm and prove that their accuracy is of O(τ + h2) and O(τmin{3–γs,2–αq,2–β}+h2), respectively. Finally, we verify our methods using two numerical examples and apply the schemes to simulate an unsteady magnetohydrodynamic (MHD) Couette flow of a generalized Oldroyd-B fluid model. Our methods are effective and can be extended to solve other non-Newtonian fluid models such as the generalized Maxwell fluid model, the generalized second grade fluid model and the generalized Burgers fluid model.

Heat transfer and fluid flow of a non-Newtonian nanofluid over an unsteady contracting cylinder employing Buongiorno’s model

2015 ◽  
Vol 25 (4) ◽  
pp. 703-723 ◽  
Author(s):  
A. Mahdy ◽  
A Chamkha
Keyword(s):  
Differential Equations ◽  
Fluid Model ◽  
Numerical Approach ◽  
Casson Fluid ◽  
Content Type ◽  
Buongiorno’S Model ◽  
Similarity Transformations ◽  
Casson Fluid Model ◽  
Two Dimensional Flow ◽  
Computer Algebra Software

Purpose – The purpose of this paper is to discuss a combined similarity-numerical approach that is used to study the unsteady two-dimensional flow of a non-Newtonian nanofluid over a contracting cylinder using Buongiorno’s model and the Casson fluid model that is used to characterize the non-Newtonian fluid behavior. Design/methodology/approach – Similarity transformations are employed to transform the unsteady Navier-Stokes partial differential equations into a system of ordinary differential equations. The transformed equations are then solved numerically by means of the very robust symbolic computer algebra software MATLAB employing the routine bvpc45. Findings – The effect of increasing values of the Casson parameter is to suppress the velocity field (in absolute sense), the temperature and concentration decrease as Casson parameter increase. The heat and mass transfer rates decrease with the increase of unsteadiness parameters and Brownian motion parameter. In addition, they increase as the Casson parameter and the thermophoresis parameter increase. Originality/value – The problem is relatively original and represents a very important contribution to the field of non-Newtonian nanofluids.

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