Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physical results in the analysis and investigations. In this work, both the ρ-Laplace homotopy transform method (ρ-LHTM) and the heat balance integral method (HBIM) are successfully combined to solve the fractional incompressible second-grade fluid differential equations. Numerical simulations and their physical interpretations of the mentioned incompressible second-grade fluid model are ensured to illustrate the main findings. It is also proposed that one can recognize the differences in physical analysis of diffusions such as ballistic diffusion, super diffusion, and subdiffusion cases by considering the impact of the orders ρ and φ.

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Dufour and Soret effects on Darcy-Forchheimer flow of second-grade fluid with the variable magnetic field and thermal conductivity

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-11-2019-0837 ◽

2020 ◽

Vol 30 (9) ◽

pp. 4331-4347 ◽

Cited By ~ 7

Author(s):

Ambreen A. Khan ◽

S. Naeem ◽

R. Ellahi ◽

Sadiq M. Sait ◽

K. Vafai

Keyword(s):

Magnetic Field ◽

Heat Transfer ◽

Thermal Conductivity ◽

Variable Magnetic Field ◽

Second Grade ◽

Second Grade Fluid ◽

Content Type ◽

Grade Fluid ◽

The Impact ◽

Forchheimer Flow

Purpose This study aims to investigate the effect of two-dimensional Darcy-Forchheimer flow over second-grade fluid with linear stretching. Heat transfer through convective boundary conditions is taken into account. Design/methodology/approach Nonlinear coupled governing equations are tackled with a homotopy algorithm, while for numerical computation the computer software package BVPh 2.0 is used. The convergence analysis is also presented for the validation of analytical and numerical results. Findings Valuation for the impact of key parameters such as variable thermal conductivity, Dufour and Soret effects and variable magnetic field in an electrically conducted fluid on the velocity, concentration and temperature profiles are graphically illustrated. It is observed from the results that temperature distribution rises by Dufour number whereas concentration distribution rises by Soret number. The Forchheimer number and porosity parameter raise the skin friction coefficient. The permeable medium has a vital impact and can help in reining the rate of heat transfer. Practical implications The permeable medium has a vital impact and can help in reining the rate of heat transfer. Originality/value To the best of the authors’ knowledge, this study is reported for the first time.

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Enhancement of heat and mass transfer of a physical model using Generalized Caputo fractional derivative of variable order and modified Laplace transform method

Journal of Mathematical Analysis and Modeling ◽

10.48185/jmam.v2i3.380 ◽

2021 ◽

Vol 2 (3) ◽

pp. 41-61

Author(s):

Muhammad Imran Asjad ◽

Maryam Aleem ◽

Waqas Ali ◽

Muhammad Abubakar ◽

Fahd Jarad

Keyword(s):

Mass Transfer ◽

Laplace Transform ◽

Heat And Mass Transfer ◽

Present Model ◽

Second Grade ◽

Variable Order ◽

Transform Method ◽

Grade Fluid ◽

The Impact ◽

Good Agreement

In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.

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Flow of a Second Grade Fluid through Constricted Tube using Integral Method

Journal of Applied Fluid Mechanics ◽

10.29252/jafm.09.06.25873 ◽

2016 ◽

Vol 9 (6) ◽

pp. 2803-2812 ◽

Cited By ~ 1

Author(s):

A A. M. Siddiqui ◽

N. Z. Khan ◽

Muhammad Afzal Rana ◽

Tahira Haroon ◽

◽

...

Keyword(s):

Integral Method ◽

Second Grade ◽

Second Grade Fluid ◽

Grade Fluid ◽

Constricted Tube

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Flow of a Dense Suspension Modeled as a Modified Second Grade Fluid

Fluids ◽

10.3390/fluids3030055 ◽

2018 ◽

Vol 3 (3) ◽

pp. 55 ◽

Cited By ~ 2

Author(s):

Wei-Tao Wu ◽

Nadine Aubry ◽

James Antaki ◽

Mehrdad Massoudi

Keyword(s):

Normal Stress ◽

Volume Fraction ◽

Variable Viscosity ◽

Fluid Model ◽

Constitutive Relationship ◽

Second Grade ◽

Simple Shear Flow ◽

Second Grade Fluid ◽

Dense Suspension ◽

Grade Fluid

In this paper, a simple shear flow of a dense suspension is studied. We propose a new constitutive relationship based on the second grade fluid model for the suspension, capable of exhibiting non-linear effects, where the normal stress coefficients are assumed to depend on the volume fraction of the particles and the shear viscosity depends on the shear rate and the volume fraction. After non-dimensionalizing the equations, we perform a parametric study looking at the effects of the normal stress coefficients and the variable viscosity. The numerical results show that for a certain range of parameters, the particles tend to form a region of high and uniform volume fraction, near the lower half of the flow.

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