scholarly journals Generalization of Thermal and Mass Fluxes for the Flow of Differential Type Fluid with Caputo–Fabrizio Approach of Fractional Derivative

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Asima Razzaque ◽  
Anam Rani ◽  
Mudassar Nazar
Keyword(s):  
Fractional Derivative ◽  
Flow Model ◽  
Integral Transform ◽  
Research Work ◽  
Vertical Surface ◽  
Physical Parameters ◽  
Governing Equations ◽  
Mass Fluxes ◽  
Generalized Momentum ◽  
Differential Type

In this research work, generalized thermal and mass transports for the unsteady flow model of an incompressible differential type fluid are considered. The Caputo–Fabrizio fractional derivative is used for the respective generalization of Fourier’s and Fick’s laws. A MHD fluid flow is considered near a flat vertical surface subject to unsteady mechanical, thermal, and mass conditions at boundary. The governing equations of flow model are solved by integral transform, and closed form results for generalized momentum, thermal, and concentration fields are obtained. Generalized thermal and mass fluxes at boundary are quantified in terms of Nusselt and Sherwood numbers, respectively, and presented in tabular form. The significance of the physical parameters over the momentum, thermal, and concentration profiles is characterized by sketching the graphs.

scholarly journals Transient Natural Convection Flow of Thermomicropolar Fluid of Micropolar Thermal Conductivity along a Nonuniformly Heated Vertical Surface

2014 ◽  
Vol 6 ◽  
pp. 141437
Author(s):  
Md. Mosharof Hossain ◽  
N. C. Roy ◽  
A. C. Mandal ◽  
M. A. Hossain
Keyword(s):  
Heat Conduction ◽  
Velocity Profiles ◽  
Vertical Surface ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Governing Equations ◽  
Layer Flow ◽  
Explicit Finite Difference ◽  
Stream Function Formulation

The unsteady free convection boundary layer flow of a thermomicropolar fluid along a vertical plate with effect of micropolar heat conduction has been investigated. The governing equations are transformed into a new form using a method of transformed coordinates. We then use an explicit finite difference scheme to solve the transformed equations. Here, the governing equations have been reduced to the forms that are valid for entire, small, and large time regimes, by using stream-function formulation. The results obtained for the above mentioned three time regimes are compared and found to be in excellent agreement. Moreover, the effects of the physical parameters such as the viscosity parameter, K, and the heat conduction parameter, α*, are presented in terms of the transient shear stress, couple stress, and surface heat transfer coefficient as well as transient velocity profiles, angular velocity profiles, and temperature profiles.

scholarly journals Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium

2013 ◽  
Vol 21 (5-6) ◽  
pp. 155-159
Author(s):  
Yury A. Rossikhin ◽  
Marina V. Shitikova
Keyword(s):  
Fractional Derivative ◽  
Viscoelastic Medium ◽  
Integral Transform ◽  
Viscous Friction ◽  
Middle Surface ◽  
Thin Body ◽  
Governing Equations ◽  
Transform Method ◽  
External Forces ◽  
The Given

AbstractDamped vibrations of elastic thin bodies, such as plates and circular cylindrical shells, embedded into a viscoelastic medium, the rheological features of which are described by fractional derivatives, are considered in the present article. Besides the forces of viscous friction, a thin body is subjected to the action of external forces dependent on the coordinates of the middle surface and time. The boundary conditions are proposed in such a way that the governing equations allow the Navier-type solution. The Laplace integral transform method and the method of expansion of all functions entering into the set of governing equations in terms of the eigenfunctions of the given problem are used as the methods of solution. It is shown that as a result of such a procedure, the systems of equations in the generalized coordinates could be reduced to infinite sets of uncoupled equations, each of which describes damped vibrations of a mechanical oscillator based on the fractional derivative Kelvin-Voigt model.

scholarly journals Fractional model of second grade fluid induced by generalized thermal and molecular fluxes with constant proportional caputo

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 207-212
Author(s):  
Yu-Ming Chu ◽  
Mushtaq Ahmad ◽  
Muhammad Asjad ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivative ◽  
Vertical Plate ◽  
Flow Model ◽  
Second Grade ◽  
Dimensionless Form ◽  
Governing Equations ◽  
Second Grade Fluid ◽  
Research Article ◽  
Grade Fluid ◽  
Molecular Profiles

In this research article, the constant proportional Caputo approach of fractional derivative is applied to derive the generalized thermal and molecular profiles for flow of second grade fluid over a vertical plate. The governing equations of the prescribed flow model are reduced to dimensionless form and then solved for temperature, concentration, and velocity via Laplace transform. Further graphs of field variables are sketched for parameter of interest. Comparison between present result and the existing results is also presented graphically.

scholarly journals First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1366
Author(s):  
Muhammad Imran Asjad ◽  
Saif Ur Rehman ◽  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
Mehdi Salimi
Keyword(s):  
Heat Transfer ◽  
Vertical Surface ◽  
Heat Transfer Analysis ◽  
Physical Parameters ◽  
Governing Equations ◽  
Fluid Properties ◽  
The Impact ◽  
The Given ◽  
Graphical Illustration ◽  
Fractional Parameter

The present study provides the heat transfer analysis of a viscous fluid in the presence of bioconvection with a Caputo fractional derivative. The unsteady governing equations are solved by Laplace after using a dimensional analysis approach subject to the given constraints on the boundary. The impact of physical parameters can be seen through a graphical illustration. It is observed that the maximum decline in bioconvection and velocity can be attained for smaller values of the fractional parameter. The fractional approach can be very helpful in controlling the boundary layers of the fluid properties for different values of time. Additionally, it is observed that the model obtained with generalized constitutive laws predicts better memory than the model obtained with artificial replacement. Further, these results are compared with the existing literature to verify the validity of the present results.

Unsteady MHD Free Convective Heat and Mass Transfer Flow Past a Vertical Porous Plate in the Presence of Radiation and Chemical Reaction

2017 ◽  
Vol 6 (10) ◽  
pp. 116
Author(s):  
J. Buggaramulu ◽  
M. Venkatakrishna ◽  
Y. Harikrishna
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Physical Parameters ◽  
Governing Equations ◽  
Vertical Porous Plate ◽  
Flow Past ◽  
Transfer Flow

The objective of this paper is to analyze an unsteady MHD free convective heat and mass transfer boundary flow past a semi-infinite vertical porous plate immersed in a porous medium with radiation and chemical reaction. The governing equations of the flow field are solved numerical a two term perturbation method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-frication coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.

Hybrid Analytical-Numerical Analysis of SAE 4150 Alloy Steel Rods Cooling

2014 ◽  
Vol 1082 ◽  
pp. 187-190 ◽  
Author(s):  
Marcelo Ferreira Pelegrini ◽  
Thiago Antonini Alves ◽  
Felipe Baptista Nishida ◽  
Ricardo A. Verdú Ramos ◽  
Cassio R. Macedo Maia
Keyword(s):  
Diffusion Equation ◽  
Alloy Steel ◽  
Integral Transform ◽  
Numerical Study ◽  
Physical Parameters ◽  
Analytical Treatment ◽  
Aspect Ratios ◽  
Rectangular Cylinders ◽  
Thermo Physical Properties ◽  
Integral Transform Technique

In this work, a hybrid analytical-numerical study was performed in cooling of rectangular rods made from SAE 4150 alloy steel (0.50% carbon, 0.85% chrome, 0.23% molybdenum, and 0.30% silicon). The analysis can be represented by the solution of transient diffusive problems in rectangular cylinders with variable thermo-physical properties in its domain under the boundary conditions of first kind (Dirichlet condition) and uniform initial condition. The diffusion equation was linearized through the Kirchhoff Transformation on the temperature potential to make the analytical treatment easier. The Generalized Integral Transform Technique (GITT) was applied on the diffusion equation in the domain in order to determine the temperature distribution. The physical parameters of interest were determined for several aspect ratios and compared with the results obtained through numerical simulations using the commercial software ANSYS/FluentTM15.

scholarly journals Effects of ohmic heating and viscous dissipation on steady MHD flow near a stagnation point on an isothermal stretching sheet

2009 ◽  
Vol 13 (1) ◽  
pp. 5-12 ◽  
Author(s):  
Pushkar Sharma ◽  
Gurminder Singh
Keyword(s):  
Stagnation Point ◽  
Viscous Dissipation ◽  
Ohmic Heating ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Governing Equations ◽  
Shooting Technique ◽  
Electrically Conducting

Aim of the paper is to investigate effects of ohmic heating and viscous dissipation on steady flow of a viscous incompressible electrically conducting fluid in the presence of uniform transverse magnetic field and variable free stream near a stagnation point on a stretching non-conducting isothermal sheet. The governing equations of continuity, momentum, and energy are transformed into ordinary differential equations and solved numerically using Runge-Kutta fourth order with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and the Nusselt number at the sheet are derived, discussed numerically, and their numerical values for various values of physical parameters are compared with earlier results and presented through tables.

The Effects of Radiation on Free Convection Flow with Ramped Wall Temperature in Brinkman Type Fluid

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Muhamad Najib Zakaria ◽  
Abid Hussanan ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Laplace Transform ◽  
Vertical Plate ◽  
Convection Flow ◽  
Physical Parameters ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
Effects Of Radiation

The present paper is on study of the influence of radiation on unsteady free convection flow of Brinkman type fluid near a vertical plate containing a ramped temperature profile. Using the appropriate variables, the basic governing equations are reduced to nondimensional equations valid with the imposed initial and boundary conditions. The exact solutions are obtained by using Laplace transform technique. The influence of radiation near a ramped temperature plate is also compared with the flow near a plate with constant temperature. The numerical computations are carried out for various values of the physical parameters such as velocity, temperature, skin friction and Nusselt number and presented graphically.

scholarly journals Consolidation Analysis of Ideal Sand-Drained Ground with Fractional-Derivative Merchant Model and Non-Darcian Flow Described by Non-Newtonian Index

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Zhongyu Liu ◽  
Penglu Cui ◽  
Jiachao Zhang ◽  
Yangyang Xia
Keyword(s):  
Fractional Derivative ◽  
Flow Model ◽  
Soft Soil ◽  
Viscoelastic Behavior ◽  
Vertical Flow ◽  
Vertical Drains ◽  
Saturated Clay ◽  
Implicit Finite Difference ◽  
Consolidation Analysis ◽  
The Ideal

To further investigate the rheological consolidation mechanism of soft soil ground with vertical drains, the fractional-derivative Merchant model (FDMM) is introduced to describe the viscoelastic behavior of saturated clay around the vertical drains, and the flow model with the non-Newtonian index is employed to describe the non-Darcian flow in the process of rheological consolidation. Accordingly, the governing partial differential equation of the ideal sand-drained ground with coupled radial-vertical flow is obtained under the assumption that the vertical strains develop freely. Then, the numerical solution to the consolidation system is conducted using the implicit finite difference method. The validity of this method is verified by comparing the results of Barron’s consolidation theory. Furthermore, the effects of the parameters of non-Darcian flow and FDMM on the rheological consolidation of ground with vertical drains are illustrated and discussed.

Verification of STACS-VOF Based Two-Phase Flow Model for Interfacial Flows

2012 ◽  
Vol 212-213 ◽  
pp. 1098-1102
Author(s):  
Bin Deng ◽  
Chang Bo Jiang ◽  
Zhi Xin Guan ◽  
Chao Shen
Keyword(s):  
Flow Model ◽  
Two Phase Flow ◽  
Three Dimensional ◽  
Test Cases ◽  
Phase Flow ◽  
Interfacial Flows ◽  
Governing Equations ◽  
Two Phase ◽  
Resolution Scheme ◽  
Volume Method

The numerical calculation and simulation of gas-liquid two-phase flows with interfacial deformations have nowadays become more and more popular issues in various scientific and industrial fields. In this study, a three-dimensional gas-liquid two-phase flow numerical model is presented for investigating interfacial flows. The finite volume method was used to discretize the governing equations. A High-resolution scheme of VOF method (STACS) is applied to capture the free surface. The paper outlines the methodology of STACS and its validation against three typical test cases used to verify its accuracy. The results show the STACS-VOF gives very satisfactory results for three-dimensional two-phase interfacial flows problem, and this scheme performs more accurate and less diffusive preserving interface sharpness and boundedness.

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