scholarly journals Exact analysis of MHD Walters’-B fluid flow with non-singular fractional derivatives of Caputo-Fabrizio in the presence of radiation and chemical reaction

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Muhammad Imran Asjad ◽  
Maryam Aleem ◽  
M. Bilal Riaz
Keyword(s):  
Fluid Flow ◽  
Newtonian Fluid ◽  
Fractional Derivatives ◽  
Fluid Model ◽  
Governing Equations ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Derivatives Of ◽  
Walters B Fluid ◽  
Transfer Study

The present article reports the applications of Caputo-Fabrizio time-fractional derivatives. This article generalizes the idea of unsteady MHD free convective flow in a Walters.-B fluid with heat and mass transfer study over an exponential isothermal vertical plate embedded in a porous medium. The governing equations are converted into dimensionless form and extended to fractional model. The generalized Walters-B fluid model has been solved analytically using the Laplace transform technique. From the general solutions we reduce limiting solutions when  to the similar motion for Newtonian fluid. The corresponding expressions for and Nusselt and Sherwood numbers are also assessed. Numerical results for velocity, temperature and concentration are demonstrated graphically for various factors of interest and discussed. As a result, we have plotted the influence of fractional parameter on fluid flow and drawn comparison between fractional Walters’-B and fractional Newtonian fluid and found that fractional Newtonian fluid is faster than fractional Walters’-B fluids.

A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives

2020 ◽  
Vol 98 (1) ◽  
pp. 89-101 ◽  
Author(s):  
Nauman Raza ◽  
Muhammad Asad Ullah
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Maxwell Fluid ◽  
Heat Transfer Analysis ◽  
Flow Parameters ◽  
Fluid Parameter ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Temperature And Velocity Fields

A comparative analysis is carried out to study the unsteady flow of a Maxwell fluid in the presence of Newtonian heating near a vertical flat plate. The fractional derivatives presented by Caputo and Caputo–Fabrizio are applied to make a physical model for a Maxwell fluid. Exact solutions of the non-dimensional temperature and velocity fields for Caputo and Caputo–Fabrizio time-fractional derivatives are determined via the Laplace transform technique. Numerical solutions of partial differential equations are obtained by employing Tzou’s and Stehfest’s algorithms to compare the results of both models. Exact solutions with integer-order derivative (fractional parameter α = 1) are also obtained for both temperature and velocity distributions as a special case. A graphical illustration is made to discuss the effect of Prandtl number Pr and time t on the temperature field. Similarly, the effects of Maxwell fluid parameter λ and other flow parameters on the velocity field are presented graphically, as well as in tabular form.

scholarly journals A new approach for the generalized fractional Casson fluid model with Newtonian heating described by the modified Riemann-Liouville fractional operator

2021 ◽  
Author(s):  
RADHAKRISHNAN BHEEMAN ◽  
Tamilarasi Mathivanan
Keyword(s):  
Fluid Model ◽  
Vertical Direction ◽  
Casson Fluid ◽  
Newtonian Heating ◽  
New Approach ◽  
Laplace Transform Technique ◽  
Casson Fluid Model ◽  
The Laplace Transform ◽  
Liouville Fractional Derivative ◽  
Oscillating Plate

This research is about the transfer of heat of a generalized fractional Casson fluid on an unsteady boundary layer which is passing through an infinite oscillating plate, in vertical direction combined with the Newtonian heating. The results are obtained by using modified Riemann-Liouville fractional derivative. The present fluid model, starts with the governing equations which are then converted to a system of partial differential equations(linear) by using some suitable non-dimensional variables. Using the method of integral balance and the Laplace transform technique, an analytical solution is obtained. The velocity and temperature expressions are derived and the effects of modelling parameters re shown in tables and graphs to validate the obtained theoretical results.

scholarly journals Mathematical fractional modeling of transpot phenomena of viscous fluid-flow between two plates

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 417-421
Author(s):  
Muhammad Asadullah ◽  
Ali Raza ◽  
Muhammad Ikram ◽  
Muhammad Asjad ◽  
Rabia Naz ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Governing Equations ◽  
Viscous Fluid Flow ◽  
Physical Behavior ◽  
Fractional Modeling ◽  
Laplace Transform Technique ◽  
Mass And Heat Transfer ◽  
Transfer Flow ◽  
Adhesive Fluid

This work is about the mass and heat transfer flow for adhesive fluid between two upright plates pulled apart by a distance, d. Fractional model of the considered problem is developed after making governing equations dimensionless. Laplace transform technique is utilized to acquire analytical solutions and some graphics are presented to see the physical behavior of embedded parameters.

Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Kuppalapalle Vajravelu ◽  
Sreedharamalle Sreenadh ◽  
Palluru Devaki ◽  
Kerehalli Prasad
Keyword(s):  
Shear Stress ◽  
Fluid Flow ◽  
Wall Shear Stress ◽  
Yield Stress ◽  
Newtonian Fluid ◽  
Power Law ◽  
Fluid Model ◽  
Elastic Tube ◽  
Yield Stress Fluid ◽  
Power Law Index

AbstractThe constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters (t 1 and t 2) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

scholarly journals On applications of Caputo k-fractional derivatives

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ghulam Farid ◽  
Naveed Latif ◽  
Matloob Anwar ◽  
Ali Imran ◽  
Muhammad Ozair ◽  
...  
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Chebyshev Inequality ◽  
Absolutely Continuous ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Type Variable

Abstract This research explores Caputo k-fractional integral inequalities for functions whose nth order derivatives are absolutely continuous and possess Grüss type variable bounds. Using Chebyshev inequality (Waheed et al. in IEEE Access 7:32137–32145, 2019) for Caputo k-fractional derivatives, several integral inequalities are derived. Further, Laplace transform of Caputo k-fractional derivative is presented and Caputo k-fractional derivative and Riemann–Liouville k-fractional integral of an extended generalized Mittag-Leffler function are calculated. Moreover, using the extended generalized Mittag-Leffler function, Caputo k-fractional differential equations are presented and their solutions are proposed by applying the Laplace transform technique.

scholarly journals Chemically reacting fluid flow induced by an exponentially accelerated infinite vertical plate in a magnetic field and variable temperature via LTT and FEM

2016 ◽  
Vol 43 (1) ◽  
pp. 49-83 ◽  
Author(s):  
Raju Srinivasa ◽  
G. Aruna ◽  
Swamy Naidu ◽  
S.V.K. Varma ◽  
M.M. Rashidi
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Vertical Plate ◽  
Flow Problem ◽  
Variable Temperature ◽  
Governing Equations ◽  
Linear Partial Differential Equations ◽  
Laplace Transform Technique ◽  
Chemically Reacting ◽  
Infinite Vertical Plate

In this research paper, we found both numerical and analytical solutions for the effect of chemical reaction on unsteady, incompressible, viscous fluid flow past an exponentially accelerated vertical plate with heat absorption and variable temperature in a magnetic field. The flow problem is governed by a system of coupled non-linear partial differential equations with suitable boundary conditions. We have solved the governing equations by an efficient, accurate, powerful finite element method (FEM) as well as Laplace transform technique (LTT). The evaluation of the numerical results are performed and graphical results for the velocity, temperature and concentration profiles within the boundary layer are discussed. Also, the expressions for the skin-friction, Nusselt number and the Sherwood number coefficients have been derived and discussed through graphs and tabular forms for different values of the governing parameters.

scholarly journals On a Study of Flow Past Non-Newtonian Fluid Bubbles

2021 ◽  
Vol 16 ◽  
pp. 74-86
Author(s):  
T. S. L. Radhika ◽  
T. Raja Rani
Keyword(s):  
Fluid Flow ◽  
Coordinate System ◽  
Newtonian Fluid ◽  
Outer Region ◽  
Considerable Effect ◽  
Governing Equations ◽  
Spherical Coordinate ◽  
Flow Past ◽  
Flow Domain ◽  
High Viscous Fluid

In the current work, we aim at finding an analytical solution to the problem of fluid flow past a pair of separated non-Newtonian fluid bubbles. These bubbles are assumed to be spherical and non-permeable with the non-Newtonian fluid, viz. the couple stress fluid filling their interior. Further, the bubbles are presumed to be static in the flow domain, where a Newtonian fluid streams past these bubbles with a constant velocity (U) along the negative x-direction. We developed a mathematical model in the bipolar coordinate system for the fluid flow outside the bubbles and the spherical coordinate system inside the bubbles to derive a separable solution for their respective governing equations. Furthermore, to evaluate the model's applicabilities on the industrial front, the data on some widely used industrial fluids are given as inputs to the model, such as density, the viscosity of air or water for the fluid flow model developed for the region outside the fluid bubbles and the data on Cyclopentane or DIDP (non-Newtonian) for that within the bubbles. Some interesting findings are: the pressure in the outer region of the bubbles is higher when filled with low viscous industrial fluid, Cyclopentane, than a high viscous fluid, DIDP. Furthermore, an increase in the viscosity of Cyclopentane did not alter the pressure distribution in the region outside the bubbles. However, there is a considerable effect on this pressure in the case of DIDP bubbles.

scholarly journals Caputo Fractional MHD Casson Fluid Flow Over an Oscillating Plate with Thermal Radiation

2021 ◽  
Vol 85 (2) ◽  
pp. 145-158
Author(s):  
Ridhwan Reyaz ◽  
Yeou Jiann Lim ◽  
Ahmad Qushairi Mohamad ◽  
Muhammad Saqib ◽  
Sharidan Shafie
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Numerical Approach ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Fractional Partial Differential Equations ◽  
Governing Equations ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Oscillating Plate

The effect of the thermal radiation on the MHD Casson fluid along with the fractional derivative in an oscillating vertical plate is elucidated. More exactly, the Caputo fractional model is utilized in developing the governing equations. Besides, the influence of the buoyancy force due to the temperature gradient has also been considered. The derived fractional partial differential equations are converted into ordinary differential equations by using the Laplace transform technique and then are solved for analytical solutions via the characteristic method. The inversion of the Laplace transformation is obtained through the numerical approach of Zakian. The effects of various physical parameters on the velocity and temperature profiles, Nusselt number, and skin friction have been analyzed and depicted in graphs and tables. The distribution of the velocity and temperature either in viscous or Casson fluid do enhance by the fractional parameter.

A Note on Exact Solutions for the Unsteady Free Convection Flow of a Jeffrey Fluid

2015 ◽  
Vol 70 (6) ◽  
pp. 397-401 ◽  
Author(s):  
Ilyas Khan
Keyword(s):  
Shear Stress ◽  
Free Convection ◽  
Exact Solutions ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform

AbstractIn this note, we investigate the unsteady free convection flow of a Jeffrey fluid past an infinite isothermal vertical plate. Exact solutions are obtained using the Laplace transform technique. These solutions are expressed in terms of exponential and complementary error functions, and satisfy all imposed initial and boundary conditions as well as the governing equations. The expression for the shear stress is also evaluated. The corresponding solutions for a Newtonian fluid can be easily obtained as a special case. It is found from the velocity and shear stress solutions that they strongly depend on the material parameters of a Jeffrey fluid. The exact solutions obtained here can be used as a benchmark for checking the correctness of other approximate or numerical solutions. In addition, this note will help in understanding the characteristics of non-Newtonian fluid flows that are subject to free convection due to buoyancy force.

scholarly journals Caputo-Fabrizio Time Fractional Derivative Applied to Visco Elastic MHD Fluid Flow in the Porous Medium

2018 ◽  
Vol 7 (4.30) ◽  
pp. 533
Author(s):  
Salah Uddin ◽  
M. Mohamad ◽  
M. A. H. Mohamad ◽  
Suliadi Sufahani ◽  
M. Ghazali Kamardan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Hartmann Number ◽  
Fluid Velocity ◽  
Axially Symmetric ◽  
Governing Equations ◽  
Permeability Parameter ◽  
The Magnetic Field

In this paper the laminar fluid flow in the axially symmetric porous cylindrical channel subjected to the magnetic field was studied. Fluidmodel was non-Newtonian and visco elastic. The effects of magnetic field and pressure gradient on the fluid velocity were studied by using a new trend of fractional derivative without singular kernel. The governing equations consisted of fractional partial differential equations based on the Caputo-Fabrizio new time-fractional derivatives NFDt. Velocity profiles for various fractional parameter a, Hartmann number, permeability parameter and elasticity were reported. The fluid velocity inside the cylindrical artery decreased with respect to Hartmann number, permeability parameter and elasticity. The results obtained from the fractional derivative model are significantly different from those of the ordinary model.  

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