scholarly journals Symmetric MHD Channel Flow of Nonlocal Fractional Model of BTF Containing Hybrid Nanoparticles

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 663 ◽  
Author(s):  
Muhammad Saqib ◽  
Sharidan Shafie ◽  
Ilyas Khan ◽  
Yu-Ming Chu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Mhd Flow ◽  
Singular Kernel ◽  
Hybrid Nanoparticles ◽  
Convection Flow ◽  
Hybrid Nanofluid ◽  
Fractional Model ◽  
Laplace Transform Technique ◽  
Local Solutions ◽  
Mhd Channel ◽  
Fractional Parameter

A nonlocal fractional model of Brinkman type fluid (BTF) containing a hybrid nanostructure was examined. The magnetohydrodynamic (MHD) flow of the hybrid nanofluid was studied using the fractional calculus approach. Hybridized silver (Ag) and Titanium dioxide (TiO2) nanoparticles were dissolved in base fluid water (H2O) to form a hybrid nanofluid. The MHD free convection flow of the nanofluid (Ag-TiO2-H2O) was considered in a microchannel (flow with a bounded domain). The BTF model was generalized using a nonlocal Caputo-Fabrizio fractional operator (CFFO) without a singular kernel of order α with effective thermophysical properties. The governing equations of the model were subjected to physical initial and boundary conditions. The exact solutions for the nonlocal fractional model without a singular kernel were developed via the fractional Laplace transform technique. The fractional solutions were reduced to local solutions by limiting α → 1 . To understand the rheological behavior of the fluid, the obtained solutions were numerically computed and plotted on various graphs. Finally, the influence of pertinent parameters was physically studied. It was found that the solutions were general, reliable, realistic and fixable. For the fractional parameter, the velocity and temperature profiles showed a decreasing trend for a constant time. By setting the values of the fractional parameter, excellent agreement between the theoretical and experimental results could be attained.

Casson Model of MHD Flow of SA-Based Hybrid Nanofluid Using Caputo Time-Fractional Models

2019 ◽  
Vol 390 ◽  
pp. 83-90 ◽  
Author(s):  
Sidra Aman ◽  
Syazwani Mohd Zokri ◽  
Zulkhibri Ismail ◽  
Mohd Zuki Salleh ◽  
Ilyas Khan
Keyword(s):  
Fractional Derivatives ◽  
Volume Fraction ◽  
Vertical Channel ◽  
Mhd Flow ◽  
Hybrid Nanoparticles ◽  
Hybrid Nanofluid ◽  
Caputo Fractional Derivatives ◽  
Fractional Models ◽  
Hybrid Nanofluids ◽  
Time Fractional Derivative

In this paper MHD flow of Casson hybrid nanofluids are investigated with Caputo time-fractional derivative. Alumina (Al) and copper (Cu) are used as nanoparticles in this study with heat, mass transfer and MHD flow over a vertical channel in a porous medium. The problem is modeled using Caputo fractional derivatives and thermophysical properties of hybrid nanoparticles. The influence of concerned parameters is investigated physically and graphically on the heat, concentration and flow. The effect of volume fraction on thermal conductivity of hybrid nanofluids is observed.

scholarly journals Exact Solutions of Heat and Mass Transfer with MHD Flow in a Porous Medium under Time Dependent Shear Stress and Temperature

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Arshad Khan ◽  
Ilyas Khan ◽  
Farhad Ali ◽  
Asma Khalid ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Shear Stress ◽  
Heat And Mass Transfer ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Convection Flow ◽  
Closed Form Solutions ◽  
Special Cases ◽  
Laplace Transform Technique

This paper aims to study the influence of thermal radiation on unsteady magnetohyrdodynamic (MHD) natural convection flow of an optically thick fluid over a vertical plate embedded in a porous medium with arbitrary shear stress. Combined phenomenon of heat and mass transfer is considered. Closed-form solutions in general form are obtained by using the Laplace transform technique. They are expressed in terms of exponential and complementary error functions. Velocity is expressed as a sum of thermal and mechanical parts. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Analytical results for the pertinent flow parameters are drawn graphically and discussed in detail. It is found that the velocity profiles of fluid decrease with increasing shear stress. The magnetic parameter develops shear resistance which reduces the fluid motion whereas the inverse permeability parameter increases the fluid flow.

scholarly journals Study of Triangular Fuzzy Hybrid Nanofluids on the Natural Convection Flow and Heat Transfer between Two Vertical Plates

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Muhammad Nadeem ◽  
Ahmed Elmoasry ◽  
Imran Siddique ◽  
Fahd Jarad ◽  
Rana Muhammad Zulqarnain ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Volume Fraction ◽  
Computational Cost ◽  
Numerical Approach ◽  
Hybrid Nanoparticles ◽  
Convection Flow ◽  
Hybrid Nanofluid ◽  
Parallel Plates ◽  
Highly Nonlinear

The prime objective of the current study is to examine the effects of third-grade hybrid nanofluid with natural convection utilizing the ferro-particle Fe 3 O 4 and titanium dioxide TiO 2 and sodium alginate (SA) as a host fluid, flowing through vertical parallel plates, under the fuzzy atmosphere. The dimensionless highly nonlinear coupled ordinary differential equations are computed adopting the bvp4c numerical approach. This is an extremely effective technique with a low computational cost. For validation, it is found that as the volume fraction of Fe 3 O 4 + TiO 2 hybrid nanoparticles rises, so does the heat transfer rate. The current and existing results with their comparisons are shown in the form of the tables. The present findings are in good agreement with their previous numerical and analytical results in a crisp atmosphere. The nanoparticles volume fraction of Fe 3 O 4 and TiO 2 is taken as uncertain parameters in terms of triangular fuzzy numbers (TFNs) [0, 0.05, 0.1]. The TFNs are controlled by α − cut and the variability of the uncertainty is studied through triangular membership function (MF).

scholarly journals MHD flow past a parabolic flow past an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction

2016 ◽  
Vol 21 (1) ◽  
pp. 95-105 ◽  
Author(s):  
R. Muthucumaraswamy ◽  
P. Sivakumar
Keyword(s):  
Thermal Radiation ◽  
Chemical Reaction ◽  
Vertical Plate ◽  
Mhd Flow ◽  
Convection Flow ◽  
Grashof Number ◽  
Linear Partial Differential Equations ◽  
Flow Past ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Abstract The problem of MHD free convection flow with a parabolic starting motion of an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction has been examined in detail in this paper. The fluid considered here is a gray, absorbing emitting radiation but a non-scattering medium. The dimensionless governing coupled linear partial differential equations are solved using the Laplace transform technique. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time on the velocity, temperature, concentration. The results are discussed graphically and qualitatively. The numerical results reveal that the radiation induces a rise in both the velocity and temperature, and a decrease in the concentration. The model finds applications in solar energy collection systems, geophysics and astrophysics, aerospace and also in the design of high temperature chemical process systems.

scholarly journals Mathematical modeling of (Cu−Al2O3) water based Maxwell hybrid nanofluids with Caputo-Fabrizio fractional derivative

2020 ◽  
Vol 12 (9) ◽  
pp. 168781402095884
Author(s):  
M Ahmad ◽  
MA Imran ◽  
M Nazar
Keyword(s):  
Maxwell Fluid ◽  
Convection Flow ◽  
Transform Method ◽  
Fractional Model ◽  
Small Times ◽  
Dimensional Parameters ◽  
Hybrid Nanofluids ◽  
Definition Of ◽  
Graphical Presentation ◽  
Fractional Parameter

In this article, a free convection flow of [Formula: see text] hybrid Maxwell nanofluids through a channel formed by two infinite vertical plates have been studied. Together with the the energy balance and heat source, a fractional model of Maxwell fluid is considered. To develop an analytical exact solution for velocity field, only the Caputo-Fabrizio definition of non-integral derivative together with application of Laplace transform method has been used. Some graphical presentation and discussion are made to see the effects of hybrid nanofluids and non-dimensional parameters on velocity boundary layer. As a result, a dual behavior of velocity was exposed due to fractional parameter for large and small times. A comparison between two kind of non-Newtonian fluids has been made and found that Brinkman fluid is more viscous than Maxwell fluid. Also, by letting Brinkman and Maxwell parameters zero, they coincides and the results obtained for Newtonian fluid showed graphically. The obtained results are realistic from the fractional model as by adjusting the values of fractional parameter can be compared with some experimental data.

An exact solution for unsteady free convection flow of chemically reacting Al2O3−SiO2/water hybrid nanofluid

2020 ◽  
pp. 095440622095771
Author(s):  
S Suganya ◽  
M Muthtamilselvan ◽  
Fahad Al-Amri ◽  
Bahaaeldin Abdalla
Keyword(s):  
Boundary Layer ◽  
Convection Flow ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Free Convection Flow ◽  
Convective Boundary ◽  
Boundary Layer Equations ◽  
Laplace Transform Technique ◽  
Chemically Reacting ◽  
Rotating Coordinates

An unsteady natural convective boundary layer fluid flow of thick incompressible [Formula: see text] water hybrid nanofluid is discussed over an oscillating permeable stretching surface. The radiative and chemically reactive hybrid nanofluid flow is induced in rotating coordinates. Essential thermophysical properties of hybrid nanofluid are utilized. The boundary layer equations governing the present phenomena are converted into nondimensional form using appropriate dimension free transformations. The non dimensionalized partial differential equations are then solved analytically by Laplace transform technique and the exact solutions are attained. The performance of all the involving parameters are surveyed and the set of mathematical outputs for temperature, velocity and concentration are graphically depicted. The expressions for skin friction, Nusselt number and Sherwood number have been derived and the numerical results are displayed through tables and graphs. Growth of heat transfer rate is observed by rising radiation parameter and frequency of oscillation. Important aspects of the present study in the physical ground are examined.

scholarly journals MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1295 ◽  
Author(s):  
Arshad Khan ◽  
Dolat Khan ◽  
Ilyas Khan ◽  
Muhammad Taj ◽  
Imran Ullah ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Temperature Profile ◽  
Sodium Alginate ◽  
Mhd Flow ◽  
Casson Fluid ◽  
Singular Kernel ◽  
Heat Transfer Analysis ◽  
Fractional Model ◽  
The Laplace Transform ◽  
Non Local

Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is taken as a specific example of Casson fluid. The fractional model of SA–NaAlg fluid using the Atangana–Baleanu fractional derivative (ABFD) of the non-local and non-singular kernel has been examined. The ABFD definition was based on the Mittag–Leffler function, and promises an improved description of the dynamics of the system with the memory effects. Exact solutions in the case of ABFD are obtained via the Laplace transform and compared graphically. The influence of embedded parameters on the velocity field is sketched and discussed. A comparison of the Atangana–Baleanu fractional model with an ordinary model is made. It is observed that the velocity and temperature profile for the Atangana–Baleanu fractional model are less than that of the ordinary model. The Atangana–Baleanu fractional model reduced the velocity profile up to 45.76% and temperature profile up to 13.74% compared to an ordinary model.

The First Stokes Problem of Radiative-Convective MHD Flow in a Porous Medium

2005 ◽  
Author(s):  
Youn-Jea Kim ◽  
Young-Wan Kim
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Stokes Problem ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Spherical Particles ◽  
Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Analytic study on the transient mixed radiative convection flow of viscous, incompressible fluids past an impulsively-started infinite vertical plate is performed. The plate is located in the transverse magnetic field embedded in a porous medium. It is assumed that the transversely applied magnetic field and the magnetic Reynolds number are very small and hence the induced magnetic field is negligible. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The Rosseland approximation is used to describe radiative heat transfer in the limit of optically thick fluids. It is also assumed here that the porous medium as an assemblage of small identical spherical particles fixed in space. The relevant transformed dimensionless governing equations are solved by using the Laplace transform technique. The obtaining results concerning velocity and temperature across the boundary layer are illustrated graphically for different values of the parameters entering into the problem under consideration. Results show that for an increase in magnetic field parameter, there is a fall in the velocity, whereas there is a rise in the velocity of the fluid for an increase in porous parameter.

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