scholarly journals ANALYSIS OF THE FLOW OF BRINKMAN-TYPE NANOFLUID USING GENERALIZED FOURIER’S AND FICK’S LAWS

Fractals ◽  
2021 ◽  
Author(s):  
NADEEM AHMAD SHEIKH ◽  
DENNIS LING CHUAN CHING ◽  
HAMZAH BIN SAKIDIN ◽  
ILYAS KHAN
Keyword(s):  
Volume Fraction ◽  
Fluid Model ◽  
Fixed Time ◽  
Physical Parameters ◽  
Fractional Partial Differential Equations ◽  
Working Ability ◽  
Transform Method ◽  
Fluid Parameter ◽  
Laplace And Fourier Transform ◽  
Fractional Parameter

The enhancement of the working ability of the industrial fluid is the need of the present era; nanofluid is an emerging field in science and technology. In this study, the Brinkman-type fluid model is used and is generalized using the Fourier’s and Fick’s laws. The graphene oxide nanoparticles are dispersed in the base fluid water. The fractional partial differential equations are then solved via the Laplace and Fourier transform method. The obtained solutions for velocity, heat transfer, and mass transfer are plotted in graphs. The results show that velocity profile decreases for Brinkman-type fluid parameter and volume fraction of the nanoparticles. The plot for the fractional parameter shows that different plots can be drawn for a fixed time and other physical parameters, which is the memory effect.

scholarly journals Shape effect on MHD flow of time fractional Ferro-Brinkman type nanofluid with ramped heating

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Saqib ◽  
Ilyas Khan ◽  
Sharidan Shafie ◽  
Ahmad Qushairi Mohamad
Keyword(s):  
Heat Dissipation ◽  
Fluid Model ◽  
Colloidal Suspension ◽  
Mhd Flow ◽  
Velocity Fields ◽  
Shape Effect ◽  
Isothermal Heating ◽  
Transform Method ◽  
Temperature And Velocity Fields ◽  
Fractional Parameter

AbstractThe colloidal suspension of nanometer-sized particles of Fe3O4 in traditional base fluids is referred to as Ferro-nanofluids. These fluids have many technological applications such as cell separation, drug delivery, magnetic resonance imaging, heat dissipation, damping, and dynamic sealing. Due to the massive applications of Ferro-nanofluids, the main objective of this study is to consider the MHD flow of water-based Ferro-nanofluid in the presence of thermal radiation, heat generation, and nanoparticle shape effect. The Caputo-Fabrizio time-fractional Brinkman type fluid model is utilized to demonstrate the proposed flow phenomenon with oscillating and ramped heating boundary conditions. The Laplace transform method is used to solve the model for both ramped and isothermal heating for exact solutions. The ramped and isothermal solutions are simultaneously plotted in the various figures to study the influence of pertinent flow parameters. The results revealed that the fractional parameter has a great impact on both temperature and velocity fields. In the case of ramped heating, both temperature and velocity fields decreasing with increasing fractional parameter. However, in the isothermal case, this trend reverses near the plate and gradually, ramped, and isothermal heating became alike away from the plate for the fractional parameter. Finally, the solutions for temperature and velocity fields are reduced to classical form and validated with already published results.

scholarly journals Convective Heat Transfer Analysis on Prandtl Fluid Model with Peristalsis

2013 ◽  
Vol 10 (4) ◽  
pp. 197-208 ◽  
Author(s):  
A. Alsaedi ◽  
Naheed Batool ◽  
H. Yasmin ◽  
T. Hayat
Keyword(s):  
Fluid Model ◽  
Perturbation Technique ◽  
Wave Length ◽  
Heat Transfer Analysis ◽  
Physical Parameters ◽  
Series Solutions ◽  
Regular Perturbation ◽  
Symmetric Channel ◽  
Long Wave ◽  
Fluid Parameter

The effects of magnetohydrodynamic (MHD) on peristaltic transport of Prandtl fluid in a symmetric channel have been studied under the assumptions of long wave length and low-Reynolds number. Channel walls are considered compliant in nature. Series solutions of axial velocity, stream function and temperature are given by using regular perturbation technique for small values of Prandtl fluid parameter. The effects of physical parameters on the velocity, streamlines and temperature are examined by plotting graphs.

scholarly journals Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier’s law

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nadeem Ahmad Sheikh ◽  
Dennis Ling Chuan Ching ◽  
Ilyas Khan ◽  
Hamzah Bin Sakidin ◽  
Muhammad Jamil ◽  
...  
Keyword(s):  
Energy Equation ◽  
Volume Fraction ◽  
Mhd Flow ◽  
Integral Transforms ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Fourier’S Law ◽  
Fractional Model ◽  
Laplace Transformations ◽  
Fourier's Law

AbstractThe present work used fractional model of Casson fluid by utilizing a generalized Fourier’s Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.

scholarly journals Melting Effect on Unsteady Hydromagnetic Flow of a Nanofluid Past a Stretching Sheet

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ali J. Chamkha ◽  
A.M. Rashad ◽  
Eisa Al-Meshaiei
Keyword(s):  
Stretching Sheet ◽  
Volume Fraction ◽  
Transverse Magnetic ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Time Histories ◽  
Nanoparticles Volume Fraction ◽  
Layer Flow ◽  
Stretching Plate ◽  
Melting Effect

This paper considers unsteady, laminar, boundary-layer flow with heat and mass transfer of a nanofluid along a horizontal stretching plate in the presence of a transverse magnetic field, melting and heat generation or absorption effects. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by an efficient implicit, iterative, finite-difference method. A parametric study illustrating the influence of various physical parameters is performed. Numerical results for the steady-state velocity, temperature and nanoparticles volume fraction profiles as well as the time histories of the skin-friction coefficient, Nusselt number and the Sherwood number are presented graphically and discussed.

Radiative Non-Coaxial Rotation of Magnetohydrodynamic Newtonian Carbon Nanofluid Flow in Porous Medium with Heat and Mass Transfer Effects

2020 ◽  
Vol 9 (4) ◽  
pp. 321-335
Author(s):  
Wan Nura’in Nabilah Noranuar ◽  
Ahmad Qushairi Mohamad ◽  
Sharidan Shafie ◽  
Ilyas Khan ◽  
Lim Yeou Jiann
Keyword(s):  
Carbon Nanotubes ◽  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Nuclear Reactor ◽  
Volume Fraction ◽  
Heating System ◽  
Transform Method ◽  
Rotation System ◽  
Walled Carbon Nanotubes

Non-coaxial rotation system has encountered in various fields such as engineering field in designing advanced cooling and heating system, food processing and mixer machines. In the present study, the effect of the non-coaxial rotation of a vertical disk on the heat and mass transfer of Newtonian nanofluids in a porous medium is analytically discussed. The influence of the magnetic field and thermal radiation is also taken into the consideration. Two different types of nanofluids which are single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with water as the base fluid are analyzed and compared. Suitable dimensionless variables are utilized to convert the governing partial differential equations associated with the initial and boundary conditions into the dimensionless form. Then, the exact solutions of the dimensionless governing equations are calculated by using the Laplace transform method. A limiting case study of the obtained analytical solutions is constructed to compare with the previously published results to verify its validity. The distributions of the velocity, temperature, and concentration along with the Skin friction, Nusselt number, and Sherwood number due to the variation of the pertinent parameters are displayed and scrutinized through graphs and tables. In the frame of non-coaxial rotation, the nanofluid with the SWCNTs nanoparticles have illustrated a higher rate of heat transfer as compared to MWCNTs nanofluid. Moreover, the heat transmission in the nanofluid has been enhanced by increasing the volume fraction of the nanoparticle and also the intensity of the radiation. This suggests that heating or cooling in a system such as a nuclear reactor can be improved by properly selecting the type of the nanofluid and also the volume fraction of the nanoparticle.

Thermo-Solutal Convection of a Nanofluid Utilizing Fourier’s-Type Compass Conditions

2020 ◽  
Vol 9 (4) ◽  
pp. 362-374
Author(s):  
J. C. Umavathi ◽  
Ali J. Chamkha
Keyword(s):  
Brownian Motion ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Temperature Fields ◽  
Physical Parameters ◽  
Surface Boundary ◽  
Perturbation Scheme ◽  
Runge Kutta ◽  
The Impact

Nanotechnology has infiltrated into duct design in parallel with many other fields of mechanical, medical and energy engineering. Motivated by the excellent potential of nanofluids, a subset of materials engineered at the nanoscale, in the present work, a new mathematical model is developed for natural convection in a vertical duct containing nanofluid. Numerical scrutiny for the double-diffusive free and forced convection within a duct encumbered with nanofluid is performed. Buongiorno’s model is deployed to define the nanofluid. Robin boundary conditions are used to define the surface boundary conditions. Thermal and concentration equations envisage the viscous, Brownian motion, thermosphores of the nanofluid, Soret and Dufour effects. Using the Boussi-nesq approximation the solutal buoyancy effect as a result of gradients in concentration are incorporated. The conservation equations which are nonlinear are numerically estimated using fourth order Runge-Kutta methodology and analytically ratifying regular perturbation scheme. The mass, heat, nanoparticle concentration and species concentration fields on eight dimensionless physical parameters such as thermal and mass Grashof numbers, Brownian motion parameter, thermal parameter, Prandtl number, Eckert number, Schmidt parameter, and Soret parameter are calculated. The impact of these parameters are outlined pictorially. The velocity and temperature fields are boosted with the thermal Grashof number. The Soret and the Schemidt parameters reduces the nanoparticle volume fraction but it heightens the momentum, temperature and concentration. At the cold wall thermal and concentration Grashof numbers reduces the Nusselt values but they increase the Nusselt values at the hot wall. The reversal consequence was attained at the hot plate. The perturbation and Runge-Kutta solutions are equal in the nonappearance of Prandtl number. The (E. Zanchini, Int. J. Heat Mass Transfer 41, 3949 (1998)). results are restored for the regular fluid. The heat transfer rate is high for nanofluid when matched with regular fluid.

ANALYTICAL APPROXIMATE SOLUTIONS OF (N + 1)-DIMENSIONAL FRACTAL HARRY DYM EQUATIONS

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850094
Author(s):  
JIANSHE SUN
Keyword(s):  
Approximate Solutions ◽  
Travelling Wave ◽  
Cantor Sets ◽  
Travelling Wave Solutions ◽  
Fractional Partial Differential Equations ◽  
Transform Method ◽  
Fractional Complex Transform ◽  
Fractal Models ◽  
Differential Transform ◽  
Harry Dym Equation

The new fractal models of the [Formula: see text]-dimensional and [Formula: see text]-dimensional nonlinear local fractional Harry Dym equation (HDE) on Cantor sets are derived and the analytical approximate solutions of the above two new models are obtained by coupling the fractional complex transform via local fractional derivative (LFD) and local fractional reduced differential transform method (LFRDTM). Fractional complex transform for functions of [Formula: see text]-dimensional variables is generalized and the theorems of [Formula: see text]-dimensional LFRDTM are supplementary extended. The travelling wave solutions of the fractal HDE show that the proposed LFRDTM is effective and simple for obtaining approximate solutions of nonlinear local fractional partial differential equations.

Eulerian Two-Phase Flow Modeling of Steam Direct Contact Condensation for the Fukushima Accident Investigation

2014 ◽  
Author(s):  
Marco Pellegrini ◽  
Giulia Agostinelli ◽  
Hidetoshi Okada ◽  
Masanori Naitoh
Keyword(s):  
Two Phase Flow ◽  
Volume Fraction ◽  
Fluid Model ◽  
Fluid Dynamic ◽  
Interfacial Region ◽  
Phase Flow ◽  
Two Phase ◽  
Fukushima Accident ◽  
Average Cell Size ◽  
Average Cell

Steam condensation is characterized by a relatively large interfacial region between gas and liquid which, in computational fluid dynamic (CFD) analyses, allows the creation of a discretized domain whose average cell size is larger than the interface itself. For this reason generally one fluid model with interface tracking (e.g. volume of fluid method, VOF) is employed for its solution in CFD, since the solution of the interface requires a reasonable amount of cells, reducing the modeling efforts. However, for some particular condensation applications, requiring the computation of long transients or the steam ejected through a large number of holes, one-fluid model becomes computationally too expensive for providing engineering information, and a two-fluid model (i.e. Eulerian two-phase flow) is preferable. Eulerian two-phase flow requires the introduction of closure terms representing the interactions between the two fluids in particular, in the condensation case, drag and heat transfer. Both terms involve the description of the interaction area whose definition is different from the typical one adopted in the boiling analyses. In the present work a simple but effective formulation for the interaction area is given based on the volume fraction gradient and then applied to a validation test case of steam bubbling in various subcooling conditions. It has been shown that this method gives realistic values of bubble detachment time, bubble penetration for the cases of interest in the nuclear application and in the particular application to the Fukushima Daiichi accident.

scholarly journals Evaluation of the suitability of synthetic polymer fuels in self-ignition engines

2019 ◽  
Vol 178 (3) ◽  
pp. 129-134
Author(s):  
Oleh KLYUS ◽  
Paweł KRAUSE ◽  
Vladimir MARKOV ◽  
Anna SKARBEK-ŻABKIN ◽  
Bowen SA
Keyword(s):  
Volume Fraction ◽  
Synthetic Polymer ◽  
Polymer Materials ◽  
Physical Parameters ◽  
Sauter Mean Diameter ◽  
Synthetic Fuels ◽  
Limit Values ◽  
Experimental Part

The article presents a method for determining the quality of spraying a mixture of oil and synthetic fuels obtained from the pro-cessing of polymer materials. Laboratory tests of physical parameters of such a mixture were carried out, which made it possible to determine the limit values for the volume fraction of synthetic fuels. The method of determining the suitability of this type of fuel takes into account the criterion numbers Re and Oh, which include physical parameters such as viscosity, density, and surface tension. The experimental part concerning the distribution of droplets of injected fuel and determination of Sauter Mean Diameter using laser diffrac-tion confirmed the usefulness of the developed method for the assessment of the possibility of using a mixture of petroleum-based and synthetic fuels in self-ignition engines.

scholarly journals Numerical simulation of the motion of a micropolar Casson fluid through a porous medium over a stretching surface

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1285-1297 ◽  
Author(s):  
Nabil El-Dabe ◽  
Galal Moatimid ◽  
Abd-Elhafez Elshekhipy ◽  
Naglaa Aballah
Keyword(s):  
Porous Medium ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Transform Method ◽  
Differential Transform ◽  
Non Linear ◽  
Linear Differential ◽  
External Uniform Magnetic Field

The present study examines the motion of a micropolar non-Newtonian Casson fluid through a porous medium over a stretching surface. The system is pervaded by an external uniform magnetic field. The heat transfer and heat generation are taken into consideration. The problem is modulated mathematically by a system of non-linear PDE which describe the equations of continuity, momentum, and energy. Suitable similarity solutions are utilized to transform the system of equation ordinary non-linear differential equations. In accordance with the appropriate boundary conditions, are numerically solved by means of the finite difference technique. Also, the system is solved by using multistep differential transform method. The effects of the various physical parameters, of the problem at hand, are illustrated through a set of diagrams.

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