scholarly journals Thermally Enhanced Darcy-Forchheimer Casson-Water/Glycerine Rotating Nanofluid Flow with Uniform Magnetic Field

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 605
Author(s):  
Anum Shafiq ◽  
Ghulam Rasool ◽  
Hammad Alotaibi ◽  
Hassan M. Aljohani ◽  
Abderrahim Wakif ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Velocity Profile ◽  
Radial Velocity ◽  
Skin Friction ◽  
Numerical Study ◽  
Tangential Velocity ◽  
Nanofluid Flow ◽  
Porosity Parameter ◽  
Forchheimer Number ◽  
The Impact

This numerical study aims to interpret the impact of non-linear thermal radiation on magnetohydrodynamic (MHD) Darcy-Forchheimer Casson-Water/Glycerine nanofluid flow due to a rotating disk. Both the single walled, as well as multi walled, Carbon nanotubes (CNT) are invoked. The nanomaterial, thus formulated, is assumed to be more conductive as compared to the simple fluid. The properties of effective carbon nanotubes are specified to tackle the onward governing equations. The boundary layer formulations are considered. The base fluid is assumed to be non-Newtonian. The numerical analysis is carried out by invoking the numerical Runge Kutta 45 (RK45) method based on the shooting technique. The outcomes have been plotted graphically for the three major profiles, namely, the radial velocity profile, the tangential velocity profile, and temperature profile. For skin friction and Nusselt number, the numerical data are plotted graphically. Major outcomes indicate that the enhanced Forchheimer number results in a decline in radial velocity. Higher the porosity parameter, the stronger the resistance offered by the medium to the fluid flow and consequent result is seen as a decline in velocity. The Forchheimer number, permeability parameter, and porosity parameter decrease the tangential velocity field. The convective boundary results in enhancement of temperature facing the disk surface as compared to the ambient part. Skin-friction for larger values of Forchheimer number is found to be increasing. Sufficient literature is provided in the introduction part of the manuscript to justify the novelty of the present work. The research greatly impacts in industrial applications of the nanofluids, especially in geophysical and geothermal systems, storage devices, aerospace engineering, and many others.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

Numerical simulation for Darcy-Forchheimer flow of carbon nanotubes due to convectively heated nonlinear curved stretching surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3290-3304 ◽  
Author(s):  
Muhammad Ijaz Khan ◽  
Khursheed Muhammad ◽  
Tasawar Hayat ◽  
Shahid Farooq ◽  
Ahmed Alsaedi
Keyword(s):  
Carbon Nanotubes ◽  
Volume Fraction ◽  
Continuous Phase ◽  
Curved Surface ◽  
Content Type ◽  
Porosity Parameter ◽  
Forchheimer Number ◽  
Forchheimer Flow ◽  
Walled Cnts ◽  
Behavior Index

Purpose This paper aims to discuss the salient aspects of the Darcy–Forchheimer flow of viscous liquid in carbon nanotubes (CNTs). CNTs are considered as nanofluid, and water is taken as the continuous phase liquid. The flow features are discussed via curved surface. Water is taken as the base liquid. Flow is generated via nonlinear stretching. Energy expression is modeled subject to heat generation/absorption. Furthermore, convective conditions are considered at the boundary. The Xue model is used in the mathematical modeling which describes the features of nanomaterials. Both types of CNTs are considered, i.e. single-walled CNTs and multi-walled CNTs. Design/methodology/approach Appropriate transformations are used to convert the flow expressions into dimensionless differential equations. The bvp4c method is used for solution development. Findings Velocity enhances via higher estimations of nanoparticles volume fraction while decays for higher Forchheimer number, curvature parameter, behavior index and porosity parameter. Furthermore, thermal field is an increasing function of nanoparticle volume fraction, behavior index, Forchheimer number and porosity parameter. Originality/value Here, the authors have discussed two-dimensional CNTs-based nanomaterial Darcy–Forchheimer flow of viscous fluid over a curved surface. The authors believe that all the outcomes and numerical techniques are original and have not been published elsewhere.

scholarly journals A Numerical Study of Chemical Reaction in a Nanofluid Flow Due to Rotating Disk in the Presence of Magnetic Field

2021 ◽  
Author(s):  
Muhammad Ramzan ◽  
Poom Kumam ◽  
Kottakkaran Sooppy Nisar ◽  
Ilyas Khan ◽  
Wasim Jamshed
Keyword(s):  
Differential Equation ◽  
Radial Velocity ◽  
Chemical Reaction ◽  
Axial Velocity ◽  
Numerical Study ◽  
Tangential Velocity ◽  
Rotating Disk ◽  
Partial Differential ◽  
Suction Parameter ◽  
Matlab Programming

Abstract In this paper, a numerical study of MHD steady flow due to the rotating disk with chemical reaction was explored. Effect of different parameters such as Schmidt number, chemical reaction parameter, Prandtl number, Suction parameter, heat absorption/generation parameter, Nano-particle concentration, Reynold number, Magnetic parameter, skin friction, shear stress, temperature distribution, Nusselt number, mass transfer rate, radial velocity, axial velocity, and tangential velocity was analyzed and discussed. For the simplification of non-linear partial differential equations (PDEs) into the nonlinear ordinary differential equation (ODEs), the method of Similarity transformation was employed, and the resulting partial differential equation was solved by using finite difference method through MATLAB programming. This work's remarkable finding is that with the expansion of nanoparticle concentration radial velocity, tangential velocity and temperature of the fluid was enhanced but reverse reaction for axial velocity. Furthermore, the present results are found to be in excellent agreement with previously published work.

Influence of carbon nanotubes on heat transfer in MHD nanofluid flow over a stretchable rotating disk: A numerical study

Heat Transfer ◽  
2020 ◽  
Vol 50 (1) ◽  
pp. 619-637
Author(s):  
Muhammad S. Iqbal ◽  
Irfan Mustafa ◽  
Iram Riaz ◽  
Abuzar Ghaffari ◽  
Waqar A. Khan
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Numerical Study ◽  
Rotating Disk ◽  
Nanofluid Flow

Radiative Heat and Mass Transfer Analysis of Micropolar Nanofluid Flow of Casson Fluid Between Two Rotating Parallel Plates With Effects of Hall Current

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Zahir Shah ◽  
Saeed Islam ◽  
Hamza Ayaz ◽  
Saima Khan
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Hall Current ◽  
Nonlinear Differential Equations ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Micropolar Nanofluid ◽  
The Impact

The present research aims to examine the micropolar nanofluid flow of Casson fluid between two parallel plates in a rotating system with effects of thermal radiation. The influence of Hall current on the micropolar nanofluids have been taken into account. The fundamental leading equations are transformed to a system of nonlinear differential equations using appropriate similarity variables. An optimal and numerical tactic is used to get the solution of the problem. The convergence and comparison have been shown numerically. The impact of the Hall current, Brownian movement, and thermophoresis phenomena of Casson nanofluid have been mostly concentrated in this investigation. It is found that amassed Hall impact decreases the operative conductivity which intends to increase the velocity field. The temperature field enhances with larger values of Brownian motion thermophoresis effect. The impacts of the Skin friction coefficient, heat flux, and mass flux have been deliberate. The skin friction coefficient is observed to be larger for k=0, as compared to the case of k=0.5. Furthermore, for conception and visual demonstration, the embedded parameters have been deliberated graphically.

scholarly journals Magnetohydrodynamic Hybrid Nanofluid Flow Past an Exponentially Stretching Sheet with Slip Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3291
Author(s):  
Abdul Samad Khan ◽  
He-Yong Xu ◽  
Waris Khan
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Slip Parameter ◽  
Nanofluid Flow ◽  
Slip Conditions ◽  
Exponentially Stretching ◽  
The Impact

This study presents the magnetized hybrid nanofluid flow with heat source/sink over an exponentially stretching/shrinking sheet. Slip conditions are implemented to analyze the hybrid nanofluid flow for both slip and no-slip conditions. Additionally, the hybrid nanofluid of alumina and copper (hybrid nanoparticles) with blood (base fluid) has been considered and discussed with both suction and injection parameters. The appropriate similarity variables are used to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and solved analytically with the help of the homotopy analysis method (HAM). The impact of different embedded parameters has been shown in the form of graphs and tables. The numerical values of skin friction and Nusselt number are presented in the form of Tables for both slip and no-slip cases. It is summarized that the upsurge of the velocity slip parameter and magnetic parameter increases the skin friction, while the rising of the thermal slip parameter and heat generation parameter decreases the Nusselt number.

scholarly journals Significance of Thermal Slip and Convective Boundary Conditions in Three Dimensional Rotating Darcy-Forchheimer Nanofluid Flow

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 741 ◽  
Author(s):  
Anum Shafiq ◽  
Ghulam Rasool ◽  
Chaudry Masood Khalique
Keyword(s):  
Activation Energy ◽  
Boundary Conditions ◽  
Skin Friction ◽  
Three Dimensional ◽  
Brownian Diffusion ◽  
Thermal Slip ◽  
Convective Boundary Conditions ◽  
Nanofluid Flow ◽  
Convective Boundary ◽  
Forchheimer Number

This article is concerned with the nanofluid flow in a rotating frame under the simultaneous effects of thermal slip and convective boundary conditions. Arrhenius activation energy is another important aspect of the present study. Flow phenomena solely rely on the Darcy–Forchheimer-type porous medium in three-dimensional space to tackle the symmetric behavior of viscous terms. The stretching sheet is assumed to drive the fluid. Buongiorno’s model is adopted to see the features of Brownian diffusion and thermophoresis on the basis of symmetry fundamentals. Governing equations are modeled and transformed into ordinary differential equations by suitable transformations. Solutions are obtained through the numerical RK45-scheme, reporting the important findings graphically. The outputs indicate that larger values of stretching reduce the fluid velocity. Both the axial and transverse velocity fields undergo much decline due to strong retardation produced by the Forchheimer number. The thermal radiation parameter greatly raises the thermal state of the field. The temperature field rises for a stronger reaction within the fluid flow, however reducing for an intensive quantity of activation energy. A declination in the concentration profile is noticed for stronger thermophoresis. The Forchheimer number and porosity factors result in the enhancement of the skin friction, while both slip parameters result in a decline of skin friction. The thermal slip factor results in decreasing both the heat and mass flux rates. The study is important in various industrial applications of nanofluids including the electro-chemical industry, the polymer industry, geophysical setups, geothermal setups, catalytic reactors, and many others.

Numerical Study on Skin Friction and Shock Inception in Various Geometries of Supersonic Nozzle

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
E.I. Jassim
Keyword(s):  
Fluid Dynamics ◽  
Skin Friction ◽  
Numerical Study ◽  
Supersonic Nozzle ◽  
Nozzle Geometry ◽  
Divergent Part ◽  
Shock Position ◽  
Nozzle Shape ◽  
The Impact ◽  
Large Disturbance

In the present study, a numerical simulation is conducted to predict the influence of convergent-divergent nozzle geometry and NPR on the skin friction and shockwave location. Various shapes of nozzles are numerically simulated using the Computational Fluid Dynamics code. The shock position is examined to demonstrate the impact of nozzle shape on its location. Skin friction is shown to be smoothly decreasing at the divergent part of the nozzle for all NPRs lower than 2.0. However, an inverse behavioural trend was observed at NPR equal to 2. This could be attributed to the fact that the large disturbance of fluid near the wall is the major factor behind such an oddity. The results also show that the shock position is reliant on the nozzle geometry at certain NPR.

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