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 sensitivity study on carbon nanotubes significance in Darcy–Forchheimer flow towards a rotating disk by response surface methodology

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anum Shafiq ◽  
Tabassum Naz Sindhu ◽  
Qasem M. Al-Mdallal
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Ethylene Glycol ◽  
Biot Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Rotating Disk ◽  
Sensitivity Study ◽  
Basic Fluid ◽  
Walled Cnts

AbstractThe current research explores incremental effect of thermal radiation on heat transfer improvement corresponds to Darcy–Forchheimer (DF) flow of carbon nanotubes along a stretched rotating surface using RSM. Casson carbon nanotubes’ constructed model in boundary layer flow is being investigated with implications of both single-walled CNTs and multi-walled CNTs. Water and Ethylene glycol are considered a basic fluid. The heat transfer rate is scrutinized via convective condition. Outcomes are observed and evaluated for both SWCNTs and MWCNTs. The Runge–Kutta Fehlberg technique of shooting is utilized to numerically solve transformed nonlinear ordinary differential system. The output parameters of interest are presumed to depend on governing input variables. In addition, sensitivity study is incorporated. It is noted that sensitivity of SFC via SWCNT-Water becomes higher by increasing values of permeability number. Additionaly, sensitivity of SFC via SWCNT-water towards the permeability number is higher than the solid volume fraction for medium and higher permeability levels. It is also noted that sensitivity of SFC (SWCNT-Ethylene-glycol) towards volume fraction is higher for increasing permeability as well as inertia coefficient. Additionally, the sensitivity of LNN towards the Solid volume fraction is higher than the radiation and Biot number for all levels of Biot number. The findings will provide initial direction for future device manufacturing.

Numerical treatment for Darcy–Forchheimer flow of nanofluid due to a rotating disk with convective heat and mass conditions

2018 ◽  
Vol 28 (11) ◽  
pp. 2531-2550 ◽  
Author(s):  
T. Hayat ◽  
Arsalan Aziz ◽  
Taseer Muhammad ◽  
A. Alsaedi
Keyword(s):  
Biot Number ◽  
Design Methodology ◽  
Rotating Disk ◽  
Random Motion ◽  
Shooting Technique ◽  
Content Type ◽  
Forchheimer Number ◽  
Opposite Trend ◽  
Lower Temperature ◽  
Forchheimer Flow

Purpose The purpose of this study is to examine the Darcy–Forchheimer flow of viscous nanoliquid because of a rotating disk. Thermophoretic diffusion and random motion aspects are retained. Heat and mass transfer features are analyzed through convective conditions. Design/methodology/approach The governing systems are solved numerically by the shooting technique. Findings Higher porosity parameter and Forchheimer number Fr depict similar trend for both velocity profiles f' and g. Both temperature and concentration profiles show increasing behavior for higher Forchheimer number Fr. An increase in Prandtl number Pr corresponds to lower temperature profile, while opposite trend is noticed for thermal Biot number. Larger concentration Biot number exhibits increasing behavior for both concentration and its associated layer thickness. Originality/value To the best of the author’s knowledge, no such consideration has been given in the literature yet.

Impact of heat generation/absorption on heat and mass transfer of nanofluid over rotating disk filled with carbon nanotubes

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Patakota Sudarsana Reddy ◽  
Paluru Sreedevi ◽  
Kavaturi Venkata Suryanarayana Rao
Keyword(s):  
Carbon Nanotubes ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Heat Generation ◽  
Volume Fraction ◽  
Rotating Disk ◽  
Numerical Code ◽  
Nanoparticle Volume Fraction ◽  
Slip Parameter ◽  
Content Type

Purpose The purpose of this paper is to know the influence of heat generation/absorption and slip effects on heat and mass transfer flow of carbon nanotubes – water-based nanofluid over a rotating disk. Two types of carbon nanotubes, single and multi-walled, are considered in this analysis. Design/methodology/approach The non-dimensional system of governing equations is constructed using compatible transformations. These equations together with boundary conditions are solved numerically by using the most prominent Finite element method. The influence of various pertinent parameters such as magnetic parameter (0.4 – 1.0), nanoparticle volume fraction parameter (0.1 – 0.6), porosity parameter (0.3 – 0.6), radiation parameter (0.1 – 0.4), Prandtl number (2.2 – 11.2), space-dependent (−3.0 – 3.0), temperature-dependent (−3.0 – 1.5), velocity slip parameter (0.1 – 1.0), thermal slip parameter (0.1 – 0.4) and chemical reaction parameter (0.3 – 0.6) on nanofluids velocity, temperature and concentration distributions, as well as rates of velocity, temperature and concentration is calculated and the results are plotted through graphs and tables. Also, a comparative analysis is carried out to verify the validation of the present numerical code and found good agreement. Findings The results indicate that the temperature of the fluid elevates with rising values of nanoparticle volume fraction parameter. Furthermore, the rates of heat transfer rise from 4.8% to 14.6% when carbon nanotubes of 0.05 volume fraction are suspended into the base fluid. Originality/value The work carried out in this analysis is original and no part is copied from other sources.

Brinkman-Forchheimer flow of SWCNT and MWCNT magneto-nanoliquids in a microchannel with multiple slips and Joule heating aspects

2018 ◽  
Vol 14 (4) ◽  
pp. 769-786 ◽  
Author(s):  
Shashikumar N.S. ◽  
Gireesha B.J. ◽  
B. Mahanthesh ◽  
Prasannakumara B.C.
Keyword(s):  
Carbon Nanotubes ◽  
Nusselt Number ◽  
Joule Heating ◽  
Microchannel Flow ◽  
Governing Equations ◽  
Content Type ◽  
Swcnts And Mwcnts ◽  
Walled Carbon Nanotubes ◽  
Multiple Slips ◽  
Forchheimer Flow

Purpose The microfluidics has a wide range of applications, such as micro heat exchanger, micropumps, micromixers, cooling systems for microelectronic devices, fuel cells and microturbines. However, the enhancement of thermal energy is one of the challenges in these applications. Therefore, the purpose of this paper is to enhance heat transfer in a microchannel flow by utilizing carbon nanotubes (CNTs). MHD Brinkman-Forchheimer flow in a planar microchannel with multiple slips is considered. Aspects of viscous and Joule heating are also deployed. The consequences are presented in two different carbon nanofluids. Design/methodology/approach The governing equations are modeled with the help of conservation equations of flow and energy under the steady-state situation. The governing equations are non-dimensionalized through dimensionless variables. The dimensionless expressions are treated via Runge-Kutta-Fehlberg-based shooting scheme. Pertinent results of velocity, skin friction coefficient, temperature and Nusselt number for assorted values of physical parameters are comprehensively discussed. Also, a closed-form solution is obtained for momentum equation for a particular case. Numerical results agree perfectly with the analytical results. Findings It is established that multiple slip effect is favorable for velocity and temperature fields. The velocity field of multi-walled carbon nanotubes (MWCNTs) nanofluid is lower than single-walled carbon nanotubes (SWCNTs)-nanofluid, while thermal field, Nusselt number and drag force are higher in the case of MWCNT-nanofluid than SWCNT-nanofluid. The impact of nanotubes (SWCNTs and MWCNTs) is constructive for thermal boundary layer growth. Practical implications This study may provide useful information to improve the thermal management of microelectromechanical systems. Originality/value The effects of CNTs in microchannel flow by utilizing viscous dissipation and Joule heating are first time investigated. The results for SWCNTs and MWCNTs have been compared.

Darcy–Forchheimer flow of nanofluid due to a curved stretching surface

2019 ◽  
Vol 29 (1) ◽  
pp. 2-20 ◽  
Author(s):  
Rai Sajjad Saif ◽  
T. Hayat ◽  
R. Ellahi ◽  
Taseer Muhammad ◽  
A. Alsaedi
Keyword(s):  
Brownian Motion ◽  
Biot Number ◽  
Motion Parameter ◽  
Content Type ◽  
Porosity Parameter ◽  
Reverse Trend ◽  
Inertia Coefficient ◽  
Curvature Parameter ◽  
Forchheimer Flow ◽  
Brownian Motion Parameter

Purpose The purpose of present communication is to analyze Darcy–Forchheimer flow of viscous nanofluid by curved stretchable surface. Flow in porous medium is characterized by Darcy–Forchheimer relation. Brownian diffusion and thermophoresis are considered. Convective heat and mass boundary conditions are also used at the curved stretchable surface. Design/methodology/approach The resulting nonlinear system is solved through shooting technique. Findings Skin friction coefficient is enhanced for larger porosity parameter and inertia coefficient while reverse trend is noticed for curvature parameter. Local Nusselt number is enhanced for higher Prandtl number and thermal Biot number, whereas the opposite trend is seen via curvature parameter, porosity parameter, inertia coefficient, thermophoresis parameter and Brownian motion parameter. Local Sherwood number is enhanced for Schmidt number, Brownian motion parameter and concentration Biot number, while reverse trend is noticed for curvature parameter, porosity parameter, inertia coefficient and thermophoresis parameter. Originality/value To the best of author’s knowledge, no such consideration has been given in the literature yet.

A comparative study of wall jet flow containing carbon nanotubes with convective heat transfer and MHD

2017 ◽  
Vol 34 (3) ◽  
pp. 739-753 ◽  
Author(s):  
Syed Zulfiqar Ali Zaidi ◽  
Syed Tauseef Mohyud-din ◽  
Bandar Bin-Mohsen
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Nusselt Number ◽  
Biot Number ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Wall Jet ◽  
Content Type ◽  
Walled Carbon Nanotubes

Purpose The purpose of this study is to conduct a comparative investigation for incompressible electrically conducting nanofluid fluid through wall jet. Single-walled carbon nanotubes (SWCNTs) and multiple-walled carbon nanotubes (MWCNTs) are considered as the nanoparticles. To record the effect of Lorentz forces, a magnetic field is applied normally with the assumption that the induced magnetic field is negligible. Design/methodology/approach Boundary layer approximation is used to convert governing equations into ordinary differential equations along with appropriate boundary conditions. To obtain the results, used homotopy analysis method (HAM) has been used as an analytical technique and to validate the obtained results a famous numerical Runge–Kutta–Fehlberg method is also exploited. It has been observed that the results obtained through both of the methods are in excellent agreement with exact solution. Findings The Hartmann number is used as controlling parameter for velocity and temperature profile. That can be recorded as its extended values help to normalize the velocity, whereas it controls the rapid increase in temperature. The temperature profile is boosted by increasing the value of the Biot number, a physical parameter. Similarly, it also increases for an increased percentage of volume fraction of particles (SWCNTs/MWCNTs). The Hartmann number plays an important role in decreasing local skin friction coefficient. The influence of the Biot number and volume fraction of nanoparticles caused similar increasing effects on the local Nusselt number. Nanoparticles of the form SWCNT provide better heat transfer as compared to MWCNTs. Influence of the Biot number and volume fraction of nanoparticles caused similar increasing effects on the local Nusselt number. Nanoparticles of the form SWCNT provide better heat transfer as compared to MWCNTs. Originality/value To gain insight into the problem, the effects of various emerging parameters and physical quantities such as Biot number, Nusselt number and skin friction coefficient, have been explored.

Physical aspects of Darcy-Forchheimer bidirectional flow in carbon nanotubes (SWCNTs and MWCNTs)

2019 ◽  
Vol 29 (6) ◽  
pp. 2032-2056 ◽  
Author(s):  
Muhammad Ijaz Khan ◽  
Madiha Rashid ◽  
Tasawar Hayat ◽  
Niaz B. Khan ◽  
Ahmed Alsaedi
Keyword(s):  
Carbon Nanotubes ◽  
Porous Medium ◽  
Three Dimensional ◽  
Stretching Surface ◽  
Optimal Homotopy Analysis Method ◽  
Content Type ◽  
Heterogeneous Effects ◽  
Swcnts And Mwcnts ◽  
Nonlinearly Stretching Surface ◽  
Walled Cnts

Purpose This paper aims to examine the three-dimensional (3D) flow of carbon nanotubes (CNTs) due to bidirectional nonlinearly stretching surface by considering porous medium. Characteristics of both single-walled CNTs and multi-walled CNTs are discussed by considering Xue model. Darcy–Forchheimer model is used for flow saturating porous medium. Design/methodology/approach Optimal homotopy analysis method is used for the development of series solutions. Findings The authors deal with 3D Darcy–Forchheimer flow of CNTs over a nonlinearly stretching surface. Heat transport mechanism is discussed in the presence of Xue model. The homogeneous and heterogeneous effects are also accounted. The mathematical modeling is computed using boundary-layer approximations. Originality/value No such work has been done yet in the literature.

Numerical simulation for entropy generation in peristaltic flow with single and multi-wall carbon nanotubes

2019 ◽  
Vol 29 (12) ◽  
pp. 4684-4705 ◽  
Author(s):  
Muhammad Ijaz Khan ◽  
Shahid Farooq ◽  
Tasawar Hayat ◽  
Faisal Shah ◽  
Ahmed Alsaedi
Keyword(s):  
Carbon Nanotubes ◽  
Entropy Generation ◽  
Volume Fraction ◽  
Fluid Flows ◽  
Second Law Of Thermodynamics ◽  
Peristaltic Flow ◽  
Content Type ◽  
Multi Wall Carbon Nanotubes ◽  
Tapered Channel ◽  
Source Sink

Purpose The novel mechanical, chemical and thermodynamics characteristics of both single- and multi-wall carbon nanotubes (CNTs) make them a subject of much attention for the scientists and engineers from all domains. Fluid flows subject to CNTs are significant in biomedical engineering, energy storage systems, domestic and industrial cooling, automobile industries and solar energy collectors, etc. Keeping such effectiveness of CNTs in mind, this paper aims to examine peristaltic flow subject to CNTs in an asymmetric tapered channel. Both single and multiple walls CNTs are considered. The viscosity of nanomaterial depends on nanoparticles volume fraction and temperature. Total entropy rate through second law of thermodynamics is calculated. Heat source/sink and nonlinear heat flux are accounted. Design/methodology/approach The complicated flow expressions are simplified through lubrication approach. The velocity, temperature and entropy expressions are numerically solved by the built-in-shooting method. Findings The solutions for entropy generation, temperature and velocity are plotted, and the influences of pertinent variables are examined. The authors noticed that entropy generation is an increasing function of the Brinkman number. Originality/value The originality of this work is to communicate peristaltic CNTs-based nanomaterial peristaltic flow of viscous fluid in an asymmetric channel. No such consideration is yet published in the literature.

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.

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