scholarly journals MHD Bioconvection Flow and Heat Transfer of Nanofluid through an Exponentially Stretchable Sheet

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 692 ◽  
Author(s):  
Mohammad Ferdows ◽  
Khairy Zaimi ◽  
Ahmed M. Rashad ◽  
Hossam A. Nabwey
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Magnetic Parameter ◽  
Volume Fraction ◽  
Lewis Number ◽  
Problem Solver ◽  
Similarity Transformations ◽  
Comparison Results ◽  
Spectral Relaxation ◽  
High Degree

Recently, bioconvection phenomenon has gained great importance in research for its use in many engineering and biological applications. Therefore, this work investigates the magnetohydrodynamic flow of a dissipative nanofluid, including gyrotactic microorganisms along an exponentially moving sheet. Since the governing equations that describe the problem are nonlinear and more complicated, similarity transformations are used to get a reduced mathematical model in which all the differential equations are ordinary and asymmetric. The computational analysis for the reduced mathematical model is carried out, employing the spectral relaxation technique (SRM) via software called MATLAB. Comparison results are also validated by using the boundary value problem solver (bvp4c) in MATLAB. The obtained results were compared with previously published researches, and a high degree of compatibility and accuracy were found symmetric. The implications of pertinent parameters on velocity, temperature, nanoparticles volume fraction, and density of the microorganism profiles are graphically presented. A decline was seen in the velocity field with augmentation in the magnetic parameter, but certain enhancement was noticed in the temperature field for augmented values of the magnetic parameter, thermophoresis, and Brownian motion parameters. A significant reduction was also noticed in the behavior of the concentration profile for augmented values of the Brownian motion parameter and Lewis number, while it was enhanced with the boost in the thermophoresis and magnetic parameters. The results also indicated that the density of the motile microorganism decreases with bioconvection Lewis number, Prandtl number, Lewis, and Peclet numbers.

scholarly journals Magnetohydrodynamic Boundary Layer Flow of Nanofluid over an Exponentially Stretching Permeable Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Krishnendu Bhattacharyya ◽  
G. C. Layek
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Volume Fraction ◽  
Lewis Number ◽  
Nanoparticle Volume Fraction ◽  
Layer Flow ◽  
Wall Mass

A mathematical model of the steady boundary layer flow of nanofluid due to an exponentially permeable stretching sheet with external magnetic field is presented. In the model, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, the wall mass transfer parameter, the Prandtl number, the Lewis number, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction. The magnetic field makes enhancement in temperature and nanoparticle volume fraction, whereas the wall mass transfer through the porous sheet causes reduction of both. For the Brownian motion, the temperature increases and the nanoparticle volume fraction decreases. Heat transfer rate becomes low with increase of Lewis number. For thermophoresis effect, the thermal boundary layer thickness becomes larger.

scholarly journals Bio-convective and chemically reactive hybrid nanofluid flow upon a thin stirring needle with viscous dissipation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Arshad Khan ◽  
Anwar Saeed ◽  
Asifa Tassaddiq ◽  
Taza Gul ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Viscous Dissipation ◽  
Flow Problem ◽  
Volume Fraction ◽  
Flow System ◽  
Lewis Number ◽  
Hybrid Nanoparticles ◽  
Hybrid Nanofluid ◽  
Buongiorno’S Model

AbstractIn this work, the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out. The chemical reaction and viscous dissipation has also considered for flow system in the presence of microorganism. The hybrid nanoparticles comprising of Copper $$\left( {Cu} \right)$$ Cu and Alumina $$\left( {Al_{2} O_{3} } \right)$$ A l 2 O 3 are considered for current flow problem. Mathematically the flow problem is formulated by employing the famous Buongiorno’s model that will also investigate the consequences of thermophoretic forces and Brownian motion upon flow system. Group of similar variables is used to transform the model equations into dimensionless form and have then solved analytically by homotopy analysis method (HAM). It has established in this work that, flow of fluid declines due to increase in bioconvection Rayleigh number, buoyancy ratio and volume fractions of nanoparticles. Thermal flow grows due to rise in Eckert number, Brownian, thermophoresis parameters and volume fraction of nanoparticles. Concentration profiles increase due to growth in Brownian motion parameter and reduces due to increase in thermophoresis parameter and Lewis number. Motile microorganism profile declines due to augmentation in Peclet and bioconvection Lewis numbers. Moreover, the percentage enhancement in the drag force and rate of heat transfer using conventional nanofluid and hybrid nanofluid are observed and discussed. The hybrid nanofluid increases the skin friction and heat transfer rate more rapidly and efficiently as compared to other traditional fluids. A comparison of the present study with the existing literature is also conducted with a closed agreement between both results for variations in thickness of the needle.

scholarly journals Optimization of Heat Transfer Properties of Nanofluid Flow Over a Shrinking Surface Through Mathematical Modeling

2020 ◽  
Vol 25 (2) ◽  
pp. 40-56 ◽  
Author(s):  
A. Bhandari ◽  
R.K. Pavan Kumar Pannala
Keyword(s):  
Magnetic Parameter ◽  
Volume Fraction ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Nanofluid Flow ◽  
Thermal Buoyancy ◽  
Similarity Transformations ◽  
Permeability Parameter ◽  
Shrinking Surface ◽  
Transfer Properties

AbstractIn the current study, a three dimensional incompressible magnetohydrodynamic (MHD) nanofluid flow over a shrinking surface with associated thermal buoyancy, thermal radiation, and heating absorption effects, as well as viscous dissipation have been investigated. The model has been represented in a set of partial differential equations and is transformed using suitable similarity transformations which are then solved by using the finite element method through COMSOL. The results for velocity and temperature profiles are provided for various values of the shrinking parameter, Biot’s number, heat generation/absorption parameter, thermal Grashof number, nanoparticle volume fraction, permeability parameter, magnetic parameter and radiation parameter.

scholarly journals Bio-convective and Chemically Reactive Hybrid Nanofluid Flow Upon a Thin Stirring Needle with Viscous Dissipation

2021 ◽  
Author(s):  
Arshad Khan ◽  
Anwar Saeed ◽  
Asifa Tassaddiq ◽  
Taza Gul
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Viscous Dissipation ◽  
Flow Problem ◽  
Volume Fraction ◽  
Flow System ◽  
Lewis Number ◽  
Hybrid Nanoparticles ◽  
Hybrid Nanofluid ◽  
Buongiorno’S Model

Abstract In this work the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out. The chemical reaction and viscous dissipation has also considered for flow system in the presence of microorganism. The hybrid nanoparticles comprising of Copper (Cu) and Alumina (Al2O3) are considered for current flow problem. Mathematically the flow problem is formulated by employing the famous Buongiorno’s model that will also investigate the consequences of thermophoretic forces and Brownian motion upon flow system. Group of similar variables is used to transform the model equations into dimensionless form and have then solved analytically by homotopy analysis method (HAM). It has established in this work that, flow of fluid declines due to increase in bioconvection Rayleigh number, buoyancy ratio and volume fractions of nanoparticles. Thermal flow grows due to rise in Eckert number, Brownian, thermophoresis parameters and volume fraction of nanoparticles. Concentration profiles increase due to growth in Brownian motion parameter and reduces due to increase in thermophoresis parameter and Lewis number. Motile microorganism profile declines due to augmentation in Peclet and bioconvection Lewis numbers. Moreover, the percentage enhancement in the drag force and rate of heat transfer using nanofluid and hybrid nanofluids are observed and discussed. The hybrid nanofluid increases the skin friction and heat transfer rate more rapidly and efficiently as compared to other traditional fluids. A comparison of the present study with the existing literature is also conducted with a closed agreement between both results for variations in thickness of the needle.

Implementation of improved Fourier's law and Fick's law for rotational flow of nanofluid over an exponentially stretching sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sumit Gupta ◽  
Sandeep Gupta ◽  
Nawal Kishor Jangid ◽  
Vijay kumar Singhal ◽  
Rohit Mukherjee ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Mass Flux ◽  
Volume Fraction ◽  
Lewis Number ◽  
Convergent Series ◽  
Deborah Number ◽  
Relaxation Parameter ◽  
Content Type ◽  
Flux Relaxation ◽  
Exponentially Stretching

PurposeThe purpose of the current article is to explore the rotational behavior on nanofluid flow over an exponentially stretching surface. Heat and mass flux are formulated upon Cattaneo–Christov theory.Design/methodology/approachEffect of thermophoretic, Brownian motion and thermally convective conditions is further retained. Novel boundary layer approximations are applied to transform the governing equations of continuity, momentum, energy and nanoparticle volume fraction. Convergent series solutions are obtained to manage the rotating flow with the aid of homotopy analysis method (HAM).FindingsDepending on the several dimensionless parameters including the local rotation parameter the Prandtl number Pr, the thermophoresis parameter, the Brownian motion parameter, the Lewis number Le, Biot number Bi, Deborah number in terms of heat flux relaxation parameter and Deborah number in terms of mass flux relaxation parameter with the dimensionless physical quantities are deliberated through graphs. Present results are also likened with the foregoing results in significance.Originality/valueNo such assumptions have been made for the development of analytical solution so far.

Unsteady Boundary Layer Flow of Nanofluid Past an Impulsively Stretching Sheet

2013 ◽  
Vol 29 (3) ◽  
pp. 423-432 ◽  
Author(s):  
M. Mustafa ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Similarity Transformations ◽  
Nanoparticles Concentration ◽  
Motion Effect ◽  
Nanoparticles Volume Fraction ◽  
Layer Flow

AbstractThe unsteady laminar boundary layer flow of nanofluid caused by a linearly stretching sheet is considered. Transport equations contain the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The relevant partial differential equations are non-dimensionalized and transformed into similar forms by using appropriate similarity transformations. The uniformly valid explicit expressions of velocity, temperature and nanoparticles volume fraction are derived. Convergence of the series solutions is carefully analyzed. It is observed that an increase in the strength of Brownian motion effect rises the temperature appreciably. However rate of heat transfer and nanoparticles concentration at the sheet is reduced when Brownian motion effect intensifies. It is also found that the temperature and nanoparticles concentration are increasing functions of the unsteady parameter.

scholarly journals On Numerical Thermal Transport Analysis of Three-Dimensional Bioconvective Nanofluid Flow

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jifeng Cui ◽  
Shahzad Munir ◽  
Umer Farooq ◽  
Mohammed Elamin Ahmed Rabie ◽  
Taseer Muhammad ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Numerical Study ◽  
Three Dimensional ◽  
Lewis Number ◽  
Dimensionless Numbers ◽  
Local Skin ◽  
Similarity Transformations ◽  
Local Skin Friction ◽  
Layer Flow ◽  
Physical Impact

In this paper, a numerical study is presented for the 3D mathematical model of bioconvective boundary layer flow having nanoparticles and motile microorganisms on a curved sheet under isothermal conditions. Using an appropriate choice of similarity transformations, the problem reduces to coupled ordinary nonlinear equations, and this system is then treated with bvp4c (a MATLAB-based solver) to get the desired solution with good accuracy. The repercussion of distinct important dimensionless numbers such as thermophoresis, buoyancy ratio, Lewis number, and Brownian number on the velocity, temperature, and volume fraction of nanoparticles is presented graphically and is discussed in context with their importance on flow dynamics. Moreover, the physical impact of various parameters on motile microorganism density, the local Sherwood number, the local Nusselt number, and the local skin friction coefficients is analyzed and presented in tables. Qualitative analysis also reveals that the Brownian motion parameter, Peclet number, and Schmidt number have an inverse impact on the density microorganisms.

scholarly journals Numerical study of nano-biofilm stagnation flow from a nonlinear stretching/shrinking surface with variable nanofluid and bioconvection transport properties

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abdulaziz Alsenafi ◽  
O. Anwar Bég ◽  
M. Ferdows ◽  
Tasveer A. Bég ◽  
A. Kadir
Keyword(s):  
Thermal Conductivity ◽  
Brownian Motion ◽  
Skin Friction ◽  
Volume Fraction ◽  
Lewis Number ◽  
Motion Parameter ◽  
Nano Particle ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter ◽  
Brownian Motion Parameter

AbstractA mathematical model is developed for stagnation point flow toward a stretching or shrinking sheet of liquid nano-biofilm containing spherical nano-particles and bioconvecting gyrotactic micro-organisms. Variable transport properties of the liquid (viscosity, thermal conductivity, nano-particle species diffusivity) and micro-organisms (species diffusivity) are considered. Buongiorno’s two-component nanoscale model is deployed and spherical nanoparticles in a dilute nanofluid considered. Using a similarity transformation, the nonlinear systems of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a central space finite difference method in the CodeBlocks Fortran platform. Graphical plots for the distribution of reduced skin friction coefficient, reduced Nusselt number, reduced Sherwood number and the reduced local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms are presented for the influence of wall velocity power-law index (m), viscosity parameter $$({c}_{2})$$ ( c 2 ) , thermal conductivity parameter (c4), nano-particle mass diffusivity (c6), micro-organism species diffusivity (c8), thermophoresis parameter $$(Nt)$$ ( N t ) , Brownian motion parameter $$(Nb)$$ ( N b ) , Lewis number $$(Le)$$ ( L e ) , bioconvection Schmidt number $$(Sc)$$ ( S c ) , bioconvection constant (σ) and bioconvection Péclet number $$(Pe)$$ ( P e ) . Validation of the solutions via comparison related to previous simpler models is included. Further verification of the general model is conducted with the Adomian decomposition method (ADM). Extensive interpretation of the physics is included. Skin friction is elevated with viscosity parameter ($${\mathrm{c}}_{2})$$ c 2 ) whereas it is suppressed with greater Lewis number and thermophoresis parameter. Temperatures are elevated with increasing thermal conductivity parameter ($${\mathrm{c}}_{4})$$ c 4 ) whereas Nusselt numbers are reduced. Nano-particle volume fraction (concentration) is enhanced with increasing nano-particle mass diffusivity parameter ($${c}_{6}$$ c 6 ) whereas it is markedly reduced with greater Lewis number (Le) and Brownian motion parameter (Nb). With increasing stretching/shrinking velocity power-law exponent ($$m),$$ m ) , skin friction is decreased whereas Nusselt number and Sherwood number are both elevated. Motile microorganism density is boosted strongly with increasing micro-organism diffusivity parameter ($${\mathrm{c}}_{8}$$ c 8 ) and Brownian motion parameter (Nb) but reduced considerably with greater bioconvection Schmidt number (Sc) and bioconvection Péclet number (Pe). The simulations find applications in deposition processes in nano-bio-coating manufacturing processes.

scholarly journals On the analytic solutions for squeezing flow of nanofluid between parallel disks

2012 ◽  
Vol 17 (4) ◽  
pp. 418-430 ◽  
Author(s):  
Meraj Mustafa Hashmi ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Brownian Motion ◽  
Volume Fraction ◽  
Concentration Field ◽  
Analytic Solutions ◽  
Squeezing Flow ◽  
Nonlinear Boundary Value Problems ◽  
Similarity Transformations ◽  
Parallel Disks ◽  
Homotopy Analysis ◽  
Convergence Control

This article investigates the magnetohydrodynamic squeezing flow of nanofluid between parallel disks. Governing partial differential equations are converted into ordinary differential system via similarity transformations. We employ homotopy analysis method (HAM) to construct analytic expressions of velocity, temperature and nanoparticles volume fraction. Convergence analysis is performed and optimal values of the convergence-control parameters are determined. The computations are validated with the built in routine for solving nonlinear boundary value problems via shooting technique through software Mathematica 8.0. The behaviors of key parameters such as suction/blowing parameter (A), squeeze parameter (S), Hartman number (M), Brownian motion parameter (Nb) and thermophoresis parameter (Nt) are thoroughly examined. It is seen that the parameters have a great impact on the concentration field for the suction flow when compared with the blowing case. An intensification in the Brownian motion and thermophoresis effects results in the appreciable increase in the temperature and nanoparticles concentration.

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.

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