scholarly journals MHD three dimensional flow of Oldroyd-B nanofluid over a bidirectional stretching sheet: DTM-Padé Solution

2019 ◽  
Vol 8 (1) ◽  
pp. 744-754 ◽  
Author(s):  
Sumit Gupta ◽  
Sandeep Gupta
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Prandtl Number ◽  
Comparative Study ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Deborah Number ◽  
Motion Parameter ◽  
Physical Parameters ◽  
Brownian Motion Parameter

Abstract Current article is devoted with the study of MHD 3D flow of Oldroyd B type nanofluid induced by bi-directional stretching sheet. Expertise similarity transformation is confined to reduce the governing partial differential equations into ordinary nonlinear differential equations. These dimensionless equations are then solved by the Differential Transform Method combined with the Padé approximation (DTM-Padé). Dealings of the arising physical parameters namely the Deborah numbers β1 and β2, Prandtl number Pr, Brownian motion parameter Nb and thermophoresis parameter Nt on the fluid velocity, temperature and concentration profile are depicted through graphs. Also a comparative study between DTM and numerical method are presented by graph and other semi-analytical techniques through tables. It is envisage that the velocity profile declines with rising magnetic factor, temperature profile increases with magnetic parameter, Deborah number of first kind and Brownian motion parameter while decreases with Deborah number of second kind and Prandtl number. A comparative study also visualizes comparative study in details.

scholarly journals Role of Brownian Motion and Thermophoresis Effects on Hydromagnetic Flow of Nanofluid Over a Nonlinearly Stretching Sheet with Slip Effects and Solar Radiation

2019 ◽  
Vol 24 (3) ◽  
pp. 489-508
Author(s):  
S.P. Anjali Devi ◽  
S. Mekala
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Velocity Slip ◽  
Physical Parameters ◽  
Nonlinear Thermal Radiation ◽  
Hydromagnetic Flow ◽  
Nonlinearly Stretching Sheet

Abstract Hydromagnetic flow of water based nanofluids over a nonlinearly stretching sheet in the presence of velocity slip, temperature jump, magnetic field, nonlinear thermal radiation, thermophoresis and Brownian motion has been studied. The article focuses on Cu water nanofluid and Ag water nanofluid. The similarity transformation technique is adopted to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations and then they are solved numerically utilizing the Nachistem – Swigert shooting method along with the fourth order Runge Kutta integration technique. The influence of physical parameters on the flow, temperature and nanoparticle volume fraction are presented through graphs. Also the values of the skin friction coefficient at the wall and nondimensional rate of heat transfer are given in a tabular form. A comparative study with previous published results is also made.

MHD Pulsating Flow of Casson Nanofluid in a Vertical Porous Space with Thermal Radiation and Joule Heating

2020 ◽  
Vol 36 (4) ◽  
pp. 535-549
Author(s):  
Challa Kalyan Kumar ◽  
Suripeddi Srinivas ◽  
Anala Subramanyam Reddy
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Motion Parameter ◽  
Porous Space ◽  
Perturbation Scheme ◽  
Casson Nanofluid ◽  
Nanoparticles Concentration ◽  
The Impact ◽  
Brownian Motion Parameter

ABSTRACTIn this investigation, the magnetohydrodynamic pulsatile flow of Casson nanofluid through a vertical channel embedded in porous medium with thermal radiation and heat generation/absorption has been analyzed using Buongiorno model. The influence of viscous and Joules dissipations are taken into account. The governing coupled partial differential equations are reduced to ordinary differential equations using perturbation scheme and then solved numerically by using Runge-Kutta fourth order technique along with shooting method. The impact of various emerging parameters on velocity, temperature, nanoparticles concentration, Nusselt number and Sherwood number distributions are analyzed in detail. Analysis indicates that the temperature distribution increases for a given increase in Brownian motion parameter and thermophoresis parameter, while it decreases with an increase in Hartmann number. Further, the nanoparticles concentration distribution decreases with an increase in the chemical reaction parameter and the Lewis number, while it increases for a given increase in the Brownian motion parameter.

Nonlinear Heat Transfer in a Two-Layer Flow With Nanofluids by OHAM

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Umer Farooq ◽  
Lin Zhi-Liang
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Mixed Convection ◽  
Vertical Channel ◽  
Motion Parameter ◽  
Physical Parameters ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Brownian Motion Parameter

The problem of fully developed steady, laminar, incompressible flow in a vertical channel is studied analytically, one region is filled with water based copper nanofluid and the other region is filled with clear viscous fluid. The resulting coupled nonlinear ordinary differential equations (ODEs) are solved by optimal homotopy analysis method (OHAM). The convergence of our results is discussed by the so-called total average squared residual error. Analytical results are presented for different values of the physical parameters, such as the mixed convection parameters, the Brownian motion parameter, and thermophoresis parameter. Reversed flow is observed for sufficiently high buoyancy (mixed convection parameter). Further we investigate the effects of the Brownian motion parameter and thermophoresis parameter on the fluid flow and heat transfer at the interface of the two regions.

scholarly journals Thin Film Flow of Couple Stress Magneto-Hydrodynamics Nanofluid with Convective Heat over an Inclined Exponentially Rotating Stretched Surface

Coatings ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 338 ◽  
Author(s):  
Asifa Tassaddiq ◽  
Ibni Amin ◽  
Meshal Shutaywi ◽  
Zahir Shah ◽  
Farhad Ali ◽  
...  
Keyword(s):  
Thin Film ◽  
Brownian Motion ◽  
Differential Equations ◽  
Prandtl Number ◽  
Ordinary Differential Equations ◽  
Couple Stress ◽  
Magnetic Parameter ◽  
Film Flow ◽  
Thin Film Flow ◽  
Brownian Motion Parameter

In this article a couple stress magneto-hydrodynamic (MHD) nanofluid thin film flow over an exponential stretching sheet with joule heating and viscous dissipation is considered. Similarity transformations were used to obtain a non-linear coupled system of ordinary differential equations (ODEs) from a system of constitutive partial differential equations (PDEs). The system of ordinary differential equations of couple stress magneto-hydrodynamic (MHD) nanofluid flow was solved using the well-known Homotopy Analysis Method (HAM). Nusselt and Sherwood numbers were demonstrated in dimensionless forms. At zero Prandtl number the velocity profile was analytically described. Furthermore, the impact of different parameters over different state variables are presented with the help of graphs. Dimensionless numbers like magnetic parameter M, Brownian motion parameter Nb, Prandtl number Pr, thermophoretic parameter Nt, Schmidt number Sc, and rotation parameter S were analyzed over the velocity, temperature, and concentration profiles. It was observed that the magnetic parameter M increases the axial, radial, drainage, and induced profiles. It was also apparent that Nu reduces with greater values of Pr. On increasing values of the Brownian motion parameter the concentration profile declines, while the thermophoresis parameter increases.

scholarly journals Sensitivity Analysis on Thermal Conductivity Characteristics of a Water-Based Bionanofluid Flow Past a Wedge Surface

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Sze Qi Chan ◽  
Fazlina Aman ◽  
Syahira Mansur
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Lewis Number ◽  
Motion Parameter ◽  
Nonlinear Ordinary Differential Equations ◽  
Shooting Technique ◽  
Wedge Surface ◽  
Water Based ◽  
Local Sherwood Number ◽  
Brownian Motion Parameter

Thermobioconvection boundary layer flow in a suspension of water-based bionanofluid holding both nanoparticles and motile microorganisms past a wedge surface was studied. The governing nonlinear partial differential equations on reference of the Buongiorno model were transformed into a set of coupled nonlinear ordinary differential equations. Shooting technique was then used to solve the transformed nonlinear ordinary differential equations numerically. The solutions were found to be contingent on several values of the governing parameters. As highlighted, the velocity profile as well as the skin friction coefficient was affected by the pressure gradient parameter, the function of the wedge angle parameter. On the other hand, the temperature, nanoparticle concentration, and density of motile microorganism’s distributions together with its corresponding local Nusselt number, local Sherwood number, and local density of the motile microorganisms change with the thermophoresis and Brownian motion parameter and so Lewis number, Schmidt number, and bioconvection Péclet number. An experimental scheme together with sensitivity analysis on the basis of Response Surface Methodology (RSM) was applied to examine the dependency of the response parameters of interest to the input parameters’ change. Obviously, local Nusselt number was more sensitive towards the Brownian motion parameter when the Brownian motion parameter was at 0.2 and 0.3. However local Sherwood number was more sensitive towards the Lewis number for all values of Brownian motion parameter. Compatibility found by comparing results between RSM and shooting technique gave confidence for the model’s accuracy. The findings would provide initial guidelines for future device fabrication. Finally, the numerical results obtained were thoroughly inspected and verified with the existing values reported by some researchers.

Chemical Reaction Effect on Forced Convection Flow of a Jeffery Fluid over a Stretching Sheet: A Numerical Study

2018 ◽  
Vol 16 ◽  
pp. 109-119
Author(s):  
A.K. Mishra ◽  
N. Senapati ◽  
S.R. Mishra ◽  
S. Bhattacharjee
Keyword(s):  
Differential Equations ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Numerical Study ◽  
Mhd Flow ◽  
Deborah Number ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Similarity Transformations

The purpose of this paper is to investigate steady two-dimensional laminar magnetohydrodynamic (MHD) flow of an incompressible Jeffrey fluid past over a linearly stretching sheet. The governing partial differential equations (PDEs) of continuity, momentum, energy and concentration are transformed into nonlinear coupled ordinary differential equations (ODEs) by using similarity transformations. Then the ODEs are solved by applying Runge-Kutta fourth order method accompanied with shooting technique. The effects of various physical parameters characterizing the flow phenomenon including Deborah number, ratio of relaxation to retardation times, magnetic parameter, porous parameter, Prandtl number, Eckert number, heat source / sink parameter, Schmidt number and chemical reaction parameter on dimensionless velocity, temperature and concentration profiles are analyzed. The numerical results are obtained and presented in graphs. The present results are compared with the earlier published results as a particular case.

scholarly journals Boundary Layer Analysis in Nanofluid Flow Past a Permeable Moving Wedge in Presence of Magnetic Field by Using Falkner – Skan Model

2018 ◽  
Vol 23 (4) ◽  
pp. 1005-1013 ◽  
Author(s):  
M. Ali ◽  
M.A. Alim
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Pressure Gradient ◽  
Ordinary Differential Equations ◽  
Velocity Ratio ◽  
Lewis Number ◽  
Motion Parameter ◽  
Gradient Parameter ◽  
Brownian Motion Parameter

Abstract In the present work, the effect of various dimensionless parameters on the momentum, thermal and concentration boundary layer are analyzed. In this respect we have considered the MHD boundary layer flow of heat and transfer over a porous wedge surface in a nanofluid. The governing partial differential equations are converted into ordinary differential equations by using the similarity transformation. These ordinary differential equations are numerically solved using fourth order Runge–Kutta method along with shooting technique. The present results have been shown in a graphical and also in tabular form. The results indicate that the momentum boundary layer thickness reduces with increasing values of the pressure gradient parameter β for different situations and also for the magnetic parameter M but increases for the velocity ratio parameter λ and permeability parameter K*. The heat transfer rate increases for the pressure gradient parameter β, velocity ratio parameter λ, Brownian motion parameter Nb and Prandtl number Pr but opposite result is found for the increasing values of the thermoporesis parameter Nt. The nanoparticle concentration rate increases with an increase in the pressure gradient parameter β, velocity ratio parameter λ, Brownian motion parameter Nb and Lewis number Le, but decreases for the thermoporesis parameter Nt. Finally, the numerical results has compared with previously published studies and found to be in good agreement. So the validity of our results is ensured.

scholarly journals Numerical and Analytical Investigation of an Unsteady Thin Film Nanofluid Flow over an Angular Surface

Processes ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 486 ◽  
Author(s):  
Haroon Rasheed ◽  
Zeeshan Khan ◽  
Ilyas Khan ◽  
Dennis Ching ◽  
Kottakkaran Nisar
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Brownian Motion ◽  
Prandtl Number ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Motion Parameter ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
Brownian Motion Parameter

In the present study, we examine three-dimensional thin film flow over an angular rotating disk plane in the presence of nanoparticles. The governing basic equations are transformed into ordinary differential equations by using similarity variables. The series solution has been obtained by the homotopy asymptotic method (HAM) for axial velocity, radial velocity, darning flow, induced flow, and temperature and concentration profiles. For the sake of accuracy, the results are also clarified numerically with the help of the BVPh2- midpoint method. The effect of embedded parameters such as the Brownian motion parameter Nb, Schmidt number Sc, thermophoretic parameter and Prandtl number Pr are explored on velocity, temperature and concentration profiles. It is observed that with the increase in the unsteadiness factor S, the thickness of the momentum boundary layer increases, while the Sherwood number Sc, with the association of heat flow from sheet to fluid, reduces with the rise in S and results in a cooling effect. It is also remarkable to note that the thermal boundary layer increases with the increase of the Brownian motion parameter Nb and Prandtl number Pr, hindering the cooling process resulting from heat transfer.

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.

Numerical study of Carreau nanofluid flow past vertical plate with the Cattaneo–Christov heat flux model

2019 ◽  
Vol 29 (2) ◽  
pp. 702-723 ◽  
Author(s):  
Vasu B. ◽  
Atul Kumar Ray
Keyword(s):  
Heat Flux ◽  
Brownian Motion ◽  
Weissenberg Number ◽  
Motion Parameter ◽  
Conduction Model ◽  
Content Type ◽  
Carreau Nanofluid ◽  
Flux Model ◽  
Heat Flux Model ◽  
Brownian Motion Parameter

PurposeTo achieve material-invariant formulation for heat transfer of Carreau nanofluid, the effect of Cattaneo–Christov heat flux is studied on a natural convective flow of Carreau nanofluid past a vertical plate with the periodic variations of surface temperature and the concentration of species. Buongiorno model is considered for nanofluid transport, which includes the relative slip mechanisms, Brownian motion and thermophoresis.Design/methodology/approachThe governing equations are non-dimensionalized using suitable transformations, further reduced to non-similar form using stream function formulation and solved by local non-similarity method with homotopy analysis method. The numerical computations are validated and verified by comparing with earlier published results and are found to be in good agreement.FindingsThe effects of varying the physical parameters such as Prandtl number, Schmidt number, Weissenberg number, thermophoresis parameter, Brownian motion parameter and buoyancy ratio parameter on velocity, temperature and species concentration are discussed and presented through graphs. The results explored that the velocity of shear thinning fluid is raised by increasing the Weissenberg number, while contrary response is seen for the shear thickening fluid. It is also found that heat transfer in Cattaneo–Christov heat conduction model is less than that in Fourier’s heat conduction model. Furthermore, the temperature and thermal boundary layer thickness expand with the increase in thermophoresis and Brownian motion parameter, whereas nanoparticle volume fraction increases with increase in thermophoresis parameter, but reverse trend is observed with increase in Brownian motion parameter.Originality/valueThe present investigation is relatively original as very little research has been reported on Carreau nanofluids under the effect of Cattaneo–Christov heat flux model.

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