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.

scholarly journals An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 637-646 ◽  
Author(s):  
Hloniphile M. Sithole ◽  
Sabyasachi Mondal ◽  
Precious Sibanda ◽  
Sandile S. Motsa
Keyword(s):  
Brownian Motion ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Linearization Method ◽  
Concentration Profiles ◽  
Nanofluid Flow ◽  
Local Linearization ◽  
Maxwell Nanofluid ◽  
The Impact ◽  
Local Linearization Method

AbstractThe main focus of this study is on unsteady Maxwell nanofluid flow over a shrinking surface with convective and slip boundary conditions. The objective is to give an evaluation of the impact and significance of Brownian motion and thermophoresis when the nanofluid particle volume fraction flux at the boundary is zero. The transformed equations are solved numerically using the spectral local linearization method. We present an analysis of the residual errors to show the accuracy and convergence of the spectral local linearization method. We explore the effect of magnetic field and thermophoresis parameters on the heat transfer rate. We show, among other results, that an increase in particle Brownian motion leads to a decrease in the concentration profiles but concentration profiles increase with the increasing value of thermophoresis parameter

scholarly journals Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1238 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stagnation Point ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Three Solutions ◽  
Convective Boundary ◽  
Suction Parameter ◽  
Stretching Surfaces ◽  
The Impact

In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.

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.

Effect of Brownian Motion and External Magnetic Field on the Effective Heat Capacity of Ferrofluids

2011 ◽  
Author(s):  
Narges Susan Mousavi Kh. ◽  
Sunil Kumar ◽  
Arvind Narayanaswamy
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Brownian Motion ◽  
Energy Equation ◽  
Volume Fraction ◽  
Physical Parameters ◽  
Effective Heat Capacity ◽  
Effective Heat ◽  
Negligible Contribution

An Eulerian formalism is used to derive the energy equation for a system of magnetic nanoparticles in a fluid (ferrofluid) in the presence of uniform magnetic field. The energy equation proposed here contains an effective heat capacity, which has contributions from: (1) Brownian motion of nanoparticles, (2) magnetic field, (3) temperature, and (4) volume fraction of particles. The modified term quantitatively shows the negligible contribution of the first three factors but the significant effect of concentration of particles in change in heat capacity of ferrofluid. In order to have a better understanding of the problem, the equation is converted to a non dimensional form from which the role of each of physical parameters can be inferred.

scholarly journals An MHD Fluid Flow over a Porous Stretching/Shrinking Sheet with Slips and Mass Transpiration

Micromachines ◽  
2022 ◽  
Vol 13 (1) ◽  
pp. 116
Author(s):  
A. B. Vishalakshi ◽  
U. S. Mahabaleshwar ◽  
Ioannis E. Sarris
Keyword(s):  
Fluid Flow ◽  
Prandtl Number ◽  
Thermal Radiation ◽  
Biot Number ◽  
Volume Fraction ◽  
Heat Transfer Analysis ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Graphical Representations ◽  
Analytical Results

In the present paper, an MHD three-dimensional non-Newtonian fluid flow over a porous stretching/shrinking sheet in the presence of mass transpiration and thermal radiation is examined. This problem mainly focusses on an analytical solution; graphene water is immersed in the flow of a fluid to enhance the thermal efficiency. The given non-linear PDEs are mapped into ODEs via suitable transformations, then the solution is obtained in terms of incomplete gamma function. The momentum equation is analyzed, and to derive the mass transpiration analytically, this mass transpiration is used in the heat transfer analysis and to find the analytical results with a Biot number. Physical significance parameters, including volume fraction, skin friction, mass transpiration, and thermal radiation, can be analyzed with the help of graphical representations. We indicate the unique solution at stretching sheet and multiple solution at shrinking sheet. The physical scenario can be understood with the help of different physical parameters, namely a Biot number, magnetic parameter, inverse Darcy number, Prandtl number, and thermal radiation; these physical parameters control the analytical results. Graphene nanoparticles are used to analyze the present study, and the value of the Prandtl number is fixed to 6.2. The graphical representations help to discuss the results of the present work. This problem is used in many industrial applications such as Polymer extrusion, paper production, metal cooling, glass blowing, etc. At the end of this work, we found that the velocity and temperature profile increases with the increasing values of the viscoelastic parameter and solid volume fraction; additionally, efficiency is increased for higher values of thermal radiation.

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.

scholarly journals Flow of non-Newtonian magneto-fluid with gold and alumina nanoparticles through a non-Darcian porous medium

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
N. S. Elgazery
Keyword(s):  
Porous Medium ◽  
Prandtl Number ◽  
Numerical Solution ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Alumina Nanoparticles ◽  
Physical Parameters ◽  
Nonlinear Odes ◽  
Similarity Transformations ◽  
First Case

AbstractThis paper is centered on a numerical solution of non-Newtonian Casson magneto-nanofluid flow underlying an axisymmetric surface through a non-Darcian porous medium with heat generation/absorption. Using similarity transformations, the system of PDEs with the corresponding boundary conditions are reduced to system of nonlinear ODEs. The Chebyshev pseudospectral (CPS) method is used to get a numerical solution for the formulated differential system. Comparisons of the present numerical results with previously published results are made, and fine agreements for some the considered values of parameters were noted. Two cases of nanofluid are considered. The first case is Newtonian nanofluid, water with suspended gold (Au) or alumina (Al2O3) nanoparticles, and representative results are obtained for β → ∞ and Pr = 6.785 (the Prandtl number of water). The second case is non-Newtonian bio-nanofluid, blood with suspended gold (Au) or alumina (Al2O3) nanoparticles, and representative results are obtained for β = 0.1 and Pr = 25 (the Prandtl number of blood). The variation of different physical parameters on non-dimensional velocity and temperature fields as well as the skin friction coefficient and the Nusselt number are discussed. It is demonstrated that the implication of a nanoparticle into bio-fluid can modify the stream design. Also, the nanoparticles with high thermal conductivity (gold) have better enhancement on heat transfer compared to alumina, i.e., the effectiveness of adding gold to the water and blood is higher than adding alumina. One of the most important applications of nanotechnology in the field of medicine is the use of nanoparticles (gold molecules) in chemotherapy to get rid of cancer cells.

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.

scholarly journals On Mixed Convection Squeezing Flow of Nanofluids

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3138 ◽  
Author(s):  
Sheikh Irfan Ullah Khan ◽  
Ebraheem Alzahrani ◽  
Umar Khan ◽  
Noreena Zeb ◽  
Anwar Zeb
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Mixed Convection ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Squeezing Flow ◽  
Physical Parameters ◽  
Gamma Alumina ◽  
Highly Nonlinear ◽  
The Impact

In this article, the impact of effective Prandtl number model on 3D incompressible flow in a rotating channel is proposed under the influence of mixed convection. The coupled nonlinear system of partial differential equations is decomposed into a highly nonlinear system of ordinary differential equations with aid of suitable similarity transforms. Then, the solution of a nonlinear system of ordinary differential equations is obtained numerically by using Runge–Kutta–Fehlberg (RKF) method. Furthermore, the surface drag force C f and the rate of heat transfer N u are portrayed numerically. The effects of different emerging physical parameters such as Hartmann number (M), Reynold’s number (Re), squeezing parameter ( β ), mixed convection parameter λ , and volume fraction ( φ ) are also incorporated graphically for γ — alumina. Due to the higher viscosity and thermal conductivity ethylene-based nanofluids, it is observed to be an effective common base fluid as compared to water. These observations portrayed the temperature of gamma-alumina ethylene-based nanofluids rising on gamma-alumina water based nanofluids.

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