scholarly journals Slip effects on squeezing flow of nanofluid between two parallel disks

2016 ◽  
Vol 21 (1) ◽  
pp. 5-20 ◽  
Author(s):  
K. Das ◽  
S. Jana ◽  
N. Acharya
Keyword(s):  
Differential Equations ◽  
Flow Characteristics ◽  
Wall Slip ◽  
Skin Friction Coefficient ◽  
Integration Scheme ◽  
Squeezing Flow ◽  
Linear Ordinary Differential Equations ◽  
Slip Conditions ◽  
Electrically Conducting ◽  
Parallel Disks

Abstract In this study, the influence of temperature and wall slip conditions on the unsteady flow of a viscous, incompressible and electrically conducting nanofluid squeezed between two parallel disks in the presence of an applied magnetic field is investigated numerically. Using the similarity transformation, the governing coupled partial differential equations are transformed into similarity non-linear ordinary differential equations which are solved numerically using the Nachtsheim and Swigert shooting iteration technique together with the sixth order Runge-Kutta integration scheme. The effects of various emerging parameters on the flow characteristics are determined and discussed in detail. To check the reliability of the method, the numerical results for the skin friction coefficient and Nusselt number in the absence of slip conditions are compared with the results reported by the predecessors and an excellent agreement is observed between the two sets of results.

scholarly journals Numerical investigation of MHD stagnation-point flow and heat transfer of sodium alginate non-Newtonian nanofluid

2019 ◽  
Vol 8 (1) ◽  
pp. 179-192 ◽  
Author(s):  
Bhuvnesh Sharma ◽  
Sunil Kumar ◽  
M.K. Paswan
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Sodium Alginate ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Analytical Approximations ◽  
Temperature Distributions ◽  
Homotopy Analysis

Abstract A rigorous analysis of unsteady magnetohydrodynamic mixed convection and electrically conducting nanofluid model with a stretching/shrinking wedge is presented. First, the governing partial differential equations for momentum and energy conservation are converted to coupled nonlinear ordinary differential equations by means of exact similarity transformation. The homotopy analysis method (HAM) is employed to obtain the analytical approximations for flow velocity and temperature distributions of alumina-sodium alginate naofluid. The solution is found to be dependent on some parameters including the nanoparticle volume fraction, unsteadiness parameter, magnetic parameter, mixed convection parameter and the generalized prandtl number. A systematic study is carried out to illustrate the effects of these parameters on the velocity and temperature distributions. Also, the value of skin friction coefficient and local Nusselt number are compared with copper-sodium alginate and titania-sodium alginate nanofluids.

scholarly journals Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet in a micropolar fluid

2013 ◽  
Vol 17 (2) ◽  
pp. 525-532
Author(s):  
Nor Yacob ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Leading Edge ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Keller Box Method ◽  
Flow And Heat Transfer ◽  
The Magnetic Field

An analysis is carried out for the steady two-dimensional mixed convection flow adjacent to a stretching vertical sheet immersed in an incompressible electrically conducting micropolar fluid. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the leading edge. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically using a finite difference scheme known as the Keller box method. The effects of magnetic and material parameters on the flow and heat transfer characteristics are discussed. It is found that the magnetic field reduces both the skin friction coefficient and the heat transfer rate at the surface for any given K and ?. Conversely, both of them increase as the material parameter increases for fixed values of M and ?.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

scholarly journals CASSON FLUID OF A STAGNATION-POINT FLOW (SPF) TOWARDS A VERTICAL SHRINKING/STRETCHING SHEET

2021 ◽  
Vol 5 (1) ◽  
pp. 16-26
Author(s):  
Winifred N. Mutuku ◽  
Anselm O. Oyem
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Fluid Model ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Integration Scheme ◽  
Shrinking Sheet ◽  
Electrically Conducting ◽  
Casson Fluid Model ◽  
Fluid Behaviour

This study presents a convectively heated hydromagnetic Stagnation-Point Flow (SPF) of an electrically conducting Casson fluid towards a vertically stretching/shrinking sheet. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour and using similarity variables, the governing partial differential equations are transformed into coupled nonlinear ordinary differential equations. The dimensionless nonlinear equations are solved numerically by Runge-Kutta Fehlberg integration scheme with shooting technique. The effects of the thermophysical parameters on velocity and temperature profiles are presented graphically and discussed quantitatively. The result shows that the flow field velocity decreases with increase in magnetic field parameter and Casson fluid parameter .

Mixed Convection in Viscoelastic Boundary Layer Flow and Heat Transfer Over a Stretching Sheet

2014 ◽  
Vol 6 (3) ◽  
pp. 359-375 ◽  
Author(s):  
Antonio Mastroberardino
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Electrically Conducting ◽  
Homotopy Analysis ◽  
Layer Flow

AbstractAn investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equations for the fluid flow and temperature are reduced to a nonlinear system of ordinary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition it is demonstrated that previously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives reported are not correct.

THERMO-DIFFUSION AND DIFFUSO-THERMO EFFECTS ON MHD SQUEEZING FLOW BETWEEN PARALLEL DISKS

2017 ◽  
Vol 24 (02) ◽  
pp. 1750022 ◽  
Author(s):  
SHEIKH IRFANULLAH KHAN ◽  
SYED TAUSEEF MOHYUD-DIN ◽  
BANDAR BIN-MOHSIN
Keyword(s):  
Skin Friction Coefficient ◽  
Squeezing Flow ◽  
Validity And Reliability ◽  
Soret And Dufour Effects ◽  
Parallel Disks ◽  
Homotopy Analysis ◽  
Number Formula ◽  
Soret Number ◽  
Dufour Number ◽  
Order Four

In this article, Magnetohydrodynamic (MHD) squeezing flow between two parallel disks is considered. The upper disk is taken to be solid and the lower one is permeable. Soret and Dufour effects are measured to explore the thermal-diffusion and diffusion-thermo effects. Governing PDEs are converted into system of ODEs with the support of suitable similarity transforms. Homotopy analysis method (HAM) has been employed to obtain the expressions for velocity, temperature and concentration profiles. Effects of different emerging parameters such as squeezing number [Formula: see text], Hartman number [Formula: see text], Prandtl number Pr, Eckert number Ec, dimensionless length [Formula: see text] and Schmidt number Sc on the flow are also discussed with the help of graphs for velocity, temperature and concentration. The local Nusselt and Sherwood numbers along with convergence of the series solutions are presented with the help of graphs. From the results obtained, we observed that the physical quantities like skin friction coefficient increases with increasing value of Hartmann number [Formula: see text] in the blowing case [Formula: see text] whereas a fall is observed in the suction case [Formula: see text]. However, the rate of heat transfer at upper wall increases with increasing values of Dufour number Du and Soret number Sr for both the suction [Formula: see text] and blowing flow [Formula: see text], whereas, for the larger values of Dufour number Du and smaller values of Soret number Sr, a rapid fall is observed in Sherwood number Sh for both the suction [Formula: see text] and blowing [Formula: see text] cases. A numerical solution is obtained by employing Runge–Kutta method of order four (RK-4) to check the validity and reliability of the developed algorithm. A well agreement is found between both the solutions.

scholarly journals Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip and Temperature Jump Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
M. G. Sobamowo ◽  
A. T. Akinshilo ◽  
A. A. Yinusa
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Temperature Jump ◽  
Squeezing Flow ◽  
Nonlinear Ordinary Differential Equations ◽  
Jump Conditions ◽  
Homotopy Perturbation ◽  
Parallel Disks

The various applications of squeezing flow between two parallel surfaces such as those that are evident in manufacturing industries, polymer processing, compression, power transmission, lubricating system, food processing, and cooling amongst others call for further study on the effects of various parameters on the flow phenomena. In the present study, effects of nanoparticle geometry, slip, and temperature jump conditions on thermo-magneto-solutal squeezing flow of nanofluid between two parallel disks embedded in a porous medium are investigated, analyzed, and discussed. Similarity variables are used to transform the developed governing systems of nonlinear partial differential equations to systems of nonlinear ordinary differential equations. Homotopy perturbation method is used to solve the systems of the nonlinear ordinary differential equations. In order to verify the accuracy of the developed analytical solutions, the results of the homotopy perturbation method are compared with the results of the numerical method using the shooting method coupled with the fourth-order Runge–Kutta, and good agreements are established. Through the approximate analytical solutions, parametric studies are carried out to investigate the effects of nanoparticle size and shape, Brownian motion parameter, nanoparticle parameter, thermophoresis parameter, Hartmann number, Lewis number and pressure gradient parameters, slip, and temperature jump boundary conditions on thermo-solutal and hydromagnetic behavior of the nanofluid. This study will enhance and advance the understanding of nanofluidics such as energy conservation, friction reduction, and micromixing of biological samples.

scholarly journals Convection heat and mass transfer in a hydromagnetic flow of a micropolar fluid over a porous medium

2014 ◽  
Vol 41 (2) ◽  
pp. 93-117
Author(s):  
B.I. Olajuwon ◽  
J.I. Oahimire ◽  
M.A. Waheed
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Micropolar Fluid ◽  
Perturbation Technique ◽  
Skin Friction Coefficient ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

This study presents a mathematical analysis of a hydromagnetic boundary layer flow, heat and mass transfer characteristics on steady twodimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field in the presence of thermal radiation. The governing system of partial differential equations is first transformed into a system of non- linear ordinary differential equation using the usual similarity transformation. The resulting coupled non-linear ordinary differential equations are then solved using perturbation technique. With the help of graphs, the effects of the various important parameters entering into the problem on the velocity, temperature and concentration fields within the boundary layer are separately discussed. The effects of the pertinent parameters on the wall temperature, wall solutal concentration, skin friction coefficient and the rate of heat and mass transfer are presented numerically in tabular form. The results obtained showed that these parameters have significant influence on the flow.

Scrutinization of Chemical Reaction Effect on Flow and Mass Transfer of Prandtl Liquid over a Riga Plate in the Presence of Solutal Slip Effect

2018 ◽  
Vol 16 (8) ◽  
Author(s):  
B.J. Gireesha ◽  
K. Ganesh Kumar ◽  
B.C. Prasannakumar
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Layer Thickness ◽  
Chemical Reaction ◽  
Boundary Layer Thickness ◽  
Skin Friction Coefficient ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Riga Plate

AbstractIn the present paper focused on flow and mass transfer of Prandtl fluid over a Riga plate. The effects of chemical reaction and solutal slip are taken into the account. The governing partial differential equations are reduced into a set of coupled non linear ordinary differential equations using suitable similarity transformations. These equations are then solved using Runge-Kutta-Fehlberg-45 method. Behaviour of emerging parameters are presented graphically and discussed for velocity and concentration distribution. Numerical values of reduced skin friction coefficient and Sherwood number are shown in table and are discussed. From the plotted results it can be observed that the solutal boundary layer thickness decreases for larger values of chemical reaction parameter and Schmidt number. Also, momentum boundary layer thickness rise with stronger modified Hartman number.

scholarly journals Convective Heat Transfer of a Hybrid Nanofluid over a Nonlinearly Stretching Surface with Radiation Effect

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2220
Author(s):  
Emad H. Aly ◽  
Alin V. Roşca ◽  
Natalia C. Roşca ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Radiation Effect ◽  
Numerical Technique ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Temperature Parameter ◽  
Nonlinearly Stretching Surface

The flow of the hybrid nanofluid (copper–titanium dioxide/water) over a nonlinearly stretching surface was studied with suction and radiation effect. The governing partial differential equations were then converted into non-linear ordinary differential equations by using proper similarity transformations. Therefore, these equations were solved by applying a numerical technique, namely Chebyshev pseudo spectral differentiation matrix. The results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that the rising of the mass flux parameter slows down the velocity and, hence, decreases the temperature. Further, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, it was mentioned that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases.

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