scholarly journals Non-Similar Solution for Magnetized Flow of Maxwell Nanofluid over an Exponentially Stretching Surface

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Raheela Razzaq ◽  
Umer Farooq ◽  
Jifeng Cui ◽  
Taseer Muhammad
Keyword(s):  
Nusselt Number ◽  
Brownian Motion ◽  
Skin Friction ◽  
Differential System ◽  
Local Nusselt Number ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Fluid Behavior ◽  
Exponentially Stretching ◽  
Physical Features

In this study, an analysis is made by studying more reliable nonsimilar magneto-hydrodynamics (MHD) flow of Maxwell fluid with nanomaterials. Nonsimilar transport is produced by extending of sheet with arbitrary velocity. Maxwell structure is marked to indicate the non-Newtonian fluid behavior. The leading nondimensional partial differential system (PDEs) is transmuted to a set of the nonlinear ordinary differential system (ODEs) through local nonsimilarity technique. The developing system is solved numerically using an implemented package known as bvp4c in MATLAB. The analysis discovers several physical features of thermal and velocity profiles. Remark the flow accelerated for greater Deborah and Hartman parameters. The influence of thermophoresis number on the thermal figure is minimal. The conducts of velocity, concentration, and thermal distribution and local Nusselt number and skin friction are illustrated graphically by taking distinct parameters. The consequences disclose that the local Nusselt number is an increasing function of Prandtl number; however, it is a decaying function for Brownian motion. The rise in skin friction is observed for increasing Brownian motion and Lewis numbers.

scholarly journals Impact of heat generation/absorption of magnetohydrodynamics Oldroyd-B fluid impinging on an inclined stretching sheet with radiation

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Fazle Mabood ◽  
Gabriella Bognár ◽  
Anum Shafiq
Keyword(s):  
Nusselt Number ◽  
Skin Friction ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Mhd Flow ◽  
Similarity Solutions ◽  
Deborah Number ◽  
Radiation Parameter ◽  
Local Skin ◽  
Local Skin Friction

Abstract In this paper, we have investigated thermally stratified MHD flow of an Oldroyd-B fluid over an inclined stretching surface in the presence of heat generation/absorption. Similarity solutions for the transformed governing equations are obtained. The reduced equations are solved numerically using the Runge–Kutta Fehlberg method with shooting technique. The influences of various involved parameters on velocity profiles, temperature profiles, local skin friction, and local Nusselt number are discussed. Numerical values of local skin friction and local Nusselt number are computed. The significant outcomes of the study are that the velocity decreases when the radiation parameter $$R_{d}$$ R d is increased while the temperature profile is increased for higher values of radiation parameter $$R_{d}$$ R d in case of opposing flow, moreover, growth in Deborah number $$\beta_{2}$$ β 2 enhance the velocity and momentum boundary layer. The heat transfer rate is decrease due to magnetic strength but increase with the increased values of Prandtl and Deborah numbers. The results of this model are closely matched with the outputs available in the literature.

MHD flow, under the kinetic postulate, of fluids that are initially liquid under thermal radiation effects

2019 ◽  
Vol 97 (6) ◽  
pp. 579-587
Author(s):  
Azad Hussain ◽  
Zainia Muneer ◽  
M.Y. Malik ◽  
Saadia Ghafoor
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Radiation Effects ◽  
Shooting Method ◽  
Porous Plate ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Runge Kutta Method

The present study focuses on the non-Newtonian magnetohydrodynamic flow, under the kinetic postulate, of fluids that are initially liquid past a porous plate in the appearance of thermal radiation effects. Resemblance transfigurations are used to metamorphose the governing equations for temperature and velocity into a system of ordinary differential equations. We then solved these differential equations subject to convenient boundary conditions by using the shooting method along with the Runge–Kutta method. Heat transfer and characteristic flow results are acquired for different compositions of physical parameters. These results are extended graphically to demonstrate interesting attributes of the physics of the problem. Nusselt number and skin friction coefficients are also discussed via graphs and tables for different values of dimensionless parameters. Decline occurs in velocity profile due to escalating values of M. Temperature profile depicts growing behavior due to acceleration in the values of λ and M. Nusselt number and skin friction curves represent rising behavior according to their parameters.

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3110-3127 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

PurposeThis paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.Design/methodology/approachThe problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.FindingsResults found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.Originality/valueThe problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

scholarly journals Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Mostafa Mahmoud ◽  
Shimaa Waheed
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Local Skin ◽  
Local Skin Friction

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

scholarly journals The Flow and Heat Transfer of a Nanofluid Past a Stretching/Shrinking Sheet with a Convective Boundary Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Syahira Mansur ◽  
Anuar Ishak
Keyword(s):  
Nusselt Number ◽  
Brownian Motion ◽  
Local Nusselt Number ◽  
Convective Boundary Condition ◽  
Motion Parameter ◽  
Shrinking Sheet ◽  
Convective Boundary ◽  
Convective Parameter ◽  
Local Sherwood Number ◽  
Brownian Motion Parameter

The boundary layer flow of a nanofluid past a stretching/shrinking sheet with a convective boundary condition is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the local Nusselt number and the local Sherwood number as well as the temperature and concentration profiles for some values of the convective parameter, stretching/shrinking parameter, Brownian motion parameter, and thermophoresis parameter. The results indicate that the local Nusselt number is consistently higher for higher values of the convective parameter. However, the local Nusselt number decreases with increasing values of the Brownian motion parameter as well as the thermophoresis parameter. In addition, the local Sherwood number increases with increasing Brownian motion parameter and decreases with increasing convective parameter and thermophoresis parameter.

Computational Study of Three-Dimensional Stagnation Point Nanofluid Bioconvection Flow on a Moving Surface With Anisotropic Slip and Thermal Jump Effect

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
M. J. Uddin ◽  
W. A. Khan ◽  
A. I. Md. Ismail ◽  
O. Anwar Bég
Keyword(s):  
Nusselt Number ◽  
Skin Friction ◽  
Stagnation Point ◽  
Local Nusselt Number ◽  
Local Density ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Slip Parameter ◽  
Moving Surface ◽  
Local Skin

The effects of anisotropic slip and thermal jump on the three-dimensional stagnation point flow of nanofluid containing microorganisms from a moving surface have been investigated numerically. Anisotropic slip takes place on geometrically striated surfaces and superhydrophobic strips. Zero mass flux of nanoparticles at the surface is applied to achieve practically applicable results. Using appropriate similarity transformations, the transport equations are reduced to a system of nonlinear ordinary differential equations with coupled boundary conditions. Numerical solutions are reported by means of very efficient numerical method provided by the symbolic code Maple. The influences of the emerging parameters on the dimensionless velocity, temperature, nanoparticle volumetric fraction, density of motile microorganism profiles, as well as the local skin friction coefficient, the local Nusselt number, and the local density of the motile microorganisms are displayed graphically and illustrated in detail. The computations demonstrate that the skin friction along the x-axis is enhanced with the velocity slip parameter along the y-axis. The converse response is observed for the dimensionless skin friction along the y-axis. The heat transfer rate is increased with greater velocity slip effects but depressed with the thermal slip parameter. The local Nusselt number is increased with Prandtl number and decreased with the thermophoresis parameter. The local density for motile microorganisms is enhanced with velocity slip parameters and depressed with the bioconvection Lewis number, thermophoresis, and Péclet number. Numerical results are validated where possible with published results and excellent correlation is achieved.

scholarly journals Magnetohydrodynamic Hybrid Nanofluid Flow Past an Exponentially Stretching Sheet with Slip Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3291
Author(s):  
Abdul Samad Khan ◽  
He-Yong Xu ◽  
Waris Khan
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Slip Parameter ◽  
Nanofluid Flow ◽  
Slip Conditions ◽  
Exponentially Stretching ◽  
The Impact

This study presents the magnetized hybrid nanofluid flow with heat source/sink over an exponentially stretching/shrinking sheet. Slip conditions are implemented to analyze the hybrid nanofluid flow for both slip and no-slip conditions. Additionally, the hybrid nanofluid of alumina and copper (hybrid nanoparticles) with blood (base fluid) has been considered and discussed with both suction and injection parameters. The appropriate similarity variables are used to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and solved analytically with the help of the homotopy analysis method (HAM). The impact of different embedded parameters has been shown in the form of graphs and tables. The numerical values of skin friction and Nusselt number are presented in the form of Tables for both slip and no-slip cases. It is summarized that the upsurge of the velocity slip parameter and magnetic parameter increases the skin friction, while the rising of the thermal slip parameter and heat generation parameter decreases the Nusselt number.

scholarly journals Three-Dimensional Flow and Heat Transfer Past a Permeable Exponentially Stretching/Shrinking Sheet in a Nanofluid

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Syahira Mansur ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Three Dimensional ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Three Dimensional Flow ◽  
Flow And Heat Transfer

The three-dimensional flow and heat transfer of a nanofluid over a stretching/shrinking sheet is investigated. Numerical results are obtained using bvp4c in MATLAB. The results show nonunique solutions for the shrinking case. The effects of the stretching/shrinking parameter, suction parameter, Brownian motion parameter, thermophoresis parameter, and Lewis number on the local skin friction coefficient and the local Nusselt number are studied. Suction increases the solution domain. Furthermore, as the sheet is shrunk in thex-direction, suction increases the skin friction coefficient in the same direction while decreasing the skin friction coefficient in they-direction. The local Nusselt number is consistently lower for higher values of thermophoresis parameter and Lewis number. On the other hand, the local Nusselt number increases as the Brownian motion parameter increases.

scholarly journals Numerical and Analytical Investigation for Darcy-Forchheimer Flow of a Williamson Fluid over a Riga Plate with Double Stratification and Cattaneo-Christov Dual Flux

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
S. Eswaramoorthi ◽  
Nazek Alessa ◽  
M. Sangeethavaanee ◽  
Ngawang Namgyel
Keyword(s):  
Nusselt Number ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Viscous Fluids ◽  
Fluid Temperature ◽  
Williamson Fluid ◽  
Injection Parameter ◽  
Riga Plate ◽  
The Impact ◽  
Forchheimer Flow

The Darcy-Forchheimer flow of a Williamson fluid over a Riga plate was analyzed in this paper. Energy and mass equations are modeled with Cattaneo-Christov theory and double stratifications. The governing PDE models are altered into ODE models. These models are numerically solved by MATLAB bvp4c and analytically solved by the homotopy analysis method. The impact of governing flow parameters on fluid velocity, fluid temperature, fluid concentration, skin-friction coefficient, local Nusselt number, and local Sherwood number is scrutinized via graphs and tables. We acknowledged that the speed of the fluid becomes diminishes for more presence of porosity parameter. Also, we noted that the thermal and solutal boundary layer thicknesses are waning due to their corresponding stratification parameters. In addition, the maximum decreasing percentage of skin friction is obtained when the suction/injection parameter varies from 0.0 to 0.4 for Williamson and viscous fluids. The maximum increasing percentage of local Nusselt number occurs when the suction/injection parameter varies from 0.4 to 0.8 for Williamson and viscous fluids.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Nurfazila Rasli ◽  
Norshafira Ramli
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Magnetohydrodynamic Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

Sign in / Sign up

Export Citation Format

Share Document