scholarly journals Influence of MHD Hybrid Ferrofluid Flow on Exponentially Stretching/Shrinking Surface with Heat Source/Sink under Stagnation Point Region

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2932
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Heat Source ◽  
Volume Fraction ◽  
Stable Solution ◽  
Boundary Layer Separation ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Stagnation Region ◽  
Analysis Of Stability ◽  
Exponentially Stretching ◽  
Source Sink

The numerical investigations of hybrid ferrofluid flow with magnetohydrodynamic (MHD) and heat source/sink effects are examined in this research. The sheet is assumed to stretch or shrink exponentially near the stagnation region. Two dissimilar magnetic nanoparticles, namely cobalt ferrite, CoFe2O4 and magnetite, Fe3O4, are considered with water as a based fluid. Utilizing the suitable similarity transformation, the governing equations are reduced to an ordinary differential equation (ODE). The converted ODEs are numerically solved with the aid of bvp4c solver from Matlab. The influences of varied parameters on velocity profile, skin friction coefficient, temperature profile and local Nusselt number are demonstrated graphically. The analysis evident the occurrence of non-unique solution for a shrinking sheet and it is confirmed from the analysis of stability that only the first solution is the stable solution. It is also found that for a stronger heat source, heat absorption is likely to happen at the sheet. Further, hybrid ferrofluid intensifies the heat transfer rate compared to ferrofluid. Moreover, the boundary layer separation is bound to happen faster with an increment of magnetic parameter, while it delays when CoFe2O4 nanoparticle volume fraction increases.

scholarly journals Mixed Convection Stagnation-Point Flow of a Nanofluid Past a Permeable Stretching/Shrinking Sheet in the Presence of Thermal Radiation and Heat Source/Sink

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 788 ◽  
Author(s):  
Anuar Jamaludin ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Heat Source ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Suction Parameter ◽  
Source Sink

In this study we numerically examine the mixed convection stagnation-point flow of a nanofluid over a vertical stretching/shrinking sheet in the presence of suction, thermal radiation and a heat source/sink. Three distinct types of nanoparticles, copper (Cu), alumina (Al2O3) and titania (TiO2), were investigated with water as the base fluid. The governing partial differential equations were converted into ordinary differential equations with the aid of similarity transformations and solved numerically by utilizing the bvp4c programme in MATLAB. Dual (upper and lower branch) solutions were determined within a particular range of the mixed convection parameters in both the opposing and assisting flow regions and a stability analysis was carried out to identify which solutions were stable. Accordingly, solutions were gained for the reduced skin friction coefficients, the reduced local Nusselt number, along with the velocity and temperature profiles for several values of the parameters, which consists of the mixed convection parameter, the solid volume fraction of nanoparticles, the thermal radiation parameter, the heat source/sink parameter, the suction parameter and the stretching/shrinking parameter. Furthermore, the solutions were presented in graphs and discussed in detail.

Hybrid nanofluid flow through an exponentially stretching/shrinking sheet with mixed convection and Joule heating

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ubaidullah Yashkun ◽  
Khairy Zaimi ◽  
Anuar Ishak ◽  
Ioan Pop ◽  
Rabeb Sidaoui
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Joule Heating ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Eckert Number ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Exponentially Stretching

Purpose This study aims to investigate the flow and heat transfer of a hybrid nanofluid through an exponentially stretching/shrinking sheet along with mixed convection and Joule heating. The nanoparticles alumina (Al2O3) and copper (Cu) are suspended into a base fluid (water) to form a new kind of hybrid nanofluid (Al2O3-Cu/water). Also, the effects of constant mixed convection parameter and Joule heating are considered. Design/methodology/approach The governing partial differential equations are transformed into ordinary differential equations (ODEs) using appropriate similarity transformations. The transformed nonlinear ODEs are solves using the bvp4c solver available in MATLAB software. A comparison of the present results shows a good agreement with the published results. Findings Dual solutions for hybrid nanofluid flow obtained for a specific range of the stretching/shrinking parameter values. The values of the skin friction coefficient increases but the local Nusselt number decreases for the first solution with the increasing of the magnetic parameter. Enhancing copper volume fraction and Eckert number reduces the surface temperature, which intimates the decrement of heat transfer rate for the first and second solutions for the stretching/shrinking sheet. In detail, the first solution results show that when the Eckert number increases as 0.1, 0.4 and 0.7 at λ = 1.5, the temperature variations reduced to 10.686840, 10.671419 and 10.655996. While in the second solution, keeping the same parameters temperature variation reduced to 9.750777, 9.557349 and 9.364489, respectively. On the other hand, the results indicate that the skin friction coefficient increases with copper volume fraction. This study shows that the thermal boundary layer thickness rises due to the rise in the solid volume fraction. It is also observed that the magnetic parameter, copper volume fraction and Eckert number widen the range of the stretching/shrinking parameter for which the solution exists. Practical implications In practice, the investigation on the flow and heat transfer of a hybrid nanofluid past an exponentially stretching/shrinking sheet with mixed convection and Joule heating is crucial and useful. The problems related to hybrid nanofluid have numerous real-life and industrial applications, such as microelectronics, manufacturing, naval structures, nuclear system cooling, biomedical and drug reduction. Originality/value In specific, this study focuses on increasing thermal conductivity using a hybrid nanofluid mathematical model. The novelty of this study is the use of natural mixed convection and Joule heating in a hybrid nanofluid. This paper can obtain dual solutions. The authors declare that this study is new, and there is no previous published work similar to the present study.

scholarly journals Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
I. Swain ◽  
S. R. Mishra ◽  
H. B. Pattanayak
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Mass Transfer Effect ◽  
Exponentially Stretching Sheet ◽  
Exponentially Stretching ◽  
Source Sink

An attempt has been made to study the heat and mass transfer effect in a boundary layer MHD flow of an electrically conducting viscous fluid subject to transverse magnetic field on an exponentially stretching sheet through porous medium. The effect of thermal radiation and heat source/sink has also been discussed in this paper. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. Graphical results are displayed for nondimensional velocity, temperature, and concentration profiles while numerical values of the skin friction local Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system.

MHD Stagnation Point Flow over Exponentially Stretching Sheet with Exponentially Moving Free-Stream, Viscous Dissipation, Thermal Radiation and Non-Uniform Heat Source/Sink

2017 ◽  
Vol 11 ◽  
pp. 182-190
Author(s):  
Gauri Shenkar Seth ◽  
Rohit Sharma ◽  
B. Kumbhakar ◽  
R. Tripathi
Keyword(s):  
Heat Source ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Free Stream ◽  
Transverse Magnetic ◽  
Stagnation Point Flow ◽  
Uniform Heat ◽  
Highly Nonlinear ◽  
Exponentially Stretching ◽  
Source Sink

An investigation is carried out for the steady, two dimensional stagnation point flow of a viscous, incompressible, electrically conducting, optically thick heat radiating fluid taking viscous dissipation into account over an exponentially stretching non-isothermal sheet with exponentially moving free-stream in the presence of uniform transverse magnetic field and non-uniform heat source/sink. The governing boundary layer equations are transformed into highly nonlinear ordinary differential equations using suitable similarity transform. Resulting boundary value problem is solved numerically with the help of 4th-order Runge-Kutta Gill method along with shooting technique. Effects of various pertinent flow parameters on the velocity, temperature field, skin friction and Nusselt number are described through figures and tables. Also, the present numerical results are compared with the earlier published results for some reduced case and a good agreement has been found among those results.

scholarly journals Stagnation-point flow past a shrinking sheet in a nanofluid

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Roslinda Nazar ◽  
Mihaela Jaradat ◽  
Norihan Arifin ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Nonlinear System ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

AbstractIn this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It was found that nanoparticles of low thermal conductivity, TiO2, have better enhancement on heat transfer compared to nanoparticles Al2O3 and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.

scholarly journals Numerical solution for thermophoresis effects on heat and mass transfer over an accelerating surface with heat source/sink

2017 ◽  
Vol 21 (6 Part B) ◽  
pp. 2719-2730
Author(s):  
Mohammad Rashidi ◽  
Ramachandran Sivaraj ◽  
Durairaj Mythili ◽  
Zhigang Yang
Keyword(s):  
Mass Transfer ◽  
Heat Source ◽  
Particle Deposition ◽  
Skin Friction Coefficient ◽  
Vital Role ◽  
Heat Transfer Characteristics ◽  
Viscous Fluid Flow ◽  
Transfer Characteristics ◽  
Implicit Finite Difference ◽  
Source Sink

A study has been carried out to analyze the thermophoretic particle deposition and heat generation/absorption effects on unsteady, free convective, viscous fluid flow over a moving flat plate. The thermal conductivity of the fluid is assumed to vary as a linear function of temperature. The governing partial differential equations are solved numerically by using an implicit finite difference method of Crank Nicolson type. Numerical results for the velocity, temperature and concentration profiles as well as for the skin-friction coefficient, Nusselt number and Sherwood number distributions are obtained and presented graphically for various parametric conditions to show interesting aspects of the solution. Results indicate that the heat source/sink plays a vital role in predicting the heat transfer characteristics of moving fluids and the thermophoretic particle deposition has notable influence on the mass transfer characteristics.

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