scholarly journals Mixed Convection of a Radiating Magnetic Nanofluid past a Heated Permeable Stretching/Shrinking Sheet in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Feleke Buta Tadesse ◽  
Oluwole Daniel Makinde ◽  
Lemi Guta Enyadene
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Volume Fraction ◽  
Flow Stability ◽  
Collective Effects ◽  
Shrinking Sheet ◽  
Convective Heating

This paper analyzes the collective effects of buoyancy force, thermal radiation, convective heating, and magnetic field on stagnation point flow of an electrically conducting nanofluid past a permeable stretching/shrinking sheet in a porous medium. Similarity transformations are used on the resulting nonlinear partial differential equations to transfer into a system of coupled nonlinear ordinary differential equations. The fourth-fifth-order Runge–Kutta–Fehlberg method with shooting technique is applied to solve numerically. Results are obtained for dimensionless velocity, temperature, and nanoparticle volume fraction as well as the skin friction and local Nusselt and Sherwood numbers. The results indicate the existence of two real solutions for the shrinking sheet in the range of λ c < λ < 0 . The fluid flow stability is maintained by increasing the magnetic field effect, whereas the porous medium parameter inflates the flow stability. It is also noted that both the skin friction coefficient and the local Sherwood number approximately decline with the intensification of thermal radiation within the range from 9.83% to 14% and the range from 48.86% to 78.66%, respectively. It is also evident in the present work that the local Nusselt number upsurges with the porous and suction/injection parameters.

scholarly journals Unsteady MHD Bionanofluid Flow in a Porous Medium with Thermal Radiation near a Stretching/Shrinking Sheet

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
M. Irfan ◽  
M. Asif Farooq ◽  
A. Mushtaq ◽  
Z. H. Shamsi
Keyword(s):  
Porous Medium ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Internal Heat ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
The Impact

This research aims at providing the theoretical effects of the unsteady MHD stagnation point flow of heat and mass transfer across a stretching and shrinking surface in a porous medium including internal heat generation/absorption, thermal radiation, and chemical reaction. The fundamental principles of the similarity transformations are applied to the governing partial differential equations (PDEs) that lead to ordinary differential equations (ODEs). The transformed ODEs are numerically solved by the shooting algorithm implemented in MATLAB, and verification is done from MATLAB built-in solver bvp4c. The numerical data produced for the skin friction coefficient, the local Nusselt number, and the local Sherwood number are compared with the available result and found to be in a close agreement. The impact of involved physical parameters on velocity, temperature, concentration, and density of motile microorganisms profiles is scrutinized through graphs. It is analyzed that the skin friction coefficient enhances with increasing values of an unsteady parameter A , magnetic parameter M , and porosity parameter Kp . In addition, we observe that the density of a motile microorganisms profile enhances larger values of the bioconvection Lewis number Lb and Peclet number Pe and decreases with the increasing values of an unsteady parameter A .

MHD mixed convection stagnation-point flow of a viscoelastic fluid towards a stretching sheet in a porous medium with heat generation and radiation

2015 ◽  
Vol 93 (5) ◽  
pp. 532-541 ◽  
Author(s):  
M. Modather M. Abdou ◽  
E. Roshdy EL-Zahar ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscoelastic Fluid ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Heat Transfer Characteristics

An analysis was carried out to study the effect of thermal radiation on magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid near the stagnation point of a vertical stretching sheet in a porous medium with internal heat generation–absorption. The flow is generated because of linear stretching of the sheet and influenced by the uniform magnetic field that is applied horizontally in the flow region. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically using an accurate implicit finite difference scheme. A comparison of the obtained results with previously published numerical results is done and the results are found to be in good agreement. The effects of the viscoelastic fluid parameter, magnetic field parameter, nonuniform heat source–sink, and the thermal radiation parameter on the heat transfer characteristics are presented graphically and discussed. The values of the skin friction coefficient and the local Nusselt number are tabulated for both cases of assisting and opposing flows.

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 Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1649
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Unsteady stagnation point flow in hybrid nanofluid (Al2O3-Cu/H2O) past a convectively heated stretching/shrinking sheet is examined. Apart from the conventional surface of the no-slip condition, the velocity slip condition is considered in this study. By incorporating verified similarity transformations, the differential equations together with their partial derivatives are changed into ordinary differential equations. Throughout the MATLAB operating system, the simplified mathematical model is clarified by employing the bvp4c procedure. The above-proposed approach is capable of producing non-uniqueness solutions when adequate initial assumptions are provided. The findings revealed that the skin friction coefficient intensifies in conjunction with the local Nusselt number by adding up the nanoparticles volume fraction. The occurrence of velocity slip at the boundary reduces the coefficient of skin friction; however, an upward trend is exemplified in the rate of heat transfer. The results also signified that, unlike the parameter of velocity slip, the increment in the unsteady parameter conclusively increases the coefficient of skin friction, and an upsurge attribution in the heat transfer rate is observed resulting from the increment of Biot number. The findings are evidenced to have dual solutions, which inevitably contribute to stability analysis, hence validating the feasibility of the first solution.

scholarly journals Thermal Radiation, Chemical Reaction, Viscous and Joule Dissipation Effects on MHD Flow Embedded in a Porous Medium

2019 ◽  
Vol 24 (3) ◽  
pp. 725-737
Author(s):  
B. Zigta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Mhd Flow ◽  
Magnetic Reynolds Number ◽  
Convection Flow ◽  
Joule Dissipation ◽  
Radiation Chemical

Abstract An analysis is presented to study the effects of thermal radiation, chemical reaction, viscous and Joule dissipation on MHD free convection flow between a pair of infinite vertical Couette channel walls embedded in a porous medium. The fluid flows by a strong transverse magnetic field imposed perpendicularly to the channel wall on the assumption of a small magnetic Reynolds number. The governing non linear partial differential equations are transformed in to ordinary differential equations and are solved analytically. The effect of various parameters viz., Eckert number, electric conductivity, dynamic viscosity and strength of magnetic field on temperature profile has been discussed and presented graphically.

EFFECT OF CHEMICAL REACTION AND THERMAL RADIATION ON AXISYMMETRIC MHD FLOW OF JEFFREY NANOFLUID THROUGH A CILIATED CHANNEL FILLED WITH POROUS MEDIUM

2021 ◽  
pp. 2150025
Author(s):  
Sidra Shaheen ◽  
Khadija Maqbool ◽  
Farah Gul ◽  
Ayesha Sohail
Keyword(s):  
Magnetic Field ◽  
Drug Delivery ◽  
Porous Medium ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Partial Differential ◽  
Radiation Chemical ◽  
Jeffrey Nanofluid

To prevent the respiratory diseases in an air ways, a defense mechanism based on mucus transport by the moving cilia plays an important role. The mucus transport is affected by the thermal radiation, chemical reaction that changes the physics of fluid due to nanoparticles and thickness of mucus, also different problems in respiratory tract may occur due to the mucus efficacy. In this study, it is observed that the mucus transport can be controlled by the magnetic field that is produced by the drug delivery of nanoparticles, thermal radiation due to temperature difference, porous medium due to respiratory infection, and diffusion of the nanoparticles (chemical reaction) due to the magnetic drug delivery. In this model, flow of Jeffrey nanofluid through the ciliated tube resembles with the mucus flow in a wind pipe. The movement of the mucus is observed by the momentum, energy and concentration equation in the presence of body forces due to magnetic field, heat source due to radiation, Darcy’s resistance due to infection and chemical reaction due to the concentration of nanoparticles. Mathematical model of this study forms a complex system of partial differential equations under the low Reynolds number and long wavelength approximation. The nonlinear set of partial differential equations is solved by the Homotopy perturbation method and software “Mathematica,” results are found for velocity, temperature and concentration profiles and concluded that the mucus flow decelerates due to magnetic field produced by the drug delivery of the nanoparticles but accelerates due to the viscoelastic parameter of Jeffrey fluid and Darcy’s resistance parameter due to infection. The heat transfer rate in the mucus flow rises by increasing the random motion and reduces by the radiation and energy loss. The diffusion of the nanoparticles in the mucus rises by the growing values of thermophoresis and chemical reaction parameter and reduces by the growing values of viscoelastic and Brownian motion parameter.

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.

Magnetohydrodynamic, Thermal Radiation and Convective Boundary Effects of Free Convection Flow Past a Vertical Plate Embedded in a Porous Medium Saturated with a Nanofluid

2015 ◽  
Vol 31 (5) ◽  
pp. 607-616 ◽  
Author(s):  
H. Ali Agha ◽  
M. N. Bouaziz ◽  
S. Hanini
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Brownian Motion ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat And Mass Transfer ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Convection Flow ◽  
Convective Boundary

AbstractA numerical analysis was performed to study the effects of combined magnetohydrodynamic and thermal radiation under convective boundary condition over a semi infinite vertical plate embedded in a non-Darcy porous medium. Coupled heat and mass transfer of free convective boundary layer with viscous nanofluid are considered. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis mechanisms, while the Darcy-Forchheimer model is used for the porous medium. The governing partial differential equations are transformed into the ordinary differential equations using the similarity transformations. The accuracy of the method is observed by a comparison with other works reduced to a common case. Many results are tabulated and representative set is displayed graphically to illustrate the influence of the various parameters of interest on different profiles. Extensive numerical investigations show that the flow field, temperature, concentration and nanoparticle volume fraction shapes are significantly influenced by magnetic parameter, regular Lewis number, Brownian motion parameter, thermophoresis parameter, regular buoyancy ratio parameter and Biot number. Heat and mass transfer rates are significantly affected by the level of the applied magnetic field and the convective heat coefficient.

scholarly journals MHD Stagnation Point Flow over a Nonlinear Stretching/Shrinking Sheet in Nanofluids

2020 ◽  
Vol 76 (3) ◽  
pp. 139-152
Author(s):  
Nor Hathirah Abd Rahman ◽  
Norfifah Bachok ◽  
Haliza Rosali
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Problem Solver ◽  
Shrinking Sheet ◽  
The Impact ◽  
The Magnetic Field

In this study, an investigation of the steady 2-D magnetohydrodynamiic (MHD) flow of stagnation point past a nonlinear sheet of stretching/shrinking within of a non-uniform transverse magnetic intensity in nanofluids had been analysed. Considered material of nanoparticles such as copper (Cu) in water base fluid with Pr = 6.2 to analyze the influence of volume fraction parameter of nanoparticles and the stretching/shrinking sheet parameter. The governing nonlinear partial differential equations (PDEs) are converted in to the nonlinear ordinary differential equations (ODEs) and use the boundary value problem solver bvp4c in Matlab program to solve numerically through the use of a similarity transformation. The impact of the parameter of the magnetic field on the coefficient of skin friction, the local number of Nusselt and the profiles of velocity and temperature are portrayed and explained physically. The analysis reveals that the magnetic field and volume fraction of nanoparticles affect the velocity and temperature. The dual solutions are achieved where for the shrinking sheet case and the solutions are non-unique, different from a stretching sheet.

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