scholarly journals Natural Convection of Viscoelastic Fluid from a Cone Embedded in a Porous Medium with Viscous Dissipation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Gilbert Makanda ◽  
O. D. Makinde ◽  
Precious Sibanda
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Differential Equations ◽  
Surface Temperature ◽  
Viscoelastic Fluid ◽  
Fourth Order ◽  
Linearization Method ◽  
Similarity Transformations ◽  
Fluid Properties ◽  
Successive Linearization Method

We study natural convection from a downward pointing cone in a viscoelastic fluid embedded in a porous medium. The fluid properties are numerically computed for different viscoelastic, porosity, Prandtl and Eckert numbers. The governing partial differential equations are converted to a system of fourth order ordinary differential equations using the similarity transformations and then solved together by using the successive linearization method (SLM). Many studies have been carried out on natural convection from a cone but they did not consider a cone embedded in a porous medium with linear surface temperature. The results in this work are validated by the comparison with other authors.

Dissipative effects on a chemically and thermally radiative heat fluid flow past a shrinking porous sheet

2020 ◽  
pp. 1-14
Author(s):  
A. Shahid ◽  
M. Ali Abbas ◽  
H.L. Huang ◽  
S.R. Mishra ◽  
M.M. Bhatti
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Linearization Method ◽  
Surface Drag ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Dissipative Effects ◽  
Successive Linearization Method

The present study analyses the dissipative influence into an unsteady electrically conducting fluid flow embedded in a pervious medium over a shrinkable sheet. The behavior of thermal radiation and chemical reactions are also contemplated. The governing partial differential equations are reformed to ordinary differential equations by operating similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the Successive linearization method (SLM) via Matlab software. The velocity, temperature, and concentration magnitudes for distant values of the governing parametric quantities are conferred, and their conduct is debated via graphical curves. The surface drag coefficient increases, whereas the local Nusselt number and Sherwood number decreases for enhancing unsteadiness parameter across suction parameter. Moreover, the magnetic and suction parameters accelerate velocity magnitudes while by raising porosity parameter, velocity decelerates. Larger numeric of thermal radiation parameter and Eckert number accelerates the temperature profile while by enhancing Prandtl number it decelerates. Schmidt number and chemical reaction parameters slowdowns the concentration distribution, and the chemical reaction parameter influences on the point of chemical reaction that benefits the interface mass transfer. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities.

BIOCONVECTION IN A NON-DARCY POROUS MEDIUM SATURATED WITH A NANOFLUID AND OXYTACTIC MICRO-ORGANISMS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450005 ◽  
Author(s):  
S. SHAW ◽  
P. K. KAMESWARAN ◽  
M. NARAYANA ◽  
P. SIBANDA
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Horizontal Plate ◽  
Nanoparticle Concentration ◽  
Transfer Rates ◽  
Similarity Transformations ◽  
Fluid Properties ◽  
Layer Flow ◽  
Micro Organisms

The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bioconvection and mixed convection on the steady boundary layer flow past a horizontal plate embedded in a porous medium filled with a water-based nanofluid. The governing partial differential equations for momentum, heat, oxygen and micro-organism conservation are reduced to a set of nonlinear ordinary differential equations using similarity transformations that are numerically solved using a built-in MATLAB ODE solver. The effects of the bioconvection parameters on the nanofluid fluid properties, nanoparticle concentration and the density of the micro-organism are analyzed. A comparative analysis of our results with those previously reported in the literature is given. Among the significant findings in this study is that bioconvection parameters highly influence heat, mass and motile micro-organism transfer rates.

scholarly journals The Effectiveness of Mass Transfer in the MHD Upper-Convected Maxwell Fluid Flow on a Stretched Porous Sheet near Stagnation Point: A Numerical Investigation

Inventions ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 64
Author(s):  
Anwar Shahid
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Maxwell Fluid ◽  
Linearization Method ◽  
The Novel ◽  
Governing Equations ◽  
Similarity Transformations ◽  
Successive Linearization Method ◽  
Linear Boundary Value Problem

The present inquiry studies the influence of mass transfer in magnetohydrodynamics (MHD) upper-convected Maxwell (UCM) fluid flow on a stretchable, porous subsurface. The governing partial differential equations for the flow problem are reformed to ordinary differential equations through similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the successive linearization method (SLM) via Matlab software. The accuracy of the SLM is confirmed through known methods, and convergence analysis is also presented. The graphical behavior for all the parametric quantities in the governing equations across the velocity and concentration magnitudes, as well as the skin friction and Sherwood number, is presented and debated in detail. A comparability inquiry of the novel proposed technique, along with the preceding explored literature, is also provided. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities and correlate with the prevailing literature.

Mixed convection over an inclined wavy surface embedded in a nanofluid saturated porous medium

2015 ◽  
Vol 25 (8) ◽  
pp. 1774-1792 ◽  
Author(s):  
D. Srinivasacharya ◽  
P. Vijay Kumar
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Mixed Convection ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Linearization Method ◽  
Wavy Surface ◽  
Content Type ◽  
Successive Linearization Method ◽  
Pseudo Spectral Method

Purpose – The purpose of this paper is to study the mixed convection in a nanofluid along an inclined wavy surface embedded in a porous medium. Design/methodology/approach – The complex wavy surface is transformed to a smooth surface by employing a coordinate transformation. Using the similarity transformation, the governing equations are transformed into a set of ordinary differential equations and then lineralized using the successive linearization method. The Chebyshev pseudo spectral method is then used to solve linearized differential equations. Findings – The effects of Brownian motion parameter, thermophoresis parameter, amplitude of the wavy surface, angle of inclination of the wavy surface for aiding and opposing flows on the non-dimensional velocity, temperature, nanoparticle volume fraction, heat and nanoparticle mass transfer rates are studied and presented graphically. Originality/value – This is the first instance in which mixed convection, inclined wavy surface and nanofluid is employed to model fluid flow.

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 The Effects of Chemical Reaction, Hall, and Ion-Slip Currents on MHD Micropolar Fluid Flow with Thermal Diffusivity Using a Novel Numerical Technique

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Fluid Flow ◽  
Thermal Diffusivity ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chemical Reaction ◽  
Numerical Technique ◽  
Linearization Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Successive Linearization Method ◽  
Ion Slip

The problem of magnetomicropolar fluid flow, heat, and mass transfer with suction through a porous medium is numerically analyzed. The problem was studied under the effects of chemical reaction, Hall, ion-slip currents, and variable thermal diffusivity. The governing fundamental conservation equations of mass, momentum, angular momentum, energy, and concentration are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is the then solved using a fairly new technique known as the successive linearization method together with the Chebyshev collocation method. A parametric study illustrating the influence of the magnetic strength, Hall and ion-slip currents, Eckert number, chemical reaction and permeability on the Nusselt and Sherwood numbers, skin friction coefficients, velocities, temperature, and concentration was carried out.

scholarly journals Insights into the Generalized Fourier's and Fick's Laws for Simulating Mixed Bioconvective Flows of Radiative-Reactive Walters-B Fluids Conveying Tiny Particles subject to Lorentz Force

2021 ◽  
Author(s):  
A. Wakif ◽  
I. L. Animasaun ◽  
Umair Khan ◽  
Ahmed Mohammed Alshehri
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Computational Cost ◽  
Energy Parameter ◽  
Linearization Method ◽  
Surface Drag ◽  
Force Coefficient ◽  
Buongiorno’S Model ◽  
Similarity Transformations ◽  
Nanoparticles Concentration

Abstract The current improvement in nanoscience and nanotechnology areas has attracted researchers' attention to biofuel, bioengineering, and biomedical and mechanical engineering applications. However, there is no report on the extension of Buongiorno's model incorporating the Cattaneo-Christov theory and the generalized Fick's law to reflect the significant impacts of Brownian motion, thermophoresis diffusion, thermal radiation, and activation energy. The governing partial differential equations (PDEs) suitable to model the case as mentioned above were converted into a unified set of ordinary differential equations (ODEs) by applying appropriate similarity transformations and solved numerically by using the Spectral Local Linearization Method (SLLM) and MATLAB in-built package. The SLLM numerical method provides robustness results with a higher level of exactness and low‐computational cost. It is worthy to conclude that the nanoparticles concentration distribution can be heightened considerably either by diminishing the Prandtl number and concentration relaxation parameter or increasing the values of nanoparticles concentration Biot number and activation energy parameter. An attractive reduction in the surface drag force coefficient is achievable via the intensifying values of the non-Newtonian parameter.

Radiation and heat source effects on MHD flow over a permeable stretching sheet through porous stratum with chemical reaction

2018 ◽  
Vol 14 (5) ◽  
pp. 1101-1114 ◽  
Author(s):  
K. Suneetha ◽  
S.M. Ibrahim ◽  
G.V. Ramana Reddy
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Working Fluid ◽  
Content Type ◽  
Source Effects ◽  
Similarity Transformations

Purpose The purpose of this paper is to investigate the steady 2D buoyancy effects on MHD flow over a permeable stretching sheet through porous medium in the presence of suction/injection. Design/methodology/approach Similarity transformations are employed to transform the governing partial differential equations into ordinary differential equations. The transformed equations are then solved numerically by a shooting technique. Findings The working fluid is examined for several sundry parameters graphically and in tabular form. It is observed that with an increase in magnetic field and permeability of porous parameter, velocity profile decreases while temperature and concentration enhances. Stretching sheet parameter reduces velocity, temperature and concentration, whereas it increases skin friction factor, Nusselt number and Sherwood number. Originality/value Till now no numerical studies are reported on the effects of heat source and thermal radiation on MHD flow over a permeable stretching sheet embedded in porous medium in the presence of chemical reaction.

scholarly journals On the Successive Linearisation Approach to the Flow of Reactive Third-Grade Liquid in a Channel with Isothermal Walls

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
S. S. Motsa ◽  
O. D. Makinde ◽  
S. Shateyi
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Linearization Method ◽  
Third Grade ◽  
Efficient Technique ◽  
Analytical Scheme ◽  
Highly Nonlinear ◽  
Successive Linearization Method ◽  
Modeling Flow

The nonlinear differential equations modeling flow of a reactive third-grade liquid between two parallel isothermal plates is investigated using a novel hybrid of numerical-analytical scheme known as the successive linearization method (SLM). Numerical and graphical results obtained show excellence in agreement with the earlier results reported in the literature. A comparison with numerical results generated using the inbuilt MATLAB boundary value solverbvp4cdemonstrates that the new SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper.

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