Bioconvection in Buoyancy Induced Flow of Williamson Nanofluid Over a Riga Plate-DTM-Padé Approach

2020 ◽  
Vol 9 (4) ◽  
pp. 269-281
Author(s):  
V. Puneeth ◽  
S. Manjunatha ◽  
B. J. Gireesha
Keyword(s):  
Group Analysis ◽  
Flow Speed ◽  
Transform Method ◽  
Gyrotactic Microorganisms ◽  
Buongiorno’S Model ◽  
Differential Transform ◽  
Riga Plate ◽  
Induced Flow ◽  
Agglomeration Of Nanoparticles ◽  
Buoyancy Induced Flow

The buoyancy induced flow of Williamson nanofluid containing Gyrotactic microorganisms along a vertical Riga plate has been investigated. This research aims at analysing the heat and mass transfer characteristics of Williamson Nanofluid in the presence of Gyrotactic microorganisms that helps in avoiding the agglomeration of nanoparticles during the nanofluid flow. The Gyrotactic microorganisms act as active mixers that help in stabilising the nanoparticles in the suspension. Also, the movement of these cells gives rise to a macro phenomenon called bioconvection that helps in preventing the agglomeration of nanoparticles. Furthermore, the magnetic field generated due to the flow of nanofluid is considered in addition to Thermophoresis and Brownian Motion to make the results more appropriate. Buongiorno’s Model has been incorporated to frame the system of equations that govern the fluid flow. Later, lie group analysis is performed to transform these equations into ordinary differential equations that are further solved using the differential transform method with Padé approximant. It is observed that the Lorentz force generated by the Riga plate in parallel to the flow helps in increasing the velocity of the nanofluid. It is also noticed that bioconvection reduces the flow speed and enhances the heat transfer rate.

scholarly journals Effects of Variable Transport Properties on Heat and Mass Transfer in MHD Bioconvective Nanofluid Rheology with Gyrotactic Microorganisms: Numerical Approach

Coatings ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 231
Author(s):  
Muhammad Awais ◽  
Saeed Ehsan Awan ◽  
Muhammad Asif Zahoor Raja ◽  
Nabeela Parveen ◽  
Wasim Ullah Khan ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Transport Properties ◽  
Heat And Mass Transfer ◽  
Group Analysis ◽  
Numerical Approach ◽  
Validity Of Results ◽  
Gyrotactic Microorganisms ◽  
Transfer Rates ◽  
Buongiorno’S Model ◽  
Density Distributions

Rheology of MHD bioconvective nanofluid containing motile microorganisms is inspected numerically in order to analyze heat and mass transfer characteristics. Bioconvection is implemented by combined effects of magnetic field and buoyancy force. Gyrotactic microorganisms enhance the heat and transfer as well as perk up the nanomaterials’ stability. Variable transport properties along with assisting and opposing flow situations are taken into account. The significant influences of thermophoresis and Brownian motion have also been taken by employing Buongiorno’s model of nanofluid. Lie group analysis approach is utilized in order to compute the absolute invariants for the system of differential equations, which are solved numerically using Adams-Bashforth technique. Validity of results is confirmed by performing error analysis. Graphical and numerical illustrations are prepared in order to get the physical insight of the considered analysis. It is observed that for controlling parameters corresponding to variable transport properties c2, c4, c6, and c8, the velocity, temperature, concentration, and bioconvection density distributions accelerates, respectively. While heat and mass transfer rates increases for convection parameter and bioconvection Rayleigh number, respectively.

NUMERICAL AND STABILITY ANALYSIS OF THE TRANSMISSION DYNAMICS OF SVIR EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE

2019 ◽  
Vol 4 (2) ◽  
pp. 349 ◽  
Author(s):  
Oluwatayo Michael Ogunmiloro ◽  
Fatima Ohunene Abedo ◽  
Hammed Kareem
Keyword(s):  
Reproduction Number ◽  
Disease Spread ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Transform Method ◽  
Globally Asymptotically Stable ◽  
Differential Transform ◽  
Mathematical Techniques ◽  
Fourth Order Method ◽  
Theoretical Results

In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results. 

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

scholarly journals A multi-step differential transform method and application to non-chaotic or chaotic systems

2010 ◽  
Vol 59 (4) ◽  
pp. 1462-1472 ◽  
Author(s):  
Zaid M. Odibat ◽  
Cyrille Bertelle ◽  
M.A. Aziz-Alaoui ◽  
Gérard H.E. Duchamp
Keyword(s):  
Chaotic Systems ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

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