scholarly journals Computational optimization for the deposition of bioconvection thin Oldroyd-B nanofluid with entropy generation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Auwalu Hamisu Usman ◽  
Noor Saeed Khan ◽  
Usa Wannasingha Humphries ◽  
Zafar Ullah ◽  
Qayyum Shah ◽  
...  
Keyword(s):  
Energy Parameter ◽  
Reynolds Numbers ◽  
Gyrotactic Microorganisms ◽  
Computational Optimization ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Spray Rate ◽  
Flow Similarity ◽  
Gyrotactic Microorganism ◽  
Transfer Flow

AbstractThe behavior of an Oldroyd-B nanoliquid film sprayed on a stretching cylinder is investigated. The system also contains gyrotactic microorganisms with heat and mass transfer flow. Similarity transformations are used to make the governing equations non-dimensional ordinary differential equations and subsequently are solved through an efficient and powerful analytic technique namely homotopy analysis method (HAM). The roles of all dimensionless profiles and spray rate have been investigated. Velocity decreases with the magnetic field strength and Oldroyd-B nanofluid parameter. Temperature is increased with increasing the Brownian motion parameter while it is decreased with the increasing values of Prandtl and Reynolds numbers. Nanoparticle’s concentration is enhanced with the higher values of Reynolds number and activation energy parameter. Gyrotactic microorganism density increases with bioconvection Rayleigh number while it decreases with Peclet number. The film size naturally increases with the spray rate in a nonlinear way. A close agreement is achieved by comparing the present results with the published results.

scholarly journals Magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abdullah Dawar ◽  
Zahir Shah ◽  
Hashim M. Alshehri ◽  
Saeed Islam ◽  
Poom Kumam
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Lewis Number ◽  
Casson Fluid ◽  
Stretching Cylinder ◽  
Concentration Difference ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Homotopy Analysis

AbstractThis study presents the magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder. The mathematical modeling is presented in the form of partial differential equations and then transformed into ordinary differential equations (ODEs) utilizing suitable similarity transformations. The analytical solution of the transformed ODEs is presented with the help of homotopy analysis method (HAM). The convergence analysis of HAM is also presented by mean of figure. The present analysis consists of five phases. In the first four phases, we have compared our work with previously published investigations while phase five is consists of our new results. The influences of dimensionless factors like a magnetic parameter, thermal radiation, curvature parameter, Prandtl number, Brownian motion parameter, Schmidt number, heat generation, chemical reaction parameter, thermophoresis parameter, Eckert number, and concentration difference parameter on physical quantities of interests and flow profiles are shown through tables and figures. It has been established that with the increasing Casson parameter (i.e. $$\beta \to \infty$$ β → ∞ ), the streamlines become denser which results the increasing behavior in the fluid velocity while on the other hand, the fluid velocity reduces for the existence of Casson parameter (i.e. $$\beta = 1.0$$ β = 1.0 ). Also, the streamlines of stagnation point Casson fluid flow are highly wider for the case of magnetized fluid as equated to non-magnetized fluid. The higher values of bioconvection Lewis number, Peclet number, and microorganisms’ concentration difference parameter reduces the motile density function of microorganisms while an opposite behavior is depicted against density number.

scholarly journals Bioconvection heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2347-2356 ◽  
Author(s):  
Bingyu Shen ◽  
Liancun Zheng ◽  
Chaoli Zhang ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Stretching Sheet ◽  
Temperature Jump ◽  
Lewis Number ◽  
Velocity Slip ◽  
Analysis Method ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Effects Of Radiation

This paper presents an investigation for bioconvection heat transfer of a nanofluid containing gyrotactic microorganisms over a stretching sheet, in which the effects of radiation, velocity slip, and temperature jump are taken into account. The non-linear governing equations are reduced into four ordinary differential equations by similarity transformations and solved by homotopy analysis method, which is verified with numerical results in good agree. Results indicate that the density of motile microorganisms and gyrotactic microorganisms increase with bioconvection Rayleigh number, while decrease with increasing in bioconvection Peclet number and bioconvection Lewis number. It is also found that the Nusselt number, Sherwood number, and gyrotactic microorganisms density depend strongly on the buoyancy, nanofluids, and bioconvection parameters.

scholarly journals Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402093046 ◽  
Author(s):  
Noor Saeed Khan ◽  
Qayyum Shah ◽  
Arif Sohail
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Mass Flux ◽  
Homotopy Analysis Method ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Transfer Flow ◽  
Insight Into

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.

scholarly journals Explicit Solutions of a Gravity-Induced Film Flow along a Convectively Heated Vertical Wall

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ammarah Raees ◽  
Hang Xu
Keyword(s):  
Film Flow ◽  
Vertical Wall ◽  
Boussinesq Approximation ◽  
Convective Boundary Condition ◽  
Convective Boundary ◽  
Similarity Transformations ◽  
Reduced Equations ◽  
Homotopy Analysis ◽  
Gravity Driven ◽  
The Mathematical Model

The gravity-driven film flow has been analyzed along a vertical wall subjected to a convective boundary condition. The Boussinesq approximation is applied to simplify the buoyancy term, and similarity transformations are used on the mathematical model of the problem under consideration, to obtain a set of coupled ordinary differential equations. Then the reduced equations are solved explicitly by using homotopy analysis method (HAM). The resulting solutions are investigated for heat transfer effects on velocity and temperature profiles.

scholarly journals Unsteady flow over an expanding cylinder in a nanofluid containing gyrotactic microorganisms

2016 ◽  
Vol 94 (5) ◽  
pp. 466-473 ◽  
Author(s):  
Hui Chen ◽  
Hongxing Liang ◽  
Tianli Xiao ◽  
Heng Du ◽  
Ming Shen
Keyword(s):  
Differential Equations ◽  
Unsteady Flow ◽  
Shooting Method ◽  
Schmidt Number ◽  
Volume Fraction ◽  
Dual Solutions ◽  
Physical Parameters ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Fifth Order

In this paper, an analysis is made for the unsteady flow due to an expanding cylinder in a nanofluid that contains both nanoparticles and gyrotactic microoganisms with suction. The nonlinear system of partial differential equations is transformed into high-order nonlinear ordinary differential equations using similarity transformations, and then solved numerically using a shooting method with fourth-fifth-order Runge–Kutta integration technique. The influences of significant physical parameters on the distributions of the velocity, temperature, nanoparticle volume fraction, as well as the density of motile microorganisms are graphically presented and discussed in detail. It is found that dual solutions exist for both stretching and shrinking cases and the range of dual solutions increases with the strength of the expansion. The results also indicate that larger bioconvection Peclet number and smaller Schmidt number lead to an increased concentration of microorganisms and thicker boundary layer thickness.

Radiation and Partial Slip Effects on Magnetohydrodynamic Jeffrey Nanofluid Containing Gyrotactic Microorganisms Over a Stretching Surface

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
K. Kumaraswamy Naidu ◽  
D. Harish Babu ◽  
S. Harinath Reddy ◽  
P. V. Satya Narayana
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Coupled System ◽  
Partial Slip ◽  
Stretching Surface ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Jeffrey Nanofluid ◽  
The Impact

Abstract In this study, the impact of thermal radiation and partial slip on magnetohydrodynamic flow of the Jeffrey nanofluid comprising motile gyrotactic microorganisms via vertical stretching surface is analyzed. The governing partial differential equations are reformed to a system of coupled ordinary differential equations by utilizing the similarity transformations. The transformed equations are of order four, which are complex to solve analytically and hence, the coupled system is solved computationally by using the shooting technique along the Runge–Kutta integrated scheme. The ramifications of different thermophysical parameters on the density of gyrotactic microorganisms, Jeffrey nanofluid velocity, nanoparticles concentration, temperature, Sherwood number, and Nusselt number are illustrated graphically. Comparing this study with the results already published favors the validity of this study. It is established that the Nusselt number is boosted on enhancing the thermal radiation parameter, and the reverse trend has been observed on increasing the Richardson number, whereas the gyrotactic microorganisms density is more in case of viscous nanofluid compared to the Jeffrey nanofluid.

scholarly journals Axisymmetric Stagnation Flow of a Micropolar Nanofluid in a Moving Cylinder

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
S. Nadeem ◽  
Abdul Rehman ◽  
K. Vajravelu ◽  
Jinho Lee ◽  
Changhoon Lee
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Flow ◽  
Finite Radius ◽  
Similarity Transformations ◽  
Moving Cylinder ◽  
Micropolar Nanofluid ◽  
Homotopy Analysis ◽  
Flow Phenomena

An analysis is carried out for axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder with finite radius. The coupled nonlinear partial differential equations of the problem are simplified with the help of similarity transformations and the resulting coupled nonlinear differential equations are solved analytically by homotopy analysis method (HAM). The features of the flow phenomena, inertia, heat transfer, and nanoparticles are analyzed and discussed.

Stagnation Flow of a Jeffrey Fluid over a Shrinking Sheet

2010 ◽  
Vol 65 (6-7) ◽  
pp. 540-548 ◽  
Author(s):  
Sohail Nadeem ◽  
Anwar Hussain ◽  
Majid K
Keyword(s):  
Jeffrey Fluid ◽  
Shrinking Sheet ◽  
Series Solutions ◽  
Analysis Method ◽  
Governing Equations ◽  
Stagnation Flow ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Equations Of Motions

January 22, 2009 The present paper describes the analytical solutions for the steady boundary layer flow of a Jeffrey fluid over a shrinking sheet. The governing equations of motions are reduced into a set of nonlinear ordinary differential equations by using similarity transformations. Two types of problems, namely, (1) two-dimensional stagnation flow towards a shrinking sheet and (2) axisymmetric stagnation flow towards an axisymmetric shrinking sheet, have been discussed. The series solutions of the problems are obtained by using the homotopy analysis method (HAM). The convergence of the obtained series solutions are analyzed and discussed in detail through graphs for various parameters of interest.

scholarly journals Flow and Heat Transfer in a Liquid Film over a Permeable Stretching Sheet

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
R. C. Aziz ◽  
I. Hashim ◽  
A. K. Alomari
Keyword(s):  
Heat Transfer ◽  
Liquid Film ◽  
Stretching Sheet ◽  
Temperature Fields ◽  
Temperature Profiles ◽  
Suction Parameter ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

An analysis has been carried out to study the flow and heat transfer in a liquid film over a permeable stretching sheet. Using similarity transformations, the time-dependent boundary layer equations are reduced to a set of nonlinear ordinary differential equations. The resulting parameter problem and velocity as well as temperature fields are solved using the homotopy analysis method (HAM). Analytic series solutions are given, and numerical results for velocity and the temperature profiles are presented through graphs of different values for pertinent parameter. The effects of unsteadiness parameter and permeability parameter on the velocity and temperature profiles are explored for different values of blowing or suction parameter.

Unsteady Flow of Third Grade Fluid With Soret and Dufour Effects

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
T. Hayat ◽  
M. Awais ◽  
S. Asghar ◽  
S. Obaidat
Keyword(s):  
Unsteady Flow ◽  
Temperature Fields ◽  
Third Grade ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Soret And Dufour Effects ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Homotopy Analysis ◽  
Grade Fluid

Unsteady flow of a third grade fluid in the presence of Soret and Dufour effects is considered. Employing similarity transformations, the governing equation for the velocity, concentration, and temperature fields is presented. The computations for the corresponding problems are performed by using a homotopy analysis method (HAM). The associated behavior of the flow parameters is discussed and important conclusions have been pointed out.

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