scholarly journals On Generalized Fourier’s and Fick’s Laws in Bio-Convection Flow of Magnetized Burgers’ Nanofluid Utilizing Motile Microorganisms

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1186
Author(s):  
Ali Saleh Alshomrani
Keyword(s):  
Temperature Field ◽  
Differential Equations ◽  
Biot Number ◽  
Control Structure ◽  
Convection Flow ◽  
Physical Parameters ◽  
Graphical Data ◽  
Fluid Parameter ◽  
Burgers Fluid ◽  
Nanoparticles Concentration

This article describes the features of bio-convection and motile microorganisms in magnetized Burgers’ nanoliquid flows by stretchable sheet. Theory of Cattaneo–Christov mass and heat diffusions is also discussed. The Buongiorno phenomenon for nanoliquid motion in a Burgers’ fluid is employed in view of the Cattaneo–Christov relation. The control structure of governing partial differential equations (PDEs) is changed into appropriate ordinary differential equations (ODEs) by suitable transformations. To get numerical results of nonlinear systems, the bvp4c solver provided in the commercial software MATLAB is employed. Numerical and graphical data for velocity, temperature, nanoparticles concentration and microorganism profiles are obtained by considering various estimations of prominent physical parameters. Our computations depict that the temperature field has direct relation with the thermal Biot number and Burgers’ fluid parameter. Here, temperature field is enhanced for growing estimations of thermal Biot number and Burgers’ fluid parameter.

scholarly journals Thermal radiation and magnetic field effects on unsteady mixed convection flow and mass transfer over a porous stretching surface with heat generation

2013 ◽  
Vol 18 (4) ◽  
pp. 1151-1164 ◽  
Author(s):  
G.V.R. Reddy ◽  
B.A. Reddy ◽  
N.B. Reddy
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Convection Flow ◽  
Physical Parameters ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Porous Stretching Surface

Abstract The effects of thermal radiation and mass transfer on an unsteady hydromagnetic boundary layer mixed convection flow along a vertical porous stretching surface with heat generation are studied. The fluid is assumed to be viscous and incompressible. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables. Numerical solutions of these equations are obtained by using the Runge-Kutta fourth order method along with the shooting technique. Velocity, temperature, concentration, the skin-friction coefficient, Nusselt number and Sherwood number for variations in the governing thermo physical parameters are computed, analyzed and discussed.

Mixed Convection Boundary Layer Flow of Williamson Fluid with Slip Conditions Over a Stretching Cylinder by Using Keller Box Method

2017 ◽  
Vol 18 (1) ◽  
pp. 9-17 ◽  
Author(s):  
T. Salahuddin ◽  
M. Y. Malik ◽  
Arif Hussain ◽  
M. Awais ◽  
S. Bilal
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Ordinary Differential Equations ◽  
Convection Flow ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Williamson Fluid ◽  
Keller Box Method ◽  
Box Method

AbstractThe aim of the present analysis is to examine the effects of slip boundary conditions and mixed convection flow of Williamson fluid over a stretching cylinder. The boundary layer partial differential equations are transformed into ordinary differential equations by using group theory transformations. The required ordinary differential equations are solved numerically by using implicit finite difference method known as Keller box method. The influence of dimensionless physical parameters on velocity and temperature profile as well as skin friction coefficient and local Nusselt number are presented graphically. Comparison has been made to the previous literature in order to check the accuracy of the method.

scholarly journals Effects of Non-Darcy Mixed Convection Over a Horizontal Cone With Different Convective Boundary Conditions Incorporating Gyrotactic Microorganisms On Dispersion

2021 ◽  
Author(s):  
M. Ferdows ◽  
Bader Alshuraiaan ◽  
Nayema Islam Nima
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Biot Number ◽  
Nonlinear Partial Differential Equations ◽  
Convection Flow ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Similarity Transformations ◽  
Strong Conclusion

Abstract This paper discusses an investigation of the influence of dispersion impact on mixed convection flow over a horizontal cone within a non-Darcy porous medium subjected to convective boundary conditions. By imposing appropriate similarity transformations, the nonlinear partial differential equations governing flow, temperature, concentration, and microbe fields are reduced to a system of ordinary differential equations, which are then solved using the MATLAB BVP4C function. In a few circumstances, the research is brought to a strong conclusion by comparing the findings of the current study to previously published works. Mixed convection parameter λ, buoyancy parameters N1,N2, Lewis parameter Le, bioconvection lewis parameter Lb, Bioconvection peclet number Pe, Biot number Bi, Biot number of Mass transfer Bi,m and also Biot number of motile microorganism transfer Bi,n are all numerically calculated for various values of the dimensionless parameters of the problem. The results also reveal that, in the presence of dispersion effects, these parameters greatly influence the heat, mass, and motile microorganism transfer rates, as well as the corresponding velocity, temperature, concentration, and motile microorganism profiles.

Fluid relaxation and retardation time properties in the flow of Burgers fluid subject to modified heat and mass flux theory

2021 ◽  
pp. 095440892110670
Author(s):  
Zahoor Iqbal ◽  
Awais Ahmed ◽  
Amina Anwar ◽  
Sivanandam Sivasankaran ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Flow Problem ◽  
Fluid Motion ◽  
Retardation Time ◽  
Linear Ordinary Differential Equations ◽  
Fluid Parameter ◽  
Burgers Fluid ◽  
Time Parameters ◽  
The Impact

In this study, the heat transport is scrutinized in the flow of magnetized Burgers fluid accelerated by stretching cylinder. Rather than, classical Fourier's and Fick's laws, the Cattaneo-Christov theory featuring the improved heat and mass conduction is utilized to investigate the energy transport. Further, the transport of thermal and solutal energy is controlled by the significant influence of heat generation/absorption and chemical reaction. The physical flow problem is modelled in the form of partial differential equations (PDEs) which are then transformed into the non-linear ordinary differential equations (ODEs) by invoking appropriate similarity variables. The numerical simulation to the system of ODE's is tackled by employing BVP-Midrich scheme in Maple. The numerical results for flow field, thermal and concentration distributions are exhibited graphically. The impact of fluid relaxation and retardation time parameters on the velocity field are observed in growing and decaying way, respectively. Both the thermal and solutal energy transport decline with higher values of retardation time parameter. The rise in Burgers fluid parameter enhances the transport of energy during the fluid motion. The effect of thermal and solutal relaxation time parameters on heat and mass transport in the fluid are noticed in the declining manner.

Simulation of nanofluid thermal radiation in Marangoni convection flow of non-Newtonian fluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2840-2853 ◽  
Author(s):  
Tasawar Hayat ◽  
Ikram Ullah ◽  
Muhammad Waqas ◽  
Ahmed Alsaedi
Keyword(s):  
Temperature Field ◽  
Heat Source ◽  
Thermal Radiation ◽  
Convective Flow ◽  
Design Methodology ◽  
Marangoni Convection ◽  
Convection Flow ◽  
Content Type ◽  
Nanoparticles Concentration ◽  
Exponential Space

Purpose The purpose of this study is to study the impacts of exponential space-dependent heat source (ESHS) and thermal radiation in Marangoni convective flow of Cross fluid. The passively controlled model is developed to exhibit the nanoparticles’ concentration on the surface. Design/methodology/approach The resulting problem under consideration is tackled by using the shooting approach. Findings Temperature field augments with enhancement of the thermophoretic, exponential-based space heat source (ESHS) and radiation parameters, whereas it decays with the increase of the Marangoni ratio parameter. Originality/value To the best of the authors’ knowledge, no such analysis has yet been reported.

scholarly journals A Numerical Exploration of Modified Second-Grade Nanofluid with Motile Microorganisms, Thermal Radiation, and Wu’s Slip

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 393 ◽  
Author(s):  
Yurong Li ◽  
Hassan Waqas ◽  
Muhammad Imran ◽  
Umar Farooq ◽  
Fouad Mallawi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Volume Fraction ◽  
Thermal Characteristics ◽  
Second Grade ◽  
Physical Parameters ◽  
Flux Boundary Condition ◽  
Shooting Technique ◽  
Automobile Engines ◽  
Nanoparticles Concentration

This study is carried out to scrutinize the gyrotactic bioconvection effects on modified second-grade nanofluid with motile microorganisms and Wu’s slip (second-order slip) features. The activation energy and thermal radiation are also incorporated. The suspended nanoparticles in a host fluid are practically utilized in numerous technological and industrial products such as metallic strips, energy enhancement, production processes, automobile engines, laptops, and accessories. Nanoparticles with high thermal characteristics and low volume fraction may improve the thermal performance of the base fluid. By employing the appropriate self-similar transformations, the governing set of partial differential equations (PDEs) are reduced into the ordinary differential equations (ODEs). A zero mass flux boundary condition is proposed for nanoparticle diffusion. Then, the transmuted set of ODEs is solved numerically with the help of the well-known shooting technique. The numerical and graphical illustrations are developed by using a collocation finite difference scheme and three-stage Lobatto III as the built-in function of the bvp4c solver via MATLAB. Behaviors of the different proficient physical parameters on the velocity field, temperature distribution, volumetric nanoparticles concentration profile, and the density of motile microorganism field are deliberated numerically as well as graphically.

scholarly journals Consequence of Heat Transfer on Free Convection Flow of Casson Fluid with Hall Effect

2019 ◽  
Vol 8 (10S) ◽  
pp. 90-95
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Free Convection ◽  
Hall Effect ◽  
Skin Friction ◽  
Casson Fluid ◽  
Temperature Fields ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Fluid Parameter

Effect of heat transfer on free convection flow of Casson fluid over a vertical plate with Hall effect has been studied. A similarity analysis method was used to transform the system of partial differential equations describing the problem into an ordinary differential equations, Analytical solutions are obtained by solving the ODE to analyze the velocity and temperature fields. Variations of interesting parameters on the velocity, heat transfer and skin friction are observed by plotting graphs. Further, it was concluded that the Casson fluid parameter and hall parameter has an retarding influence on velocity profile and also in the skin friction.

Chemical Reaction Effect on Forced Convection Flow of a Jeffery Fluid over a Stretching Sheet: A Numerical Study

2018 ◽  
Vol 16 ◽  
pp. 109-119
Author(s):  
A.K. Mishra ◽  
N. Senapati ◽  
S.R. Mishra ◽  
S. Bhattacharjee
Keyword(s):  
Differential Equations ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Numerical Study ◽  
Mhd Flow ◽  
Deborah Number ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Similarity Transformations

The purpose of this paper is to investigate steady two-dimensional laminar magnetohydrodynamic (MHD) flow of an incompressible Jeffrey fluid past over a linearly stretching sheet. The governing partial differential equations (PDEs) of continuity, momentum, energy and concentration are transformed into nonlinear coupled ordinary differential equations (ODEs) by using similarity transformations. Then the ODEs are solved by applying Runge-Kutta fourth order method accompanied with shooting technique. The effects of various physical parameters characterizing the flow phenomenon including Deborah number, ratio of relaxation to retardation times, magnetic parameter, porous parameter, Prandtl number, Eckert number, heat source / sink parameter, Schmidt number and chemical reaction parameter on dimensionless velocity, temperature and concentration profiles are analyzed. The numerical results are obtained and presented in graphs. The present results are compared with the earlier published results as a particular case.

scholarly journals Mathematical analysis of the flow and heat transfer of Ag-Cu hybrid nanofluid over a stretching/shrinking surface with convective boundary condition and viscous dissipation

2020 ◽  
Vol 1 (01) ◽  
pp. 11-22
Author(s):  
R. Jusoh ◽  
K. Naganthran ◽  
A. Jamaludin ◽  
M.H. Ariff ◽  
M.F.M. Basir ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Biot Number ◽  
Convective Boundary Condition ◽  
Hybrid Nanofluid ◽  
Convective Boundary ◽  
Nanoparticles Concentration ◽  
The Impact

Hybrid nanofluid has a vast potential of applications in the cooling system due to the high thermal conductivity. This study emphasizes on the impact of the convective boundary condition and viscous dissipation to the heat transfer of Ag-Cu hybrid nanofluid. A suitable similarity transformation is used to transform the partial differential equations of mass, momentum and energy into the ordinary differential equations. A finite difference code known as bvp4c in Matlab is employed to generate the numerical solutions. Stability analysis is conducted since dual solutions are generated in this study and the first solution exhibits the stability properties. The influence of variations in the suction parameter, viscous dissipation, nanoparticles concentration and Biot number on the on the temperature and velocity profiles of the hybrid nanofluid are portrayed. The rate of heat transfer is prominently higher with the augmentation of the Biot number and Ag nanoparticles concentration.

Flow and heat transfer of non-Newtonian power-law fluids over a stretching surface with variable thermal conductivity

2019 ◽  
Vol 15 (4) ◽  
pp. 686-698 ◽  
Author(s):  
Meng Yang ◽  
Yanhai Lin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Field ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Physical Parameters ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Power Law Fluids

Purpose The purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features. Design/methodology/approach The governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method. Findings As the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids. Originality/value Unlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

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