scholarly journals Magnetohydrodynamic flow of nanofluid over permeable stretching sheet with convective boundary conditions

2016 ◽  
Vol 20 (6) ◽  
pp. 1835-1845 ◽  
Author(s):  
Tasawar Hayat ◽  
Maria Imtiaz ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Mass Transfer Process ◽  
Convergent Series ◽  
Convective Boundary ◽  
Layer Flow ◽  
Type Boundary ◽  
Mhd Boundary Layer Flow

Analysis has been carried out for the magnetohydrodynamic (MHD) boundary layer flow of nanofluid. The flow is caused by a permeable stretching sheet. Convective type boundary conditions are employed in modeling the heat and mass transfer process. Appropriate transformations reduce the nonlinear partial differential equations to ordinary differential equations. The convergent series solutions are constructed. Graphical results of different parameters are discussed. The behaviors of Brownian motion and thermophoretic diffusion of nanoparticles have been examined. The dimensionless expressions of local Nusselt and local Sherwood numbers have been evaluated and discussed.

scholarly journals Finite Element Simulation of Multi-Slip Effects on Unsteady MHD Bioconvective Micropolar Nanofluid Flow Over a Sheet with Solutal and Thermal Convective Boundary Conditions

Coatings ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 842 ◽  
Author(s):  
Liaqat Ali ◽  
Xiaomin Liu ◽  
Bagh Ali ◽  
Saima Mujeed ◽  
Sohaib Abdal
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fluid Velocity ◽  
Mesh Size ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Micropolar Nanofluid ◽  
Layer Flow ◽  
Buoyancy Ratio

In this article, the intention is to explore the flow of a magneto-hydrodynamic (MHD) bioconvective micro-polar Nanofluid restraining microorganism. The numerical solution of 2-D laminar bioconvective boundary layer flow of micro-polar nanofluids are presented. The phenomena of multi-slip, convective thermal and Solutal boundary conditions have been integrated. A system of non-linear partial differential equations are transformed into the system of coupled nonlinear ordinary differential equations by applying appropriate transformations, the transformed equations are then solved by applying the variational finite element method (FEM). The fascinating features of assorted velocity parameter, microrotation, temperature, microorganism compactness, solutal and nanoparticles concentration have been inspected. The rate of heat transfer, the skin friction coefficient, couple stress and Sherwood number for microorganisms have also been discussed graphically and numerically. The investigations illustrated that increase in material parameters causes a reduction in microorganism compactness, concentration and temperature. As a result of enhancement in the unsteadiness parameter, the fluid velocity, concentration of microorganisms and the temperature are observed to be declines. Energy and microorganism compactness profile affected by the improvement in the buoyancy ratio parameter. As the improvement in results of buoyancy ratio parameter effects on improvement in the energy and the microorganism compactness profile while the velocity profile is condensed. In the end, rationalized convergence of the finite element solution has been inspected; the computations are found out via depreciating the mesh size.

scholarly journals On Convective Dusty Flow Past a Vertical Stretching Sheet with Internal Heat Absorption

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Raj Nandkeolyar ◽  
Precious Sibanda
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Internal Heat ◽  
Transverse Magnetic ◽  
Convective Heating ◽  
Joule Dissipation ◽  
Highly Nonlinear ◽  
Layer Flow

The steady two-dimensional boundary layer flow of a viscous, incompressible, and electrically conducting dusty fluid past a vertical permeable stretching sheet under the influence of a transverse magnetic field with the viscous and Joule dissipation is investigated. The fluid particles are assumed to be heat absorbing and the temperature at the surface of the sheet is a result of convective heating. The governing nonlinear partial differential equations are transformed to a set of highly nonlinear coupled ordinary differential equations using a suitable similarity transformation and the resulting system is then solved numerically. It is found inter alia that the contributions of viscous and Joule dissipation in the flow are to increase the thickness of the thermal boundary layer.

Flow Over a Stretching Sheet in a Dusty Fluid With Radiation Effect

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
G. K. Ramesh ◽  
B. J. Gireesha
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Radiation Effect ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Particle Interaction ◽  
Dusty Fluid ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Fifth Order

The radiation effect on a steady two-dimensional boundary layer flow of a dusty fluid over a stretching sheet is analyzed. The governing nonlinear partial differential equations have been transformed by a similarity transformation into a system of nonlinear ordinary differential equations and then solved numerically by applying Runge Kutta Fehlberg fourth-fifth order method (RKF45 method). The effect of fluid particle interaction parameter, Prandtl number, Eckert number, and radiation parameter on heat transfer characteristics in two different general cases, namely (1) the prescribed surface temperature (PST) and (2) the prescribed heat flux (PHF) are presented graphically and discussed. The rate of heat transfer is computed and tabulated for various values of the different parameters. Comparison of the obtained numerical results is made with previously published results.

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.

scholarly journals MHD Boundary Layer Flow over a Stretching Sheet: A New Stochastic Method

2021 ◽  
Vol 2021 ◽  
pp. 1-26
Author(s):  
Hakeem Ullah ◽  
Imran Khan ◽  
Mehreen Fiza ◽  
Nawaf N. Hamadneh ◽  
M. Fayz-Al-Asad ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Industrial Applications ◽  
Deborah Number ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

In this study, a new computing model is developed using the strength of feed-forward neural networks with the Levenberg–Marquardt scheme-based backpropagation technique (NN-BLMS). It is used to find a solution for the nonlinear system obtained from the governing equations of the magnetohydrodyanmic (MHD) boundary layer flow over a stretching sheet. Moreover, the partial differential equations (PDEs) for the MHD boundary layer flow over a stretching sheet are converting into ordinary differential equations (ODEs) with the help of similarity transformation. A dataset for the proposed NN-BLMM-based model is generated at different scenarios by a variation of various embedding parameters: Deborah number β and magnetic parameter (M). The training (TR), testing (TS), and validation (VD) of the NN-BLMS model are evaluated in the generated scenarios to compare the obtained results with the reference results. For the fluidic system convergence analysis, a number of metrics, such as the mean square error (MSE), error histogram (EH), and regression (RG) plots, are utilized for measuring the effectiveness and performance of the NN-BLMS infrastructure model. The experiments showed that comparisons between the results of proposed model and the reference results match in terms of convergence up to E-02 to E-10. This proves the validity of the NN-BLMS model. Furthermore, the results demonstrated that there is a decrease in the thickness of the boundary layer by increasing the Deborah number and magnetic parameter. The importance of the experiment can be seen due to its industrial applications such as MHD power generation, MHD generators, and MHD pumps.

scholarly journals Influence of Thermal Radiation on Magnetohydrodynamic (MHD) Boundary Layer Flow of a Viscous Fluid Over an Exponentially Stretching Sheet

2016 ◽  
Vol 21 (3) ◽  
pp. 581-592 ◽  
Author(s):  
A.S. Idowu ◽  
S. Usman
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Exponentially Stretching Sheet ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Exponentially Stretching ◽  
Mhd Boundary Layer Flow

Abstract Radiation on a magnetohydrodynamic (MHD) boundary layer flow of a viscous fluid over an exponentially stretching sheet was considered together with its effects. The new technique of homotopy analysis method (nHAM) was used to obtain the convergent series expressions for velocity and temperature, where the governig system of partial differential equations was transformed into ordinary differential equations. The interpretation of these expressions is shown physically through graphs. We observed that the effects of the Prandtl and magnetic number act in opposite to each other on the temperature.

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