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 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 Boundary layer flow of magneto-micropolar nanofluid flow with Hall and ion-slip effects using variable thermal diffusivity

2017 ◽  
Vol 65 (3) ◽  
pp. 383-390 ◽  
Author(s):  
M. Bilal ◽  
S. Hussain ◽  
M. Sagheer
Keyword(s):  
Thermal Diffusivity ◽  
Differential Equations ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Similarity Transformations ◽  
Slip Effects ◽  
Micropolar Nanofluid ◽  
Ion Slip ◽  
Layer Flow ◽  
Linear Differential

AbstractIn the present article, magneto-micropolar nanofluid flow with suction or injection in a porous medium over a stretching sheet for the heat and mass transfer is analyzed numerically. Both Hall and ion-slip effects are considered along with variable thermal diffusivity. The governing partial differential equations are transformed to ordinary differential equations using usual similarity transformations. These coupled non-linear differential equations are solved using the shooting method. Effects of prominent parameter on velocities, temperature and concentration are discussed graphically. Numerical values of skin-friction coefficient, local Nusselt number and local Sherwood number are also tabulated and discussed.

3D flow and heat transfer of micropolar fluid suspended with mixture of nanoparticles (Ag-CuO/H2O) driven by an exponentially stretching surface

2020 ◽  
Vol 16 (6) ◽  
pp. 1691-1707
Author(s):  
S. Manjunatha ◽  
B. Ammani Kuttan ◽  
G.K. Ramesh ◽  
B.J. Gireesha ◽  
Emad H. Aly
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Vertical Direction ◽  
Convective Boundary Condition ◽  
Moving Plate ◽  
Convective Boundary ◽  
Content Type ◽  
Similarity Transformations ◽  
Micropolar Nanofluid ◽  
Layer Flow

PurposeThe purpose of this paper is to discuss the 3D micropolar hybrid (Ag-CuO/H2O) nanofluid past rapid moving surface, where porous medium has been considered.Design/methodology/approachThe model of problem was represented by highly partial differential equations which were deduced by using suitable approximations (boundary layer). Then, the governing model was converted into five combined ordinary differential equations applying proper similarity transformations. Therefore, the eminent iterative Runge–Kutta–Fehlberg method (RKF45) has been applied to solve the resulting equations.FindingsHigher values of vortex viscosity, spin gradient viscosity and micro-inertia density parameters are reduced in horizontal direction, whereas opposite behaviour is noticed for vertical direction.Originality/valueThe work has not been done in the area of hybrid micropolar nanofluid. Hence, this article culminates to probe how to improve the thermal conduction and fluid flow in 3D boundary layer flow of micropolar mixture of nanoparticles driven by rapidly moving plate with convective boundary condition.

Impact of Convective Boundary Condition on Heat and Mass Transfer of Nanofluid Flow Over a Thin Needle Filled with Carbon Nanotubes

2020 ◽  
Vol 9 (4) ◽  
pp. 282-292
Author(s):  
P. Sreedevi ◽  
P. Sudarsana Reddy
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Finite Element Scheme ◽  
Convective Boundary ◽  
Non Linear ◽  
Layer Flow ◽  
Linear Differential

In the current study, we have scrutinized the sway of non-linear thermal radiation and Biot number on boundary layer flow along a continuously moving thin needle filled with carbon based nanotubes by considering water as regular fluid. The main system of partial differential equations is first reduced to the system of ordinary non-linear differential equations with the help of similarity conversion technique. The transmuted boundary layer ordinary differential equations are answered numerically by implementing Finite element scheme. The influence of pertinent constraints involved on heat, hydro-dynamic and solutal boundary layers are analysed in depth and the outcomes are revealed through plots. Moreover, the effect of these parameters on the values of Sherwood number, Nusselt number and skin-friction coefficient is also inspected and the results are exposed through tables. It is seen that velocity sketches depreciates with improving values of size of the needle parameter.

scholarly journals Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 74 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Umair Khan ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Numerical Comparison ◽  
Convective Boundary ◽  
Suction Parameter ◽  
Stress Coefficient ◽  
Micropolar Nanofluid

The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative).

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

scholarly journals Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1238 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stagnation Point ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Three Solutions ◽  
Convective Boundary ◽  
Suction Parameter ◽  
Stretching Surfaces ◽  
The Impact

In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.

Slip flow over a non-Newtonian fluid through a Darcy–Forchheimer medium: Numerical approach

2019 ◽  
Vol 33 (35) ◽  
pp. 1950448
Author(s):  
K. Ganesh Kumar ◽  
M. N. Khan ◽  
M. Osman ◽  
Abdulaziz R. Alharbi ◽  
Mohammad Rahimi-Gorji ◽  
...  
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Convective Boundary Condition ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Liquid Suspension

This work focused on slip flow over a non-Newtonian nanofluid fluid flow past a stretching sheet with particles–liquid suspension. The convective boundary condition is taken into account. Similarity transformations are utilized to reduce the nonlinear partial differential equations into a set of nonlinear ordinary differential equations. Runge–Kutta–Fehlberg scheme is used to get the numerical solution. Important parameters are analyzed through graphs and skin friction coefficient. Nusselt numbers are presented in tables. Investigation reveals that slip parameter decreases the velocity field and Biot number increases the temperature field.

scholarly journals A Study on Non-Newtonian Transport Phenomena in Mhd Fluid Flow From a Vertical Cone With Navier Slip and Convective Heating

2019 ◽  
Vol 8 (1) ◽  
pp. 534-545 ◽  
Author(s):  
CH. Amanulla ◽  
Abderrahim Wakif ◽  
Zoubair Boulahia ◽  
Syed Fazuruddin ◽  
S. Noor Mohammed
Keyword(s):  
Differential Equations ◽  
Transport Phenomena ◽  
Conductive Polymer ◽  
Convective Heating ◽  
Vertical Cone ◽  
Convective Boundary ◽  
Radial Magnetic Field ◽  
Navier Slip ◽  
Significant Acceleration ◽  
Layer Flow

Abstract In the current study is to examine numerically the effects of presence of a radial magnetic field, slip and jump conditions on the steady two-dimensional free convective boundary layer flow over an external surface of a vertical cone for an electro-conductive polymer. A proper non-similarity transformation simplifies the system of partial differential equations into a system of ordinary differential equations. The collocation formula in the MATLAB software then solves the system of non-similarity equations. The finding results show that, a weak elevation in temperature is accompanied with the increase in the Carreau fluid parameter, whereas a significant acceleration in the flow is computed near the cone surface. The study is relevant to smart coating transport phenomena.

Existence of Dual Solutions and Melting Phenomenon in Unsteady Nanofluid Flow and Heat Transfer over a Stretching Surface

2019 ◽  
Vol 35 (5) ◽  
pp. 705-717
Author(s):  
S. Ghosh ◽  
S. Mukhopadhyay ◽  
K. Vajravelu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Stretching Surface ◽  
Melting Phenomenon ◽  
Runge Kutta Method ◽  
Layer Flow

ABSTRACTThe problem of unsteady boundary layer flow of a nanofluid over a stretching surface is studied. Heat transfer due to melting is analyzed. Using a similarity transformation the governing coupled nonlinear partial differential equations of the model are reduced to a system of nonlinear ordinary differential equations, and then solved numerically by a Runge-Kutta method with a shooting technique. Dual solutions are observed numerically and their characteristics are analyzed. The effects of the pertinent parameters such as the acceleration parameter, the Brownian motion parameter, the thermophoresis parameter, the Prandtl number and the Lewis number on the velocity, temperature and concentration fields are discussed. Also the effects of these parameters on the skin friction coefficient, the Nusselt number and the Sherwood number are analyzed through graphs. It is observed that the melting phenomenon has a significant effect on the flow, heat and mass transfer characteristics.

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