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

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.

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A boundary layer flow analysis of a magnetohydrodynamic fluid over a shrinking sheet

Advances in Mechanical Engineering ◽

10.1177/1687814019835069 ◽

2019 ◽

Vol 11 (3) ◽

pp. 168781401983506 ◽

Cited By ~ 1

Author(s):

Cheng-Hsing Hsu ◽

Te-Hui Tsai ◽

Ching-Chuan Chang ◽

Wen-Han Huang

Keyword(s):

Magnetic Field ◽

Boundary Layer ◽

Differential Equations ◽

Boundary Layer Flow ◽

Flow Analysis ◽

Shear Thickening ◽

Transformation Method ◽

Skin Friction Coefficient ◽

Shrinking Sheet ◽

Layer Flow

A steady-state boundary layer flow analysis of a non-Newtonian magnetic fluid over a shrinking sheet was studied. The boundary layer thickness and the velocity distribution in the layer were studied under the conditions of a uniform magnetic field normal to the shrinking sheet and/or a vertical uniform mass suction across the sheet. The similarity transformation method was used to transform the governing partial differential equations to ordinary differential equations. The shooting method with Newton’s algorithm and Runge–Kutta integration method were used to obtain the solutions of the equations. The results showed that the variation of the flow velocity profiles in the boundary layer was significant, the thickness of the boundary layer was thinner, and the skin friction coefficient was bigger for either shear thinning or shear thickening magnetic fluids under the conditions of a stronger magnetic field or a larger mass suction effect.

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Series Solutions of Boundary Layer Flow of a Micropolar Fluid Near the Stagnation Point Towards a Shrinking Sheet

Zeitschrift für Naturforschung A ◽

10.1515/zna-2009-9-1006 ◽

2009 ◽

Vol 64 (9-10) ◽

pp. 575-582 ◽

Cited By ~ 17

Author(s):

Sohail Nadeem ◽

Saeid Abbasbandy ◽

Majid Hussain

Keyword(s):

Boundary Layer ◽

Boundary Layer Flow ◽

Micropolar Fluid ◽

Skin Friction Coefficient ◽

Shrinking Sheet ◽

Local Skin ◽

Similarity Transformations ◽

Homotopy Analysis ◽

Local Skin Friction ◽

Layer Flow

An analysis has been carried out to obtain the series solution of boundary layer flow of a micropolar fluid towards a shrinking sheet. The governing equations of micropolar fluid are simplified using suitable similarity transformations and then solved by homotopy analysis method (HAM). The convergence of the HAM solutions has been obtained by using homotopy-pade approximation. The effects of various parameters such as porosity parameter R, the ratio λ and the microinertia K on the velocity and microinertia profiles as well as local skin friction coefficient are presented graphically and in tabulated form.

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Boundary layer flow on permeable flat surface in Ag-Al2O3/water hybrid nanofluid with viscous dissipation

Data Analytics and Applied Mathematics (DAAM) ◽

10.15282/daam.v2i1.6431 ◽

2021 ◽

Vol 2 (1) ◽

pp. 11-19

Author(s):

MUHAMMAD KHAIRUL ANUAR MOHAMED ◽

A. Hussanan ◽

H.T. Alkasasbeh ◽

B. Widodo ◽

M.Z. Salleh

Keyword(s):

Boundary Layer ◽

Differential Equations ◽

Viscous Dissipation ◽

Boundary Layer Flow ◽

Flat Surface ◽

Volume Fraction ◽

Transfer Characteristic ◽

Hybrid Nanofluid ◽

Water Based ◽

Layer Flow

Seeking the better performance nanofluid but with low cost of production, presence challenged. Metal nanomaterial is good in both thermal and electric conductivity but expensive while oxide nanomaterial does oppositely. The present study solved numerically the laminar boundary layer flow over a permeable flat surface in a blended metal-oxide hybrid nanofluid plate with viscous dissipation effects. The similarity equations in the form of the set of ordinary differential equations are reduced from the non-linear partial differential equations before being solved numerically using the Runge-Kutta-Fehlberg method in MAPLE. The numerical solution is obtained for the reduced skin friction coefficient and reduced Nusselt number as well as the temperature and velocity profiles. The flow features and the heat transfer characteristic for the Eckert number, permeability parameter and nanoparticle volume fraction are analyzed and discussed. The Ag-Al2O3 water-based hybrid nanofluid tested in this study shows competitive results with the Ag water-based nanofluid in certain cases.

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DUAL SOLUTIONS OF BOUNDARY LAYER FLOW WITH HEAT AND MASS TRANSFERS OVER AN EXPONENTIALLY SHRINKING CYLINDER: STABILITY ANALYSIS

Latin American Applied Research - An international journal ◽

10.52292/j.laar.2020.535 ◽

2020 ◽

Vol 50 (4) ◽

pp. 247-253

Author(s):

Debasish Dey ◽

Rupjyoti Borah

Keyword(s):

Boundary Layer ◽

Stability Analysis ◽

Differential Equations ◽

Boundary Layer Flow ◽

Numerical Results ◽

Dual Solutions ◽

Suction Parameter ◽

Similarity Transformations ◽

Layer Flow ◽

Mass Transfers

Boundary layer flow with heat and mass transfers over a stretching/shrinking cylinder has been investigated. The governing partial differential equations are converted into a set of ordinary differential equations using suitable similarity transformations and have been solved numerically using MATLAB built in bvp4c solver technique. The numerical results are graphically discussed in the form of velocity, temperature and concentration distributions for various values of flow parameters. Numerical results show that dual solutions are possible in specific range of the suction parameter. A stability analysis is executed to obtain which solution is linearly stable and physically realizable.

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Magnetohydrodynamic Boundary Layer Flow and Heat Transfer of Nanofluids Past a Bidirectional Exponential Permeable Stretching/Shrinking Sheet With Viscous Dissipation Effect

Journal of Heat Transfer ◽

10.1115/1.4041800 ◽

2018 ◽

Vol 141 (1) ◽

Cited By ~ 15

Author(s):

Rahimah Jusoh ◽

Roslinda Nazar ◽

Ioan Pop

Keyword(s):

Heat Transfer ◽

Thermal Conductivity ◽

Boundary Layer ◽

Viscous Dissipation ◽

Boundary Layer Flow ◽

Volume Fraction ◽

Shrinking Sheet ◽

Suction Parameter ◽

Flow And Heat Transfer ◽

Layer Flow

The problem of boundary layer flow and heat transfer of magnetohydrodynamic (MHD) nanofluids which consist of Fe3O4, Cu, Al2O3, and TiO2 nanoparticles and water as the base fluid past a bidirectional exponentially permeable stretching/shrinking sheet is studied numerically. The mathematical model of the nanofluid incorporates the effect of viscous dissipation in the energy equation. By employing a suitable similarity transformation, the conservative equations for mass, momentum, and energy are transformed into the ordinary differential equations. These equations are then numerically solved with the utilization of bvp4c function in matlab. The effects of the suction parameter, magnetic parameter, nanoparticle volume fraction parameter, Eckert number, Prandtl number, and temperature exponent parameter to the reduced skin friction coefficient as well as the local Nusselt number are graphically presented. Cu is found to be prominently good in the thermal conductivity. Nevertheless, higher concentration of nanoparticles leads to the deterioration of heat transfer rate. The present result negates the previous literature on thermal conductivity enhancement with the implementation of nanofluid. Stability analysis is conducted since dual solutions exist in this study, and conclusively, the first solution is found to be stable.

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MHD Laminar Boundary Layer Flow of a Jeffrey Fluid Past a Vertical Plate Influenced by Viscous Dissipation and a Heat Source/Sink

Mathematics ◽

10.3390/math9161896 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1896

Author(s):

Hillary Muzara ◽

Stanford Shateyi

Keyword(s):

Boundary Layer ◽

Differential Equations ◽

Heat Source ◽

Viscous Dissipation ◽

Laminar Boundary Layer ◽

Boundary Layer Flow ◽

Vertical Plate ◽

Jeffrey Fluid ◽

Physical Parameters ◽

Layer Flow

This study investigates the effects of viscous dissipation and a heat source or sink on the magneto-hydrodynamic laminar boundary layer flow of a Jeffrey fluid past a vertical plate. The governing boundary layer non-linear partial differential equations are reduced to non-linear ordinary differential equations using suitable similarity transformations. The resulting system of dimensionless differential equations is then solved numerically using the bivariate spectral quasi-linearisation method. The effects of some physical parameters that include the Schmidt number, Eckert number, radiation parameter, magnetic field parameter, heat generation parameter, and the ratio of relaxation to retardation times on the velocity, temperature, and concentration profiles are presented graphically. Additionally, the influence of some physical parameters on the skin friction coefficient, local Nusselt number, and the local Sherwood number are displayed in tabular form.

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Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

Sains Malaysiana ◽

10.17576/jsm-2021-5012-24 ◽

2021 ◽

Vol 50 (12) ◽

pp. 3753-3764

Author(s):

Nurul Amira Zainal ◽

Roslinda Nazar ◽

Kohilavani Naganthran ◽

Ioan Pop

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Volume Fraction ◽

Skin Friction Coefficient ◽

Hybrid Nanofluid ◽

Similarity Transformations ◽

Flow And Heat Transfer ◽

Theoretical Investigations ◽

Suitable Form ◽

Layer Flow

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

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The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid

International Journal of Engineering Mathematics ◽

10.1155/2013/581507 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 6

Author(s):

D. R. V. S. R. K. Sastry ◽

A. S. N. Murti ◽

T. Poorna Kantha

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Differential Equations ◽

Boundary Layer Flow ◽

Numerical Solutions ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Convection Boundary Layer ◽

Similarity Transformations ◽

Layer Flow

The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.

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Mixed Convection in Viscoelastic Boundary Layer Flow and Heat Transfer Over a Stretching Sheet

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2013.m303 ◽

2014 ◽

Vol 6 (3) ◽

pp. 359-375 ◽

Cited By ~ 5

Author(s):

Antonio Mastroberardino

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Differential Equations ◽

Mixed Convection ◽

Boundary Layer Flow ◽

Skin Friction Coefficient ◽

Convection Boundary Layer ◽

Electrically Conducting ◽

Homotopy Analysis ◽

Layer Flow

AbstractAn investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equations for the fluid flow and temperature are reduced to a nonlinear system of ordinary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition it is demonstrated that previously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives reported are not correct.

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Three-dimensional MHD boundary layer flow due to an axisymmetric shrinking sheet with radiation, viscous dissipation and heat source/sink

International Journal of Applied Mechanics and Engineering ◽

10.1515/ijame-2016-0024 ◽

2016 ◽

Vol 21 (2) ◽

pp. 393-406

Author(s):

M. Madhu ◽

B. Balaswamy ◽

N. Kishan

Keyword(s):

Boundary Layer ◽

Differential Equations ◽

Heat Source ◽

Boundary Layer Flow ◽

Three Dimensional ◽

Shrinking Sheet ◽

Mhd Boundary Layer ◽

Layer Flow ◽

Source Sink ◽

Mhd Boundary Layer Flow

AbstractAn analysis is made to study a three dimensional MHD boundary layer flow and heat transfer due to a porous axisymmetric shrinking sheet. The governing partial differential equations of momentum and energy are transformed into self similar non-linear ordinary differential equations by using the suitable similarity transformations. These equations are, then solved by using the variational finite element method. The flow phenomena is characterised by the magnetic parameterM, suction parameterS, porosity parameterKp, heat source/sink parameterQ, Prandtl number Pr, Eckert number Ec and radiation parameterRd. The numerical results of the velocity and temperature profiles are obtained and displayed graphically.

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