Boundary layer flow of a dusty fluid over a permeable shrinking surface

2017 ◽  
Vol 27 (4) ◽  
pp. 758-772 ◽  
Author(s):  
Rohana Abdul Hamid ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Particle Interaction ◽  
Engine Oil ◽  
Shrinking Sheet ◽  
Suction Parameter ◽  
Content Type ◽  
Dusty Fluid ◽  
Boundary Layer Problem ◽  
Shrinking Surface ◽  
Layer Problem

Purpose The purpose of this paper is to numerically study the boundary layer problem for the case of two-dimensional flow of dusty fluid over a shrinking surface in the presence of the fluid suction at the surface. Design/methodology/approach The governing equations of the problem are reduced to the system of ordinary differential equations using the similarity transformation and then solved using the bvp4c method in the Matlab software. Findings The effects of the drag coefficient parameter L, the fluid–particle interaction parameter δ, the suction parameter s and the particle loading parameter ω on the flow of the permeable shrinking sheet are investigated. It is found that the aforementioned parameters have different effects in the shrinking sheet flow. This study has also succeeded in discovering the second solution, and through the stability analysis, it is suggested that the solution is unstable and not physically realizable in practice. Practical implications The current findings add to a growing body of literature on the boundary layer problem in the dusty fluid. The dusty fluid is significant in various practical applications such as in the transporting suspended powdered materials through pipes, propulsion and combustion in rockets, the flow of blood in arteries, wastewater treatment and as corrosive particles in engine oil flow. Originality/value Even though the dusty fluid problem has been extensively studied in the flow of the stretching sheet, limited findings can be found over a shrinking flow. In fact, this is the first study to discover the second solution in the dusty fluid problem.

MHD Marangoni boundary layer problem for hybrid nanofluids with thermal radiation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Emad H. Aly ◽  
Abdelhalim Ebaid
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Copper Nanoparticles ◽  
Volume Fraction ◽  
Content Type ◽  
Boundary Layer Problem ◽  
Nanoparticles Volume Fraction ◽  
Hybrid Nanofluids ◽  
Marangoni Boundary Layer ◽  
Layer Problem

Purpose The purpose of this paper is to study flow of the Marangoni boundary layer pasta surface embedded in a porous medium saturated by a hybrid nanofluid in the presence of a magnetic field and thermal radiation. Design/methodology/approach The governing model was converted into ordinary differential equations applying proper similarity transformations. Therefore, Laplace transform was used to exactly solve the resulted equations. Hence, the influence of the velocity profile and temperature distribution was investigated under impacts of the involved parameters. Findings In the case of regular fluid, i.e. the solid volume fractions are zeros, the current results are in a very good agreement with those in the literature. It was found that the velocity decreases (increases) on increasing the parameters of copper-nanoparticles volume fraction, magnetic field and suction (permeability and injection). Further, the temperature increases (decreases) with an increase of the copper-nanoparticles volume fraction, magnetic field, injection and radiation (permeability and suction). Originality/value The current results of the Marangoni boundary layer problem for hybrid nanofluids are new, original and extend the previous problems investigated by many authors for the case of regular/nano fluids.

scholarly journals Boundary Layer of a Dusty Fluid Flow Over A Stretching Sheet

2018 ◽  
Vol 7 (4.30) ◽  
pp. 462
Author(s):  
Noorzehan F. M. S ◽  
Anati A ◽  
Syahira M ◽  
Radiah M ◽  
Nurul A. J
Keyword(s):  
Boundary Layer ◽  
Interaction Parameter ◽  
Stretching Sheet ◽  
Particle Interaction ◽  
Fluid Phase ◽  
Fluid Particle ◽  
Physical Parameters ◽  
Suction Parameter ◽  
Dusty Fluid ◽  
Linear Ordinary Differential Equations

A numerical analysis has been carried out to investigate the effects of suction parameter and fluid-particle interaction parameter on boundary layer of dusty fluid towards the stretching sheet. The governing equations of boundary layer were transformed into system of coupled non-linear ordinary differential equations with the help of similarity transformation. The transformed equations then solved numerically using bvp4c solver of MATLAB software. The effects of physical parameters on velocity profile of fluid phase and dust particle phase were obtained and analysed through several plots. Useful discussion were carried out with the help of plotted graphs and tables. The numerical results obtain were compared and found to be in good agreement with the previous study. It is observed that the presence of suction increase the velocity of fluid meanwhile opposite with velocity of particle. Besides that, the fluid-particle interaction parameter increase the velocity of particle. These findings will be used for future studies involving nanofluid.

Numerical Study of Boundary Layers With Reverse Wedge Flows Over a Semi-Infinite Flat Plate

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
R. Ahmad ◽  
K. Naeem ◽  
Waqar Ahmed Khan
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Study ◽  
Boundary Layer Equation ◽  
Wedge Angle ◽  
Adverse Pressure Gradient ◽  
Problem Solution ◽  
Weighted Residual Method ◽  
Boundary Layer Problem ◽  
Layer Problem

This paper presents the classical approximation scheme to investigate the velocity profile associated with the Falkner–Skan boundary-layer problem. Solution of the boundary-layer equation is obtained for a model problem in which the flow field contains a substantial region of strongly reversed flow. The problem investigates the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. Optimized results for the dimensionless velocity profiles of reverse wedge flow are presented graphically for different values of wedge angle parameter β taken from 0≤β≤2.5. Weighted residual method (WRM) is used for determining the solution of nonlinear boundary-layer problem. Finally, for β=0 the results of WRM are compared with the results of homotopy perturbation method.

On a Boundary Layer Problem

2002 ◽  
Vol 108 (4) ◽  
pp. 369-398 ◽  
Author(s):  
R. Wong ◽  
Heping Yang
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Layer Problem

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.

The boundary layer over an impulsively started flat plate

1969 ◽  
Vol 310 (1502) ◽  
pp. 401-414 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Surface Shear Stress ◽  
Unsteady State ◽  
Similarity Condition ◽  
Surface Shear ◽  
Boundary Layer Problem ◽  
Independent Variables ◽  
Selection Of ◽  
Layer Problem

A numerical solution has been obtained for the development of the flow from the initial unsteady state described by Rayleigh to the ultimate steady state described by Blasius. The usual formulation of the problem in two independent variables is dropped, and three independent variables, in space and time, are reverted to. The boundary-layer problem is unconventional in that the boundary conditions are not completely known. Instead, it is known that the solution should satisfy a similarity condition, and use is made of this to obtain a solution by iteration. A finite-difference technique of a mixed, explicit-implicit, type is employed. The iteration converges rapidly. It is terminated where the maximum errors are estimated to be about 0.04%. A selection of the results for the velocity profiles and the surface shear stress is presented. One striking feature is the rapidity of the transition from the Rayleigh to the Blasius state. The change is practically complete, at a given station on the plate, by the time the plate has moved a distance equal to four times the distance from the station to the leading edge of the plate.

Three-dimensional flow of radiative hybrid nanofluid past a permeable stretching/shrinking sheet with homogeneous-heterogeneous reaction

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Najiyah Safwa Khashi'ie ◽  
Norihan Md Arifin ◽  
Natalia C. Rosca ◽  
Alin V. Rosca ◽  
Ioan Pop
Keyword(s):  
Heterogeneous Reaction ◽  
Three Dimensional ◽  
Heterogeneous Reactions ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Three Dimensional Flow ◽  
Suction Parameter ◽  
Content Type ◽  
Fluid Concentration ◽  
The Stability

Purpose The purpose of this paper is to study the effects of thermal radiation and homogeneous-heterogeneous reactions in the three-dimensional hybrid nanofluid flow past a permeable stretching/shrinking sheet. Design/methodology/approach The combination of aluminum oxide (Al2O3) and copper (Cu) nanoparticles with total volumetric concentration is numerically analyzed using the existing correlations of hybrid nanofluid. With the consideration that both homogeneous and heterogeneous reactions are isothermal while the diffusion coefficients of both autocatalyst and reactant are same, the governing model is simplified into a set of differential (similarity) equations. Findings Using the bvp4c solver, dual solutions are presented, and the stability analysis certifies the physical/real solution. The findings show that the suction parameter is requisite to induce the steady solution for shrinking parameter. Besides, the fluid concentration owing to the shrinking sheet is diminished with the addition of surface reaction. Originality/value The present findings are novel and can be a reference point to other researchers to further analyze the heat transfer performance and stability of the working fluids.

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