scholarly journals Exploring the magnetohydrodynamic stretched flow of Williamson Maxwell nanofluid through porous matrix over a permeated sheet with bioconvection and activation energy

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Sohaib Abdal ◽  
Imran Siddique ◽  
Dalal Alrowaili ◽  
Qasem Al-Mdallal ◽  
Sajjad Hussain
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Density Profile ◽  
Maxwell Fluid ◽  
Computational Procedure ◽  
Active Role ◽  
Porous Matrix ◽  
Skin Friction Coefficient ◽  
Linear Partial Differential Equations ◽  
Similarity Transformations

AbstractThe evolution of compact density heat gadgets demands effective thermal transportation. The notion of nanofluid plays active role for this requirements. A comparative account for Maxwell nanofluids and Williamson nanofluid is analyzed. The bioconvection of self motive microorganisms, non Fourier heat flux and activation energy are new aspects of this study. This article elaborates the effects of viscous dissipation, Cattaneo–Christov diffusion for Maxwell and Williamson nanofluid transportation that occurs due to porous stretching sheet. The higher order non-linear partial differential equations are solved by using similarity transformations and a new set of ordinary differential equations is formed. For numerical purpose, Runge–Kutta method with shooting technique is applied. Matlab plateform is used for computational procedure. The graphs for various profiles .i.e. velocity, temperature, concentration and concentration of motile micro-organisms are revealed for specific non-dimensional parameters. It is observed that enhancing the magnetic parameter M, the velocity of fluid decreases but opposite behavior happens for temperature, concentration and motile density profile. Also the motile density profile decrease down for Pe and Lb. The skin friction coefficient is enhanced for both the Williamson and Maxwell fluid.

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.

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 New Numerical Solution of Maxwell Fluid over a Shrinking Sheet in the Region of a Stagnation Point

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
S. S. Motsa ◽  
Y. Khan ◽  
S. Shateyi
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Maxwell Fluid ◽  
Shrinking Sheet ◽  
Two Dimensional ◽  
Similarity Transformations ◽  
The Mathematical Model ◽  
Successive Linearisation Method ◽  
Fluid Parameters

The mathematical model for the incompressible two-dimensional stagnation flow of a Maxwell fluid towards a shrinking sheet is proposed. The developed equations are used to discuss the problem of being two dimensional in the region of stagnation point over a shrinking sheet. The nonlinear partial differential equations are transformed to ordinary differential equations by first-taking boundary-layer approximations into account and then using the similarity transformations. The obtained equations are then solved by using a successive linearisation method. The influence of the pertinent fluid parameters on the velocity is discussed through the help of graphs.

scholarly journals Role of Slip Velocity in a Magneto-Micropolar Fluid Flow from a Radiative Surface with Variable Permeability: A Numerical Study

2017 ◽  
Vol 22 (3) ◽  
pp. 637-651
Author(s):  
B.K. Sharma ◽  
V. Tailor ◽  
M. Goyal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Numerical Study ◽  
Slip Flow ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Variable Permeability

AbstractAn analysis is presented to describe the hydromagnetic mixed convection flow of an electrically conducting micropolar fluid past a vertical plate through a porous medium with radiation and slip flow regime. A uniform magnetic field has been considered in the study which absorbs the micropolar fluid with a varying suction velocity and acts perpendicular to the porous surface of the above plate. The governing non-linear partial differential equations have been transformed into linear partial differential equations, which are solved numerically by applying the explicit finite difference method. The numerical results are presented graphically in the form of velocity, micro-rotation, concentration and temperature profiles, the skin-friction coefficient, the couple stress coefficient, the rate of heat and mass transfers at the wall for different material parameters.

scholarly journals Analytical solution of MHD free convective flow of couple stress fluid in an annulus with Hall and ion-slip effects

2011 ◽  
Vol 16 (4) ◽  
pp. 477-487 ◽  
Author(s):  
Darbhashayanam Srinivasacharya ◽  
Kolla Kaladhar
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Circular Cylinders ◽  
Couple Stress Fluid ◽  
Electrically Conducting ◽  
Linear Partial Differential Equations ◽  
Similarity Transformations ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Ion Slip

This paper presents the Hall and Ion-slip effects on electrically conducting couple stress fluid flow between two circular cylinders in the presence of a temperature dependent heat source. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and then solved using homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, Ion-slip parameter and couple stress fluid parameter on velocity and  temperature are discussed and shown graphically.

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

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.

scholarly journals Insights into the Generalized Fourier's and Fick's Laws for Simulating Mixed Bioconvective Flows of Radiative-Reactive Walters-B Fluids Conveying Tiny Particles subject to Lorentz Force

2021 ◽  
Author(s):  
A. Wakif ◽  
I. L. Animasaun ◽  
Umair Khan ◽  
Ahmed Mohammed Alshehri
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Computational Cost ◽  
Energy Parameter ◽  
Linearization Method ◽  
Surface Drag ◽  
Force Coefficient ◽  
Buongiorno’S Model ◽  
Similarity Transformations ◽  
Nanoparticles Concentration

Abstract The current improvement in nanoscience and nanotechnology areas has attracted researchers' attention to biofuel, bioengineering, and biomedical and mechanical engineering applications. However, there is no report on the extension of Buongiorno's model incorporating the Cattaneo-Christov theory and the generalized Fick's law to reflect the significant impacts of Brownian motion, thermophoresis diffusion, thermal radiation, and activation energy. The governing partial differential equations (PDEs) suitable to model the case as mentioned above were converted into a unified set of ordinary differential equations (ODEs) by applying appropriate similarity transformations and solved numerically by using the Spectral Local Linearization Method (SLLM) and MATLAB in-built package. The SLLM numerical method provides robustness results with a higher level of exactness and low‐computational cost. It is worthy to conclude that the nanoparticles concentration distribution can be heightened considerably either by diminishing the Prandtl number and concentration relaxation parameter or increasing the values of nanoparticles concentration Biot number and activation energy parameter. An attractive reduction in the surface drag force coefficient is achievable via the intensifying values of the non-Newtonian parameter.

Effects of Chemical Reaction, Activation Energy and Thermal Energy on Magnetohydrodynamics Maxwell Fluid Flow in Rotating Frame

2021 ◽  
Vol 10 (1) ◽  
pp. 67-74
Author(s):  
Hunegnaw Dessie
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Heat Radiation ◽  
Rotating Frame ◽  
Rotational Parameter ◽  
The Impact

The purpose of this research is to see how chemical processes, activation energy, and heat radiation affect MHD flow of Maxwell fluid in a rotating frame. Using applicable similarity transformations, the partial differential equations that regulate the flow are reduced to extremely nonlinear ordinary differential equations. Graphs and tables are used to study the impact of monitoring parameters on velocity, temperature, concentration profiles, reduced Nusselt number, reduced Sherwood numbers, and skin friction coefficients. Outstanding agreement is obtained when the present findings of the study is compared with the previous related research works. In the study, it is noted that an increase of the thermal radiation parameters contributes to an increase of the flow temperature region. When a fluid is subjected to a greater rotation parameter, the thermal boundary layer thickens and the heat transfer rate decrease. Moreover, a decline of mass transfer rate is observed for a rise of Prandl number, rotational parameter or Deborah number.

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.

Casson Liquid Flow due to Porous Stretching Sheet with Suction/Injection

2018 ◽  
Vol 388 ◽  
pp. 420-432
Author(s):  
Vinay Kumar Poorigaly Nanjundaswamy ◽  
Ulavathi Shettar Mahabaleshwar ◽  
Patil Mallikarjun ◽  
Mohaddeseh Mousavi Nezhad ◽  
Giulio Lorenzini
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Theoretical Study ◽  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Boundary Layer Flows ◽  
Similarity Transformations ◽  
Casson Fluid Model

The theoretical study of laminar boundary layer flows of a non-Newtonian fluid past a stretching sheet in an embedded porous medium in the presence of suction/injection is of significant importance in the crystal growing, geothermal, metallurgical, polymer extrusion and several other technological processes. Casson fluid model is one such fluid model used to characterize the behaviour of non-Newtonian fluids. The present article discusses the Casson fluid flow past a permeable stretching sheet in the presence of mass transpiration. The physical problem is modelled into a system of nonlinear partial differential equations which are analytically solved by transforming them into nonlinear ordinary differential equations with constant coefficient by means of similarity transformations. The analysis reveals the effect of Casson parameter on the velocity boundary. In fact, the increasing Casson parameter results in the suppression of velocity boundary. It is found that the skin friction coefficient decreases with the decreasing values of Casson parameter. The effects of Darcy drag force and the mass transpiration are also analyzed by means of various plots.

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