scholarly journals Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. M. Ajayi ◽  
A. J. Omowaye ◽  
I. L. Animasaun
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Newtonian Fluid ◽  
Dynamic Viscosity ◽  
Casson Fluid ◽  
Stratified Medium ◽  
Internal Space ◽  
Melting Surface

The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy) and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases inRex1/2Cfxis guaranteed withStwhen magnitude ofβis large.Rex1/2Cfxdecreases withEcandm.

scholarly journals Dual Solutions of Non-Newtonian Casson Fluid Flow and Heat Transfer over an Exponentially Permeable Shrinking Sheet with Viscous Dissipation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Aurang Zaib ◽  
Krishnendu Bhattacharyya ◽  
Md. Sharif Uddin ◽  
Sharidan Shafie
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Flow ◽  
Viscous Dissipation ◽  
Newtonian Fluid ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Shrinking Sheet ◽  
Nonlinear Odes ◽  
Flow And Heat Transfer

The two-dimensional boundary layer flow of a non-Newtonian Casson fluid and heat transfer due to an exponentially permeable shrinking sheet with viscous dissipation is investigated. Using similarity transformations, the governing momentum and energy equations are transformed to self-similar nonlinear ODEs and then those are solved numerically by very efficient shooting method. The analysis explores many important aspects of flow and heat transfer of the aforesaid non-Newtonian fluid flow dynamics. For the steady flow of non-Newtonian Casson fluid, more amount of wall mass suction through the porous sheet is required in comparison to that of Newtonian fluid flow. Dual similarity solutions are obtained for velocity and temperature. The viscous dissipation effect has major impact on the heat transfer characteristic. In fact, heat absorption at the surface occurs and it increases due to viscous dissipation. For higher Prandtl number, the temperature inside the boundary layer reduces, but with larger Eckert number (viscous dissipation) it is enhanced.

scholarly journals Nonviscous Oblique Stagnation Point Flow towards Riga Plate

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sobia Akbar ◽  
Azad Hussain
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Stagnation Point ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Riga Plate ◽  
Mathematical Techniques

Purpose. The flow of nonviscous Casson fluid is examined in this study over an oscillating surface. The model of the fluid flow has been inspected in the presence of oblique stagnation point flow. The scrutiny is subsumed for the Riga plate by considering the effects of magnetohydrodynamics. The Riga plate is considered as an electromagnetic lever which carries eternal magnets and a stretching line up of alternating electrodes coupled on a plane surface. We have considered nonboundary layer two-dimensional incompressible flow of the fluid. The fluid flow model is analyzed in the fixed frame of reference. Motivation. The motivation of achieving more suitable results has always been a quest of life for scientists; the capability of determining the boundary layer of flow on aircraft which either stays laminar or turns turbulent has encouraged the researcher to study compressible flow in depth. The compressible fluid with boundary layer flow has been utilized by numerous researchers to reduce skin friction and enhance thermal and convectional heat exchange. Design/Approach/Methodology. The attained partial differential equations will be critically inspected by using suitable similarity transformation to transform these flows thrived equations into higher nonlinear ordinary differential equations (ODE). Then, these equations of motion are intercepted by mathematical techniques such as the bvp4c method in Maple and Matlab. The graphical and tabular representation of different parameters is also given. Findings. The behavior of β and modified Hartmann number M increases by positively increasing the values of both parameters for F η , while ω decreases with increasing the values of ω for F η . The graph of β shows upward behavior for distinct values for both G η and G ′ η for velocity portray. Prandtl number and β for the temperature profile of θ η and θ 1 η goes downward with increasing parameters.

scholarly journals Radiative Boundary Layer Flow of Casson Fluid Over an Exponentially Permeable Slippery Riga Plate with Viscous Dissipation

2020 ◽  
Vol 21 (1) ◽  
pp. 41-51
Author(s):  
Nur Syamila Yusof ◽  
Siti Khuzaimah Soid ◽  
Mohd Rijal Illias ◽  
Ahmad Sukri Abd Aziz ◽  
Nor Ain Azeany Mohd Nasir
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Numerical Results ◽  
Thermal Slip ◽  
Slip Parameter ◽  
Riga Plate

This study is aimed to analyze the steady of stagnation point flow and radiative heat transfer of a non-Newtonian fluid which is Casson fluid passing over an exponentially permeable slippery Riga plate in presence of thermal radiation, magnetic field, velocity slip, thermal slip, and viscous dissipation effects. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation then solved numerically by boundary value problem solver (BVP4C) in MATLAB software package. The numerical results are evaluated with previous researches to reach an agreement with the parameters of the current study. This study is discussing the behavior of the velocity and temperature profiles as well as skin friction coefficient and local Nusselt number for various physical parameters such as magnetic field, radiation, suction, thermal slip, velocity slip, Prandtl number, Eckert number and modified Hartmann number. Numerical results are shown graphically for each parameter with different values. It is found that the momentum boundary layer thickness increases with increasing the values of Casson parameter. The temperature decreases when the velocity slip parameter and thermal slip parameter are increased.

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 Ohmic and Viscous Dissipation Effect on Free and Forced Convective Flow of Casson Fluid in a Channel

2021 ◽  
Vol 12 (1) ◽  
pp. 132-148
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Convective Flow ◽  
Casson Fluid ◽  
Pictorial Representation ◽  
Physical Parameters ◽  
Partial Differential ◽  
Buoyancy Parameter ◽  
Forced Convective Flow

Analytical study of the free and forced convective flow of Casson fluid in the existence of viscous dissipation, ohmic effect and uniform magnetic field in a porous channel to the physical model. The nonlinear coupled partial differential equations are converted to linear partial differential equations using similarity transformation and the classical perturbation method. The physical parameters such as Prandtl number (Pr), viscous dissipation (Vi), Schmidt number (Sc), Reynolds number (R), thermal buoyancy parameter (λ), Ohmic number (Oh), Casson fluid parameter (β), Darcy number (Da), Hartmann number (M2), the concentration of buoyancy parameter (N), chemical reaction rate (γ) effect on velocity, temperature and concentration have been studied with pictorial representation. For the particular case, the present paper analysis is compared with the previous work and is found good agreement.

Similarity solution of second grade fluid flow over a moving cylinder

2021 ◽  
Author(s):  
Nadeem Abbas ◽  
M. Y. Malik ◽  
Sohail Nadeem ◽  
Shafiq Hussain ◽  
A. S. El-Shafa
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Material Parameter ◽  
Second Grade ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Second Grade Fluid ◽  
Moving Cylinder ◽  
Grade Fluid

Stagnation point flow of viscoelastic second grade fluid over a stretching cylinder under the thermal slip and magnetic hydrodynamics effects are studied. The mathematical model has been developed under the assumption of non-Newtonian viscoelastic fluid flow over a stretching cylinder by means of the boundary layer approximations. The developed model further reduced through the similarity transformations and constructs the model of nonlinear ordinary differential equations. The system of nonlinear differential equations is dimensionless and solved through the numerical technique bvp5c methods. The results of the physical parameters are found and interpreted in the form of tables and graphs. The velocity shows that the graph of curves enhances away from the surface when the values material parameter [Formula: see text] increase, which means the momentum boundary layer increases for enhancing the material parameter [Formula: see text]. The temperature gradient reduced due enhancing the values of material parameter [Formula: see text] because thermal boundary layer reduced for higher values of material parameter [Formula: see text].

scholarly journals Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Shooting Method ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Stagnation Point Flow ◽  
Stretching Surfaces

Abstract In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.

Two-parameter Lie convective Casson fluid scale study with MHD, joule heating and viscous dissipation influences

2020 ◽  
pp. 095440622096484
Author(s):  
Muhammad Nazim Tufail ◽  
Musharafa Saleem ◽  
Qasim Ali Chaudhry
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Casson Fluid ◽  
Graphical Analysis ◽  
Thermal Transfer ◽  
Fluid Parameter ◽  
Two Parameters ◽  
Unsteady Effects ◽  
Physical Quantities

The model encountered an unsteady laminar and two-dimensional convective flow of Casson fluid passing through an inclined permeable vertical stretching sheet. The momentum, thermal and concentrated boundary layers (BLs) are used to analyze the unsteady effects of magnetohydrodynamics (MHD) (neglecting induced magnetic field), viscous dissipation, Joule heating and chemical reactions. The governed partial differential equations (PDEs) of the model are reduced to the ordinary differential equations (ODEs). The ξ and χ are selected as the two parameters of the scaling transformations. By using bvp4c with MATLAB, the ODEs are solved numerically and represent their results through the graphs and tables. After the non-dimensionalizing of the equations system, we get the emerging dimensionless parameters. The concentration process was enhanced by the Casson fluid parameter but it reduced the fluid flow and thermal transfer that can be found through the graphical results. The effect of Buoyancy is highlighted as it reduced the velocity profile function, but it is a growing function of the thermal and concentrated profiles. The physical quantities are integrated through the table and graphical analysis. In the center of the wall, the number Shx versus Sc decreases, but at the end it increases.

scholarly journals Magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abdullah Dawar ◽  
Zahir Shah ◽  
Hashim M. Alshehri ◽  
Saeed Islam ◽  
Poom Kumam
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Lewis Number ◽  
Casson Fluid ◽  
Stretching Cylinder ◽  
Concentration Difference ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Homotopy Analysis

AbstractThis study presents the magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder. The mathematical modeling is presented in the form of partial differential equations and then transformed into ordinary differential equations (ODEs) utilizing suitable similarity transformations. The analytical solution of the transformed ODEs is presented with the help of homotopy analysis method (HAM). The convergence analysis of HAM is also presented by mean of figure. The present analysis consists of five phases. In the first four phases, we have compared our work with previously published investigations while phase five is consists of our new results. The influences of dimensionless factors like a magnetic parameter, thermal radiation, curvature parameter, Prandtl number, Brownian motion parameter, Schmidt number, heat generation, chemical reaction parameter, thermophoresis parameter, Eckert number, and concentration difference parameter on physical quantities of interests and flow profiles are shown through tables and figures. It has been established that with the increasing Casson parameter (i.e. $$\beta \to \infty$$ β → ∞ ), the streamlines become denser which results the increasing behavior in the fluid velocity while on the other hand, the fluid velocity reduces for the existence of Casson parameter (i.e. $$\beta = 1.0$$ β = 1.0 ). Also, the streamlines of stagnation point Casson fluid flow are highly wider for the case of magnetized fluid as equated to non-magnetized fluid. The higher values of bioconvection Lewis number, Peclet number, and microorganisms’ concentration difference parameter reduces the motile density function of microorganisms while an opposite behavior is depicted against density number.

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