Analysis of Carreau fluid flow by convectively heated disk with viscous dissipation effects

AbstractThe primary motive of this study is to examine boundary layer flow of Carreau fluid over a convectively heated disk stretching with nonlinear velocity. The flow is assumed to be two dimensional. Moreover, viscous dissipation possessions are taken into description. The dominating nonlinear differential equations involving partial derivatives are changed into nonlinear differential equations involving ordinary derivatives by applying suitable transformations. Numerical outcomes for velocity and temperature are obtained from MATLAB’s built-in solver bvp4c and presented graphically and in tabular form.

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

Journal of Advanced Research in Fluid Mechanics and Thermal Sciences ◽

10.37934/arfmts.88.2.6479 ◽

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.

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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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Comparison of Numerical Methods for Nano Boundary Layer Flow

Zeitschrift für Naturforschung A ◽

10.5560/zna.2011-0006 ◽

2011 ◽

Vol 66 (8-9) ◽

pp. 539-542

Author(s):

Nader Y. Abd Elazem ◽

Abdelhalim Ebaid

Keyword(s):

Boundary Layer ◽

Numerical Methods ◽

Differential Equations ◽

Boundary Layer Flow ◽

Nonlinear Differential Equations ◽

The Other ◽

Chebyshev Collocation ◽

Collocation Scheme ◽

Layer Flow

Abstract The nonlinear differential equations describing the nano boundary layer flow is investigated in this paper utilizing Chebyshev collocation scheme. The results obtained in this research are compared with those obtained by the other published works.

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Viscous Dissipation and Heat Transfer Effect on MHD Boundary Layer flow past a Wedge of Nano fluid Embedded in a Porous media

Turkish Journal of Computer and Mathematics Education (TURCOMAT) ◽

10.17762/turcomat.v12i4.1208 ◽

2021 ◽

Vol 12 (4) ◽

pp. 1352-1366

Author(s):

N. Amar, Et. al.

Keyword(s):

Boundary Layer ◽

Porous Media ◽

Differential Equations ◽

Viscous Dissipation ◽

Nano Fluid ◽

Flow Parameters ◽

Flow Past ◽

Dimensional Boundary ◽

Layer Flow ◽

Mhd Boundary Layer Flow

In this investigation the steady of laminar magnetohydrodynamic(MHD) heat and mass transfer two dimensional boundary layer nanofluid flow past a wedge embedded in a porous media in the availability of the viscous dissipation, thermophoresis and Brownian motion effects are taken into account. With the assistance of the similarity transformation, the governing partial differential equations (PDE) are transformed into nonlinear ordinary differential equations (ODE). The solution of the problem is solved numerically by using the MATLAB in built package solver bvp4c. The method's accuracy is examined against recently discussed results and outstanding agreement was reached. The impacts of the pertinent flow parameters are examined through graphs and tabular form.

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Linear Stability on the Local Thermal Nonequilibrium Model of Mixed Convection Boundary Layer Flow over a Moving Wedge in a Porous Medium: Viscous Dissipation and Radiation Effects

Journal of Heat Transfer ◽

10.1115/1.4049514 ◽

2021 ◽

Vol 143 (4) ◽

Author(s):

Shashi Prabha Gogate S. ◽

Bharathi M. C. ◽

Ramesh B. Kudenatti

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Porous Medium ◽

Differential Equations ◽

Mixed Convection ◽

Viscous Dissipation ◽

Boundary Layer Flow ◽

Convection Boundary Layer ◽

Convection Boundary ◽

Layer Flow

Abstract This paper studies the local thermal nonequilibrium (LTNE) model for two-dimensional mixed convection boundary-layer flow over a wedge, which is embedded in a porous medium in the presence of radiation and viscous dissipation. It is considered that the temperature of the fluid and solid phases is not identical; hence, we require two energy equations: one for each phase. The motion of the mainstream and wedge is approximated by the power of distance from the leading boundary layer. The flow and heat transfer in the LTNE phase is governed by the coupled partial differential equations, which are then reduced to nonlinear ordinary differential equations via suitable similarity transformations. Numerical simulations show that when the interphase rate of heat transfer is large, the system attains the local thermal equilibrium (LTE) state and so is for porosity scaled conductivity. When LTNE is strong, the fluid phase reacts faster to the mainstream temperature than the corresponding solid phase. The state of LTE rather depends on radiation and viscous dissipation of the model. Further, numerical solutions successfully predicted the upper and lower branch solutions when the velocity ratio is varied. To assess which of these solutions is practically realizable, an asymptotic analysis on unsteady perturbations for a large time leading to linear stability needs to be performed. This shows that the upper branch solutions are always stable and practically realizable. The physical dynamics behind these results are discussed in detail.

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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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MHD Boundary Layer Flow over a Cone Embedded in Porous Media with Joule Heating and Viscous Dissipation

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.401.131 ◽

2020 ◽

Vol 401 ◽

pp. 131-139

Author(s):

Santosh Devi ◽

Mukesh Kumar Sharma

Keyword(s):

Boundary Layer ◽

Differential Equations ◽

Viscous Dissipation ◽

Joule Heating ◽

Boundary Layer Flow ◽

Flowing Fluid ◽

Coupled Equations ◽

Mhd Boundary Layer ◽

Layer Flow ◽

Mhd Boundary Layer Flow

Aim of the paper is to study the Magnetohydrodynamic boundary layer flow over a cone under the effect of joule heating and viscous dissipation. The surface of the cone is cooled and heated by the flowing fluid having constant temperature along with variable heat transfer coefficient.The surface of the cone is subjected under the convective heat flux. The governing equation for MHD boundary layer flow are non-linear partial differential equations, are transformed into ordinary differential equations using similarity techniques. The reduced ordinary coupled equations are solved with Runge-Kutta’s fourth order method followed by shooting techniques. The effects on flow and heat convection of various physical parameters pertinent to the modeled problem are computed and analyzed and shown through graphs. Keywords: Mixed convection, cone, Boundary layer, Joule Heating, Convective boundary condition.

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Magnetohydrodynamic Boundary Layer Flow of a Viscoelastic Fluid Past a Nonlinear Stretching Sheet in the Presence of Viscous Dissipation Effect

Coatings ◽

10.3390/coatings9080490 ◽

2019 ◽

Vol 9 (8) ◽

pp. 490

Author(s):

Ahmad Banji Jafar ◽

Sharidan Shafie ◽

Imran Ullah

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Differential Equations ◽

Viscous Dissipation ◽

Viscoelastic Fluid ◽

Boundary Layer Flow ◽

Stretching Sheet ◽

Dissipation Effect ◽

Layer Flow ◽

Nonlinear Stretching

This paper numerically investigates the viscous dissipation effect on the boundary layer flow of an electrically-conducting viscoelastic fluid (Walter’s B liquid) past a nonlinear stretching sheet. The partial differential equations governing the flow problem are transformed into ordinary differential equations through similarity variables. The transformed equations are then solved using the Keller box method. A careful evaluation of the influence of the pertinent parameters on the velocity field and temperature distributions through various plots is done for the prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions. The computed coefficient of skin friction, the rate of heat transfer (Nusselt number), and the temperature at the wall are also presented in tabular form. It is revealed from this table that the magnitude of the heat transfer is reduced with the increase in the Eckert number E c , viscoelastic parameter K, and magnetic parameter M for the PST case by about 12%, 20%, and 29%, respectively. Similarly, the temperature at the wall for the PHF case also decreases with the increase in E c and M by about 8% and 24%, respectively. It is obvious that the application of the PST condition excels at keeping the viscoelastic fluid warmer than the PHF condition. This implies that applying the PHF condition is better for cooling the sheet faster. The temperature at the wall is unchanged with the changes in the pertinent parameters in the PST case, and it is ascertained that the present results are in close agreement with the previous published results.

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On the Study of Viscoelastic Walters' B Fluid in Boundary Layer Flows

Mathematical Problems in Engineering ◽

10.1155/2012/861508 ◽

2012 ◽

Vol 2012 ◽

pp. 1-18 ◽

Cited By ~ 7

Author(s):

Seyed Ali Madani Tonekaboni ◽

Ramin Abkar ◽

Reza Khoeilar

Keyword(s):

Boundary Layer ◽

Differential Equations ◽

Order Approximation ◽

Nonlinear Differential Equations ◽

Boundary Layer Flows ◽

Sakiadis Flow ◽

Stream Functions ◽

Layer Flow ◽

Walter’S B Fluid ◽

Walters B Fluid

Viscoelastic Walters' B fluid flows for three problems, stagnation-point flow, Blasius flow, and Sakiadis flow, have been investigated. In each problem, Cauchy equations are changed to a nondimensional differential equations using stream functions and with assumption of boundary layer flow. The fourth-order predictor-corrector finite-difference method for solving these nonlinear differential equations has been employed. The results that have been obtained using this method are compared with the results of the last studies, and it is clarified that this method is more accurate. It is also shown that the results of last study about Sakiadis flow of Walter's B fluid are not true. In addition, the effects of order of discretization in the boundaries are investigated. Moreover, it has been discussed about the valid region of Weissenberg numbers for the second-order approximation of viscoelastic fluids in each case of study.

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