scholarly journals Analysis of Williamson nanofluid with velocity and thermal slips past over a stretching sheet by Lobatto IIIA numerically

2021 ◽  
pp. 159-159
Author(s):  
Sharafat Ali ◽  
Muhammad Raja ◽  
Tahir Cheema ◽  
Iftikhar Ahmad ◽  
Numan Mian ◽  
...  
Keyword(s):  
Stretching Sheet ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Williamson Fluid ◽  
Numerical Computing ◽  
Relative Errors ◽  
Buongiorno Model ◽  
The Impact ◽  
The Mathematical Model

A novel numerical computing framework through Lobatto IIIA method is presented for the dynamical investigation of nanofluidic problem with Williamson fluid flow on a stretching sheet by considering the thermal slip and velocity. The impact of thermophoresis and brownian motion on phenomena of heat transfer are explored by using Buongiorno model. The governing nonlinear partial differential system representing the mathematical model of the Williamson fluid is transformed in to a system of ODEs by incorporating the competency of non-dimensional similarity variables. The dynamics of the transformed system of ODEs are evaluated through the Lobatto IIIA numerically. Sufficient graphical and numerical illustrations are portrayed in order to investigate and analyze the influence of physical parameters; Williamson parameter, Prandtl number, Lewis number, Schmidt number, ratio of diffusivity parameter and ratio of heat capacitance parameter on velocity, temperature and concentration fields. The numerically computed values of local Nusselt number, local Sherwood number and Skin friction coefficient are also inspected for exhaustive assessment. Moreover, the accuracy, efficiency and stability of the proposed method is analyzed through relative errors.

scholarly journals MHD Flow and Heat Transfer over Vertical Stretching Sheet with Heat Sink or Source Effect

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 297 ◽  
Author(s):  
Ibrahim Alarifi ◽  
Ahmed Abokhalil ◽  
M. Osman ◽  
Liaquat Lund ◽  
Mossaad Ayed ◽  
...  
Keyword(s):  
Stretching Sheet ◽  
Hartmann Number ◽  
Velocity Ratio ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Normal System ◽  
Integration Algorithm ◽  
Nonlinear Normal ◽  
The Impact

A steady laminar flow over a vertical stretching sheet with the existence of viscous dissipation, heat source/sink, and magnetic fields has been numerically inspected through a shooting scheme based Runge—Kutta–Fehlberg-integration algorithm. The governing equation and boundary layer balance are expressed and then converted into a nonlinear normal system of differential equations using suitable transformations. The impact of the physical parameters on the dimensionless velocity, temperature, the local Nusselt, and skin friction coefficient are described. Results show good agreement with recent researches. Findings reveal that the Nusselt number at the sheet surface augments, since the Hartmann number, stretching velocity ratio A, and Hartmann number Ha increase. Nevertheless, it reduces with respect to the heat generation/absorption coefficient δ.

scholarly journals Melting Effect on Unsteady Hydromagnetic Flow of a Nanofluid Past a Stretching Sheet

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ali J. Chamkha ◽  
A.M. Rashad ◽  
Eisa Al-Meshaiei
Keyword(s):  
Stretching Sheet ◽  
Volume Fraction ◽  
Transverse Magnetic ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Time Histories ◽  
Nanoparticles Volume Fraction ◽  
Layer Flow ◽  
Stretching Plate ◽  
Melting Effect

This paper considers unsteady, laminar, boundary-layer flow with heat and mass transfer of a nanofluid along a horizontal stretching plate in the presence of a transverse magnetic field, melting and heat generation or absorption effects. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by an efficient implicit, iterative, finite-difference method. A parametric study illustrating the influence of various physical parameters is performed. Numerical results for the steady-state velocity, temperature and nanoparticles volume fraction profiles as well as the time histories of the skin-friction coefficient, Nusselt number and the Sherwood number are presented graphically and discussed.

A Model of Solar Radiation and Joule Heating in Flow of Third Grade Nanofluid

2015 ◽  
Vol 70 (3) ◽  
pp. 177-184 ◽  
Author(s):  
Tariq Hussain ◽  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Ahmed Alsaedi ◽  
Bin Chen
Keyword(s):  
Solar Radiation ◽  
Joule Heating ◽  
Shear Thickening ◽  
Radiation Energy ◽  
Skin Friction Coefficient ◽  
Third Grade ◽  
Physical Parameters ◽  
Convective Conditions ◽  
Grade Fluid ◽  
The Impact

AbstractThe flow problem resulting from the stretching of a surface with convective conditions in a magnetohydrodynamic nanofluid with solar radiation is examined. Both heat and nanoparticle mass transfer convective conditions are employed. An incompressible third grade fluid which exhibits shear thinning and shear thickening characteristics is used as a base fluid. Concept of convective nanoparticle mass condition is introduced. Effects of Brownian motion and thermophoresis on magnetohydrodynamic flow of nanofluid are accounted in the presence of thermal radiation. Energy equation incorporates the features of Joule heating. The impact of physical parameters on the temperature and nanoparticle concentration has been pointed out. Numerical values of skin-friction coefficient are presented and analysed. It is hoped that this present investigation serves as a stimulus for the next generation of solar film collectors, heat exchangers technology, material processing, geothermal energy storage, and all those processes which are highly affected by the heat enhancement concept.

scholarly journals Heat Transfer of Thin Film Flow Over an Unsteady Stretching Sheet with Dynamic Viscosity

2021 ◽  
Vol 81 (2) ◽  
pp. 67-81
Author(s):  
Ali R ehman ◽  
Zabidin Salleh ◽  
Taza Gul
Keyword(s):  
Differential Equation ◽  
Dynamic Viscosity ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Nonlinear Ordinary Differential Equation ◽  
Thin Film Flow ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
The Impact

This research paper explains the impact of dynamics viscosity of water base GO-EG/GO-W nanofluid over a stretching sheet. The impact of different parameter for velocity and temperature are displayed and discussed. The similarity transformation is used to convert the partial differential equation to nonlinear ordinary differential equation. The solution of the problem is obtained by using the optimal homotopy analysis method (OHAM). The BVPh 2.0 package function of Mathematica is used to obtain the numerical results. The result of important parameter such as magnetic parameter, Prandtl number, Eckert number, dynamic viscosity, nanoparticles volume fraction and unsteady parameter for both velocity and temperature profiles are plotted and discussed. The BVPh 2.0 package is used to obtain the convergences of the problem up to 25 iteration. The skin friction coefficient and Nusselt number is explained in table form.

scholarly journals Analysis of entropy generation minimization (EGM) in flow of Ree-Eyring nanofluid between two coaxially rotating disks

2020 ◽  
pp. 57-57
Author(s):  
Muhammad Khan ◽  
Riaz Muhammad ◽  
Sumaira Qayyum ◽  
Niaz Khan ◽  
M. Jameel
Keyword(s):  
Ohmic Heating ◽  
Skin Friction Coefficient ◽  
Random Motion ◽  
Brownian Diffusion ◽  
Physical Parameters ◽  
Rotating Disks ◽  
Rotational Parameter ◽  
Transfer Rates ◽  
Homotopy Analysis ◽  
Buongiorno Model

The present communication addresses MHD radiative nanomaterial flow of Ree-Eying fluid between two coaxially rotating disks. Both disks are stretchable. Buongiorno model is used for nanofluids. Nanofluid aspects comprise random motion of particles (Brownian diffusion) and thermophoresis. MHD fluid is considered. Furthermore, dissipation, radiative heat flux and Ohmic heating effects are considered to model the energy equation. Total entropy rate is calculated through implementation of second thermodynamics law. Series solutions are developed through homotopy analysis method. Impacts of physical parameters on the velocity, temperature, entropy and concentration fields are discussed graphically. Skin friction coefficient and heat and mass transfer rates are numerically calculated through Tables 2-4. It is noticed that the velocity of liquid particles decreases versus higher estimations of magnetic parameter while it enhances via larger rotational parameter. Temperature field significantly increases in the presence of both Brownian diffusion and thermophoresis parameters.

scholarly journals Heat Transfer and Flow Characteristics of Pseudoplastic Nanomaterial Liquid Flowing over the Slender Cylinder with Variable Characteristics

Crystals ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 27
Author(s):  
Azad Hussain ◽  
Aysha Rehman ◽  
Naqash Ahmed ◽  
A. S. El-Shafay ◽  
Sahar A. Najati ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Variable Viscosity ◽  
Flow Characteristics ◽  
Skin Friction Coefficient ◽  
Weissenberg Number ◽  
Nano Particles ◽  
Nonlinear Flow ◽  
Physical Parameters ◽  
Flow Equations ◽  
Buongiorno Model

The present article investigates heat transfer and pseudoplastic nanomaterial liquid flow over a vertical thin cylinder. The Buongiorno model is used for this analysis. The problem gains more significance when temperature-dependent variable viscosity is taken into account. Using suitable similarity variables, nonlinear flow equations are first converted into ordinary differential equations. The generating structure is solved by the MATLAB BVP4C algorithm. Newly developed physical parameters are focused. It is observed that the heat transfer rate and the skin friction coefficient is increased remarkably because of mixing nano-particles in the base fluid by considering γb=1, 2, 3, 4 and λ=1, 1.5, 2, 2.5,3. It is found that the temperature field increases by inclining the values of thermophoresis and Brownian motion parameters. It is also evaluated that the velocity field decreases by increasing the values of the curvature parameter, Weissenberg number and buoyancy ratio characteristics.

scholarly journals Assisting and Opposing Stagnation Point Pseudoplastic Nano Liquid Flow towards a Flexible Riga Sheet: A Computational Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Aysha Rehman ◽  
Azad Hussain ◽  
Sohail Nadeem
Keyword(s):  
Brownian Motion ◽  
Mixed Convection ◽  
Hartmann Number ◽  
Lewis Number ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Diverse Range ◽  
Flow Equations ◽  
Buongiorno Model

Nanofluids are used as coolants in heat transport devices like heat exchangers, radiators, and electronic cooling systems (like a flat plate) because of their improved thermal properties. The preeminent perspective of this study is to highlight the influence of combined convection on heat transfer and pseudoplastic non-Newtonian nanofluid flow towards an extendable Riga surface. Buongiorno model is incorporated in the present study to tackle a diverse range of Reynolds numbers and to analyze the behavior of the pseudoplastic nanofluid flow. Nanofluid features are scrutinized through Brownian motion and thermophoresis diffusion. By the use of the boundary layer principle, the compact form of flow equations is transformed into component forms. The modeled system is numerically simulated. The effects of various physical parameters on skin friction, mass transfer, and thermal energy are numerically computed. Fluctuations of velocity increased when modified Hartmann number and mixed convection parameter are boosted, where it collapses for Weissenberg number and width parameter. It can be revealed that the temperature curve gets down if modified Hartmann number, mixed convection, and buoyancy ratio parameters upgrade. Concentration patterns diminish when there is an incline in width parameter and Lewis number; on the other hand, it went upward for Brownian motion parameter, modified Hartmann, and Prandtl number.

scholarly journals Biomathematical analysis for the carbon nanotubes effects in the stagnation point flow towards a nonlinear stretching sheet with homogeneous-heterogeneous reaction

2020 ◽  
Vol 17 (1) ◽  
pp. 67-77
Author(s):  
S. R. Reddisekhar Reddy ◽  
P. Bala Anki Reddy
Keyword(s):  
Carbon Nanotubes ◽  
Stretching Sheet ◽  
Heterogeneous Reaction ◽  
Skin Friction Coefficient ◽  
Heterogeneous Reactions ◽  
Single Wall Carbon Nanotubes ◽  
Published Data ◽  
Physical Parameters ◽  
Local Skin ◽  
Nonlinear Stretching

The main objective of this paper is to study the homogeneous-heterogeneous reactions in magnetohydrodynamic flow due to a nonlinear stretching sheet. Analysis for single wall carbon nanotubes with water and pure blood are taken as the base fluids. The governing non-linear partial differential equations are transformed into ordinary which are solved numerically by utilizing the fourth order Runge-Kutta method with shooting technique. Graphical results have been presented for velocity profile, temperature, concentration, local skin friction coefficient and local Nusselt number profiles for various physical parameters of interest. Comparisons with previously published data are performed and the results are found to be excellent agreement.

scholarly journals Numerical Treatment for the Three-Dimensional Eyring-Powell Fluid Flow over a Stretching Sheet with Velocity Slip and Activation Energy

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Umar ◽  
Rizwan Akhtar ◽  
Zulqurnain Sabir ◽  
Hafiz Abdul Wahab ◽  
Zhu Zhiyu ◽  
...  
Keyword(s):  
Activation Energy ◽  
Nonlinear System ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Lewis Number ◽  
Velocity Slip ◽  
Dynamical Analysis ◽  
Physical Parameters ◽  
Similarity Transformations ◽  
Computational Paradigm

In this manuscript, a computational paradigm of technique shooting is exploited for investigation of the three-dimensional Eyring-Powell fluid with activation energy over a stretching sheet with slip arising in the field of fluid dynamics. The problem is modeled and resulting nonlinear system of PDEs is transformed into nonlinear system of ODEs using well-known similarity transformations. The strength of shooting based computing approach is employed to analyze the dynamics of the system. The proposed technique is well-designed for different scenarios of the system based on three-dimensional non-Newtonian fluid with activation energy over a stretching sheet. Slip condition is also incorporated to enhance the physical and dynamical analysis of the system. The proposed results are compared with the bvp4C method for the correctness of the solver. Graphical and numerical illustrations are used to envisage the behavior of different proficient physical parameters of interest including magnetic parameter, stretching rate parameter, velocity slip parameter, Biot number on velocity, and Lewis number on temperature and concentration.

Entropy Generation with nonlinear heat and Mass transfer on MHD Boundary Layer over a Moving Surface using SLM

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
M. M. Bhatti ◽  
M. M. Rashidi ◽  
I. Pop
Keyword(s):  
Boundary Layer ◽  
Chemical Reaction ◽  
Entropy Generation ◽  
Skin Friction Coefficient ◽  
Momentum Equation ◽  
Physical Parameters ◽  
Numerical Comparison ◽  
Moving Surface ◽  
Mhd Boundary Layer ◽  
The Impact

AbstractIn this article, entropy generation with combined effects of thermal radiation and chemical reaction on MHD boundary layer over a moving surface has been investigated. The governing flow comprises of linear momentum equation, energy, and concentration equations which are modified with the help of similarity variables. The reduced resulting nonlinear coupled ordinary differential equations are solved with the help of Successive linearization method (SLM) and Chebyshev spectral collocation method. The impact of all the physical parameters is demonstrated numerically and graphically. A detailed analysis have been given for all the pertinent parameters such as Hartmann number, porosity parameter, Prandtl number, radiation parameter, suction/injection parameter, moving parameter, Brinkmann number, Reynolds number, chemical reaction parameter and Schmidt number on velocity, temperature, concentration and entropy profile as well as the Skin friction coefficient, Nusselt number and Sherwood number are also conducted. The numerical comparison has also been given to the existing published literature.

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