scholarly journals Dual solutions for three-dimensional magnetohydrodynamic nanofluid flow with entropy generation

2019 ◽  
Vol 6 (4) ◽  
pp. 657-665 ◽  
Author(s):  
Hiranmoy Mondal ◽  
Mohammed Almakki ◽  
Precious Sibanda
Keyword(s):  
Brownian Motion ◽  
Entropy Generation ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Linearization Method ◽  
Dissipation Function ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Temperature Profiles ◽  
Residual Errors

Abstract This paper presents a formulation for simulating magnetohydrodynamic three-dimensional convective flow and heat transfer in a nanofluid by incorporating the complete viscous dissipation function in the energy equation. A novel feature of this investigation of entropy generation and dual solutions is the use of the spectral quasilinearization method to solve the conservation equations. The results are compared with exact solutions or higher order solutions and a good agreement is achieved. The accuracy is determined by calculation of residual errors and the method of solution is shown to produce smaller residual errors than those achieved by the fifth-order Runge-Kutta Fehlberg method for nonlinear differential equations. The dual solutions for different Prandtl number, and Brownian motion and thermophoresis parameters are shown graphically and discussed. It is found that the temperature profiles as well as thermal boundary layer thickness increase with the Brownian motion parameter for first and the second solutions. The temperature profiles increase with the thermophoresis parameter for the first and second solutions. The entropy generation increases with the Reynolds number. Highlights Combined effects of entropy generation and MHD nanofluid are proposed. Spectral quasi-linearization method (SQLM) is used for computer simulations. Use axisymmetric stretching/shrinking sheet for dual solution. Validate the accuracy and convergence using residual error analysis.

Viscous and Joule Heating in the Stagnation Point Nanofluid Flow Through a Stretching Sheet With Homogenous–Heterogeneous Reactions and Nonlinear Convection

2013 ◽  
Vol 4 (4) ◽  
Author(s):  
R. Nandkeolyar ◽  
S. S. Motsa ◽  
P. Sibanda
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
Joule Heating ◽  
Volume Fraction ◽  
Nonlinear Differential Equations ◽  
Linearization Method ◽  
Heterogeneous Reactions ◽  
Problem Solver ◽  
Shrinking Sheet ◽  
Temperature Relation

The combined effects of viscous and Joule heating on the stagnation point flow of a nanofluid through a stretching/shrinking sheet in the presence of homogeneous–heterogeneous reactions are investigated. The nanoparticle volume fraction model is used to describe the nanofluid. In this study, the density temperature relation is nonlinear which causes a nonlinear convective heat transfer. The surface of the sheet is assumed to be convectively heated with a hot fluid. The governing nonlinear differential equations are solved using the successive linearization method (SLM), and the results are validated by comparison with numerical approximations obtained using the Matlab in-built boundary value problem solver bvp4c and with existing results in literature. The nanofluid problem finds applications in heat transfer devices where the density and temperature relations are complex and the viscosity of the fluid has significant effect on the heat transfer rate.

scholarly journals On Unsteady Three-Dimensional Axisymmetric MHD Nanofluid Flow with Entropy Generation and Thermo-Diffusion Effects

2017 ◽  
Author(s):  
Mohammed Almakki ◽  
Sharadia Dey ◽  
Sabyasachi Mondal ◽  
Precious Sibanda
Keyword(s):  
Nusselt Number ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Three Dimensional ◽  
Linearization Method ◽  
Physical Parameters ◽  
Particle Volume ◽  
Nanofluid Flow

We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasilinearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account when the nanofluid particle volume fraction on the boundary in passively controlled. The results show that as the Hartman number increases, both the Nusselt number and the Sherwood number decrease whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with the physical parameters.

An Analytic Solution for Electrical Magneto-Hydrodynamics Darcy–Forchheimer Three Dimensional Non-Newtonian Nanofluid Flow with Convective Boundary Conditions

2020 ◽  
Vol 9 (4) ◽  
pp. 257-268
Author(s):  
Gossaye Aliy Adem
Keyword(s):  
Brownian Motion ◽  
Velocity Profile ◽  
Electric Field ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Slip Parameter ◽  
Convective Boundary ◽  
Strongly Nonlinear ◽  
Biot Numbers

In this article, the treatment of three-dimensional non-Newtonian Williamson fluid has been carried out under examination. Using the standard transformation, the governing equations are converted into universal similarity equations which have been solved by the optimal homotopy asymptotic method. We observed that the method is effective, reliable, consistent and efficient in solving strongly nonlinear differential equations. The influence of embedded parameters on the fluid flow has discovered graphically and using table. The velocity profile in the x-direction is increased with magnetic and electric field parameters and decreased with the increased stretching parameter, coefficient of inertia, velocity slip parameter L1 and porosity parameters. The velocity profile in the y-direction is increased with magnetic and electric field parameters, the distended stretching parameter, while reduced with the velocity slip parameter L2, coefficient of inertia, and porosity parameters. The temperature profile is increased with the radiation, thermophoresis and Brownian motion parameters, and Biot number. The profile of concentration is rising with the enlarged Biot numbers and thermophoresis parameter, while reduced with the Brownian motion parameter.

scholarly journals Entropy generation as a practical tool of optimisation for non-Newtonian nanofluid flow through a permeable stretching surface using SLM

2016 ◽  
Vol 4 (1) ◽  
pp. 21-28 ◽  
Author(s):  
Muhammad Mubashir Bhatti ◽  
Tehseen Abbas ◽  
Mohammad Mehdi Rashidi
Keyword(s):  
Brownian Motion ◽  
Entropy Generation ◽  
Stretching Sheet ◽  
Flow Problem ◽  
Similarity Transformation ◽  
Linearization Method ◽  
Physical Parameters ◽  
Nanoparticle Concentration ◽  
Suction Parameter ◽  
Successive Linearization Method

Abstract In this article, entropy generation on non-Newtonian Eyring-Powell nanofluid has been analysed through a permeable stretching sheet. The governing flow problem is based on linear momentum, thermal energy, and nanoparticle concentration equation which are simplified with the help of similarity transformation variables. The resulting coupled nonlinear ordinary differential equations are solved numerically with the help of Successive Linearization method (SLM) and Chebyshev Spectral collocation method. The novel characteristics of all the physical parameters are discussed with the help of graphs and tables. The expression for local Nusselt number and local Sherwood number is also taken into account. It is observed that velocity profile increases due to the greater influence of suction parameter. Moreover, Brownian motion and thermophoresis parameter significantly enhance the temperature profile, however Brownian motion parameter shows converse behaviour on nanoparticle concentration profile. Entropy profile acts as an increasing function of all the pertinent parameters. Highlights This study analyses entropy generation on non-Newtonian Eyring-Powell nanofluid through a permeable stretching sheet. The governing flow problem is modelled with the help of similarity transformation variables. The physical behavior of all parameters of the problem is discussed. Comparison with an existing results shows the validity of the present methodology.

Thermomechanical Coupling of a Hyper-viscoelastic Truck Tire and a Pavement Layer and its Impact on Three-dimensional Contact Stresses

2021 ◽  
pp. 036119812110171
Author(s):  
Angeli Jayme ◽  
Imad L. Al-Qadi
Keyword(s):  
Contact Stress ◽  
Contact Area ◽  
Three Dimensional ◽  
Interaction Model ◽  
Rolling Resistance ◽  
Contact Stresses ◽  
Thermomechanical Coupling ◽  
Temperature Profiles ◽  
Near Surface ◽  
Truck Tire

A thermomechanical coupling between a hyper-viscoelastic tire and a representative pavement layer was conducted to assess the effect of various temperature profiles on the mechanical behavior of a rolling truck tire. The two deformable bodies, namely the tire and pavement layer, were subjected to steady-state-uniform and non-uniform temperature profiles to identify the significance of considering temperature as a variable in contact-stress prediction. A myriad of ambient, internal air, and pavement-surface conditions were simulated, along with combinations of applied tire load, tire-inflation pressure, and traveling speed. Analogous to winter, the low temperature profiles induced a smaller tire-pavement contact area that resulted in stress localization. On the other hand, under high temperature conditions during the summer, higher tire deformation resulted in lower contact-stress magnitudes owing to an increase in the tire-pavement contact area. In both conditions, vertical and longitudinal contact stresses are impacted, while transverse contact stresses are relatively less affected. This behavior, however, may change under a non-free-rolling condition, such as braking, accelerating, and cornering. By incorporating temperature into the tire-pavement interaction model, changes in the magnitude and distribution of the three-dimensional contact stresses were manifested. This would have a direct implication on the rolling resistance and near-surface behavior of flexible pavements.

Magneto convective flow of casson nanofluid due to Stefan blowing in the presence of bio-active mixers

2021 ◽  
pp. 239779142110166
Author(s):  
Venkatesh Puneeth ◽  
Sarpabhushana Manjunatha ◽  
Bijjanal Jayanna Gireesha ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Convective Flow ◽  
Three Dimensional ◽  
Induced Magnetic Field ◽  
Density Profiles ◽  
Casson Nanofluid ◽  
And Brownian Motion ◽  
Similarity Transformations ◽  
The Mathematical Model

The induced magnetic field for three-dimensional bio-convective flow of Casson nanofluid containing gyrotactic microorganisms along a vertical stretching sheet is investigated. The movement of these microorganisms cause bioconvection and they act as bio-active mixers that help in stabilising the nanoparticles in the suspension. The two forces, Thermophoresis and Brownian motion are incorporated in the Mathematical model along with Stefan blowing. The resulting model is transformed to ordinary differential equations using similarity transformations and are solved using [Formula: see text] method. The Velocity, Induced Magnetic field, Temperature, Concentration of Nanoparticles, and Motile density profiles are interpreted graphically. It is observed that the Casson parameter decreases the flow velocity and enhances the temperature, concentration, and motile density profiles and also it is noticed that the blowing enhances the nanofluid profiles whereas, suction diminishes the nanofluid profiles. On the other hand, it is perceived that the rate of heat conduction is enhanced with Thermophoresis and Brownian motion.

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

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