scholarly journals Impact of Nanofluid Flow over an Elongated Moving Surface with a Uniform Hydromagnetic Field and Nonlinear Heat Reservoir

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Haroon U. R. Rasheed ◽  
Saeed Islam ◽  
Zeeshan Khan ◽  
Sayer O. Alharbi ◽  
Hammad Alotaibi ◽  
...  
Keyword(s):  
Mathematical Formulation ◽  
Heat Rate ◽  
Lewis Number ◽  
Physical Parameters ◽  
Flow Equations ◽  
Heat Transfer Fluids ◽  
Differential Flow ◽  
Global Demand ◽  
Flow Features ◽  
Limiting Case

The increasing global demand for energy necessitates devoted attention to the formulation and exploration of mechanisms of thermal heat exchangers to explore and save heat energy. Thus, innovative thermal transport fluids require to boost thermal conductivity and heat flow features to upsurge convection heat rate, and nanofluids have been effectively employed as standard heat transfer fluids. With such intention, herein, we formulated and developed the constitutive flow laws by utilizing the Rossland diffusion approximation and Stephen’s law along with the MHD effect. The mathematical formulation is based on boundary layer theory pioneered by Prandtl. Governing nonlinear partial differential flow equations are changed to ODEs via the implementation of the similarity variables. A well-known computational algorithm BVPh2 has been utilized for the solution of the nonlinear system of ODEs. The consequence of innumerable physical parameters on flow field, thermal distribution, and solutal field, such as magnetic field, Lewis number, velocity parameter, Prandtl number, drag force, Nusselt number, and Sherwood number, is plotted via graphs. Finally, numerical consequences are compared with the homotopic solution as a limiting case, and an exceptional agreement is found.

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.

Carbon Nanotubes Flow Induced by Rotating Stretching Disk with Non-Linear Radiations and Slip

2021 ◽  
Vol 24 ◽  
Author(s):  
Uzma Sultana ◽  
M. Mushtaq ◽  
Ilyas Khan
Keyword(s):  
Carbon Nanotubes ◽  
Mathematical Formulation ◽  
Practical Importance ◽  
Rotating Disk ◽  
Single Wall Carbon Nanotubes ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Flow Equations ◽  
Similarity Transformations ◽  
Keller Box Method

Background: The phenomena of rotating disks involving flows serve as a crucial element in the field of fluid mechanics. Due to its massive practical importance in engineering and industry, considerable attention is being paid to the extensions of the problems associated with rotating stretching disks. In this regard, Carbon nanotubes (CNT) are chosen as the best example of true nanotechnology. CNTs have an incredible range of applications due to their extraordinary characteristics. But single rotating-stretching disk with CNTs fluid flow has not been plowed yet. Objective: The objective of this work is to outstretch the study of a viscous fluid with carbon nanotubes (CNTs) and transfer of heat due to radially stretching and rotating disk contingent to Navier slip, nonlinear radiations, and convective boundary conditions. Methods: Cylindrical coordinates are utilized in the modeling and the mathematical formulation of the flow equations. These flow equations take the form of ordinary differential equations by means of similarity transformations. The emanated equations are solved by two numerical methods, i.e., the shooting method and the Keller box method, respectively. Xue model of carbon nanotubes is incorporated to carry out the research. Results: The acquired solutions are tabulated, and precise values of the physical parameters with excellent matching results are shown. These results are juxtaposed with CNTs of multi-wall and single-wall carbon nanotubes, while water is taken as a base fluid. Conclusion: Results reveal a significant depletion in skin friction with an increase in the slip parameter. Slip, nonlinear radiation, and Biot number proved as liable factors in escalating the rate of heat transfer.

Outlining the impact of second-order slip and multiple convective condition on nanofluid flow: A new statistical layout

2018 ◽  
Vol 96 (1) ◽  
pp. 104-111 ◽  
Author(s):  
Nilankush Acharya ◽  
Kalidas Das ◽  
Prabir Kumar Kundu
Keyword(s):  
Second Order ◽  
Physical Parameters ◽  
Convective Condition ◽  
Nanofluid Flow ◽  
Shooting Technique ◽  
Slip Mechanism ◽  
Runge Kutta Method ◽  
Differential Flow ◽  
Flow Features ◽  
The Impact

An analysis exploring the influence of second-order slip mechanism on nanofluid flow passing over a permeable stretching surface is investigated. Additionally we have captured the flow features including the presence of realistic thermal and solutal boundary conditions. Applying the similarity transformation procedure leads us to convert the partial differential flow related equations into nonlinear ordinary ones. After that we solved them numerically using the fourth-order Runge–Kutta method in conjunction with the shooting technique. Parametric study has been performed through tables and diagrams to highlight the consequence of velocity, temperature, and concentration profile. Moreover, a statistical attempt is made to illustrate the correlation of physical parameters within the flow system.

scholarly journals Numerical simulation of periodic MHD casson nanofluid flow through porous stretching sheet

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Abdullah Al-Mamun ◽  
S. M. Arifuzzaman ◽  
Sk. Reza-E-Rabbi ◽  
Umme Sara Alam ◽  
Saiful Islam ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Lewis Number ◽  
Stability And Convergence ◽  
Radiation Absorption ◽  
Physical Parameters ◽  
Theoretical Idea ◽  
Prostate Cancer Therapy ◽  
Flow Through ◽  
Explicit Finite Difference ◽  
The Stability

AbstractThe perspective of this paper is to characterize a Casson type of Non-Newtonian fluid flow through heat as well as mass conduction towards a stretching surface with thermophoresis and radiation absorption impacts in association with periodic hydromagnetic effect. Here heat absorption is also integrated with the heat absorbing parameter. A time dependent fundamental set of equations, i.e. momentum, energy and concentration have been established to discuss the fluid flow system. Explicit finite difference technique is occupied here by executing a procedure in Compaq Visual Fortran 6.6a to elucidate the mathematical model of liquid flow. The stability and convergence inspection has been accomplished. It has observed that the present work converged at, Pr ≥ 0.447 indicates the value of Prandtl number and Le ≥ 0.163 indicates the value of Lewis number. Impact of useful physical parameters has been illustrated graphically on various flow fields. It has inspected that the periodic magnetic field has helped to increase the interaction of the nanoparticles in the velocity field significantly. The field has been depicted in a vibrating form which is also done newly in this work. Subsequently, the Lorentz force has also represented a great impact in the updated visualization (streamlines and isotherms) of the flow field. The respective fields appeared with more wave for the larger values of magnetic parameter. These results help to visualize a theoretical idea of the effect of modern electromagnetic induction use in industry instead of traditional energy sources. Moreover, it has a great application in lung and prostate cancer therapy.

scholarly journals Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1866
Author(s):  
Zahid Javid ◽  
Ulas Karaagac ◽  
Ilhan Kocar ◽  
Ka Wing Chan
Keyword(s):  
Fixed Point ◽  
Power Flow ◽  
Low Voltage ◽  
Mathematical Formulation ◽  
Distribution Networks ◽  
Load Flow ◽  
Banach Fixed Point Theorem ◽  
Loading Conditions ◽  
Flow Equations ◽  
Uniqueness Of The Solution

There is an increasing interest in low voltage direct current (LVDC) distribution grids due to advancements in power electronics enabling efficient and economical electrical networks in the DC paradigm. Power flow equations in LVDC grids are non-linear and non-convex due to the presence of constant power nodes. Depending on the implementation, power flow equations may lead to more than one solution and unrealistic solutions; therefore, the uniqueness of the solution should not be taken for granted. This paper proposes a new power flow solver based on a graph theory for LVDC grids having radial or meshed configurations. The solver provides a unique solution. Two test feeders composed of 33 nodes and 69 nodes are considered to validate the effectiveness of the proposed method. The proposed method is compared with a fixed-point methodology called direct load flow (DLF) having a mathematical formulation equivalent to a backward forward sweep (BFS) class of solvers in the case of radial distribution networks but that can handle meshed networks more easily thanks to the use of connectivity matrices. In addition, the convergence and uniqueness of the solution is demonstrated using a Banach fixed-point theorem. The performance of the proposed method is tested for different loading conditions. The results show that the proposed method is robust and has fast convergence characteristics even with high loading conditions. All simulations are carried out in MATLAB 2020b software.

Nonlinear mixed convective Williamson nanofluid flow with the suspension of gyrotactic microorganisms

2021 ◽  
pp. 2150145
Author(s):  
Shuang-Shuang Zhou ◽  
M. Ijaz Khan ◽  
Sumaira Qayyum ◽  
B. C. Prasannakumara ◽  
R. Naveen Kumar ◽  
...  
Keyword(s):  
Heat Source ◽  
Lewis Number ◽  
Solution Procedure ◽  
Energy Concentration ◽  
Gyrotactic Microorganisms ◽  
Dimensionless Parameters ◽  
Flow Equations ◽  
Fluid Parameter ◽  
Source Sink ◽  
The Impact

This investigation aims to present the thermally developed bioconvection flow of Williamson nanoliquid over an inclined stretching cylinder in presence of linear mixed convection and nonuniform heat source/sink. The activation energy and suspension of gyrotactic microorganisms are accounted with applications of bioconvection phenomenon. Appropriate nondimensional variables are opted to attain the dimensionless form of flow equations. The resulting momentum, energy, concentration and motile density equations are abridged to highly coupled and nonlinear in nature. The numerical treatment is followed for the solution procedure by employing the shooting method. The influence of some relevant dimensionless parameters is discoursed graphically along with physical justifications. Moreover, the impact of several dimensionless parameters on skin friction and Nusselt number is obtained and listed in tables. It is observed that the velocity of fluid shows a decreasing variation for Williamson fluid parameter. The change in unsteadiness parameter and heat source parameter enhanced the nanofluid temperature. The motile microorganisms profile declines with bioconvection constant and bio-convection Lewis number.

scholarly journals EFFECT OF HEAT AND MASS TRANSFER AND THERMAL RADIATION ON A STEADY MHD CONVECTIVE FLOW WITH VISCOUS DISSIPATION AND SUCTION/INJECTION

2022 ◽  
Vol 52 (1) ◽  
pp. 35-41
Author(s):  
Silpisikha Goswami ◽  
Kamalesh Kumar Pandit ◽  
Dipak Sarma
Keyword(s):  
Nusselt Number ◽  
Thermal Radiation ◽  
Temperature Profile ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Sherwood Number ◽  
Fluid Velocity ◽  
Physical Parameters ◽  
Flow Equations ◽  
The Impact

Our motive is to examine the impact of thermal radiation and suction or injection with viscous dissipation on an MHD boundary layer flow past a vertical porous stretched sheet immersed in a porous medium. The set of the flow equations is converted into a set of non-linear ordinary differential equations by using similarity transformation. We use Runge Kutta method and shooting technique in MATLAB Package to solve the set of equations. The impact of non-dimensional physical parameters on flow profiles is analysed and depicted in graphs. We observe the influence of non-dimensional physical quantities on the Nusselt number, the Sherwood number, and skin friction and presented in tables. A comparison of the obtained numerical results with existing results in a limiting sense is also presented. We enhance radiation to observe the deceleration of fluid velocity and temperature profile for both suction and injection. While enhancing porosity parameter accelerates velocity whereas decelerates temperature profile. As the heat source parameter increases, the temperature of the fluid decreases for both suction and injection, it has been found. With the increasing values of the radiation parameter, the skin friction and heat transfer rate decreases. Increasing magnetic parameter decelerates the skin friction, Nusselt number, and Sherwood number.

Numerical simulation of nonlinear thermal radiation on the 3D flow of a couple stress Casson nanofluid due to a stretching sheet

2020 ◽  
pp. 1-28
Author(s):  
P. V. Satya Narayana ◽  
Tarakaramu Nainaru ◽  
G. Sarojamma ◽  
Isaac Lare Animasaun
Keyword(s):  
Heat Transfer ◽  
Couple Stress ◽  
Three Dimensional ◽  
Casson Fluid ◽  
Industrial Applications ◽  
Physical Parameters ◽  
Nonlinear Thermal Radiation ◽  
Scaling Analysis ◽  
Nonlinear Odes ◽  
Limiting Case

Abstract Little is known on the three-dimensional flow of couple stress Casson fluid conveying nanoparticles when the significance of Lorentz force, chaotic gesture of those minute particles and thermophoresis are significant. The intent of this investigation is to focus on the flow of such fluid along a horizontal surface due to dual stretching and internal heating. The dimensional nonlinear equations are reduced into a system of coupled nonlinear ODEs employing scaling analysis and later they are solved numerically. The results are discussed graphically for various emerged physical parameters through different plots. The results in the absence of stretching ratio factor indicate that the heat absorption parameter and Prandtl number accelerate the heat transfer rate. The temperature of the non- Newtonian couple stress fluid is found to be bigger than that of viscous case. It may be suggested that Casson couple stress nanofluid can be substituted for the corresponding viscous fluid in industrial applications for greater heat transfer. The outcomes are closely matched with the studies available in the literature as a limiting case.

An Overview on a Nonideal System With Three and a Half Degrees of Freedom

2005 ◽  
Author(s):  
Karen de Lolo Guilherme ◽  
Jose´ Manoel Balthazar ◽  
Paulo Roberto Gardel Kurka ◽  
Masayoshi Tsuchida
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Dynamical Behavior ◽  
Mathematical Formulation ◽  
Rotation Frequency ◽  
Steady State Solution ◽  
Dc Motor ◽  
Physical Parameters ◽  
Phase Coordinates ◽  
Limited Power

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor.

scholarly journals Numerical Study for the Effects of Temperature Dependent Viscosity Flow of Non-Newtonian Fluid with Double Stratification

2020 ◽  
Vol 10 (2) ◽  
pp. 708 ◽  
Author(s):  
Hafiz Abdul Wahab ◽  
Hussan Zeb ◽  
Saira Bhatti ◽  
Muhammad Gulistan ◽  
Seifedine Kadry ◽  
...  
Keyword(s):  
Newtonian Fluid ◽  
Numerical Study ◽  
Mathematical Formulation ◽  
Nano Particles ◽  
Physical Parameters ◽  
Concentration Profiles ◽  
Temperature Dependent ◽  
Double Stratification ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

The main aim of the current study is to determine the effects of the temperature dependent viscosity and thermal conductivity on magnetohydrodynamics (MHD) flow of a non-Newtonian fluid over a nonlinear stretching sheet. The viscosity of the fluid depends on stratifications. Moreover, Powell–Eyring fluid is electrically conducted subject to a non-uniform applied magnetic field. Assume a small magnetic reynolds number and boundary layer approximation are applied in the mathematical formulation. Zero nano-particles mass flux condition to the sheet is considered. The governing model is transformed into the system of nonlinear Ordinary Differential Equation (ODE) system by using suitable transformations so-called similarity transformation. In order to calculate the solution of the problem, we use the higher order convergence method, so-called shooting method followed by Runge-Kutta Fehlberg (RK45) method. The impacts of different physical parameters on velocity, temperature and concentration profiles are analyzed and discussed. The parameters of engineering interest, i.e., skin fraction, Nusselt and Sherwood numbers are studied numerically as well. We concluded that the velocity profile decreases by increasing the values of S t , H and M. Also, we have analyzed the variation of temperature and concentration profiles for different physical parameters.

Sign in / Sign up

Export Citation Format

Share Document