Insight into the dynamics of non-Newtonian Carreau fluid when viscous dissipation,entropy generation,convective heating and diffusion are significant

The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation optimization.The novel dynamic of viscous dissipation is utilized to analyze the thermal mechanism of magnetized flow.The convective boundary assumptions are directed in order to examine the heat and mass transportation of nanofluid.The thermal concept of thermophoresis and Brownian movements has been re-called with the help of Buongiorno model.The problem formulated in dimensionless form is solved by NDSolve MATHEMATICA.The graphical analysis for parameters governed by the problem is performed with physical applications.The affiliation of entropy generation and Bejan number for different parameters is inspected in detail.The numerical data for illustrating skin friction,heat and mass transfer rate is also reported.The motion of the fluid is highest for the viscosity ratio parameter.The temperature of the fluid rises via thermal Biot number.Entropy generation rises for greater Brinkman number and diffusion parameter.

FlowBreakdown of Hybrid Nanofluid on a Rigid Surface with Power Law Fluid as Lubricated Layers

Thiswork investigates an oblique stagnation point flowof hybrid nanofluid over a rigid surface with power lawfluidas lubricated layers. Copper (Cu) and Silver (Ag) solid particles are used as hybrid particles acting in water H2O asa base fluid. The mathematical formulation of flow configuration is presented in terms of differential systemthat isnonlinear in nature. The thermal aspects of the flow field are also investigated by assuming the surface is a heatedsurface with a constant temperature T. Numerical solutions to the governing mathematical model are calculatedby the RK45 algorithm. The results based on the numerical solution against various flow and thermal controllingparameters are presented in terms of line graphs. The specific results depict that the heat flux increases over thelubricated-indexed parameter.

Biomathematical study of time-dependent flow of a Carreau nanofluid through inclined catheterized arteries with overlapping stenosis

This work is concerned with the analysis of blood flow through inclined catheterized arteries having a balloon(angioplasty) with time-variant overlapping stenosis. The nature of blood in small arteries is analyzed mathematically by considering it as a Carreau nanofluid. The highly nonlinear momentum equations of nanofluid model are simplified by considering the mild stenosis case. The formulated problem is solved by a homotopy perturbation expansion in terms of a variant of the Weissenberg number to obtain explicit forms for the axial velocity, the stream function, the pressure gradient, the resistance impedance and the wall shear stress distribution. These solutions depend on the Brownian motion number, thermophoresis number, local temperature Grashof number G_r and local nanoparticle Grash of number B_r. The results were also studied for various values of the physical parameters, such as the Weissenberg number W_i, the power law index n, the taper angle φ, the maximum height of stenosis δ~*, the angle of inclination α, the maximum height of balloon σ~*, the axial displacement of the balloon z_d~*,the flow rate F and the Froud number Fr. The obtained results show that the transmission of axial velocity curves through a Newtonian fluid(Wi=0, n=1, Gr=0, Br=0, Nt=0, Nb≠0) is substantially lower than that through a Carreau nanofluid near the wall of balloon while the inverse occurs in the region between the balloon and stenosis. The streamlines have a clearly distinguished shifting toward the stenotic region and this shifting appears near the wall of the balloon, while it has almost disappeared near the stenotic wall and the trapping bolus in the case of horizontal arteries and Newtonian fluid(Wi=0, n=1, Gr=0, Br=0, Nt=0, Nb≠0) does not appear but for the case of Carreau nanofluid bolus appears.

Flow of Casson nanofluid with viscous dissipation and convective conditions: A mathematical model

The magnetohydrodynamic(MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated.Convective conditions of temperature and nanoparticle concentration are employed in the formulation. The flow is generated due to exponentially stretching surface. The governing boundary layer equations are reduced into the ordinary differential equations. Series solutions are presented to analyze the velocity, temperature and nanoparticle concentration fields. Temperature and nanoparticle concentration fields decrease when the values of Casson parameter enhance. It is found that the Biot numbers arising due to thermal and concentration convective conditions yield an enhancement in the temperature and concentration fields. Further, we observed that both the thermal and nanoparticle concentration boundary layer thicknesses are higher for the larger values of thermophoresis parameter. The effects of Brownian motion parameter on the temperature and nanoparticle concentration are reverse.

Three-dimensional boundary layer flow of Maxwell nanofluid:mathematical model

The present research explores the three-dimensional boundary layer flow of the Maxwell nanofluid. The flow is generated by a bidirectional stretching surface. The mathematical formulation is carried out through a boundary layer approach with the heat source/sink, the Brownian motion, and the thermophoresis effects. The newly developed boundary conditions requiring zero nanoparticle mass flux at the boundary are employed in the flow analysis for the Maxwell fluid. The governing nonlinear boundary layer equations through appropriate transformations are reduced to the coupled nonlin- ear ordinary differential system. The resulting nonlinear system is solved. Graphs are plotted to examine the effects of various interesting parameters on the non-dimensional velocities, temperature, and concentration fields. The values of the local Nusselt number are computed and examined numerically.

A Mathematical Model for Studying the Slip Effect on Peristaltic Motion with Heat and Mass Transfer

A mathematical model is presented with an interest to examine the peristaltic motion in an asymmetric channel by taking into account the slip,heat and mass transfer.Constitutive relationships for a micropolar fluid are used.The solution procedure for nonlinear analysis is given under long wavelength and low Reynolds number approximations.The effects of sundry parameters entering into the expressions of axial velocity,temperature and concentration are explored.Pumping and trapping phenomena are discussed.

Designing Pair of Nonlinear Components of a Block Cipher over Gaussian Integers

In block ciphers,the nonlinear components,also known as sub-stitution boxes(S-boxes),are used with the purpose of inducing confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the points of elliptic curves has been published.The main purpose of these studies is to hide data and improve the security levels of crypto algorithms.In this work,we design pair of nonlinear components of a block cipher over the residue class of Gaussian integers(GI).The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters.But the prime field dependent on the Elliptic curve(EC)provides one S-box at a time by fixing three parameters a,b,and p.The newly designed pair of S-boxes are assessed by various tests like nonlinearity,bit independence criterion,strict avalanche criterion,linear approximation probability,and differential approximation probability.

Asymmetric Key Cryptosystem for Image Encryption by Elliptic Curve over Galois Field GF(2^(n))

Protecting the integrity and secrecy of digital data transmitted through the internet is a growing problem.In this paper,we introduce an asymmetric key algorithm for specifically processing images with larger bit values.To overcome the separate flaws of elliptic curve cryptography(ECC)and the Hill cipher(HC),we present an approach to picture encryption by combining these two encryption approaches.In addition,to strengthen our scheme,the group laws are defined over the rational points of a given elliptic curve(EC)over a Galois field(GF).The exclusive-or(XOR)function is used instead of matrix multiplication to encrypt and decrypt the data which also refutes the need for the inverse of the key matrix.By integrating the inverse function on the pixels of the image,we have improved system security and have a wider key space.Furthermore,through comprehensive analysis of the proposed scheme with different available analyses and standard attacks,it is confirmed that our proposed scheme provides improved speed,security,and efficiency.

A Novel Approach for Security Enhancement of Data Encryption Standard

Data Encryption Standard(DES)is a symmetric key cryptosystem that is applied in different cryptosystems of recent times.However,researchers found defects in the main assembling of the DES and declared it insecure against linear and differential cryptanalysis.In this paper,we have studied the faults and made improvements in their internal structure and get the new algorithm for Improved DES.The improvement is being made in the substitution step,which is the only nonlinear component of the algorithm.This alteration provided us with great outcomes and increase the strength of DES.Accordingly,a novel 6×6 good quality S-box construction scheme has been hired in the substitution phase of the DES.The construction involves the Galois field method and generates robust S-boxes that are used to secure the scheme against linear and differential attacks.Then again,the key space of the improved DES has been enhanced against the brute force attack.The out-comes of different performance analyses depict the strength of our proposed substitution boxes which also guarantees the strength of the overall DES.

Nonlinear Components of a Block Cipher over Eisenstein Integers

In block ciphers,the nonlinear components,also known as substitution boxes(S-boxes),are used with the purpose to induce confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the points of elliptic curves,chaotic maps,and Gaussian integers has been published.The main purpose of these studies is to hide data and improve the security levels of crypto algorithms.In this work,we design pair of nonlinear components of a block cipher over the residue class of Eisenstein integers(EI).The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters.However,in the same way,by taking three fixed parameters only one S-box is obtained through a prime field-dependent Elliptic curve(EC),chaotic maps,and Gaussian integers.The newly designed pair of S-boxes are assessed by various tests like nonlinearity,bit independence criterion,strict avalanche criterion,linear approximation probability,and differential approximation probability.

不同pH条件下硫化钼纳米片吸附Cd(Ⅱ)的微观机制研究

本研究结合静态实验和X射线吸收精细结构谱学(EXAFS)评估了硫化钼纳米片对重金属Cd(Ⅱ)的吸附行为和微观机制。结果表明:Cd(Ⅱ)在硫化钼纳米片上的吸附受溶液pH、反应时间和温度的显著影响,但不受离子强度的影响。在pH 3.3~9.6范围内, pH升高显著促进了硫化钼对Cd(Ⅱ)的吸附量,但不改变吸收速率、吸附等温线和热力学。二级动力学模型能更好地拟合该吸附平衡,且内表面颗粒扩散模型显示了吸附过程中的三个典型阶段。等温线和热力学分析说明Cd(Ⅱ)在硫化钼上的吸附是异质性的、自发的、吸热的和不可逆的过程。EXAFS光谱学分析揭示了该吸附存在两种类型:在较低的pH(3.56,6.48)条件下,内表面络合以Cd–S配位键为主;在较高的pH(9.57)条件下,出现Cd(OH)2沉淀,且配位键以Cd–O和Cd–Cd的形式存在。这些研究结果对于评估重金属离子和硫化钼纳米片在分子水平上的作用机理提供了新的视野。

Simulation of the Second Grade Fluid Model for Blood Flow through a Tapered Artery with a Stenosis

我们通过一根逐渐变细的动脉分析血流动，假定血是第二个顺序液体模型。结果部分微分方程的非线性的含蓄的系统被不安方法解决。表情为砍应力，速度，流动率，墙砍应力和纵的阻抗被获得。不同参数的物理行为也被讨论，作为正在套住现象。[从作者抽象]

Boundary layer flow of third grade nanofluid with Newtonian heating and viscous dissipation

Two-dimensional boundary layer flow of an incompressible third grade nanofluid over a stretching surface is investigated.Influence of thermophoresis and Brownian motion is considered in the presence of Newtonian heating and viscous dissipation.Governing nonlinear problems of velocity, temperature and nanoparticle concentration are solved via homotopic procedure.Convergence is examined graphically and numerically. Results of temperature and nanoparticle concentration are plotted and discussed for various values of material parameters, Prandtl number, Lewis number, Newtonian heating parameter, Eckert number and thermophoresis and Brownian motion parameters. Numerical computations are performed. The results show that the change in temperature and nanoparticle concentration distribution functions is similar when we use higher values of material parameters β1 andβ2. It is seen that the temperature and thermal boundary layer thickness are increasing functions of Newtonian heating parameter γ.An increase in thermophoresis and Brownian motion parameters tends to an enhancement in the temperature.

Peristaltic flow in an asymmetric channel with convective boundary conditions and Joule heating

The peristaltic transport of viscous fluid in an asymmetric channel is concentrated. The channel walls exhibit convective boundary conditions. Both cases of hydrodynamic and magnetohydrodynamic(MHD) fluids are considered. Mathematical analysis has been presented in a wave frame of reference. The resulting problems are non-dimensionalized. Long wavelength and low Reynolds number approximations are employed. Joule heating effect on the thermal equation is retained. Analytic solutions for stream function and temperature are constructed. Numerical integration is carried out for pressure rise per wavelength. Effects of influential flow parameters have been pointed out through graphs.

MHD three-dimensional flow of Jeffrey fluid with Newtonian heating

The magnetohydrodynamic(MHD) three-dimensional flow of Jeffrey fluid in the presence of Newtonian heating is investigated. Flow is caused by a bidirectional stretching surface. Series solutions are constructed for the velocity and temperature fields. Convergence of series solutions is ensured graphically and numerically. The variations of key parameters on the physical quantities are shown and discussed in detail. Constructed series solutions are compared with the existing solutions in the limiting case and an excellent agreement is noticed. Nusselt numbers are computed with and without magnetic fields. It is observed that the Nusselt number decreases in the presence of magnetic field.

Convective heat and mass transfer in MHD mixed convection flow of Jeffrey nanofluid over a radially stretching surface with thermal radiation

Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed.

Effects of partial slip on flow of a third grade fluid

This paper is an analytical study of the rotating flow of a third grade fluid past a porous plate with partial slip effects. It serves as a flow model for the study of polymers. The analytic solution has been determined using homotopy analysis method （HAM）.

Mixed convective heat and mass transfer analysis for peristaltic transport in an asymmetric channel with Soret and Dufour effects

The present investigation addresses the simultaneous effects of heat and mass transfer in the mixed convection peristaltic flow of viscous fluid in an asymmetric channel. The channel walls exhibit the convective boundary conditions. In addition, the effects due to Soret and Dufour are taken into consideration. Resulting problems are solved for the series solutions. Numerical values of heat and mass transfer rates are displayed and studied. Results indicate that the concentration and temperature of the fluid increase whereas the mass transfer rate at the wall decreases with increase of the mass transfer Biot number. Furthermore, it is observed that the temperature decreases with the increase of the heat transfer Biot number.

Thin Film Flow of a Second Grade Fluid over a Stretching/Shrinking Sheet with Variable Temperature-Dependent Viscosity

在一张水平多孔的拉长表上的一部薄电影的流动和热转移上的可变粘性的效果被分析。为动量和热精力的稳定的边界层方程被使用类似转变简化。结果并且联合了非线性的微分方程被 Homotopy 分析解决方法。结果图形地被介绍解释处于这个问题出现的各种各样的物理参数。

Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis

Non-Newtonian fluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper.The Jeffrey fluid has two parameters,the relaxation time λ1 and retardation time λ2.The governing equations are simplified using the case of mild stenosis.Perturbation method is used to solve the resulting equations.The effects of non-Newtonian nature of blood on velocity profile,temperature profile,wall shear stress,shearing stress at the stenotsis throat and impedance of the artery are discussed.The results for Newtonian fluid are obtained as special case from this model.