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The elevated convective heat transfer process plays vital role in performance of electronic and engineering equipment’s. Over the years various attempts have been executed in this regards, including the insertion of nano elements in poorly conducting liquids. Initially, improvement in thermophysical characteristics of ordinary fluids was observed but with advancement in nanoparticles structuring new classifications in nano elements are found. Among these discoveries experimentations have explored highly fascinating and intrinsically featured class of nanomaterials renowned as ferromagnetic nano constituents. So, the motivation regarding this investigation is execution about change in thermal features of base liquid with insertion of different ferrite particles. Here, water is considered as based liquid and Nickel Zinc Ferrite (NiZnFe2O4) and magnetite ferrite (Fe2O4) as solid particles are inserted. Impact of magnetic dipole is also envisioned to produce optimized effectiveness of ferrite particles. Energy transmission in flow domain is depicted by incorporation of Cattaneo-Christov heat flux model. Mathematical formulation containing thermo mechanical features of ferrite particles are attained in complexly structured partial differential system and afterwards similarity transformations are implemented for transmutation into ODES. Constructed problem is simulated by implementing numerical approaches. Influence of involved variables on associated distributions are displayed through graphs and tables. It is demonstrated that momentum as well as heat transfer of base fluid augments with inclusion of Nickel Zinc ferrite as compared magnetite ferrite. It is inferred that velocity shows declining behavior against Curie temperature whereas reverse behavior is seen for temperature profile. It is divulged that viscous dissipation imparts diminishing impact on momentum whereas contrary behavior is depicted in case of temperature profile. In addition, increment in wall drag magnitude and thermal flux is manipulated by incorporation of (NiZnFe2O4) rather than (Fe2O4).

The purpose of this article is to theoretically discuss the unsteady hemo-dynamics of blood through a catheterized overlapping stenotic vessel with nanoparticles. The nature of the blood is characterized by the constitutive Cross model equation. This study is conducted under the assumption of mild stenotic conditions and the equations of momentum and temperature are simplified after making this assumption. Explicit finite difference method is employed to obtain the numerical results of the governing equations. Results for different values of emerging parameters, such as Weissenberg number, Lewis number, thermophoresis parameter, and Brownian motion parameter are shown at different locations of an arterial cross section. These results demonstrate a pictorial way to comprehend the theoretical biomedical problem. These results reveal that Lewis number (Le) and visco-elastic parameter Weissenberg number (We) both are decreasing functions of velocity profiles at each arterial cross section. Furthermore, it is also noted that the thermophoresis parameter (Nt) quantitatively decreases the flow of blood inside the vessel while the Brownian motion parameter (Nb) shows the opposite effects on blood flow; it increases the magnitude of velocity.

In this paper we have considered a staggered cavity. It is equipped with purely viscous fluid. The physical design is controlled through mathematical formulation in terms of both the equation of continuity and equation of momentum along with boundary constraints. To be more specific, the Navier-Stokes equations for two dimensional Newtonian fluid flow in staggered enclosure is formulated and solved by well trusted method named finite element method. The novelty is increased by considering the motion of upper and lower walls of staggered cavity case-wise namely, in first case we consider that the upper wall of staggered cavity is moving and rest of walls are kept at zero velocity. In second case we consider that the upper and bottom walls are moving in a parallel way. Lastly, the upper and bottom walls are considered in an antiparallel direction. In all cases the deep analysis is performed and results are proposed by means of contour plots. The velocity components are explained by line graphs as well. The kinetic energy examination is reported for all cases. It is trusted that the findings reported in present pagination well serve as a helping source for the upcoming studies towards fluid flow in an enclosure domains being involved in an industrial areas.

This study is based on the idea that education forms a quadratic relationship with the income inequality. To evaluate it for South Asian Association for Regional Cooperation (SAARC) countries, this study uses the panel data from 1990 to 2015. Long run panel data necessitated the use of panel co-integration approach, followed up with fully modified OLS model to generate long-run coefficients. The results depict that initially primary and secondary enrollment increases inequality while tertiary enrollment decreases it. However, after a certain threshold level of enrollment (76% for primary, 42% for secondary and 7% for tertiary), their effect reverses. Thus, it makes inverted U shape for primary and secondary enrollment and U shape for tertiary enrollment. Hence education shows diminishing marginal return effect. Only the countries of India, Sri Lanka, Maldives and Nepal in SAARC economies have high enough education enrollments to cause a negative effect on income inequality.

In this paper, numerical simulations are performed in a single and double lid driven square cavity to study the flow of a Bingham viscoplastic fluid. The governing equations are discretized with the help of finite element method in space and the nonconforming Stokes elementQ~1/Q0is utilized which gives 2nd-order accuracy for velocity and 1st-order accuracy for pressure. The discretized systems of nonlinear equations are treated by using the Newton method and the inner linear subproablems are solved by the direct solver UMFPACK. A qualitative comparison is done with the results reported in the literature. In addition to these comparisons, some new reference data for the kinetic energy is generated. All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations.

The present study describes MHD micropolar fluid as a result of curved stretching surface with Cattaneo-Christov theory of heat diffusion. The new heat model with the relaxation time is employed in this paper, in spite of classical theory of heat flux presented by Fourier. The curvilinear coordinates are used to model the governing equations. The nonlinear PDE’s are changed into ODE’s by using suitable transformation. The nonlinear ODE’s are solved with the help of OHAM by using BVPh2. The variation of several parameters are indicated and examined graphically. We observed that the pressure and velocity rises by enhancing the radius of curvature.

Objective The present investigation is concerned with hybrid mediated blood flow model through atherosclerotic bifurcated artery with slip effects by considering the properties of compliant walls. Design/approach In human body, the circulatory system is made up of a network of blood vessels that include the bifurcation therefore the influence of hybrid nanoparticles on parent artery with mild stenosis, at apex and in the region of daughter arteries (after being bifurcated) is observed. Blood streaming along the segment of vessel is considered to be Newtonian. The compliant nature of the atherosclerotic artery wall is also considered to create association with permeability aspects for the thickness of arterial wall. Property of heat transfer with convective impacts is taken into account to weaken the stenotic lesions. Through phase flow model approach, a mathematical model is develop with the phenomena of hybrid nanofluid. Findings For theoretical research of designed equations experimentally determined values of nanoparticles and base fluid are used. Further, flow configurations of hemodynamics are figure out to analyze the blood flow through bifurcated stenotic artery. The comparison in parent and daughter artery is plotted for velocity profile. These patterns provide us a graphical way to recognize the importance of theoretical assistance of this model to biomedical field. At the end, it is concluded from graphical results that slip to the boundary reduces the resistance to flow for atherosclerotic bifurcated artery. Conclusions In bifurcated artery, blood circulation is assumed due to difference of pressure between atherosclerotic and non-atherosclerotic portions. Slip impacts are more effective to reduce the hemodynamics effects of stenosis for bifurcated artery. Bifurcation angle reduces the shear stress for daughter artery whereas opposite behavior is observed for parent artery. Compliant wall parameters reduces the inner bolus size in stenotic region while number of bolus increases in bifurcated region. Reduction in the amplitude of shear stress for convective parameter is more prominent in the parent artery as compared to daughter artery.

In this article we consider a smooth channel with infinite length. A circular cylinder is placed in the channel as an obstacle. A fluid satisfying Newton’s law of viscosity is taken in the channel with two different classes of velocity profiles at the inlet namely, a linear (constant) velocity profile and a parabolic profile. The mathematical model is structured by using the fundamental laws involved in the field of fluid rheology. Since the flow-describing differential equations are nonlinear in nature, a computational scheme is executed to report the primitive flow field quantities that is the pressure and the velocity. The numerical method used in this case is the finite-element method. The obtained outcomes are given by way of graphical trends. For a clear insight both the contour plots and line graphs are added. Further, the benchmark quantities namely, the drag and the lift coefficients are evaluated around the outer surface of the obstacle through the line integration. For accuracy the numerical data subject to both the drag and the lift coefficients is recorded up to nine different refinement mesh levels. Finally, the findings are concluded with the potential remark that the flow in a channel (having no-slip condition at both the lower and upper walls) with the parabolic velocity profile initiated at the inlet is the more realistic approach as compared to the linear (constant) profile being considered at the inlet.

The present case study contains evaluation of hydrodynamic forces experienced by uniformly heated square cylinder being placed fixed in a partially heated moon shaped cavity. To be more specific, the partially heated moon shaped cavity is achieved by merging two circular enclosures with different radii and common center. The left uniformly heated arc length is treated as inlet of moon shaped cavity while the right cold arc length is taken as an outlet. The uniformly heated square shaped cylinder is taken as an obstacle in between cavity. The no-slip condition is implemented at outer boundary of obstacle. The problem is mathematically modelled in terms of partial differential equations. For solution purpose the hybrid meshed finite element method is utilized. The solution is report for four different inclinations of uniformly heated square obstacle in moon shaped cavity. The primitive variable namely, velocity, pressure and temperature are studies by way of contour plots. The hydrodynamic forces subject to case-wise installation of obstacle are evaluated by adopting line integration around the uniformly heated square cylinder. It is noticed that the drag force experienced by uniformly heated square obstacle at α = 0 0 is greater as compared other inclinations.

It is a well-known fact that the interaction of ongoing Shear-thinning and Shear thickening liquid streams towards natural or manmade installed hitches holds the complex differential formulation. To seek the solution for the interpretation of the flowing shear thinning/thickening liquids stream seems difficult and hence it remains to be better understood. Therefore, the present study is case-wise mathematical devotion to fill the gap subject to evaluation of hydrodynamic forces in a corrugated domain experienced by uniformly heated triangular, square and circular shaped hitches. To be more specific, the non-Newtonian fluid named power-law fluid is taken in the corrugated channel. The flow is initiated from the left wall with a specific velocity profile. The outlet is manifested with Neumann and adiabatic conditions. The externally applied magnetic field is taken against the power-law fluid flow. The physical illustration is controlled mathematically in terms of coupled partial differential equations. The finite element method is adopted to report the solution. The three different flow modes namely, the shear thinning, Newtonian and shear thickening subject to the power-law index are examined subject to each obstacle namely triangle, square and circle. The velocity, pressure, and temperature are owned as quantities of interest for each flow mode. The obtained results are shared as contour plots. The uniformly heated obstacles are installed in each flow mode with an externally applied magnetic field and the experienced hydrodynamic forces are evaluated. It is done by adopting line integration around heated installed obstacles at various hybrid meshing levels. It is observed that the lift force as a lift coefficient for all installed obstacles is found an increasing function of the magnetic field parameter. It is trusted that the present attempt will serve as a helping directory to investigate the flows having abundant enrollments in both an engineering and natural settings.

This paper presents the stationary Bingham fluid flow simulations past a circular cylinder placed in a channel. The governing equations of motion are discretized using the mixed finite element method. The biquadratic element Q2 is used to approximate the velocity space and Pdisc for the pressure space. This LBB-stable finite element pair $$Q_{2} /P_{1}^{\text{disc}}$$ leads to an accuracy of third and second order in L2-norm for velocity and pressure approximations, respectively. The discrete version of the nonlinear system is linearized by the Newton’s method, and the linear subproblems as an inner loop are coped with UMFPACK solver. Code validation and grid independence study is also presented to confirm the reliability of the results. Simulations are carried out for various values of dimensionless Bingham number Bn, and its impact is investigated with great detail by demonstrating the velocity, viscosity and pressure contours. The benchmark quantities like drag coefficient (CD) and lift coefficient (CL) are also discussed graphically and quantitatively. Moreover, two different locations of the circular cylinder are considered for the analysis of hydrodynamic forces.

The magnetized flow field statistics of hydrodynamic forces subject to the grooved channel is debated in the present pagination. To be more specific, the grooved channel as a computational domain is considered. The fluid flow is initiated with the parabolic velocity profile at an inlet of the grooved channel. The right wall of the channel is entertained with notable Neumann condition. The velocity of the rest of the walls is taken zero. Both square and circular shaped cylinders are placed fixed in between the grooved channel. The whole design is mathematically controlled in terms of coupled non-linear differential equations. The numerical solution is proposed by utilizing the finite element method commercially. The LBB-stable finite pair is used for the approximation of primitive variables namely, the velocity and pressure. The obtained outcomes are offered through both the line graphs and contour plots. The drag and lift forces are evaluated by carrying line integration around the outer surface of square and circular shaped obstacles. It is noticed that in the grooved channel the obstacles experience an extreme maximum drag force. Further, the drag force is found to be an increasing function of the Hartmann number.

In this paper, we implement the non-conforming finite elements for the simulation of two dimensional incompressible Newtonian fluid flows. The classical driven cavity benchmark problem is simulated on a very fine uniform grid. In order to discretize the governing partial differential equations (PDEs) we employ the rotated bilinear Q ˜ 1 element for velocity and piecewise constant Q 0 element for the pressure on the general quadrilateral meshes. In L 2 -norm this pair is 2 nd order accurate for velocity and provides 1st order accuracy for pressure approximations. For the solution of non-linear systems arising from the discretization, Newton’s method is used as an outer nonlinear iteration and for the inner linear sub problems, the direct solver UMFPACK is utilized. The results have been compared with the reference data present in the literature and a good agreement is found.

This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved analytically by means of the homotopy analysis method (HAM). An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of physical parameters γ and Prandtl number Pr on the local Nusselt number and momentum thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.

The unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat sheet have been investigated. The partial differential equations governing the flows have been solved analytically by means of an analytic technique for strongly non-linear problems, namely the homotopy analysis method (HAM). This analytic approach gives us the convergent series solution uniformly valid for all dimensionless time in the whole spatial region 0 ≤ x ∞ and 0 ≤ y ∞ . To the best of our knowledge, such a kind of series solution has never been obtained. The skin friction coefficient and the boundary-layer thickness are also analyzed for different dimensionless time τ .

We have examined the behavior of solid particles in particulate flows. The interaction of particles with each other and with the fluid is analyzed. Solid particles can move freely through a fixed computational mesh using an Eulerian approach. Fictitious boundary method (FBM) is used for treating the interaction between particles and the fluid. Hydrodynamic forces acting on the particle’s surface are calculated using an explicit volume integral approach. A collision model proposed by Glowinski, Singh, Joseph and coauthors is used to handle particle-wall and particle-particle interactions. The particulate flow is computed using multigrid finite element solver FEATFLOW. Numerical experiments are performed considering two particles falling and colliding and sedimentation of many particles while interacting with each other. Results for these experiments are presented and compared with the reference values. Effects of the particle-particle interaction on the motion of the particles and on the physical behavior of the fluid-particle system has been analyzed.We have examined the behavior of solid particles in particulate flows. The interaction of particles with each other and with the fluid is analyzed. Solid particles can move freely through a fixed computational mesh using an Eulerian approach. Fictitious boundary method (FBM) is used for treating the interaction between particles and the fluid. Hydrodynamic forces acting on the particle’s surface are calculated using an explicit volume integral approach. A collision model proposed by Glowinski, Singh, Joseph and coauthors is used to handle particle-wall and particle-particle interactions. The particulate flow is computed using multigrid finite element solver FEATFLOW. Numerical experiments are performed considering two particles falling and colliding and sedimentation of many particles while interacting with each other. Results for these experiments are presented and compared with the reference values. Effects of the particle-particle interaction on the motion of the particles and on the physical behavior ...

The non-similarity solution for natural convection from a permeable isothermal vertical wall is considered. The governing boundary-layer equations for non-similarity flow and temperature fields are solved using the homotopy analysis method. The homotopy-Pade technique is applied to accelerate the convergence of the homotopy-series solution. The influence of physical parameters on the non-similarity flows is investigated in detail. Different from the previous analytic results, the homotopy-series solutions are convergent and valid for all physical parameters in the whole domain 0 ⩽ x < ∞ and 0 ⩽ y < ∞.