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.

In this paper, we offer a numerical study on heated non-Newtonian fluid with a Newtonian heating effect towards thermally stable stretching surfaces. A comparative analysis for two stretched surfaces, namely, plate and cylinder, is offered. The Casson fluid model is considered to be a non-Newtonian fluid model. By applying the suitable set of transformations, the non-linear coupled PDEs are transformed into non-linear ODEs. It is difficult to obtain the exact solution of such non-linear differential equations; therefore, we used the shooting method along with Runge–Kutta scheme. The influence of pertinent flow variables on velocity and temperature is presented through graphs. Notably from the results, heat generation parameters, Newtonian heating, and magnetic parameters enhanced the temperature profile, whereas Casson fluid and magnetic field parameters reduced the fluid velocity. It is also observed that increases in fluid temperature were more influenced at the cylindrical surface as compared with the flat plate. Moreover, we obtained remarkable results for the heat transfer rate by imposing Newtonian heating conditions at the surface; tables are used to present variations in the skin friction coefficient and Nusselt number at the thermally stable surfaces.

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.

The present article summarized the effects of double magnetic dipole for chemically reactive viscoelastic fluid in the presence of two different ferromagnetic particles, namely, nickel zinc ferrite (NiZnFe₂O₄) and magnetite ferrite (Fe₃O₄). Due to double magnetic dipole, an external magnetic field is applied normal to the flow. Blood is used as base fluid due to its viscoelastic fluid properties. The Cattaneo‐Christov heat flux model is used for heat transport phenomena. The physical model is formulated in the form of partial differential equations which are then converted into ordinary differential equations using the suitable transformations. The system is solved numerically using shooting method along with Runge‐Kutta‐Fehlberg method. The characteristics of different parameters like the strength of homogeneous‐heterogeneous reactions (k₁ and k₂), ferrohydrodynamic interaction (β₁), Schmidt number (S_c), Deborah number (α_1a), and thermal relaxation time (α_1c) on velocity, temperature, and concentration profiles are analyzed through graphs and in tabular form. It has been observed that as magnetic dipole creates a force which attracts the ferrite particles, hence, it slows down the velocity profile. Concentration field depresses due to the presence of strength of heterogeneous reaction parameter k₂.It is also noted that by expanding values of thermal relaxation time (α_1c), the temperature profile shows a reverse behavior.