The objective of this article is to study the physics of slip effect at the boundary of a vertical plate in starting the flow of Casson fluid with the combined effect of radiative heat and mass transfer in the presence of first-order chemical reaction. The problem has been modeled in terms of partial differential equations along with appropriate initial and boundary conditions. The dimensionless governing equations have been solved by means of the Laplace transform technique. Exact solutions have been obtained for velocity, temperature and concentration profiles. The obtained velocity has been computed in tabular form for steady and transient velocities. The physics of velocity profile has been studied for various physical parameters through numerical computation and displayed in graphs. From obtained solutions, the well-known published results in the open literature have been recovered and displayed in graphs and tables.

Heat and mass transfer phenomena in the flow of Casson fluid over an infinite oscillating plate in the presence of first-order chemical reaction and slip effect

Coupling of the Crank–Nicolson scheme and localized meshless technique for viscoelastic wave model in fluid flow

Existence of solutions of the abstract Cauchy problem of fractional order

Micropolar fluids had many industrial applications such as polymer solutions, lubricant fluids, and biological structures. However, the present study deals with the drug delivery in the cardiovascular system where the blood particles are considered as microparticles included their self-rotation (mainly red blood cells) and interaction. The nanoparticles may be used as drug carrier particles. In the present problem, nanoparticles are considered as metallic oxides, e.g., Alumina (
 $${\text {Al}} _2{\text {O}} _3$$
 ), Titania (
 $${\text {TiO}} _2$$
 ), and Magnetite (
 $${\text {Fe}} _3{\text {O}} _4$$
 ) with water as base fluid. The magnetohydrodynamic micropolar fluid flow between two parallel squeezing plates is considered. Further, the analysis is carried out in the presence of viscous dissipation and Joule heating effects. With the aid of a similarity transformation, the flow governing Navier–Stokes equations is transformed into a system of coupled nonlinear ordinary differential equations. Fourth-order Runge–Kutta method with shooting approach is used to solve the nonlinear coupled boundary value problem. The profiles of flow field variables are acquired for key parameters arising in the present problem. It is noticed that, when the plates are fixed, the viscous drag of the base fluid is the same as that of nanofluid. Further, it is observed that increasing volume fraction results a decrement in microrotation and thereby causing an increase in temperature of Titania–water nanofluid which is in contrast to the behavior of other nanofluids.

Unsteady 3D micropolar nanofluid flow through a squeezing channel: application to cardiovascular disorders

This study develops an optimized finite difference iterative (OFDI) scheme for the two-dimensional (2D) viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition (POD) method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.

Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation

The unsteady, two-dimensional laminar flow of an incompressible micropolar fluid in a channel with expanding or contracting porous walls is investigated. The governing equations are transformed into a coupled nonlinear two-points boundary value problem by a suitable similarity transformation. Unlike the classic Berman problem (Berman in J. Appl. Phys. 24:1232-1235, 1953), three new solutions (totally six solutions) and no-solution interval, which is one of important characteristics for the laminar flow through porous pipe with stationary wall (Terrill and Thomas in Appl. Sci. Res. 21:37-67, 1969), are found numerically for the first time. The multiplicity of the solutions is strictly dependent on the expansion ratio. Furthermore, the asymptotic solutions are constructed by the Lighthill method, which eliminates the singularity of the similarity solution, for large injection and by the matching theorem for the suction Reynolds number, respectively. The analytical solutions also are compared with the numerical ones and the results agree well.

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Jianhui Zhou

Papers

The solutions for the flow of micropolar fluid through an expanding or contracting channel with porous walls