The hydromagnetic mixed convection flow of Cassonnano fluid under the influence of chemical reaction,thermal radiation and heat generation or absorption is investigated. The flow is induced due to unsteady nonlinearly stretching sheet saturated in a porous medium. The governing nonlinear coupled partial differential equations are converted into the system of coupled ordinary differential equations using similarity transformations and then solved numerically via Keller box method. The effects of pertinent parameters on velocity, temperature and nanoparticles concentration as well as wall shear stress, heat and mass transfer rate are analyzed and displayed graphically. The results for skin friction coefficient and local Nusselt number are compared with previously published work and found to be in good agreement. Findings demonstrate that increase in Casson parameter enhanced the friction factor and heat transfer rate. It is noticed that the heat transfer rate is declined with increment in Brownian motion and thermophoresis parameters. The nanoparticles concentration is seen to be higher in generative chemical reaction and opposite effect is observed in destructive chemical reaction. Increase in unsteadiness parameter decreased the fluid velocity, temperature and nanoparticles concentration. The magnitude of wall shear stress is also reduced with increase in unsteadiness and porous medium parameters.
Invadopodia are finger-like protrusions located at subcellular membrane which can lead to cancer cell invasion. The formation of invadopodia involves several steps such as actin polymerizations, degradation of extracellular matrix which produce ligand and signal stimulation that is occurred from the binding of ligand with epidermal growth factor receptor. In this paper, a mathematical model of signal transduction is investigated. Both signal and ligand are represented by Laplace equation with Dirichlet boundary condition for each region. The cell membrane is treated as free boundary surface to separate any activity that occurred in intracellular and extracellular regions. The motion of the interface is taken as gradient of interior signal and the cell membrane is set as zero level set function. The problem is solved numerically using finite difference scheme of upwind, interpolation and extrapolation methods. The results showed that the formation of invadopodia is formed when protrusions exist on the cell membrane.