Hall current effect in bioconvection Oldroyd-B nanofluid flow through a porous medium with Cattaneo-Christov heat and mass flux theory.

Bioconvection due to microorganisms is important area of research, considerably importance for environment and sustainable fuel cell technologies. Buongiorno nanofluid model for Cattaneo-Christov heat and mass flux theory taken into account the Oldroyd-B nanofluid and gyrotactic microorganisms in a rotating system with the effects of Hall current, and Darcy porous medium is scrutinized. The constitutive equations of the problem are transformed into nondimensional equations with the help of similarity transformations. Homotopy analysis method is used to obtain the solution. Graphs and table support the comprehesive representation of the achieved results. Radial velocity is reduced with the increasing values of relaxation time, retardation time and magnetic field parameters while heat transfer is augmented with thermal relaxation time parameter. The nanoparticles concentration is reduced with the increasing values of Schmidt number and the gyrotactic microorganisms concentration is enhanced with the increasing values of Peclet number. A nice agreement is obtained while comparing the present results numerically with the published results. The proposed mathematical model is used in biochemical engineering, meteorology, power and transportation production, optoelectronic and sensing microfabrication.

The Effect of Stenotic Geometry and Non-newtonian Property of Blood Flow through Arterial Stenosis.

BACKGROUND: A mathematical model of blood flow is a way to study the blood flow behavior. In this research work, a mathematical model of non-Newtonian blood flow through different stenosis, namely bell shape and cosine shape, is considered. The physiologically important flow quantities of blood flow behavior to describe the blood flow phenomena are obtained such as resistance to flow, skin friction and blood flow rate. METHODS: Mathematical methods are used to analyze a mathematical model of blood flow through stenosed artery. The resistance to flow, skin friction and blood flow rate were obtained to describe the blood flow in stenosis. The resistance to flow is a relation between pressure and blood flow rate while the skin friction is the friction at the artery membrane. Resutls: The blood flow in cosine geometry exhibits higher resistance to flow and flow rate than in the bell geometry, while the blood flow in bell geometry gives a higher skin friction than in cosine geometry. Not only the effect of stenotic geometry was studied but also the effect of stenosis depth and stenosis height on the flow quantities Moreover, the power law index was adjusted to explore the non-Newtonian behavior. When blood exhibits Newtonian behavior, the resistance to flow and skin friction decrease but the blood flow rate increases. CONCLUSION: The stenosed artery geometry, the stenosis length, stenosis depth and the power law index (non-Newtonian behavior) are important factors affecting the blood flow through the stenosed artery. This work provides some potential aspects to further study the causes and development of cardiovascular diseases.

Mathematical analysis of non-Newtonian blood flow in stenosis narrow arteries.

The flow of blood in narrow arteries with bell-shaped mild stenosis is investigated that treats blood as non-Newtonian fluid by using the K-L model. When skin friction and resistance of blood flow are normalized with respect to non-Newtonian blood in normal artery, the results present the effect of stenosis length. When skin friction and resistance of blood flow are normalized with respect to Newtonian blood in stenosis artery, the results present the effect of non-Newtonian blood. The effect of stenosis length and effect of non-Newtonian fluid on skin friction are consistent with the Casson model in which the skin friction increases with the increase of either stenosis length or the yield stress but the skin friction decreases with the increase of plasma viscosity coefficient. The effect of stenosis length and effect of non-Newtonian fluid on resistance of blood flow are contradictory. The resistance of blood flow (when normalized by non-Newtonian blood in normal artery) increases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length. The resistance of blood flow (when normalized by Newtonian blood in stenosis artery) decreases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.

Mesoscale modeling technique for studying the dynamics oscillation of Min protein: pattern formation analysis with lattice Boltzmann method.

We presented an application of the Lattice Boltzmann method (LBM) to study the dynamics of Min proteins oscillations in Escherichia coli. The oscillations involve MinC, MinD and MinE proteins, which are required for proper placement of the division septum in the middle of a bacterial cell. Here, the LBM is applied to a set of the deterministic reaction diffusion equations which describes the dynamics of the Min proteins. This determines the midcell division plane at the cellular level. We specifically use the LBM to study the dynamic pole-to-pole oscillations of the Min proteins in two dimensions. We observed that Min proteins' pattern formation depends on the cell's shape. The LBM numerical results are in good agreement with previous findings, using other methods and agree qualitatively well with experimental results. Our results indicate that the LBM can be an alternative computational tool for simulating the dynamics of these Min protein systems and possibly for the study of complex biological systems which are described by reaction-diffusion equations. Moreover, these findings suggest that LBM could also be useful for the investigation of possible evolutionary connection between the cell's shape and cell division of E. coli. The results show that the oscillatory pattern of Min protein is the most consistent with experimental results when the dimension of the cell is 1 x 2. This suggests that as the cell's shape is close to being a square, the oscillatory pattern no longer places the cell division of E. coli at the proper location. These findings may have a significant implication on why, by natural selection, E. coli is maintained in a rod shape or bacillus form.