Balswaroop Bhatt

Two-phase fluid flow in a porous tube: a model for blood flow in capillaries

A theoretical study of blood flow, under the influence of a body force, in a capillary is presented. Blood is modeled as a two-phase fluid consisting of a core region of suspension of all erythrocytes, represented by a micropolar fluid and a plasma layer free from cells modeled as a Newtonian fluid. The capillary is modeled as a porous tube consisting of a thin transition Brinkman layer overlying a porous Darcy region. Analytical expressions for the pressure, microrotation, and velocities for the different regions are given. Plots of pressure, microrotation, and velocities for varying micropolar parameters, hydraulic resistivity, and Newtonian fluid layer thickness are presented. The overall system was found to be sensitive to variations in micropolar coupling number. It was also discovered that high values of hydraulic resistivity result in an overall slower velocity of the micropolar and Newtonian fluid.

A modified predator-prey model for the interaction of police and gangs

A modified predator–prey model with transmissible disease in both the predator and prey species is proposed and analysed, with infected prey being more vulnerable to predation and infected predators hunting at a reduced rate. Here, the predators are the police and the prey the gang members. In this system, we examine whether police control of gangs is possible. The system is analysed with the help of stability analyses and numerical simulations. The system has five steady states—four of which involve no core gang members and one in which all the populations coexist. Thresholds are identified which determine when the predator and prey populations survive and when the disease remains endemic. For parameter values where the spread of disease among the police officers is greater than the death of the police officers, the diseased predator population survives, when it would otherwise become extinct.

Heat Transfer of Coupled Fluid Flow Within a Channel With a Permeable Base

We examine the heat transfer in a Newtonian fluid confined within a channel with a lower permeable wall. The upper wall of the channel is impermeable and driven by an accelerating surface velocity. Through a similarity solution, the Navier-Stokes equations are reduced to a fourth-order differential equation; the analytical solutions of which determined for small Reynolds numbers show dependence of the temperature and heat transfer profiles on the slip parameter based on the properties of the porous channel base. For larger Reynolds numbers, numerical solutions for three main groups of solutions show that the Reynolds number strongly influences the heat transfer profile. However, the slip conditions associated with the porous base of the channel can be used to alter these heat transfer profiles for large Reynolds numbers. The presence of a porous base in a channel can thus serve as an effective means of reducing or enhancing heat transfer performance in model systems.

The movement of single large liquid bubbles in vertical porous tubes

The motion of single large liquid bubbles (exhibiting micropolar behaviour) surrounded by a liquid under gravity in closed vertical porous tube has been studied. The effect of slip parameter and porosity parameter has been studied on pressure gradient, velocity distribution for given film thickness. A possible application of the result for detecting the pressure fluctuations of a human body has been suggested.

Switching effect of predation on a small size prey species living in two different habitats

A Mathematical model with one prey species living in two different habitats and a predator where the predatory rate diminishes at low population density of prey is investigated. Two habitats are separated by a barrier and prey species is able to disperse among two different habitats at some cost of the population. The stability analysis is carried out for non-zero equilibrium values. Using rate of conversion of the prey to predator as bifurcation parameter, the necessary and sufficient condition for a Hopf bifurcation to occur are derived. It is shown numerically that predation rate does not always have stabilizing effect for the prey-predator system.

Switching Effect of Predation on Prey Species Living in Different Habitats with Arbitrary Predatory Rates II

The present paper extends previous work by Bhatt et al. [J. Phys. Soc. Jpn. 69 (2000) 3133] referred as Part I. It deals with the switching effect of predation on prey species living in two habitats when the predatory rates are arbitrary. The predator feeds preferentially on the more abundant habitats population. Two habitats have been separated by a barrier so that the prey species is able to disperse among them at some cost of the population. The stability analysis has been carried out for non-zero equilibrium values. Using the conversion rate of the prey to predator as a bifurcation parameter, necessary and sufficient conditions for a Hopf bifurcation to occur have been derived. Two particular cases of predatory rates, namely, (i) multiplicative case and (ii) exponential case have been derived.