K. V. Prasad

Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity

Abstract This paper deals with the study of boundary layer flow and heat transfer of a visco-elastic fluid immersed in a porous medium over a non-isothermal stretching sheet. The fluid viscosity is assumed to vary as a function of temperature. The presence of variable viscosity of the fluid leads to the coupling and the non-linearity in the boundary value problem. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge–Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. An analysis has been carried out for two different cases namely (1) prescribed surface temperature (PST), and (2) prescribed heat flux (PHF), to get the effect of fluid viscosity, permeability parameter and visco-elastic parameter for various situations. The important finding of our study is that the effect of fluid viscosity parameter is to decrease the wall temperature profile significantly when flow is through a porous medium. Further, the effect of permeability parameter is to decrease the skin friction on the sheet.

Diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet

Abstract The influence of reaction rate on the transfer of chemically reactive species in the laminar visco-elastic fluid flow immersed in a porous medium over a stretching sheet is considered. The flow is caused solely by the linearly stretching sheet and the reactive species is emitted from this sheet and undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. A similarity transformation is introduced, which reduces the concentration conservation equation to an ordinary differential equation. An exact analytical solution due to Siddappa and Abel (Z. Angew. Math. Phys. 36 (1985) 890) is adopted for velocity, where as the concentration equation is obtained numerically for higher-order reactions. The numerical computations show that the effect of destructive chemical reaction is to reduce the thickness of concentration boundary layer and increase the mass transfer rate from the sheet to the surrounding fluid. This effect is more effective for zero- and first-order reaction than second- and third-order reactions.

Momentum and heat transfer in visco‐elastic fluid flow in a porous medium over a non‐isothermal stretching sheet

Visco‐elastic fluid flow and heat transfer in a porous medium over a non‐isothermal stretching sheet have been investigated. The flow is influenced by linearly stretching the sheet in the presence of suction, blowing and impermeability of the wall. Thermal conductivity is considered to vary linearly with temperature. The intricate non‐linear problem has been solved numerically by shooting technique with fourth order Runge‐Kutta algorithm after using perturbation method. The zeroth order solutions are obtained analytically in the form of Kummer’s function. An analysis has been carried out for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF) to get the effect of porosity and visco‐elasticity at various physical situations. The important finding is that the effect of visco‐elasticity and porosity is to increase the wall temperature in case of blowing and to decrease in both the cases of suction and when the stretching sheet is impermeable.

The effect of variable viscosity on the flow and heat transfer of a viscous Ag-water and Cu-water nanofluids

A numerical study is carried out to study the effects of the temperature dependent viscosity on the flow and heat transfer of a nanofluid over a flat surface in the presence of viscous dissipation. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, and are solved numerically by the Keller-box method. The numerical results indicate that the effect of nanoparticle volume fraction is to increase the heat transfer and hence enhance the thermal boundary layer thickness. This is true even in the presence of variable viscosity and the viscous dissipation. Furthermore, the results obtained for heat transfer characteristics with nanoparticles reveal many interesting behaviors that warrant further study on the effects of the “nano-solid-particles”.

Axisymmetric magneto-hydrodynamic (MHD) flow and heat transfer at a non-isothermal stretching cylinder

Abstract An investigation is made to study the effects of transverse curvature and the temperature dependent thermal conductivity on the magneto-hydrodynamic (MHD) axisymmetric flow and heat transfer characteristics of a viscous incompressible fluid induced by a non-isothermal stretching cylinder in the presence of internal heat generation/absorption. It is assumed that the cylinder is stretched in the axial direction with a linear velocity and the surface temperature of the cylinder is subjected to vary non-isothermally. Here the thermal conductivity is assumed to vary linearly with temperature. Using a similarity transformation, the governing system of partial differential equations is first transformed into coupled non-linear ordinary differential equations with variable coefficients. The resulting intricate non-linear boundary value problem is solved numerically by a second order finite difference scheme for different values of the pertinent parameters for two cases: (i) the prescribed surface temperature (PST case) and (ii) the prescribed heat flux (PHF case). Numerical results are obtained for two different cases namely, zero and non-zero values of the curvature parameter to get the effects on the velocity and temperature fields. The combined effects of the curvature parameter and the thermal conductivity parameter are examined. The physical significances of the numerical results are presented for several limiting cases.

Convective heat and mass transfer in a visco‐elastic fluid flow through a porous medium over a stretching sheet

Presents a numerical solution of the two‐dimensional laminar boundary layer problem on free and forced convection of an incompressible visco‐elastic fluid immersed in a porous medium over a stretching sheet. Here, the driving force for the flow is provided by an impermeable sheet stretched with a velocity proportional to the distance from a slit and buoyancy effects due to both temperature and concentration gradients. The resultant governing boundary layer equations are highly non‐linear and coupled form of partial differential equations, and they have been solved by employing a numerical shooting technique with fourth order Runge‐Kutta integration scheme. Numerical computations are carried out for the non‐dimensional physical parameters. The results are analyzed for the effect of different physical parameters like visco‐elasticity, permeability of the porous medium, Grashof number, Schmidt number and Prandtl number on the flow, heat and mass transfer characteristics. One of the several important observations is that the combined effect of thermal diffusion and diffusion of species is to increase the horizontal velocity profile and to decrease the temperature and concentration profiles in the boundary layer flow field.

Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

The constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress τ0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters (t1 and t2) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Diffusion of a chemically reactive species of a power-law fluid past a stretching surface

Abstract A numerical solution for the steady magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a continuously moving surface with species concentration and chemical reaction has been obtained. The viscous flow is driven solely by the linearly stretching sheet, and the reactive species emitted from this sheet undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. Using a similarity transformation, the governing non-linear partial differential equations are transformed into coupled nonlinear ordinary differential equations. The governing equations of the mathematical model show that the flow and mass transfer characteristics depend on six parameters, namely, the power-law index, the magnetic parameter, the local Grashof number with respect to species diffusion, the modified Schmidt number, the reaction rate parameter, and the wall concentration parameter. Numerical solutions for these coupled equations are obtained by the Keller–Box method, and the solutions obtained are presented through graphs and tables. The numerical results obtained reveal that the magnetic field significantly increases the magnitude of the skin friction, but slightly reduces the mass transfer rate. However, the surface mass transfer strongly depends on the modified Schmidt number and the reaction rate parameter; it increases with increasing values of these parameters. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Effects of variable fluid properties on the thin film flow of Ostwald-de Waele fluid over a stretching surface

We investigate, in this paper, the effects of thermo-physical properties on the flow and heat transfer in a thin film of a power-law liquid over a horizontal stretching surface in the presence of a viscous dissipation. The fluid properties, namely the fluid viscosity and the fluid thermal conductivity, are assumed to vary with temperature. Using a similarity transformation, the governing partial differential equations with a time dependent boundary are converted into coupled non-linear Ordinary Differential Equations (ODEs) with variable coefficients. Numerical solutions of the coupled ODEs are obtained by a finite difference scheme known as the Keller-box method. Results for the velocity and temperature distributions are presented graphically for different values of the pertinent parameters. The effects of unsteady parameter on the skin friction, the wall temperature gradient and the film thickness are presented and analyzed for zero and non-zero values of the temperature-dependent thermo-physical properties. The results obtained reveal many interesting features that warrant further study on the non-Newtonian thin film fluid flow phenomena, especially the shear-thinning phenomena.

Parenteral formulation of zopiclone.

The present study was undertaken with an intention to develop a stable and effective parenteral formulation, containing the drug zopiclone. Since zopiclone is a water insoluble drug, various methods such as co-solvency, pH control and hydrotrophy have been tried in order to enhance its solubility. When all these methods could not give adequate solubility enhancement of the drug, a hydrochloride salt was prepared, and it was found to be thermostable. Various batches of zopiclone hydrochloride injection formulation were prepared in order to assess the influence of light, atmospheric oxygen and antioxidant on the stability of the drug and the formulations were also subjected to accelerated stability testing in order to predict approximate shelf-life of the product.