This study attempts to analyze the effect of diverse parameters of the peristaltic flow of second grade DUSTY FLUID through a curved configuration. Stream function conversions are used to model the separate system of equations for the dust particles and FLUID. The Perturbation technique is used to get the analytical solutions and the results are verified through graphs. It is noticeable that the trapped bolus, compresses both the dust particles and FLUID with an increase in `the second grade parameter'. Moreover, a surge in `the Reynolds number' Re effects the bolus trapped in the lower portion of the channel for FLUID. Decrement in the velocity is observed with a rise in `the wave number' \delta and `the second grade parameter' \alpha_1.

The paper considers the influence of thermal Marangoni convection on boundary layer flow of two-phase DUSTY FLUID along a vertical wavy surface. The dimensionless boundary layer equations for two-phase problem are reduced to a convenient form by primitive variable transformations (PVF) and then integrated numerically by employing the implicit finite difference method along with the Thomas Algorithm. The effect of thermal Marangoni convection, DUSTY water and sinusoidal waveform are discussed in detail in terms of local heat transfer rate, skin friction coefficient, velocity and temperature distributions. This investigation reveals the fact that the water-particle mixture reduces the rate of heat transfer, significantly.

The present work illustrates the variable viscosity of dust nanoFLUID runs over a permeable stretched sheet with thermal radiation. The problem has been modelled mathematically introducing the mixed convective condition and magnetic effect. Additionally analysis of entropy generation and Bejan number provides the fine points of the flow. The of model equations are transformed into non-linear ordinary differential equations which are then transformed into linear form using the spectral quasi-linearization method (SQLM) for direct Taylor series expansions that can be applied to non-linear terms in order to linearize them. The spectral collocation approach is then applied to solve the resulting linearized system of equations. The validity of our model is established using relative entropy generation analysis. A convergence schematic was obtained graphically. Consequence of various parameters on flow features have been delivered via graphs. Some important findings reported in this study that entropy generation analysis have significant impact in controlling the rate of heat transfer in the boundary layer region. The paper acquires realistic numerical explanations for rapidly convergent solutions using the Spectral quasi-linearization method. Convergence of the numerical solutions was monitored using the convergence graph. The initial guess values are automatically satisfied the boundary conditions. The resulting equations are then integrated using the Spectral quasi-linearization methods. The influence of radiation, heat and mass parameters on the flow are made appropriately via graphs. The effects of varying certain physical parameters of interest are examined and presented.

In the present study, transient MHD Couette flow and heat transfer of DUSTY FLUID between two parallel plates and the effect of the temperature dependent properties has been investigated. The thermal conductivity and viscosity of the FLUID are assumed as linear and exponential functions of temperature, respectively. A constant pressure gradient and an external uniform magnetic field are considered in the main flow direction and perpendicular to the plates, respectively. A hybrid treatment based on finite difference method (FDM) and differential transform method (DTM) is used to solve the coupled flow and heat transfer equations. The effects of the variable properties, Hartman number, Hall current, Reynolds number and suction velocity on the Nusselt number and skin friction factor have been discussed. It is found that when Hartman number increases, skin friction of the upper and lower plates increases.

The unsteady flow and heat transfer of a viscous incompressible, electrically conducting DUSTY FLUID past vertical plate under the influence of a transverse magnetic field is studied with a view to examine the combined effects of suction, heat absorption and ramped wall temperature. The temperature of the wall is assumed to have a temporarily ramped profile which goes on increasing up to a certain time limit and then becomes constant. To investigate the effect of rampedness in wall temperature, the solution for the flow past an isothermal wall is also obtained. The governing partial differential equations are solved using Laplace transformation technique in which the inversion is obtained numerically using Matlab. To validate the results of numerical inversion a comparison between the numerical and analytical values of FLUID and particle temperatures and Nusselt number is also presented. The effects of pertinent flow parameters affecting the flow and heat transfer are investigated with the help of graphs and tables. It is found that the increase in suction, heat absorption and particle concentration contribute in thinning the thermal and momentum boundary layers and the velocity and temperature for both the FLUID and particle phases are higher in the case of a flow past an isothermal plate than that of a flow past a plate with ramped temperature.

The FLUID description is employed to investigate the instability of Newtonian viscous shear DUSTY plasma system in hydrodynamic regime, taking into account both viscosity and collision effects. Describing the equilibrium configuration in the presence of the binary collision terms between dust grains and neutral particles and using the local approximation method, the dispersion relation is obtained by applying the generalized hydrodynamic equation to find the spatial dependence of the initial velocity in equilibrium state. Analyzing the obtained dispersion relation shows that the main factor of free energy source to arise the instability of the system is due to the viscous force. While the collision effect plays a stabilizing role for the system by reducing the growth rate of the instability of the Newtonian strongly coupled DUSTY plasma system in the hydrodynamic regime.

The steady three-dimensional boundary layer flow and heat transfer of a DUSTY FLUID towards a stretching sheet with convective boundary conditions are investigated using similarity solution approach. The free stream along zdirection impinges on the stretching sheet to produce a flow with different velocity components. The governing equations are reduced into ordinary differential equations using appropriate similarity variables. Reduced nonlinear ordinary differential equations subjected to the associated boundary conditions are solved numerically using Runge– Kutta fourth-fifth order method along with shooting technique. The effects of the physical parameters like magnetic parameter, velocity ratio, FLUID and thermal particle interaction parameter, Prandtl number, Eckert number and Biot number on flow and heat characteristics are examined, illustrated graphically, and discussed in detail. The results indicate that the FLUID phase velocity is always greater than that of the particle phase and temperature profiles of the FLUID and dust phases increase with the increase of the Eckert number.

This paper presents the CAS wavelet based numerical technique for the solution of non-linear system of differential equations arising in the analysis of an unsteady DUSTY tangent hyperbolic FLUID flow over a stretching sheet through porous medium with magnetic dipole effect, quadratic convection, non-linear radiation, convective boundary and entropy generation. Initially, the proposed method is implemented on the test problem having the exact solution. The results obtained are very close to the exact solution in comparison with the Runge-Kutta Fehlberg 4th – 5th order method. The considered DUSTY FLUID problem is solved by using the proposed technique. The solutions obtained for certain fixed parameters are compared and found to be coinciding with the solutions given in the literature. The comparisons and convergence analysis validate the method. The flow behaviour of DUSTY tangent hyperbolic FLUID is analysed and the impact of various factors on the velocity and thermal profile of the FLUID are studied. It is inferred that the Weissenberg number, power law index and Ferro-hydrodynamic interaction parameter declines the velocity and improves the temperature. Opposite behaviour is observed for mixed convection and quadratic convection parameters. The temperature increases for the Biot number. The Weissenberg number declines the entropy generation and enhances the Bejan number. A reverse trend is noticed for Brinkman number. CAS wavelet based numerical technique is simple, reliable, highly accurate, efficient and effective tool to solve the non-linear system of differential equations arising in DUSTY FLUID flow problems.