Viscous Dusty Fluid Flow with Constant Velocity Magnitude

We consider the viscous dusty fluid, where the velocity of the dust particle is everywhere parallel to that of the fluid with velocity magnitude of the fluid is constant along each individual streamline. Also it is assumed that number density of the dust particle is constant and the dust particles are uniform in size and shape and bulk concentration of the dust is small. Hodograph and Legendre transform of stream function is employed to get the solutions and the geometry of streamlines for these flows by using the resulting partial differential equations when the Jacobian is zero and nonzero cases. In each case the variation of pressure is analyzed graphicall

Nonlinear Radiative Heat Transfer of Cu-Water Nanoparticles over an Unsteady Rotating Flow under the Influence of Particle Shape

A 3D study on Cu-water-rotating nanofluid over a permeable surface in the presence of nonlinear radiation is presented. Particle shape and thermophysical properties are considered in this study. The governing equations in partial forms are reduced to a system of nonlinear ordinary differential equations using suitable similarity transformations. An effective Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique is applied to attain the solution. The effects of flow parameters on the flow field and heat transfer characteristics were obtained and are tabulated. Useful discussions were carried out with the help of plotted graphs and tables. It is found that the rate of heat transfer is more enhanced in column-shaped nanoparticles when compared to tetrahedron- and sphere-shaped nanoparticles. Higher values of rotating parameter enhance the velocity profile and corresponding boundary layer thickness. It has quite the opposite behavior in angular velocity profile. Further, unsteady parameter increases the velocity profile and corresponding boundary layer thickness

Thermal Conductivity in the Boundary Layer of Non-Newtonian Fluid with Particle Suspension

The present chapter is focused on studies concerned with three-dimensional flow and heat transfer analysis of Carreau fluid with nanoparticle suspension. The heat transfer analysis in the boundary was carried out with the fluid flow over a stretching surface under the influence of nonlinear thermal radiation, mixed convection and convective boundary condition. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. The equations in non-linear form are then solved numerically using Runge-Kutta-Fehlberg fourth fifth-order method with the help of symbolic algebraic software MAPLE. The results so extracted are well tabulated and adequate discussions on the parameters affecting flow and heat transfer analysis were carried out with the help of plotted graphs

Effects of variable viscosity and thermal conductivity on MHD flow and heat transfer of a dusty fluid

The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible and electrically conducting dusty fluid over an unsteady stretching sheet is analyzed numerically. The fluid viscosity and thermal conductivity are assumed to vary as an exponential function of temperature. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations using similarity transformations. The obtained similarity equations are solved numerically using RKF-45 method. Numerical computation has been carried out for horizontal velocity profiles, temperature, Nusselt number and skin friction coefficient for various values of the flow parameters that are presented for both VWT and VHF respectively. A comparison with previously published work is performed and the results are found to be in good agreement

Scrutinization of thermal radiation, viscous dissipation and Joule heating effects on Marangoni convective two-phase flow of Casson fluid with fluid-particle suspension

The impact of Marangoni convection on dusty Casson fluid boundary layer flow with Joule heating and viscous dissipation aspects is addressed. The surface tension is assumed to vary linearly with temperature. Physical aspects of magnetohydrodynamics and thermal radiation are also accounted. The governing problem is modelled under boundary layer approximations for fluid phase and dust particle phase and then Runge-Kutta-Fehlberg method based numeric solutions are established. The momentum and heat transport mechanisms are focused on the result of distinct governing parameters. The Nusselt number is also calculated. It is established that the rate of heat transfer can be enhanced by suspending dust particles in the base fluid. The temperature field of fluid phase and temperature of dust phase are quite reverse for thermal dust parameter. The radiative heat, viscous dissipation and Joule heating aspects are constructive for thermal fields of fluid and dust phases. The velocity of dusty Casson fluid dominates the velocity of dusty fluid while this trend is opposite in the case of temperature. Moreover qualitative behaviour of fluid phase and dust phase temperature/velocity are similar. Keywords: Marangoni convection, Dusty fluid, Casson fluid, Joule heating, Viscous dissipation, Two-phase flow, Thermal radiatio

Influence of heat source/sink on a Maxwell fluid over a stretching surface with convective boundary condition in the presence of nanoparticles

In this article, heat source/sink effects on the steady boundary layer flow of a Maxwell fluid over a stretching sheet with convective boundary condition in the presence of nanoparticles are reported. An appropriate similarity transformation is employed to transform the governing equations in partial differential equations form to similarity equations in ordinary differential equations form. The resulting equations are then solved numerically using shooting technique. Results for the velocity, temperature and concentration distributions are presented graphically for different values of the pertinent parameters. It is found that the local Nusselt number is smaller and local Sherwood number is higher for Maxwell fluids compared to Newtonian fluids

Thermal Marangoni convection in two-phase flow of dusty Casson fluid

This paper deals with the thermal Marangoni convection effects in magneto-Casson liquid flow through suspension of dust particles. The transpiration cooling aspect is accounted. The surface tension is assumed to be fluctuating linearly with temperature. The fluid and dust particle’s temperature of the interface is chosen as a quadratic function of interface arc length. The governing problem is modelled by conservation laws of mass, momentum and energy for fluid and dust particle phase. Stretching transformation technique is utilized to form ordinary differential equations from the partial differential equations. Later, the numerical solutions based on Runge-Kutta-Fehlberg method are established. The momentum and heat transport distributions are focused on the outcome of distinct governing parameters. The results of Nusselt number is also presented and discussed. It is established that the heat transfer rate is higher in the case of dusty non-Newtonian fluid than dusty Newtonian fluid. The rate of heat transfer can be enhanced by suspending dust particles in a base liquid. Keywords: Marangoni convection, Dusty fluid, Casson fluid, Two-phase flow, Runge-Kutta-Fehlberg metho

Cattaneo-Christov heat flux on UCM nanofluid flow across a melting surface with double stratification and exponential space dependent internal heat source

Melting and exponential space dependent internal heat source effects on magnetohydrodynamic of upper convected Maxwell liquid towards a horizontal flat surface are addressed. The combined effect of Brownian motion and thermophoresis in nanofluid modeling are retained. The Cattaneo-Christov heat flux model is imposed. Impacts of thermal and solutal stratifications are also accounted. A set of similarity variables are utilized to form ordinary differential system from the prevailing partial differential equations. The problem of ordinary differential system is analyzed numerically through Runge-Kutta-Fehlberg based shooting method. Graphical results of pertinent parameters on the velocity, temperature and nanoparticle concentration are studied. Skin friction coefficient, local Nusselt number and Sherwood number are also addressed

Radiated flow of chemically reacting nanoliquid with an induced magnetic field across a permeable vertical plate

Impact of induced magnetic field over a flat porous plate by utilizing incompressible water-copper nanoliquid is examined analytically. Flow is supposed to be laminar, steady and two-dimensional. The plate is subjected to a regular free stream velocity as well as suction velocity. Flow formulation is developed by considering Maxwell–Garnetts (MG) and Brinkman models of nanoliquid. Impacts of thermal radiation, viscous dissipation, temperature dependent heat source/sink and first order chemical reaction are also retained. The subjected non-linear problems are non-dimensionalized and analytic solutions are presented via series expansion method. The graphs are plotted to analyze the influence of pertinent parameters on flow, magnetism, heat and mass transfer fields as well as friction factor, current density, Nusselt and Sherwood numbers. It is found that friction factor at the plate is more for larger magnetic Prandtl number. Also the rate of heat transfer decayed with increasing nanoparticles volume fraction and the strength of magnetism. Keywords: Induced magnetic field, Nanoliquids, Heat source/sink, Series expansion method, Chemical reaction, Thermal radiatio

Scrutinization of Joule Heating and Viscous Dissipation on MHD Flow and Melting Heat Transfer Over a Stretching Sheet

The present paper deals with an analysis of the combined effect of Joule heating and viscous dissipation on an MHD boundary layer flow and melting heat transfer of a micro polar fluid over a stretching surface. Governing equations of the problem are transformed into a set of coupled nonlinear ordinary differential equations by applying proper transformations and then they are solved numerically using the RKF-45 method. The method is verified by a comparison with the established results with limiting solution. The influence of the various interesting parameters on the flow and heat transfer is analyzed in detail through plotted graphs