Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and ion-slip effects

The Hall and ion-slip effects on fully developed electrically conducting couple stress fluid flow between vertical parallel plates in the presence of a temperature dependent heat source are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the homotopy analysis method （HAM）. The effects of the magnetic parameter, Hall parameter, ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically

Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection

The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer as- sumptions are taken into account to govern the mathematical model of the flow analy- sis. Some suitable similarity variables are introduced to transform the partial differen- tial equations into ordinary differential systems. fifth-order techniques with the shooting method The Runge-Kutta-Fehlberg fourth- and are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the non- linear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation.

Application of First-Order Differential Equation to Heat Convection in Fluid

Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mathematical form of ordinary differential equations (ODEs). In this research, we determine heat transferred by convection in fluid problems by first-order ordinary differential equations. So in this research work first we discuss the solution of ordinary homogeneous and non-homogeneous differential equation and then apply the solution of first-order ODEs to heat transferring particularly in heat convection in fluid.

Soret and Dufour Effects on Unsteady Free Convection Fluid Flow in the Presence of Hall Current and Heat Flux

Unsteady MHD natural convective heat and mass transfer flow through a semi-infinite vertical porous plate in a rotating system have been investigated with the combined Soret and Dufour effects in the presence of Hall current and constant heat flux. It is considered that the porous plate is subjected to constant heat flux. The obtained non-dimensional, non-similar coupled non-linear and partial differential equations have been solved by explicit finite difference technique. Numerical solutions for velocities, temperature and concentration distributions are obtained for various parameters by the above mentioned technique. The local and average shear stresses, Nusselt number as well as Sherwood number are also investigated. The stability conditions and convergence criteria of the explicit finite difference scheme are established for finding the restriction of the values of various parameters to get more accuracy. The obtained results are illustrated with the help of graphs to observe the effects of various legitimate parameters.

Flow of Casson nanofluid with viscous dissipation and convective conditions: A mathematical model

The magnetohydrodynamic(MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated.Convective conditions of temperature and nanoparticle concentration are employed in the formulation. The flow is generated due to exponentially stretching surface. The governing boundary layer equations are reduced into the ordinary differential equations. Series solutions are presented to analyze the velocity, temperature and nanoparticle concentration fields. Temperature and nanoparticle concentration fields decrease when the values of Casson parameter enhance. It is found that the Biot numbers arising due to thermal and concentration convective conditions yield an enhancement in the temperature and concentration fields. Further, we observed that both the thermal and nanoparticle concentration boundary layer thicknesses are higher for the larger values of thermophoresis parameter. The effects of Brownian motion parameter on the temperature and nanoparticle concentration are reverse.

MHD flow and mass transfer of chemically reactive upper convected Maxwell fluid past porous surface

The magnetohydrodynamic （MHD） flow and mass transfer of an electrically conducting upper convected Maxwell （UCM） fluid at a porous surface are studied in the presence of a chemically reactive species. The governing nonlinear partial differential equations along with the appropriate boundary conditions are transformed into nonlinear ordinary differential equations and numerically solved by the Keller-box method. The effects of various physical parameters on the flow and mass transfer characteristics are graphically presented and discussed. It is observed that the order of the chemical reaction is to increase the thickness of the diffusion boundary layer. Also, the mass transfer rate strongly depends on the Schmidt number and the reaction rate parameter. Furthermore, available results in the literature are obtained as a special case.

Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction

The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.

Free Convective Nonaligned Non-Newtonian Flow with Non-linear Thermal Radiation

The present study explores the free convective oblique Casson fluid over a stretching surface with non-linear thermal radiation effects. The governing physical problem is modelled and transformed into a set of coupled non-linear ordinary differential equations by suitable similarity transformation, which are solved numerically with the help of shooting method keeping the convergence control of 10^(-5) in computations. Influence of pertinent physical parameters on normal, tangential velocity profiles and temperature are expressed through graphs. Physical quantities of interest such as skin friction coefficients and local heat flux are investigated numerically.