Slip effects on a mixed convection flow of a third-grade fluid near the orthogonal stagnation point on a vertical surface

A mixed convection flow of a third-grade fluid near the orthogonal stagnation point on a vertical surface with slip and viscous dissipation effects is investigated. The governing partial differential equations for the third-grade fluid are converted into a system of nonlinear ordinary differential equations by using a similarity transformation. The effects of various parameters, including the Weissenberg number, third-grade parameter, local Reynolds number, Prandtl number, Eckert number, mixed convection parameter, velocity slip, and thermal slip on the velocity and temperature profiles, local skin friction coefficient, and local Nusselt number are discussed.     

Heat transfer and entropy generation analysis of non-Newtonian fluid flow through vertical microchannel with convective boundary condition

The entropy generation and heat transfer characteristics of magnetohydrodynamic(MHD) third-grade fluid flow through a vertical porous microchannel with a convective boundary condition are analyzed. Entropy generation due to flow of MHD non-Newtonian third-grade fluid within a microchannel and temperature-dependent viscosity is studied using the entropy generation rate and Vogel's model. The equations describing flow and heat transport along with boundary conditions are first made dimensionless using proper non-dimensional transformations and then solved numerically via the finite element method(FEM). An appropriate comparison is made with the previously published results in the literature as a limiting case of the considered problem.The comparison confirms excellent agreement. The effects of the Grashof number, the Hartmann number, the Biot number, the exponential space-and thermal-dependent heat source(ESHS/THS) parameters, and the viscous dissipation parameter on the temperature and velocity are studied and presented graphically. The entropy generation and the Bejan number are also calculated. From the comprehensive parametric study, it is recognized that the production of entropy can be improved with convective heating and viscous dissipation aspects. It is also found that the ESHS aspect dominates the THS aspect.     

Criticality and transition for a steady reactive plane couette flow of a viscous fluid

Numerical integration is used to determine critical and transitional values of parameters for steady, reactive, viscous, one dimensional plane Couette flow of an incompressible, homogeneous fluid of third-grade with the lower plate at rest while the upper is in uniform motion. The solutions are found for the following cases: (i) Bimolecular (ii) Arrhenius and (iii) Sensitized temperature dependence. Specifically, it is shown that the parameter Λ controlling the non-Newtonian fluid does not affect the flow velocity in any sense while the influence on the viscous dissipation parameter Γ is examined. The results obtained are then compared with similar results in the literature.     

Approximate analytical solutions for the flow of a third-grade fluid in a pipe

The flow of a third-grade fluid in a pipe with heat transfer is considered. Constant viscosity, Reynold's model viscosity and Vogel's model viscosity cases are treated separately. Approximate analytical solutions are presented for each case using perturbations. The criteria for which the solutions are valid are determined for the dimensionless parameters involved. The analytical solutions are contrasted with the finite difference solutions given in Massoudi and Christie (Int. J. Non-Linear Mech. 30 (1995) 687-699) and within admissible parameter range, a close match is achieved.     

On thin film flow of a third-grade fluid down an inclined plane

An exact solution for the thin film flow of a third-grade fluid on an inclined plane is presented. This is a corrected version of the solution obtained by Hayat et al. (Chaos Solitons Fractals 38:1336–1341, 2008). An alternative parametric form for the solution is also derived. The variation of the dimensionless velocity and average velocity is given for a wide range of parameter values. An asymptotic solution for large parameter values is obtained giving rise to a boundary-layer structure at the free surface.     

Disappearance of criticality for reactive third-grade fluid with Reynold's model viscosity in a flat channel

In this paper, we consider how a model for the motion with exponential viscosity of a third-grade fluid flowing between parallel plates, under the action of externally imposed pressure gradient, affects the fully developed and laminar reactive flow. The non-dimensional form of the coupled equations are solved numerically. The temperature distribution is presented for various viscosity variational parameters and the number is related to the Frank-Kamenetskii parameter. The criticality and disappearance of criticality (transition) of physical parameters and the competing effects of viscous dissipation, viscosity variational number, heat generation and non-Newtonian are discussed.     

MHD flow of a third-grade fluid due to eccentric rotations of a porous disk and a fluid at infinity

The problem of magnetohydrodynamics (MHD) flow of a conducting, incompressible third-grade fluid due to non-coaxial rotations of a porous disk and a fluid at infinity in the presence of a uniform transverse magnetic field is considered. An exact analysis is carried out to model the governing non-linear partial differential equation. A numerical solution of the third-order non-linear partial differential equation has been obtained. Several graphs and tables have been drawn to show the influence of porosity ε, magnetic parameter N, material parameters α and β on the velocity distribution.     

Rotating flow of a third grade fluid in a porous space with Hall current

This study investigates the rotating magnetohydrodynamic (MHD) flow of a third-grade fluid in a porous space. Modified Darcy's law has been utilized for the flow modeling. The Hall effects are taken into consideration. The basic equations governing the flow are reduced to a highly nonlinear ordinary differential equation. This equation has been solved analytically by employing the homotopy analysis method (HAM). The effects of the various interesting parameters on the velocity distribution have been discussed.     

Exact flow of a third-grade fluid on a porous wall

The flow of a third-grade fluid occupying the space over a wall is studied. At the surface of the wall suction or blowing velocity is applied. By introducing a velocity field, the governing equations are reduced to a non-linear partial differential equation. The resulting equation is analysed analytically using Lie group methods.     

Approximate Analytical Solutions for Flow of a Third-Grade Fluid Through a Parallel-Plate Channel Filled with a Porous Medium

The flow of a non-Newtonian fluid through a porous media in between two parallel plates at different temperatures is considered. The governing momentum equation of third-grade fluid with modified Darcy’s law and energy equation have been derived. Approximate analytical solutions of momentum and energy equations are obtained by using perturbation techniques. Constant viscosity, Reynold’s model viscosity, and Vogel’s model viscosity cases are treated separately. The criteria for validity of approximate solutions are derived. A numerical residual error analysis is performed for the solutions. Within the validity range, analytical and numerical solutions are in good agreement.     

Thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined plane

This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy are obtained and solved by using a new computational approach based on a special type of Hermite-Padé approximation technique implemented in MAPLE. This semi-numerical scheme offers some advantages over solutions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.     

Unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid with Joule heating,chemical reaction and radiation effects

The effects of Joule-heating, chemical reaction and thermal radiation on unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid are analyzed. The partial differential equations governing the flow and heat and mass transfer have been solved numerically using an implicit finite-difference scheme. The case corresponding to vanishing of the anti-symmetric part of the stress tensor that represents weak concentrations is considered. The numerical results are validated by favorable comparisons with previously published results. A parametric study of the governing parameters, namely the magnetic field parameter, suction/injection parameter, radiation parameter, chemical reaction parameter, vortex viscosity parameter and the Eckert number on the linear velocity, angular velocity, temperature and the concentration profiles as well as the skin friction coefficient, wall couple stress coefficient, Nusselt number and the Sherwood number is conducted. A selected set of numerical results is presented graphically and discussed.     

Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimen- sionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are preSented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ the order of.the chemical reaction parameter m, the Soret number St, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.     

Stability of steady plane-parallel convective motion of a chemically active medium

A study is made of a vertical plane layer of reacting fluid whose boundaries are maintained at constant equal temperatures. As a result of heating due to a chemical reaction of zeroth order taking place in the fluid a steady plane-parallel convective flow develops in the layer, and if the internal heat release is sufficiently intense this can become unstable. The linear stability of this motion has hitherto been considered only in the hydro-dynamic formulation [1], in which one can ignore the thermal perturbations and their influence on the development of the hydrodynamic perturbations (the region of small Prandtl numbers). In the present paper, the stability boundary is determined for arbitrary values of the Prandtl number and the Frank-Kamenetskii parameter FK characterizing the steady plane-parallel regime. An important difference between this flow and the types of convective motion hitherto studied [2] is that the basic planeparallel flow of the reacting medium is possible only in a definite range of the parameter FK: At values of the parameter exceeding a critical value, there is a thermal explosion — abrupt strong heating of the fluid. This is due to the essentially nonlinear dependence of the heat release of a chemical reaction on the temperature.     

Cattaneo-Christov heat flux model for third-grade fluid flow towards exponentially stretching sheet

The Cattaneo-Christov heat flux in the two-dimensional (2D) flow of a third-grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temperature gradient while reduces the temperature profile.     

MHD free convective flow and mass transfer over a stretching sheet with chemical reaction

The effect of chemical reaction on free convective flow and mass transfer of a viscous, incompressible and electrically conducting fluid over a stretching surface is investigated in the presence of a constant transverse magnetic field. The non-linear boundary layer equations with the boundary conditions are transferred by a similarity transformation into a system of non-linear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth order Runge-Kutta scheme with the shooting method. Numerical results of the skin friction coefficient, the local Nusselt number Nu, the local Sherwood number Sh, as will as the velocity, temperature and concentration profiles are presented for gases with a Prandtl number of 0.71 for various values of chemical reaction parameter, order of reaction, magnetic parameter and Schmidt number.     

Analytical solutions of the helical flow of non newtonian fluid in eccentric annular space

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Heat transfer characteristics for the Maxwell fluid flow past an unsteady stretching permeable surface embedded in a porous medium with thermal radiation

An unsteady boundary layer flow of a non-Newtonian fluid over a continuously stretching permeable surface in the presence of thermal radiation is investigated. The Maxwell fluid model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained. The transformed boundary layer equations are then solved numerically by the shooting method. The flow features and heat transfer characteristics for different values of the governing parameters (unsteadiness parameter, Maxwell parameter, permeability parameter, suction/blowing parameter, thermal radiation parameter, and Prandtl number) are analyzed and discussed in detail.     

Visco-elastic fluid flow past an infinite vertical porous plate in the presence of first-order chemical reaction

An analysis has been developed to study the unsteady free convection flow of an incompressible visco-elastic fluid on a continuously moving vertical porous plate in the presence of a first-order chemical reaction. The governing equations are solved numerically using an implicit finite difference technique. The obtained numerical solutions are compared with the analytical solutions. The velocity profiles are presented. A parametric analysis is performed to illustrate the influences of the visco-elastic parameter, the dimensionless chemical reaction parameter, and the plate moving velocity on the steady state velocity profiles, the time dependent friction coefficient, the Nusselt number, and the Sherwood number.     

Radiation effect on forced convective flow and heat transfer over a porous plate in a porous medium

Heat transfer analysis has been presented for the boundary layer forced convective flow of an incompressible fluid past a plate embedded in a porous medium. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. In case of porous plate, fluid velocity increases for increasing values of suction parameter whereas due to injection, fluid velocity is noticed to decrease. The non-dimensional temperature increases with the increasing values of injection parameter. A novel result of this investigation is that the flow separation occurred due to suction/injection may be controlled by increasing the permeability parameter of the medium. The effect of thermal radiation on temperature field is also analyzed.