Corina Fetecau

General Solutions for Magnetohydrodynamic Natural Convection Flow with Radiative Heat Transfer and Slip Condition over a Moving Plate

General solutions for the magnetohydrodynamic (MHD) natural convection flow of an incompressible viscous fluid over a moving plate are established when thermal radiation, porous effects, and slip condition are taken into consideration. These solutions, obtained in closed-form by Laplace transform technique, depend on the slip coefficient and the three essential parameters Gr, Preff, and Keff. They satisfy all imposed initial and boundary conditions and can generate a large class of exact solutions corresponding to different fluid motions with technical relevance. For illustration, two special cases are considered and some interesting results from the literature are recovered as limiting cases. The influence of pertinent parameters on the fluid motion is graphically underlined.

Radiative and Porous Effects on Free Convection Flow near a Vertical Plate that Applies Shear Stress to the Fluid

General solutions for the unsteady free convection flow of an incompressible viscous fluid due to an infinite vertical plate that applies a shear stress f (t) to the fluid are established when thermal radiation and porous effects are taken into consideration. They satisfy all imposed initial and boundary conditions and can generate a large class of exact solutions corresponding to different motions with technical relevance. The velocity is presented as a sum of thermal and mechanical components. Finally, some special cases are brought to light, and effects of pertinent parameters on the fluid motion are graphically underlined.

Natural Convection Flow near a Vertical Plate that Applies a Shear Stress to a Viscous Fluid

The unsteady natural convection flow of an incompressible viscous fluid near a vertical plate that applies an arbitrary shear stress to the fluid is studied using the Laplace transform technique. The fluid flow is due to both the shear and the heating of the plate. Closed-form expressions for velocity and temperature are established under the usual Boussinesq approximation. For illustration purposes, two special cases are considered and the influence of pertinent parameters on the fluid motion is graphically underlined. The required time to reach the steady state in the case of oscillating shear stresses on the boundary is also determined.

First Exact Solutions for Flows of Rate Type Fluids in a Circular Duct that Applies a Constant Couple to the Fluid

Rotational flow of an Oldroyd-B fluid induced by an infinite circular cylinder that applies a constant couple to the fluid is studied by means of integral transforms. Such a problem is not solved in the existing literature for rate type fluids and the present solutions are based on a simple but important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easy be reduced to the similar solutions corresponding to Maxwell, second-grade, and Newtonian fluids performing the same motion. Finally, the influence of material parameters on the velocity and shear stress distributions is graphically underlined.

Magnetohydrodynamic Natural Convection Flow with Newtonian Heating and Mass Diffusion over an Infinite Plate that Applies Shear Stress to a Viscous Fluid

Abstract Unsteady magnetohydrodynamic natural convection flow with Newtonian heating and constant mass diffusion over an infinite vertical plate that applies an arbitrary time-dependent shear stress to a viscous optically thick fluid is studied in the presence of a heat source. Radiative effects are taken into consideration and exact solutions for the dimensionless velocity and temperature are established under Boussinesq approximation. The solutions that have been obtained, uncommon in the literature, satisfy all imposed initial and boundary conditions and can generate exact solutions for any motion problem with technical relevance of this type. For illustration, a special case is considered and the influence of pertinent parameters on the fluid motion is graphically underlined.

Starting solutions for the flow of second grade fluids in a rectangular channel due to an oscillating shear stress

The unsteady motion of a second grade fluid between two parallel side walls perpendicular to a plate is studied by means of the Fourier sine and cosine transforms. Initially, the fluid is at rest and at time t = 0+, the plate applies an oscillating shear to the fluid. The solutions that have been obtained, presented under integral and series form and written as a sum between steady time-periodic and transient solutions can be easily reduced to the similar solutions for Newtonian fluids performing the same motion. They describe the motion of the fluid some time after its initiation. After that time, when the transient solutions disappear, the motion of the fluid is described by the steady time-periodic solutions that are independent of the initial conditions. In the absence of side walls, more exactly when the distance between walls tends to infinity, all solutions reduce to those corresponding to the motion over an infinite plate. As it was to be expected, the steady time-periodic solutions corresponding to sine and cosine oscillations of the shear stress on the boundary differ by a phase shift. Finally, the influence of side walls on the fluid motion, the required time to reach the steady periodic flow, as well as the distance between walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence are established by numerical calculus and graphical illustrations. As expected, the time needed to reach the steady periodic flows is lower in the presence of side walls. It is lower for Newtonian fluids in comparison with second grade fluids and greater for sine oscillations in comparison to the cosine oscillations of the boundary shear.The unsteady motion of a second grade fluid between two parallel side walls perpendicular to a plate is studied by means of the Fourier sine and cosine transforms. Initially, the fluid is at rest and at time t = 0+, the plate applies an oscillating shear to the fluid. The solutions that have been obtained, presented under integral and series form and written as a sum between steady time-periodic and transient solutions can be easily reduced to the similar solutions for Newtonian fluids performing the same motion. They describe the motion of the fluid some time after its initiation. After that time, when the transient solutions disappear, the motion of the fluid is described by the steady time-periodic solutions that are independent of the initial conditions. In the absence of side walls, more exactly when the distance between walls tends to infinity, all solutions reduce to those corresponding to the motion over an infinite plate. As it was to be expected, the steady time-periodic solutions corresponding ...

EXACT ANALYTIC SOLUTIONS FOR THE FLOW OF A GENERALIZED BURGERS FLUID INDUCED BY AN ACCELERATED SHEAR STRESS

This article has been retracted.

On the Motion Induced by a Flat Plate That Applies Oscillating Shear Stresses to an Oldroyd-B Fluid: Applications

Starting solutions corresponding to the motion induced by an infinite flat plate that applies oscillating shear stresses to an Oldroyd-B fluid are developed using the Laplace and Fourier sine transforms. These solutions, presented as a sum between steady-state and transient solutions, describe the motion of the fluid some time after its initiation. After that time, when the transients disappear, the starting solutions tend to the steady-state solutions which are periodic in time and independent of the initial conditions. However, they satisfy the governing equation and boundary conditions. As a check of results, the known solution corresponding to the motion due to an infinite plate that applies a constant shear to the fluid is obtained as a limiting case of our cosine solution. Exact solutions for Maxwell and Newtonian fluids performing the same motions are obtained as special cases of general solutions. Furthermore, as an application, the solutions corresponding to the motion produced by an oscillating plate are provided.