Magnetohydrodynamic flow in a rectangular duct with suction and injection

Summary The effects of suction or injection on an incompressible laminar flow in a rectangular duct with nonconducting walls in the presence of an imposed transverse magnetic field are examined. Analytical solutions are obtained for the velocity and magnetic field, which are useful for obtaining the current density and electric field strength.     

Stability of fluid flow in a plane channel with uniform injection or suction through porous walls

The stability of laminar flow in a channel with porous walls is analyzed within the scope of the linear theory.Notation x distance from entrance cross section - y transverse coordinate measured from axis - u_x, u_y longitudinal and transverse velocity components of main flow - h half-width of channel - kinematic viscosity coefficient - U₀ average velocity in entrance cross section - V suction or injection rate (positive for suction) - U=U₀–V_x/h local average velocity - amplitude of flow disturbances - wave number - c complex phase velocity of disturbances - c_r real propagation velocity of disturbances, =y/h - Re=Uh/ Reynolds number of main flow - R=Vh/ injection or suction Reynolds number - m=U/¦V¦ injection rate parameter Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 436–440, September, 1981.     

Hydromagnetic flow between rotating eccentric cylinders with suction at the porous walls

The effect of a radial magnetic field on the flow of a viscous, incompressible fluid between two eccentric rotating cylinders with suction at both the cylinders, for very small clearance ratio is investigated. The expressions for the stream function and pressure are obtained using perturbation analysis. Conclusions are drawn from the streamlines and pressure plots which are shown graphically for various values of flow parameters.     

Heat transfer in MHD flow with pressure gradient,suction and injection

Summary Numerical solutions to the MHD Falkner-Skan equation and the corresponding heat transfer equation have been obtained on taking into consideration the effects of suction and injection and the pressure gradient parameter . Velocity and temperature profiles are shown on graphs and the numerical values of the skin friction and the rate of heat transfer are given in the form of tables. It has been observed that an increase inN _m (magnetic field parameter) leads to an increase in velocity, skin friction, rate of heat transfer and a fall in temperature. Also an increase in suction leads to a fall in the value of the skin friction and the rate of heat transfer, opposite to the case of injection.     

Variational approach to free convection boundary-layer flow with suction and injection

The Gyarmati variational principle — a significant development in the field of the thermodynamics of irreversible processes — is employed to study suction and injection effects in flow and heat transfer in a free convection boundary layer over a cone. The velocity and temperature distributions inside respective boundary layers are considered as simple polynomial functions, and with the use of the perturbation procedure the variational principle is formulated. The Euler-Lagrange equations are reduced to coupled polynomial equations in terms of boundary-layer thicknesses. The skin-friction (shear-stress) and heat-transfer (Nusselt number) values with constant wall temperature are computed for various values of the suction and injection parameters and the cone-angle parameter. The comparison of the present solution with an available numerical solution shows good agreement. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 6, pp. 109–115, November–December, 2007.     

Laminar flow of a non-Newtonian fluid in channels with wall suction or injection

The one-dimensional approximate equation in the rectangular Cartesian coordinates governing flow of a non-Newtonian fluid confined in two large plates separated by a small distance of h, with the upper plate stationary while the lower plate is uniformly porous and moving in the x-direction with constant velocity, is derived by accounting for the order of magnitude of terms as well as the accompanying approximations to the full-blown three-dimensional equations by using scaling arguments, asymptotic techniques and assuming the cross-flow velocity is much less than the axial velocity. The one-dimensional governing equation for a power-law fluid flow confined between parallel plates, with the upper plate is stationary and the bottom plate subjected to sudden acceleration with a constant velocity in the x-direction and uniformly porous, is solved analytically for a Newtonian fluid case (n = 1) and numerically for various values of power-law index to determine the transient velocity and thus the overall transient velocity distribution. The effects of mass suction/injection at the porous bottom plate on the flow of non-Newtonian fluids are examined for various values of time and power-law index. The results obtained from the present analysis are compared with the data available in the literature.     

Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts

 The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical–analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied. Received 16 March 2000     

The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls

Summary A numerical investigation is made to establish whether multiple solutions exist for laminar, incompressible, steady flow in a parallel plate porous channel with uniform suction at both walls. For values of the wall suction Reynolds number,R, greater than 12.165 three numerical solutions are observed for eachR, while forR less than 12.165 only one solution for eachR can be found. A method involving the inclusion of exponentially small terms in a perturbation series is used to find two of the solutions analytically, while an appeal to the numerical results gives an indication of how the third solution can be obtained. The series involving the exponentially small terms, as well as predicting dual solutions, gives more accurate analytic results for the skin friction at the channel walls.     

Thermal boundary layers over a wedge with uniform suction or injection in forced flow

Summary The behavior of incompressible laminar boundary layers in forced flow over a wedge with uniform suction or injection was theoretically investigated. The boundary layer equations along a wedge are transformed into non-similar partial differential ones, and the ordinary differential equations were obtained by means of the difference-differential method. The solutions of the resulting equations are expressed in a form of integral equations which are in turn solved by iterative numerical quadratures. The numerical results are given for the velocity distribution, temperature distribution and the coefficient of skin friction and heat transfer for various values of suction/injection parameter.     

Free convection boundary layer flow with uniform suction or injection over a cone

Summary The effect of uniform suction or injection on free convection boundary layer over a cone was theoretically investigated. The non-linear ordinary differential equations were obtained by the difference-differential method after transforming it to an equivalent two-dimensional problem by Mangler's transformation. The solutions of the resulting equations can be expressed in the form of integral equations. Numerical calculations were performed solving the integral equations by the iterative numerical quadrature. The velocity profiles, temperature profiles, skin friction parameters and heat transfer parameters with constant wall temperature were computed for various values of suction/injection parameter and cone angle parameter.     

Non-newtonian secondary flows in ducts of rectangular cross-section

Summary A numerical study of the secondary flows which occur in the laminar pressure-driven motion of dilute polymer solutions in ducts of rectangular cross-section is presented. The full nonlinear equations of motion for a Maxwell fluid with shear thinning are solved by an explicit finite-difference technique. Results are presented in an inertial framing which indicate the existence of the previously observed eight-vortex secondary flow in ducts of various aspect ratios. In addition, the effect of spanwise rotations on the strength and the structure of the secondary flow is examined. The results indicate that even the mere presence of the diurnal rotation of the earth can give rise to a double-vortex secondary flow which is of a comparable order of magnitude to the viscoelastic secondary flows in dilute polymer solutions. Specific computations are presented which illustrate the distortional effect that the imposition of a spanwise rotation has on the viscoelastic secondary flow structure in square ducts. The implications that these results can have on laboratory experiments are discussed briefly along with other possible applications to rotating and curved flows.With 15 Figures     

Natural convection in a rectangular enclosure in the presence of a magnetic field with uniform heat flux from the side walls

Summary A numerical study is presented for magnetohydrodynamic free convection of an electrically conducting fluid in a two-dimensional rectangular enclosure in which two side walls are maintained at uniform heat flux condition. The horizontal top and bottom walls are thermally insulated. A finite difference scheme comprising of modified ADI (Alternating Direction Implicit) method and SOR (Successive-Over-Relaxation) method is used to solve the governing equations. Computations are carried out over a wide range of Grashof number, Gr and Hartmann number, Ha for an enclosure of aspect ratio 1 and 2. The influences of these parameters on the flow pattern and the associated heat transfer characteristics are discussed. Numerical results show that with the application of an external magnetic field, the temperature and velocity fields are significantly modified. When the Grashof number is low and Hartmann number is high, the central streamlines are elongated and the isotherms are almost parallel representing a conduction state. For sufficiently large magnetic field strength the convection is suppressed for all values of Gr. The average Nusselt number decreases with an increase of Hartmann number and hence a magnetic field can be used as an effective mechanism to control the convection in an enclosure.List of symbols Ar aspect ratio,H/L - B ₀ induction magnetic field - H ₀ magnetic field,H ₀=B ₀/ _m - g gravitational acceleration - Gr Grashof number,gq(L/k)L ³/v ² - H height of the enclosure - Ha Hartmann number, - k thermal conductivity - Nu local Nusselt number - average Nusselt number - p pressure - Pr Prandtl number, / - q heat flux - t time - T dimensionless temperature, (–₀)/q(L/k) - u vertical velocity - U dimensionless vertical velocity,uL/ - v horizontal velocity - V dimensionless horizontal velocity,vL/ - x vertical coordinate - X dimensionless vertical coordinate,x/L - y horizontal coordinate - Y dimensionless horizontal coordinate,y/L - thermal diffusivity - thermal expansion coefficient - temperature - ₀ reference temperature - density - kinematic viscosity - viscosity - _m magnetic permeability - electrical conductivity - stream function - dimensionless stream function, / - dimensionless time,t/L ² - vorticity - dimensionless vorticity, L ²/ - X grid spacing inX-direction - Y grid spacing inY-direction - time increment - ² Laplacian operator     

Theoretical analysis on mixed convection boundary layer flow over a wedge with uniform suction or injection

Summary Forced and free mixed convection boundary layer flow over a wedge with uniform suction or injection is theoretically investigated. Nonsimilar partial differential equations are transformed into ordinary differential equations by means of difference-differential method. The solutions of the resulting equations are obtained in integral forms and are calculated by iterative numerical procedures. The results were given for velocity profiles, temperature profiles, friction and heat transfer parameters for various values of suction/injection parameter, pressure gradient parameter and buoyancy parameter.     

Forced and free mixed convection boundary layer flow with uniform suction or injection on a vertical flat plate

Summary A laminar forced and free mixed convection flow on a flat plate with uniform suction or injection was theoretically investigated. Nonsimilar partial differential equations are transformed into nonsimilar ordinary ones by means of difference-differential method. The solutions of the resulting equations are obtained with integral forms, and are calculated by the method of successive iteration. The velocity profiles, temperature profiles, friction coefficient and heat transfer coefficient are obtained for various values of suction/injection parameter and buoyancy parameter.     

Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection

Van Dyke's singular perturbation technique has been used to study the heat transfer in the flow of a micropolar fluid past a curved surface with suction and injection. The conditions for similar solutions of the thermal boundary layer equations have been obtained. In addition to the usual “no slip” condition for velocity, the two types of boundary conditions used for microrotation are: (i) no relative spin on the boundary; (ii) the anti-symmetric part of the stress tensor vanishes at the boundary. The effect of suction or injection on velocity, microrotation, temperature, skin friction coefficient, wall couple stress coefficient, displacement and momentum thicknesses, rate of heat transfer and adiabatic wall temperature have been studied. It is observed that with the increase of injection velocity, the thickness of the boundary layer is increased and the local drag is reduced. A comparison with the results obtained for a Newtonian fluid reveals that the microelements present in the fluid reduce the velocity and frictional drag, and cool the boundary.     

On the steady flow produced by a rotating disc with either surface suction or injection

Summary A series solution is presented for the steady, laminar flow produced by a rotating disc. The series consists solely of exponential terms with negative exponents. It is shown that this approach yields uniformly valid solutions of high accuracy for all cases of suction and for low values of injection at the disc surface. The radius of convergence of the series is determined. For those injection cases for which the direct series method fails, an integral method is presented which is based on the properties of the series. The latter method consists of obtaining differential equations which represent the behaviour of the sums of the series. This method allows the solution of the governing differential equations as an initial value problem.     

Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field

The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct with one conducting and one insulating pair of opposite walls under an external magnetic field parallel to the conducting walls, is investigated. The MHD equations are coupled in terms of velocity and magnetic field and cannot be decoupled with conducting wall boundary conditions since then boundary conditions are coupled and involve an unknown function. The boundary element method (BEM) is applied here by using a fundamental solution which enables to treat the MHD equations in coupled form with the most general form of wall conductivities. Also, with this fundamental solution it is possible to obtain BEM solution for values of Hartmann number (M) up to 300 which was not available before. The equivelocity and induced magnetic field contours which show the well-known characteristics of MHD duct flow are presented for several values of M.