Incompressible boundary layer for longitudinal flow over a cylinder with an applied magnetic field

The flow, heat and mass transfer problem for a steady laminar incompressible boundary layer flow in an electrically conducting fluid over a longitudinal cylinder with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The results are found to be strongly dependent on the magnetic field and dissipation parameter. The effect of the mass transfer is more pronounced on the skin friction than on the heat transfer. The results have been compared with those of the series solution, the asymptotic solution, the Glauert and Lighthill's solution, local similarity, local nonsimilarity and difference-differential methods. Good agreement is found with all of them, except with the results of the local similarity and series solution methods.

On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

A new algorithm for parallel solution of linear equations

Abstract is not available.

Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

A multi-microprocessor architecture for solving partial differential equations

This paper presents the architecture of a fault-tolerant, special-purpose multi-microprocessor system for solving Partial Differential Equations (PDEs). The modular nature of the architecture allows the use of hundreds of Processing Elements (PEs) for high throughput. Its performance is evaluated by both analytical and simulation methods. The results indicate that the system can achieve high operation rates and is not sensitive to inter-processor communication delay.

Derivation of the solution of certain singular integral equations

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.

Unsteady laminar compressible stagnation-point boundary-layer flow over a three-dimensional body: Higher order effects

The unsteady laminar compressible three-dimensional stagnation-point boundary-layer flow with variable properties has been studied when the velocity of the incident stream, mass transfer and wall temperature vary arbitrarily with time. The second-order unsteady boundary-layer equations for all the effects have been derived by using the method of matched asymptotic expansions. Both nodal and saddle point flows as well as cold and hot wall cases have been considered. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for an accelerating stream, a decelerating stream and a fluctuating stream. The results indicate that the unsteady free stream velocity distributions, the nature of the stagnation point, the mass transfer, the wall temperature and the variation of the density-viscosity product across the boundary significantly affect the skin friction and heat transfer. The variation of the wall temperature with time strongly affects the heat transfer whereas its effect is comparatively less on skin friction. Suction increases the skin friction and heat transfer but injection does the opposite. The skin friction in the x direction due to the combined effects of first- and second-order boundary layers is less than the skin-friction in the x direction due to the first-order boundary layers for all the parameters. The overall skin friction in the z direction and heat transfer are more or less than the first-order boundary layers depending upon the values of the various parameters.

Mass transfer effects on the generalised vortex flow over a stationary surface with or without magnetic field

The effect of injection and suction on the generalised vortex flow of a steady laminar incompressible fluid over a stationary infinite disc with or without magnetic field under boundary-layer approximations has been studied. The coupled nonlinear ordinary differential equations governing the self-similar flow have been numerically solved using the finite-difference scheme. The results indicate that the injection produces a deeper inflow layer and de-stabilises the motion while suction or magnetic field suppresses the inflow layer and produces stability. The effect of decreasingn, the parameter characterising the nature of vortex flow, is similar to that of increasing the injection rate.

Unsteady three-dimensional boundary layer flow over a flat plate with attached cylinder

The unsteady laminar incompressible three-dimensional boundary layer flow and heat transfer on a flat plate with an attached cylinder have been studied when the free stream velocity components and wall temperature vary inversely as linear and quadratic functions of time, respectively. The governing semisimilar partial differential equations with three independent variables have been solved numerically using a quasilinear finite-difference scheme. The results indicate that the skin friction increases with parameter λ which characterizes the unsteadiness in the free stream velocity and the streamwise distance Image , but the heat transfer decreases. However, the skin friction and heat transfer are found to change little along Image . The effect of the Prandtl number on the heat transfer is found to be more pronounced when λ is small, whereas the effect of the dissipation parameter is more pronounced when λ is comparatively large.

Generalized Burgers equations and Euler-Painlev transcendents. I

Initial-value problems for the generalized Burgers equation (GBE) ut+u betaux+lambdaualpha =(delta/2)uxx are discussed for the single hump type of initial data both continuous and discontinuous. The numerical solution is carried to the self-similar ``intermediate asymptotic'' regime when the solution is given analytically by the self-similar form. The nonlinear (transformed) ordinary differential equations (ODE's) describing the self-similar form are generalizations of a class discussed by Euler and Painlevé and quoted by Kamke. These ODE's are new, and it is postulated that they characterize GBE's in the same manner as the Painlev equations categorize the Kortweg-de Vries (KdV) type. A connection problem for some related ODE's satisfying proper asymptotic conditions at x=±[infinity], is solved. The range of amplitude parameter is found for which the solution of the connection problem exists. The other solutions of the above GBE, which display several interesting features such as peaking, breaking, and a long shelf on the left for negative values of the damping coefficient lambda, are also discussed. The results are compared with those holding for the modified KdV equation with damping. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Compressible 2nd-order boundary-layers for 3-dimensional stagnation point flows with mass-transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.

Unsteady Self-similar Stagnation Point Boundary Layers for Micropolar Fluids

The self-similar solution of the unsteady laminar incompressible two-dimensional and axisymmetric stagnation point boundary layers for micropolar fluids governing the flow and heat transfer problem has been obtained when the free stream velocity and the square of the mass transfer vary inversely as a linear function of time. The nonlinear ordinary differential equations governing the flow have been solved numerically using a quasilinear finite-Difference scheme. The results indicate that the coupling parameter, mass transfer and unsteadiness in the free stream velocity strongly affect the skin friction, microrotation gradient and heat transfer whereas the effect of microrotation parameter is strong only on the microrotation gradient. The heat transfer is strongly dependent on the prandtl number whereas the skin friction gradient are unaffected by it.

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Spinup or spindown of a rotating electrically conducting fluid in a magnetic field

The hydromagnetic spinup or spindown of an incompressible, rotating, electrically conducting fluid over an infinite insulated disk with an applied magnetic field is studied when the impulsive motion is imparted either to the fluid or to the disk. The nonlinear partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. It is found that the spinup (or spindown) time due to impulsive motion of the disk is much shorter than the spinup (or spindown) time due to the impulsive motion of the distant fluid. The spinup (or spindown) time for the hydromagnetic case is comparatively smaller than the corresponding nonmagnetic case. Spindown is not merely a mirror reflection of spinup. Physics of Fluids is copyrighted by The American Institute of Physics.