Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface

1988 ◽  
Vol 110 (3) ◽  
pp. 590-595 ◽  
Author(s):  
K. N. Lakshmisha ◽  
S. Venkateswaran ◽  
G. Nath
Keyword(s):  
Mass Transfer ◽  
Nodal Point ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Constant Heat Flux ◽  
Stretching Surface ◽  
Boundary Layer Equations ◽  
Self Similar Solution ◽  
Self Similar ◽  
Unsteady Fluid

A numerical solution of the unsteady boundary layer equations under similarity assumptions is obtained. The solution represents the three-dimensional unsteady fluid motion caused by the time-dependent stretching of a flat boundary. It has been shown that a self-similar solution exists when either the rate of stretching is decreasing with time or it is constant. Three different numerical techniques are applied and a comparison is made among them as well as with earlier results. Analysis is made for various situations like deceleration in stretching of the boundary, mass transfer at the surface, saddle and nodal point flows, and the effect of a magnetic field. Both the constant temperature and constant heat flux conditions at the wall have been studied.

Inhomogeneous thermal conduction equations

1978 ◽  
Vol 56 (7) ◽  
pp. 928-935
Author(s):  
C. S. Lai
Keyword(s):  
Differential Equations ◽  
Thermal Conduction ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Self Similar Solution ◽  
Self Similar ◽  
A New Technique ◽  
The One

The method of self-similar solution of partial differential equations is applied to the one-, two-, and three-dimensional inhomogeneous thermal conduction equations with the thermometric conductivities χ ~ rmWn. Analytical solutions are obtained for the case that the total amount of heat is conserved. For the case that the temperature is maintained constant at r = 0, a new technique of the series solution about the point of intercept is proposed to solve the resultant nonlinear differential equations. The solutions obtained are useful in studying the thermal conduction characteristics of some incompressible fluids.

scholarly journals Formation of corner waves in the wake of a partially submerged bluff body

2015 ◽  
Vol 771 ◽  
pp. 547-563 ◽  
Author(s):  
P. Martínez-Legazpi ◽  
J. Rodríguez-Rodríguez ◽  
A. Korobkin ◽  
J. C. Lasheras
Keyword(s):  
Bluff Body ◽  
Physical Mechanism ◽  
Essential Feature ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Point Of View ◽  
Similar Solution ◽  
Physical Point ◽  
Self Similar Solution ◽  
Self Similar

We study theoretically and numerically the downstream flow near the corner of a bluff body partially submerged at a deadrise depth ${\rm\Delta}h$ into a uniform stream of velocity $U$, in the presence of gravity, $g$. When the Froude number, $\mathit{Fr}=U/\sqrt{g{\rm\Delta}h}$, is large, a three-dimensional steady plunging wave, which is referred to as a corner wave, forms near the corner, developing downstream in a similar way to a two-dimensional plunging wave evolving in time. We have performed an asymptotic analysis of the flow near this corner to describe the wave’s initial evolution and to clarify the physical mechanism that leads to its formation. Using the two-dimensions-plus-time approximation, the problem reduces to one similar to dam-break flow with a wet bed in front of the dam. The analysis shows that, at leading order, the problem admits a self-similar formulation when the size of the wave is small compared with the height difference ${\rm\Delta}h$. The essential feature of the self-similar solution is the formation of a mushroom-shaped jet from which two smaller lateral jets stem. However, numerical simulations show that this self-similar solution is questionable from the physical point of view, as the two lateral jets plunge onto the free surface, leading to a self-intersecting flow. The physical mechanism leading to the formation of the mushroom-shaped structure is discussed.

Transient Heat and Mass Transfer to a Drop in an Electric Field

1977 ◽  
Vol 99 (2) ◽  
pp. 269-273 ◽  
Author(s):  
F. A. Morrison
Keyword(s):  
Mass Transfer ◽  
Electric Field ◽  
Transfer Rate ◽  
Similarity Transformation ◽  
Fluid Motion ◽  
Sudden Change ◽  
Drop Surface ◽  
Concentration Difference ◽  
Boundary Layer Equations ◽  
Surrounding Fluid

A circulating fluid motion is generated by an electric field imposed on a dielectric drop in another dielectric liquid. The motion of the drop surface may be from the poles to the equator or from the equator to the poles. Transient heat or mass transfer results in response to a sudden change in the temperature difference or concentration difference between the drop and the surrounding fluid. The low Reynolds number, high Peclet number response is analyzed. The boundary layer equations are solved exactly using a similarity transformation. Results are obtained for both directions of circulation. While local fluxes differ greatly when the flow reverses, and despite a lack of symmetry, the overall transfer rate is independent of the direction of flow. This result applies to the transient as well as the steady state.

scholarly journals Far Field of a Three-Dimensional Laminar Wall Jet

2021 ◽  
Vol 56 (6) ◽  
pp. 812-823
Author(s):  
I. I. But ◽  
A. M. Gailfullin ◽  
V. V. Zhvick
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Plane Surface ◽  
Three Dimensional ◽  
The Self ◽  
Similar Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar

Abstract We consider a steady submerged laminar jet of viscous incompressible fluid flowing out of a tube and propagating along a solid plane surface. The numerical solution of Navier–Stokes equations is obtained in the stationary three-dimensional formulation. The hypothesis that at large distances from the tube exit the flowfield is described by the self-similar solution of the parabolized Navier–Stokes equations is confirmed. The asymptotic expansions of the self-similar solution are obtained for small and large values of the coordinate in the jet cross-section. Using the numerical solution the self-similarity exponent is determined. An explicit dependence of the self-similar solution on the Reynolds number and the conditions in the jet source is determined.

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