Mathematical modeling of a thin viscous layer adhering to an infinite plate withdrawn at an angle

1994 ◽  
Vol 71 (5) ◽  
pp. 2670-2673
Author(s):  
A. Sh. Bakhtovarshoev ◽  
A. V. Kuz'min
Keyword(s):  
Mathematical Modeling ◽  
Infinite Plate ◽  
Viscous Layer

scholarly journals Modeling methodology of locally non-equilibrium heat conductivity processes

Vestnik IGEU ◽  
2020 ◽  
pp. 65-71
Author(s):  
A.V. Eremin
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Equation ◽  
Exact Analytical Solution ◽  
Separation Of Variables ◽  
Infinite Plate ◽  
Transfer Processes ◽  
Non Equilibrium

With the development of laser technologies and the ability to carry out processing steps under extreme conditions (ul-trahigh temperatures, pressures and their gradients), the interest in studying the processes that occur under locally non-equilibrium conditions has grown significantly. The key directions for the description of locally non-equilibrium pro-cesses include thermodynamic, kinetic and phenomenological ones. The locally non-equilibrium transfer equations can also be derived from the Boltzmann equation by using the theory of random walks and molecular-kinetic methods. It should be noted that some options of locally non-equilibrium processes lead to conflicting results. This study aims to develop a method for mathematical modeling of locally nonequilibrium heat conduction processes in solids, which allows determining their temperature with high accuracy during fast and high-intensity heat transfer processes. As applied to heat transfer processes in solids, a generalized heat equation that takes into account the relaxation properties of materials is formulated. The exact analytical solution is obtained using the Fourier method of separation of variables. The methodology for mathematical modeling of locally non-equilibrium transfer processes based on modified conservation laws has been developed. The generalized differential heat equation which allows performing N-fold relaxation of the heat flow and temperature in the modified heat balance equation has been formulated. For the first time, an exact analytical solution to the unsteady heat conduction problem for an infinite plate was obtained taking into account many-fold relaxation. The analysis of the solution to the boundary value problem of locally nonequilibrium heat conduction enabled to conclude that it is impossible to instantly has establish a boundary condition of the first kind. It has been demonstrated that each of the following terms in the relaxed heat equation has an ever smaller effect on the heat transfer process. The obtained results can be used by the scientific and technical personnel of organizations and higher educational institutions in the study of fuel ignition processes, the development of laser processing of materials, the design of highly efficient heat transfer equipment and the description of fast-flowing heat transfer processes.

Mathematical Modeling of Mechanized Technologies Soldering

2016 ◽  
Vol 870 ◽  
pp. 573-577
Author(s):  
V.N. Shtennikov
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Heat Flow ◽  
Solder Joints ◽  
Electronic Devices ◽  
Infinite Plate ◽  
Surface Warming ◽  
Wave Soldering ◽  
Laser Soldering ◽  
Regular Mode

The possibility of compliance with the required technological soldering conditions and ensuring their reproducibility for wave soldering, laser soldering, convection soldering have been researched. Comparing the experimental data to the results of mathematical modeling allowed selectng optimal modes of the wave, convection and laser soldering of electronic devices. The conclusion about the prospects of the analytical dependencies to improve mechanical soldering of electronic devices for any purpose. When heating by convection or wave solder, the temperature along the depth of the solder joints is less than when the contact or laser soldering. It was found that the temperature of the solder joints with infrared and laser soldering can be estimated based on the heat equation for a semi-infinite plate with a given heat flow on the surface. Warming up of the printing unit and, consequently, the solder joints when soldering, convection can be described by equations of the regular mode.

Flow Transient Near the Leading Edge of a Flat Plate Moving Through a Viscous Fluid

1974 ◽  
Vol 41 (4) ◽  
pp. 919-924 ◽  
Author(s):  
R. B. Kinney ◽  
M. A. Paolino
Keyword(s):  
Free Stream ◽  
Infinite Plate ◽  
Leading Edge ◽  
Viscous Flows ◽  
Stream Velocity ◽  
Viscous Layer ◽  
Two Dimensional Flow ◽  
Essential Input ◽  
Vorticity Production ◽  
Vorticity Transport

An investigation is made of the unsteady flow in the leading-edge region of a semi-infinite plate impulsively started from rest. Based entirely on the vorticity concepts outlined by Lighthill, numerical results are obtained for the complete two-dimensional flow field by solving the single vorticity transport equation. An essential input to the calculations is the distribution of vorticity production at the plate surface. This is determined at each instant of time from the no-slip condition at the plate and represents a departure from conventional numerical analyses of viscous flows. Departing further from conventional approaches, the velocity field is computed from the law of induced velocities (Biot-Savart law) rather than the stream function. Because of vorticity diffusion well ahead of the plate, a significant disturbance propagates upstream, thereby destroying the uniformity of the approaching flow. Calculations are carried sufficiently forward in time for an approximately steady state to be reached at a distance downstream of the leading edge equal to the thickness of the viscous layer. As viewed by an observer moving with the plate, the flow transient exhibits a velocity overshoot relative to the apparent free-stream velocity. This effect was unexpected for a semi-infinite plate and represents a novel aspect of the flow not found in transient analyses based on the boundary-layer approximations.

Cerebral Blood Circulation in Premature Infants by Means of Mathematical Modeling

2015 ◽  
Vol 46 (S 01) ◽  
Author(s):  
R. Lampe ◽  
N. Botkin ◽  
V. Turova ◽  
T. Blumenstein ◽  
A. Alves-Pinto
Keyword(s):  
Mathematical Modeling ◽  
Premature Infants ◽  
Blood Circulation ◽  
Cerebral Blood Circulation
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