One-dimensional dispersion in unsteady flow in an adsorbing porous medium: An analytical solution

1990 ◽  
Vol 4 (2) ◽  
pp. 189-196 ◽  
Author(s):  
Raja Ram Yadava ◽  
Ram Raj Vinda ◽  
Naveen Kumar
Keyword(s):  
Porous Medium ◽  
Analytical Solution ◽  
Unsteady Flow ◽  
One Dimensional

A Semi-analytical Solution for One-Dimensional Oil Displacement by Miscible Gas in a Homogeneous Porous Medium

2019 ◽  
pp. 81-95
Author(s):  
Luana C. M. Cantagesso ◽  
Luara K. S. Sousa ◽  
Tamires A. Marotto ◽  
Anna M. Radovanovic ◽  
Adolfo Puime Pires ◽  
...  
Keyword(s):  
Porous Medium ◽  
Analytical Solution ◽  
One Dimensional ◽  
Oil Displacement ◽  
Homogeneous Porous Medium

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

Calculation of two-dimensional dispersion in a gas in unsteady flow in a porous medium

1983 ◽  
Vol 17 (5) ◽  
pp. 704-710
Author(s):  
E. G. Basanskii ◽  
V. M. Kolobashkin ◽  
N. A. Kudryashov
Keyword(s):  
Porous Medium ◽  
Unsteady Flow ◽  
Two Dimensional

Building Vertical Walls by Deposition of Molten Metal Droplets

2005 ◽  
Author(s):  
M. Fang ◽  
S. Chandra ◽  
C. B. Park
Keyword(s):  
Surface Layer ◽  
Analytical Solution ◽  
Substrate Temperature ◽  
Layer By Layer ◽  
Droplet Temperature ◽  
Droplet Generator ◽  
One Dimensional ◽  
Metallurgical Bonding ◽  
Experimental Parameters ◽  
Vertical Walls

Experiments were conducted to determine conditions under which good metallurgical bonding was achieved in vertical walls composed of multiple layers of droplets that were fabricated by depositing tin droplets layer by layer. Molten tin droplets (0.75 mm diameter) were deposited using a pneumatic droplet generator on an aluminum substrate. The primary parameters varied in experiments were those found to most affect bonding between droplets on different layers: droplet temperature (varied from 250°C to 325°C) and substrate temperature (varied from 100°C to 190°C). Considering the cooling rate of droplet is much faster than the deposition rate previous deposition layer cooled down too much that impinging droplets could only remelt a thin surface layer after impact. Assuming that remelting between impacting droplets and the previous deposition layer is a one-dimensional Stefan problem with phase change an analytical solution can be found and applied to predict the minimum droplet temperature and substrate temperature required for local remelting. It was experimentally confirmed that good bonding at the interface of two adjacent layers could be achieved when the experimental parameters were such that the model predicted remelting.

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