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Flow from a source above a sloping base

We consider the outflow of water from the peak of a triangular ridge into a channel of finite depth. Solutions are computed for different flow rates and bottom angles. A numerical method is used to compute the flow from the source for small values of flow rate and it is found that there is a maximum flow rate beyond which steady solutions do not seem to exist. Limiting flows are computed for each geometrical configuration. One application of this work is as a model of saline water being returned to the ocean after desalination. References Craya, A. ''Theoretical research on the flow of nonhomogeneous fluids''. La Houille Blanche, (1):22–55, 1949. doi:10.1051/lhb/1949017 Dun, C. R. and Hocking, G. C. ''Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary''. J. Eng. Math. 29:1–10, 1995. doi:10.1007/bf00046379 Hocking, G. ''Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom''. ANZIAM J. 26:470–486, 1985. doi:10.1017/s0334270000004665 Hocking, G. C. and Forbes, L. K. ''Subcritical free-surface flow caused by a line source in a fluid of finite depth''. J. Eng. Math. 26:455-466, 1992. doi:10.1007/bf00042763 Hocking, G. C. ''Supercritical withdrawal from a two-layer fluid through a line sink", J. Fluid Mech. 297:37–47, 1995. doi:10.1017/s0022112095002990 Hocking, G. C., Nguyen, H. H. N., Forbes, L. K. and Stokes,T. E. ''The effect of surface tension on free surface flow induced by a point sink''. ANZIAM J., 57:417–428, 2016. doi:10.1017/S1446181116000018 Landrini, M. and Tyvand, P. A. ''Generation of water waves and bores by impulsive bottom flux'', J. Eng. Math. 39(1–4):131-170, 2001. doi:10.1023/A:1004857624937 Lustri, C. J., McCue, S. W. and Chapman, S. J. ''Exponential asymptotics of free surface flow due to a line source''. IMA J. Appl. Math., 78(4):697–713, 2013. doi:10.1093/imamat/hxt016 Stokes, T. E., Hocking, G. C. and Forbes, L.K. ''Unsteady free surface flow induced by a line sink in a fluid of finite depth'', Comp. Fluids, 37(3):236–249, 2008. doi:10.1016/j.compfluid.2007.06.002 Tuck, E. O. and Vanden-Broeck, J.-M. ''A cusp-like free-surface flow due to a submerged source or sink''. ANZIAM J. 25:443–450, 1984. doi:10.1017/s0334270000004197 Vanden-Broeck, J.-M., Schwartz, L. W. and Tuck, E. O. ''Divergent low-Froude-number series expansion of nonlinear free-surface flow problems". Proc. Roy. Soc. A., 361(1705):207–224, 1978. doi:10.1098/rspa.1978.0099 Vanden-Broeck, J.-M. and Keller, J. B. ''Free surface flow due to a sink'', J. Fluid Mech, 175:109–117, 1987. doi:10.1017/s0022112087000314 Yih, C.-S. Stratified flows. Academic Press, New York, 1980. doi:10.1016/B978-0-12-771050-1.X5001-3

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Publication Date
Tue Dec 21 2021
Journal Name
Journal Of Engineering Mathematics
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Publication Date
Wed May 10 2023
Journal Name
Journal Of Engineering
ANALYTICAL SOLUTION OF UNSATURATED SOIL WATER FLOW FROM A POINT SOURCE

Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation and Darcy’s laws. The Richards’ equation may be written in three forms,where the dependent variable is pressure head or moisture content, and the constitutive relationships between water content and pressure head allow for conversion of one form into the other. In the present paper, the “moisture-based" form of Richards’ equation is linearized by applying Kirchhoff’s transformation, which
combines the soil water diffusivity and soil water content. Then the similarity method is used to obtain the analytical solution of wetting front position. This exact solution is obtained by means of Lie’s

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Publication Date
Mon Jul 01 2019
Journal Name
Applied Mathematical Modelling
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Publication Date
Thu Feb 01 2018
Journal Name
Applied Mathematical Modelling
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Publication Date
Sun Oct 30 2022
Journal Name
Iraqi Journal Of Science
Peristaltic Flow with Nanofluid under Effects of Heat Source, and Inclined Magnetic Field in the Tapered Asymmetric Channel through a Porous Medium

     In this present paper , a special model was built to govern the equations of  two dimensional peristaltic transport to nanofluid  flow of a heat source in a tapered  considered in an asymmetric channel. The equations of dimensionless temperature concentration are analytical solve under assumption slow Reynolds number and long wave length. Furthermore, the results that receive by expressing the maximum pressure rise  communicates increased in case of  non-Newtonian fluid when equated with Newtonian fluid. Finally, MATHEMATICA  11 program has been used to solve such system after obtaining the initial conditions.  Most of the results  of drawing  for many are obtained via above program .

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Publication Date
Wed Aug 09 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A Study of the Change of the Total Solar Radiation Above Baghdad City for the Period from 1985.1989 By Using Satellite Antenna Data

 The solar radiation plays an important role on the energy balance of the earthatmosphere, which is the main source of energy.  Also the solar radiation is a main factor of all applications which use a solar energy as renewable energy source.  The purpose of this research is to study the monthly average changes for solar radiation for the period from 1985 to 1989 by using satellite Antenna Alignment from (NASA). The result shows that the monthly average radiation changes from one year to another because of the changing of it component of atmosphere, (gases, clouds and Aerosols) and as an enhancement for this conclusion, we compared the results with the monthly average radiation at clear atmosphere where the change was slig

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Publication Date
Wed Dec 30 2020
Journal Name
Iraqi Journal Of Science
Expansion Velocities of Elementary Gas in Comet Panstarrs Above 30000 Km from Nucleus

The coma gasses consist of molecules liberated from the nucleus by solar heating and relative sublimation. Once they have left the nucleus, these molecules in the coma are exposed to direct solar radiation and can be damaged in various ways due to the combined action of these reactions.

   One of some complex problems facing the research in this field is that the Maxwell-Boltzmann equation gives distribution function for one kind of particles which have same masses, but the gas has multi-groups of particles (Carbon, Neon, Sodium … etc.), where all these components must be in one program to extract average velocity of all and calculate particles velocity to each band. This problem is solved here by Matlab program a

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Publication Date
Fri Jan 01 2016
Journal Name
Animal Nutrition And Feed Technology
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Publication Date
Thu Jan 24 2019
Journal Name
Journal Of Education College Wasit University
“They’ve damaged your uniqueness”: Technology as a Source of Dystopia in Caryl Churchill’s A Number

This study focuses on the impact of technology on creating a dystopian world as presented by the English playwright Caryl Churchill in her play A Number (2002). This dramatic work came as a reaction to the most crucial and valuable turning point in the scientific achievements of human engineering, namely, the cloning of the sheep called Dolly. Therefore, A Number is a play that presents an analytical stage for imagining the biotechnological and scientific future. This dramatic vignette captures the playwright’s fears towards the abnormal progress of technology and science and how far such technological progress affects human relationships and identity. It also portrays how technological progress results in the feeling of a lack of

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Publication Date
Thu Oct 01 2020
Journal Name
Chemical Engineering And Processing - Process Intensification
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