A particular solution of the two and three dimensional unsteady state thermal or mass diffusion equation is obtained by introducing a combination of variables of the form,
η = (x+y) / √ct , and η = (x+y+z) / √ct, for two and three dimensional equations
respectively. And the corresponding solutions are,
θ (t,x,y) = θ0 erfc (x+y)/√8ct and θ( t,x,y,z) =θ0 erfc (x+y+z/√12ct)
In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.
DAIRMD Professor Hayder R. Al-Hamamy, **Professor Adil A. Noaimi, **Dr. Ihsan A. Al-Turfy, IOSR Journal of Dental and Medical Sciences (IOSR-JDMS), 2015
Theoretical and experimental investigations of the transient heat transfer parameters of constant heat flux source subjected to water flowing in the downward direction in closed channel are conducted. The power increase transient is ensured by step change increase in the heat source power. The theoretical investigation involved a mathematical modeling for axially symmetric, simultaneously developing laminar water flow in a vertical annulus. The mathematical model is based on one dimensional downward flow. The boundary conditions of the studied case are based on adiabatic outer wall, while the inner wall is subjected to a constant heat flux. The heat & mass balance equation derived for specified element of bulk water within the annulu
... Show MoreThe insulation system of a machine coil includes several layers made of materials with different characteristics. The effective insulation design of machine coils, especially in the machine end winding, depends upon an accurate model of the stress grading system. This paper proposes a modeling approach to predict the transient overvoltage, electric field, and heat generation in machine coils with a stress grading system, considering the variation of physical properties in the insulation layers. A non-uniform line model is used to divide the coil in different segments based on material properties and lengths: overhang, stress grading and slot. The cascaded connection of chain matrices is used to connect segments for the representation of the
... Show MoreIn this research, some probability characteristics functions (probability density, characteristic, correlation and spectral density) are derived depending upon the smallest variance of the exact solution of supposing stochastic non-linear Fredholm integral equation of the second kind found by Adomian decomposition method (A.D.M)
This research aims to modify the components of stainless steel alloy by the method of surface engineering through the single diffusion coating technique in order to obtain new alloys with high efficiency in resisting harsh environmental conditions. Steam a mixture of sodium chloride ( ) and sodium sulfate ( ) at a temperature of 900 and then compare it with the base alloy. The results showed that the alloys produced in this way are very efficient. The results showed that the aluminum coating showed high efficiency in resisting oxidation and provided better protection for a longer time compared to the uncoated alloy due to the oxide crust layer formed with high adhesion as well as the aluminum-rich phases, whether the phase
... Show MoreBackground: The accuracy of fitness of any dental casting is imperative for the success of any prosthodontic treatment. From the time that dental casting was first introduced, efforts have been made to produce more accurate and better fitted castings with minimal marginal discrepancy. The aim of this in vitro study was to evaluate the effects of three different investing and burnout techniques on the vertical marginal discrepancies ofceramometalcopings invested with two types of phosphate- bonded investments. Materials and methods: Sixty wax patterns were fabricated on a standardized prepared brass die representing an upper central incisor by the aid of a custom-made split mold. Three different investing and burnout techniques were applied
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