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)
The presented work includes the Homotopy Transforms of Analysis Method (HTAM). By this method, the approximate solution of nonlinear Navier- Stokes equations of fractional order derivative was obtained. The Caputo's derivative was used in the proposed method. The desired solution was calculated by using the convergent power series to the components. The obtained results are demonstrated by comparison with the results of Adomain decomposition method, Homotopy Analysis method and exact solution, as explained in examples (4.1) and (4.2). The comparison shows that the used method is powerful and efficient.
Objective: the aim of this study is to invest age and determine the effect of using (2) packing
technique (conventional and new tension technique) on hardness of (2) types of heat cure acrylic
resin which are (Ivoclar and Qual dental type).
Methodology : this study was intended the using of two types of heat cure acrylic (IVoclar and
Qual dental type) which are used in construction of complete denture which packed in two different
packing technique (conventional and new tension technique) and accomplished by using a total of
(40) specimens in diameter of ( 2mm thickness, 2 cm length and 1 cm width) . This specimens were
sectioned and subdivide into (4) group each (10) specimens for one group , then signed as (A, Al B
The non static chain is always the problem of static analysis so that explained some of theoretical work, the properties of statistical regression analysis to lose when using strings in statistic and gives the slope of an imaginary relation under consideration. chain is not static can become static by adding variable time to the multivariate analysis the factors to remove the general trend as well as variable placebo seasons to remove the effect of seasonal .convert the data to form exponential or logarithmic , in addition to using the difference repeated d is said in this case it integrated class d. Where the research contained in the theoretical side in parts in the first part the research methodology ha
... Show MoreThe basic goal of this research is to utilize an analytical method which is called the Modified Iterative Method in order to gain an approximate analytic solution to the Sine-Gordon equation. The suggested method is the amalgamation of the iterative method and a well-known technique, namely the Adomian decomposition method. A method minimizes the computational size, averts round-off errors, transformation and linearization, or takes some restrictive assumptions. Several examples are chosen to show the importance and effectiveness of the proposed method. In addition, a modified iterative method gives faster and easier solutions than other methods. These solutions are accurate and in agreement with the series
... Show MoreBackground: The fracture of instruments within root canal during endodontic treatment is a common incidence, fracture because of fatigue through flexure occurs due to metal fatigue, this study aimed to assess the effect of curvature angle and rotational speed on the cyclic fatigue of different type of Endodontic NiTi Rotary Instruments and compare among them. Materials and method: Three types of rotary instruments with tip size 0.25: ProTaPer F2 (Densply, Malifier) Revo-S SU( 0.06 taper, MicroMega) and RaCe system (0.06 taper, FKG, Dentaire), Forty file of each instrument were used within two canals with angle of curvature (40 &60 )at two speed (250&400)RPM, twelve group were formed for all instruments(total number=120),ten file fo
... Show MoreThe electrical resistivity method is one of the geophysical methods for detecting weak subsurface zone. The 2D resistivity data were used to compare three electrode configurations, Wenner, Dipole-dipole, and Schlumberger, to detect weak subsurface zones along a profile south of Baghdad near the Bismayah pumping station. The results show many zones of low resistivity that may be weak zones. A dipole-dipole array is a large number of measurements and is more sensitive than others. The Wenner-Schlumberger array has a depth also higher than other arrays. Wenner array has higher signal strength than other arrays. Because it is more sensitive to horizontal and vertical structures, the dipole-dipole array is the optimum for mapping sub
... Show MoreIn this paper, the methods of weighted residuals: Collocation Method (CM), Least Squares Method (LSM) and Galerkin Method (GM) are used to solve the thin film flow (TFF) equation. The weighted residual methods were implemented to get an approximate solution to the TFF equation. The accuracy of the obtained results is checked by calculating the maximum error remainder functions (MER). Moreover, the outcomes were examined in comparison with the 4th-order Runge-Kutta method (RK4) and good agreements have been achieved. All the evaluations have been successfully implemented by using the computer system Mathematica®10.