This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-up times for three numerical experiments. Moreover, we calculate the error bounds and the numerical order of convergence arise from using these methods. Finally, we carry out the numerical simulations to the discrete graphs obtained from using these methods to support the numerical results and to confirm some known blow-up properties for the studied problems.
Different parameters of double pipe helical coil were investigation experimentally. Four coils were used; three with a curvature ratio (0.037, 0.031, and 0.028) and 11mm diameter of the inner tube while the fourth with 0.033 curvature ratio and 13 mm diameter of the inner tube. The hot water flow in the inner tube whereas the cold water flows in the annulus. The inlet temperatures of hot and cold water are 50 0C and 18 0C respectively. The inner mass flow rate ranges from 0.0167 to 0.0583 kg/s. The results show the Nusselt number increase with increase curvature ratio. The Nusselt number of the coil with 0.037 curvature ratio increases by approximately 12.3 % as compare with 0.028 curvature ratio. The results also r
... Show MoreThe fouling depositions of crude oil stream were studied theoretically in a shell and tube heat exchanger to investigate the effect of depositions on the heat transfer process. The employed heat exchanger was with steam flowing in the inner tubes and crude oil in the shell at different velocities and bulk temperatures. It is assumed that fouling occurs only on the heated stream side (crude oil). The analysis was carried out for turbulent flow heat transfer conditions with wide range of Reynolds number, bulk temperature and time. Many previously proposed models for fouling resistance were employed to estimate a new model for fouling rate. It is found that the fouling rate and consequently the heat transfer coefficient were affected by Rey
... Show MoreThis paper is concerned with studying the numerical solution for the discrete classical optimal control problem (NSDCOCP) governed by a variable coefficients nonlinear hyperbolic boundary value problem (VCNLHBVP). The DSCOCP is solved by using the Galerkin finite element method (GFEM) for the space variable and implicit finite difference scheme (GFEM-IFDS) for the time variable to get the NS for the discrete weak form (DWF) and for the discrete adjoint weak form (DSAWF) While, the gradient projection method (GRPM), also called the gradient method (GRM), or the Frank Wolfe method (FRM) are used to minimize the discrete cost function (DCF) to find the DSCOC. Within these three methods, the Armijo step option (ARMSO) or the optimal step opt
... Show MoreThis study is an attempt to investigate the conceptual metaphor of UP and DOWN commonly used in Iraqi community. Some of the metaphorical expressions in Iraqi colloquial Arabicarewidely used by Iraqi speakers in everyday language. Ithas been analyzed by following the cognitive theory of metaphor (Lakoff& Johnson,1980).The study indicates that the Iraqi speakerexperiences more of the metaphorical expressions of UP and DOWN to referto many of the abstract concepts that shape his/her impression of everyday life situations.
The obligatory duty must be fulfilled for attachment to the discharge, whatever the reasons for the missingness, whether it is left by mistake or omission or deliberate, whether with or without excuse. What is likely in this research to spend Ramadan on laxity.
The one who delayed making up Ramadaan fasts until he realized another Ramadaan, fasted the second and spent the first after him, and no ransom on him, either with an excuse or without an excuse.
The technique of adding Carbon Nano-Tubes to What liquids is a new important method used to enhance the thermal properties of liquids such as specific heat and heat capacity.
The experimental part was carried out using water-based nanoparticles such as Carbon Nano Tubes, with different concentrations at (0.1, 0.3, o.5and 0.7wt %) of MWCNT (Multi Wall Carbon Nanotubes) and distilled water as a base, in different temperatures. The change in the value of heat capacity of a liquid was investigated. The value of heat capacity for Nano fluids increased with increasing the Carbon NanoTubes particles,when as compared with the value of heat capacity for distilled water . The best concentration of MWCNTs was improved with heat capacity about 60
An experimental and computational study is conducted to analyze the thermal performance of heat sinks and to pick up more profound information in this imperative field in the electronic cooling. One important approach to improve the heat transfer on the air-side of the heat exchanger is to adjust the fin geometry. Experiments are conducted to explore the impact of the changing of diverse operational and geometrical parameters on the heat sink thermal
performance. The working fluid used is air. Operational parameters includes: air Reynolds number (from 23597 to 3848.9) and heat flux (from 3954 to 38357 W/m
2 ). Conformational parameters includes: change the direction of air flow and the area of conduct
We examine the integrability in terms of Painlevè analysis for several models of higher order nonlinear solitary wave equations which were recently derived by Christou. Our results point out that these equations do not possess Painlevè property and fail the Painlevè test for some special values of the coefficients; and that indicates a non-integrability criteria of the equations by means of the Painlevè integrability.
In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials.
This article dealt with identifying the importance of heat stress in poultry flocks and the damages resulting from the production of eggs and meat and the spread of pathogens, in addition to that ways to mitigate the harmful effects of heat stress, including physiological, nutritional, engineering and genetics, in order to ensure preservation of the product and reduce damages