Performance analysis of solar powered absorption refrigeration system

The present work provides a detailed thermodynamic analysis of a 10 kW solar absorption refrigeration system using ammonia-water mixtures as a working medium. This analysis includes both first law and second law of thermodynamics. The coefficient of performance (COP), exergetic coefficient of performance (ECOP) and the exergy losses (ΔE) through each component of the system at different operating conditions are obtained. The minimum and maximum values of COP and ECOP were found to be at 110 and 200°C generator temperatures respectively. About 40% of the system exergy losses were found to be in the generator. The maximum exergy losses in the absorber occur at generator temperature of 130°C for all evaporator temperatures. A computer simulation model is developed to carry out the calculations and to obtain the results of the present study.     

On the numerical computation of blowing‐up solutions for semilinear parabolic equations

Theoretical aspects related to the approximation of the semilinear parabolic equation: $u_t=\Delta u+f(u)$\nopagenumbers\end , with a finite unknown ‘blow‐up’ time T_b have been studied in a previous work. Specifically, for ε a small positive number, we have considered coupled systems of semilinear parabolic equations, with positive solutions and ‘mass control’ property, such that: \def\ve{^\varepsilon}$$u_t\ve=\Delta u\ve+f(u\ve)v\ve\qquad v_t\ve=\Delta v\ve‐\varepsilon f(u\ve)v\ve$$\nopagenumbers\end The solution \def\ve{^\varepsilon}$$\{u\ve,v\ve\}$$\nopagenumbers\end of such systems is known to be global. It is shown that $$\|(u^\varepsilon‐u)(\, .\, ,t)\|_\infty\leq C(M_T)\varepsilon$$\nopagenumbers\end , \def\lt{\char'74}$t\leq T \lt T_b$\nopagenumbers\end where $M_T=\|u(\, .\, ,T)\|_\infty$\nopagenumbers\end and $C(M_T)$\nopagenumbers\end is given by (6). In this paper, we suggest a numerical procedure for approaching the value of the blow‐up time T_b and the blow‐up solution u. For this purpose, we construct a sequence $\{M_\eta\}$\nopagenumbers\end , with $\lim_{\eta\rightarrow 0}M_\eta=\infty$\nopagenumbers\end . Correspondingly, for $\varepsilon\leq1/2C(M_\eta+1)=\eta^\alpha$\nopagenumbers\end and \def\lt{\char'74}$0\lt\alpha\lt\,\!1$\nopagenumbers\end , we associate a specific sequence of times $\{T_\varepsilon\}$\nopagenumbers\end , defined by $\|u^\varepsilon(\, .\, ,T_\varepsilon)\|_\infty=M_\eta$\nopagenumbers\end . In particular, when $\varepsilon=\eta\leq\eta^\alpha$\nopagenumbers\end , the resulting sequence $\{T_\varepsilon\equiv T_\eta\}$\nopagenumbers\end , verifies, $\|(u‐u^\eta)(\, .\, ,t)\|_\infty\leq{1\over2}(\eta)^{1‐\alpha}$\nopagenumbers\end , \def\lt{\char'74}$0\leq t\leq T_\eta\lt T_{\rm b}$\nopagenumbers\end with $\lim_{\eta\rightarrow 0}T_\eta=T_{\rm b}$\nopagenumbers\end . The two special cases of a single‐point blow‐up where $f(u)=\lambda{\rm e}^u$\nopagenumbers\end and $f(u)=u^p$\nopagenumbers\end are then studied, yielding respectively sequences $\{M_\eta\}$\nopagenumbers\end of order $O(\ln|\ln(\eta)|)$\nopagenumbers\end and $O(\{|\ln(\eta)|\}^{1/p‐1})$\nopagenumbers\end . The estimate $|T_\eta‐T_{\rm b}|/T_{\rm b}=O(1/|\ln(\eta)|)$\nopagenumbers\end is proven to be valid in both cases. We conduct numerical simulations that confirm our theoretical results. Copyright © 2001 John Wiley & Sons, Ltd.     

Mössbauer Spectroscopy Study of Fe–Si Solid Solution Prepared by Mechanical Milling

A specimen of Fe–Si solid solution is prepared by ball milling of proper amounts of the pure elements (3Fe:Si) for different milling times. X-ray diffraction and Mössbauer spectroscopy have been used to characterize the solid solution. The Mössbauer spectra show four different sites corresponding to Fe atoms in a bcc structure having 0, 1, 2 and 3 Si atoms in the 1st nearest-neighbor (nn) shell. The hyperfine magnetic field decreases by 31 kOe for each Si atom in the 1st nn shell. A magnetic component with hyperfine field around (180 kOe) characterized by a broadened sextet was observed which could be due to iron sites having more than 3 Si atoms in the 1st nn. A theoretical model based on the binomial distribution was adopted to analyze the data. Good agreement between the experimental and the theoretical hyperfine field distribution in the high hyperfine field region was found, and the silicon content in the disordered A2 phase is deduced from the parameters which give the best agreement.     

Numerical analysis of semi-linear parabolic systems in diffusion–reaction problems

In this paper, we investigate problems of approximation for the solution of a system of coupled semi-linear parabolic partial differential equations that model diffusion-reaction problems in chemical engineering. Given that the solutions belong to H^s (0, ∞), we consider finite-element approximations on bounded domains (0, R(h)) such that lim_h→0[R(h)] = ∞. Optimal convergence estimates are found to depend on the asymptotic behaviour of the solution and its regularity near t = 0. In the L²-norm, they cannot exceed an order of O((;h²/t^3/4) + h²[In h]²). For that purpose, a Wheeler-type argument is also generalized to non-coercive elliptic forms. Fully discrete schemes that preserve the positivity of the solutions are also considered. Due to the singularity at t = 0, they lead to estimates of the order O(τ^1/4 + h²/t^3/4).