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Vapor compression refrigeration (VCR) systems operating in hot climates suffer from high condenser temperatures that reduce their performance. One interesting approach being investigated to improve VCR performance is incorporating phase change materials (PCMs) into VCR systems that have not yet been expanded experimentally. So, this work experimentally studies the effect of using tubular PCM heat exchanger to cool the VCR condenser. The impact of two PCMs types suitable for warm climate conditions: SP24 and SP26, and combination of them on the VCR energy and exergy performance is investigated for two inlet ambient air temperatures. The impact on the exit air and PCMs temperatures, and VCR unit's pressure-enthalpy curve, VCR coefficient of performance, and power consumption is also examined. The results show that PCM-equipped systems significantly enhance the VCR exergy efficiency and coefficient of performance, especially at higher ambient temperature. Compared to the system without PCM, the power consumption can be reduced by up to 10.4% with PCM, while the exergy efficiency and coefficient of performance can be improved by 13.7% and 13.4%, respectively. While PCM SP24 provides the best performance, PCM SP26 has longer effective cooling period. A combination of SP24 and SP26 balances the performance and effective cooling period.

In this paper, a new scheme based on the exponential fitting technique is presented for solving the nonlinear time-fractional Swift-Hohenberg equation, where the first and second-order derivatives are replaced by Caputo fractional derivative. The exponential fitting technique depends on a parameter that led to getting high-order accuracy. The convergence and unconditional stability will be discussed using the Fourier method and the analysis is built on uniform and nonuniform time steps, to solve initial singularity by using the graded meshes. Applicability and theoretical results will be demonstrated and enhanced with numerical examples.

In this article, fractional linear electrical systems are investigated. Analytical solutions of the fractional models are derived using Laplace transform method. Also, numerical simulations using Grünwald–Letnikov definition are proposed. Comparisons between fractional and classical electrical systems are illustrated using Laplace transform and nonstandard finite difference method.