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The parabolic trough solar collector (PTSC) is a medium-temperature solar system that operates in the temperature range of 60–400 ºC. This technology is utilized dominantly for heat and power generation. Recently, numerous theoretical and numerical investigations have been carried out to evaluate and enhance the performance of PTSCs. This review paper provides fundamentals of PTSC systems, mathematical models, discretization methods, and turbulence models utilized for the simulation of PTSCs. Challenges in the field and future directions are presented to provide a perspective for researchers to achieve more accurate numerical results with lower computational costs. [ABSTRACT FROM AUTHOR]

In this paper, we explore the effect of the stochastic environmental fluctuations on the dynamics of an HIV system with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity. First, the existence and uniqueness of the global positive solution and the stochastically ultimate boundedness of the stochastic HIV system are discussed. Then, by constructing a series of suitable Lyapunov functions and using some differential inequality techniques, the long-time asymptotic properties of the stochastic delayed system are investigated. These properties reveal that the solution of the stochastic system oscillates around the equilibrium points of the deterministic system when the intensity of environmental perturbations is appropriate. In addition, the sufficient condition for persistence in mean and extinction of the stochastic system are established under the suitable condition. At last, numerous numerical simulations show that the HIV will disappear if the intensity of environmental fluctuations is sufficiently large. This means that appropriate stochastic environmental fluctuations can effectively suppress the outbreak of HIV. • A stochastic delay HIV system with humoral immunity is proposed. • Asymptotic properties,persistence in mean and extinction, are investigated. • A series of Lyapunov functions and differential inequality are constructed and used. • Numerical simulations confirmed the effects of stochastic fluctuations on HIV. • Stochastic fluctuations can effectively suppress the outbreak of HIV. [ABSTRACT FROM AUTHOR]