Mathematical Modeling of Heat Transfer in Energy Conversion Systems
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Abstract
This study presents the development and numerical implementation of a mathematical model for analyzing heat transfer in parabolic trough collectors (PTCs), a widely adopted technology in solar thermal energy conversion. The model integrates conduction, convection, and radiation mechanisms, formulating an energy balance along the absorber tube through which a heat transfer fluid (HTF) circulates. Governing equations for the fluid domain were coupled with boundary conditions for absorber wall interactions, including radiative and convective losses to the environment. The model was discretized and solved in Python, employing a one-dimensional approach to capture axial temperature variations under steady-state conditions. Simulations were conducted for a 100 m collector length using pressurized water as the HTF, with an inlet temperature of 250 °C and a mass flow rate of 0.5 kg/s under a direct normal irradiance (DNI) of 850 W/m². Results indicate a fluid temperature rise of approximately 110 °C, yielding an outlet temperature of 360 °C. The overall thermal efficiency was calculated as 54.5%, which, while slightly lower than experimental benchmarks such as the DISS project (65–75%), reflects the expected physical trends and validates the simplified modeling approach. The study highlights the significance of optical and external thermal losses in limiting efficiency and underscores the importance of effective heat transfer between the absorber wall and the HTF. The findings provide a computationally efficient framework for evaluating PTC performance and establish a foundation for future model refinements incorporating temperature-dependent properties, transient behavior, and experimental validation to enhance predictive accuracy and applicability in system design and optimization.
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