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Thermal expansion and Thermal stress: Problem Solving01:27

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San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
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Linear extrapolation method based on multiple equiproportional models for thermal performance prediction of

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    A new linear extrapolation method based on multiple equiproportional models (LEM-MEM) efficiently predicts thermal performance for ultra-large photothermal (PT) arrays. This method significantly reduces computation time and memory usage for complex thermal engineering problems.

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    Area of Science:

    • Thermal engineering
    • Materials science
    • Computational physics

    Background:

    • Growing demand for ultra-large photothermal (PT) and electrothermal devices necessitates efficient performance prediction.
    • Traditional finite element method (FEM) models are computationally intensive for ultra-large arrays, limiting optimization.
    • Periodic boundary conditions can introduce significant errors in simulating local heating on large periodic arrays.

    Purpose of the Study:

    • To develop a computationally efficient method for predicting the thermal performance of ultra-large periodic arrays.
    • To overcome the limitations of traditional FEM for large-scale thermal simulations.
    • To provide a facile and efficient prediction strategy for optimizing PT transducers and other thermal engineering applications.

    Main Methods:

    • Proposed a linear extrapolation method based on multiple equiproportional models (LEM-MEM).
    • Constructed several reduced-size FEM models for simulation and extrapolation, avoiding direct modeling of ultra-large arrays.
    • Fabricated and tested a PT transducer with over 4000 × 4000 pixels to validate the LEM-MEM predictions.

    Main Results:

    • LEM-MEM demonstrated high predictability for thermal performance in PT transducers.
    • The maximum percentage error in average temperature prediction was within 5.22% across four different pixel patterns.
    • The fabricated PT transducer exhibited a response time within 2 ms.

    Conclusions:

    • LEM-MEM offers a significant reduction in computation consumption for thermal performance prediction in ultra-large arrays.
    • The method provides valuable design guidance for optimizing PT transducers and similar devices.
    • LEM-MEM is applicable to a wide range of thermal engineering problems requiring efficient prediction strategies for large-scale systems.