A local discontinuous Galerkin (LDG) scheme coupled with a third-order strong stability-preserving (SSP) Runge–Kutta time integration, is proposed for the numerical simulation of non-Fourier heat transfer in longitudinal fins subject to temperature-dependent convective and radiative heat transfer incorporating direct interaction between the fin surface and the base. The mathematical model is based on the Maxwell–Cattaneo–Vernotte (MCV) hyperbolic heat conduction framework, which accounts for the finite speed of thermal wave propagation via a relaxation time parameter. Three representative fin profiles — trapezoidal, rectangular, and dovetail — are considered by varying the taper ratio. The scheme is verified against exact solutions and achieves third-order accuracy. Moreover, it accurately captures the sharp wavefront without oscillations. The effects of the key physical parameters on the transient temperature distribution and fin efficiency are systematically examined. It is found that the thermal wave speed is primarily governed by the relaxation parameter Ve and the thermal conductivity parameter β, but is independent of the surface heat transfer mechanisms and fin geometry. Both convection and radiation effects play an important role in the process of heat transfer, and strengthening these effects will enhance heat loss and increase heat transfer rate. The time-averaged fin efficiency increases with Ve and is consistently higher for the dovetail fin than for both the rectangular and trapezoidal fins under the same operating conditions.
Thermal management represents a critical challenge for the reliability and lifespan of modern power electronics, such as medium-power photovoltaic (PV) inverters. This work presents a self-organizing generative design methodology for air-cooled heat sinks embedded within a realistic PV inverter enclosure, driven deterministically by the Constructal Law. Numerical simulations of conjugate heat transfer and turbulent flow are conducted utilizing the chtMultiRegionFoam solver within the OpenFOAM framework, closed with the standard κ−ϵ turbulence model. Instead of tuning predefined geometries, a specialized construction algorithm progressively expands the heat exchanger surfaces based on a local thermodynamic opportunity function. The evolution of the fluid-solid interfaces is systematically investigated across a family of solution paths under four distinct fin thickness constraints. Results demonstrate a stark continuous drop in global thermal resistance for all configurations. This trend establishes a performance trade-off where the massive gain in wetted perimeter completely outweighs the local convective degradation caused by the decay of the channel's hydraulic diameter. Among the analyzed paths, the configurations with thinner fin thicknesses (1.5 mm and 2.5 mm) yield the superior physical designs, achieving a significant reduction in the peak operation temperature compared to the conventional commercial baseline and also a substantial reduction in total material volume. This work demonstrates that allowing the geometry to grow freely in pursuit of greater currents provides a natural path to minimize systemic thermal resistance, directly embodying the Constructal Law by adapting the flow architecture to maximize performance while ensuring a rational and reduced use of material.
