In the paper the general boundary element method for numerical solution of the dual-phase lag equation with temperature-dependent thermophysical parameters and supplemented by appropriate boundary-initial conditions is presented. In the discussed differential equation there are two delay times called the relaxation and thermalization ones.In the second chapter of the paper the dual phase lag equation (DPLE) with temperature-dependent parameters (volumetric specific heat and thermal conductivity) is discussed in detail. The equation considered also contains the terms related to the internal heat sources that occur both in the models of ultra-thin metal films heating and in the problems related to the heat transfer in the domains of biological tissues. The boundary and initial conditions are also formulated.Next, the numerical algorithm based on the general boundary element method (for 1D problems) is discussed. The presented method is used to model the heating of a metal layer (gold and nickel) exposed to a laser beam, and also the thermal processes in a layer of biological tissue heated by an external heat source are considered.The results of numerical simulations are compared with repeatedly verified solutions using the finite difference method and, where possible, with the experimental data, and a very good agreement between the solutions based on GBEM and FDM is obtained. The results of numerical simulations for temperature-dependent and average values of thermophysical parameters are also compared and appropriate conclusions are formulated.
Flame spread under lateral airflow exhibits distinct flame behaviors and heat transfer mechanisms compared to concurrent and opposed flow configurations, yet this scenario remains insufficiently understood. In this work, flame spread behaviors under lateral flow for different pool widths were systematically investigated. Results show that the increasing flow speed causes a transition from pulsating to uniform flame spread, accompanied by the emergence and evolution of flame streaks regardless of pool width. Flame spread rate displays a non-monotonic dependence on the lateral flow speed, leading to three distinct stages based on the evolution of dominant mechanisms of heat transfer. Heat transfer measurements reveal that subsurface convective heat transfer in liquid phase dominates in narrow pool, whereas gas-phase heat feedback becomes significant in wide pool. Accordingly, a model of subsurface flow velocity for narrow pool is established incorporating sidewall viscosity effects. Moreover, flame convective heat transfer is enhanced while radiation is suppressed with enhanced lateral flow, resulting in convective dominance in the gas-phase heat feedback. Additionally, an equation of convective heat flux is proposed using the lateral heating length and mix-flow theory. Finally, a theoretical model for predicting flame spread rate is proposed in narrow and wide pools respectively based on the dominant heat transfer mechanisms.
The introduction of hot streak inflows at turbine inlets creates pronounced nonuniformity in the mainstream temperature field. In engineering practice, the adiabatic wall temperature of a film cooled vane is often predicted by combining the film cooling effectiveness obtained under uniform inlet conditions with the mainstream recovery temperature under hot streak conditions. In this study, numerical simulations were performed to investigate the mechanisms responsible for adiabatic wall temperature superposition deviations under hot streak conditions. The superposition method captures the overall trend of the adiabatic wall temperature, but notable quantitative deviations remain. When the hot streak is aligned with the leading edge, the maximum spanwise mean deviations on the pressure and suction sides reach 68.2 K and 17.8 K, respectively. The additional thermophysical property effect induced by the hot streak alters the discharge conditions of the film holes and redistributes coolant mass flow, causing the actual film cooling state to deviate from that under uniform inflow and constituting an important source of the superposition deviation. When the hot streak is aligned with the leading edge, pressure side, and suction side, the contributions of this effect to the total deviation are 76.1%–89.0%, 76.1%–93.0%, and 66.7%–93.2%, respectively. In all three cases, the contribution decreases as the coolant mass flow rate increases, indicating a strong dependence on hot streak position and coolant mass flow rate. In addition to this effect, the remaining deviation is mainly associated with mainstream temperature gradients. These gradients alter mixing between the coolant and mainstream. The spanwise temperature gradient causes asymmetric mixing on the two sides of the film jet, whereas the temperature gradient normal to the wall can transport cooler mainstream fluid from the outer region toward the wall through vortex entrainment. Hot streak inflow can therefore alter the transport and mixing of the coolant and mainstream and should be considered when improving the reliability of adiabatic wall temperature prediction and optimizing cooling design.
When subcritical fuel is injected into a supercritical environment, transcritical phase transition may occur, which serves as a fundamental problem in advanced combustion engines. In this work, gradient theory modeling of transient transcritical phase transition of hydrocarbon fuel droplets is performed under various ambient conditions. Results show that the evaporative mass transfer and the temporal evolution of liquid-gas interfacial stability jointly determines the phase transition pathway. Under supercritical ambient conditions, the rapid increase of interfacial temperature reduces the liquid-gas density contrast and weakens the thermodynamic non-uniformity across the interface. This leads to a sharp decrease in the grand-potential density difference and the tangential-pressure depression relative to the equilibrium pressure, thereby driving surface tension decay and the transition from a sharp liquid-gas interface to a diffuse mixing layer. The transient characteristics of the interface is largely affected by the ambient temperature, pressure, and fuel vapor mass fraction. Specifically, the ambient temperature accelerates heat and mass transfer, the ambient pressure enhances gas dissolution and promotes interfacial thickening, while the ambient fuel vapor is capable of suppressing subcritical evaporation yet promoting transcritical mixing at elevated temperature and pressure. Finally, a phase transition criterion is proposed based on the residual liquid-core mass ratio, showing good agreement with the phenomenological classification obtained from experimental results.
