Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries

This paper investigates the effect of gravity modulation on Rayleigh–Bénard convection using the rigid isothermal boundary conditions. We calculate heat transfer results using the Nusselt and mean Nusselt numbers through the finite-amplitude of convection, which we got from the Ginzburg–Landau equation (GLE). The Ginzburg–Landau equation is derived analytically from the Fredholm solvability condition at third order. The finite amplitude equation (GLE) is a function of system parameters and solved numerically. The gravity modulation considered in terms of steady and sinusoidal parts. The sinusoidal part defines gravity modulation in terms of amplitude and frequency. Our study shows that gravity modulation controls the heat transfer results. The amplitude of modulation enhances heat transfer for low frequencies and diminishes for high frequencies. Further, we found that rigid isothermal boundary conditions are diminishing heat transfer than free and isothermal boundaries. Finally, we concluded that rigid isothermal boundary conditions and gravity modulation controls heat transfer results.

Delayed Detached-Eddy Simulations of a High Pressure Turbine Vane

The flow in a generic, high-pressure turbine vane was simulated using an in-house DDES code. Two different operating conditions were simulated with one leading to a shock wave while the other does not. One case was used to validate the capability of the DDES method to capture shock waves and other flow structures using an inlet Reynolds number of 271,000 and an exit Mach number of 0.840. The test conditions for the other case were an inlet Reynolds number of 265,000 and an exit Mach number of 0.927, which is representative of a transonic, high pressure turbine vane which was used to further investigate the flow field. The DDES simulations from the first case are compared with published experimental data, RANS simulations and LES simulations. Then, DDES results for two cases with adiabatic and isothermal boundary conditions are compared. The numerical simulations with the isothermal boundary condition are further used to study the flow phenomena with wake vortices, shock waves, pressure waves, wake-shock interactions, and wake-pressure wave interactions. The effects of the pressure waves on the vane heat transfer are also analyzed.

Modeling Thermal Microspreading Resistance in Via Arrays

As thermal management techniques for three-dimensional (3D) chip stacks and other high-power density electronic packages continue to evolve, interest in the thermal pathways across substrates containing a multitude of conductive vias has increased. To reduce the computational costs and time in the thermal analysis of through-layer via (TXV) structures, much research to date has focused on defining effective anisotropic thermal properties for a pseudohomogeneous medium using isothermal boundary conditions. While such an approach eliminates the need to model heat flow through individual vias, the resulting properties are found to depend on the specific boundary conditions applied to a unit TXV cell. More specifically, effective properties based on isothermal boundary conditions fail to capture the local “microspreading” resistance associated with more realistic heat flux distributions and local hot spots on the surface of these substrates. This work assesses how the thermal microspreading resistance present in arrays of vias in interposers, substrates, and other package components can be properly incorporated into the modeling of these arrays. We present the conditions under which spreading resistance plays a major role in determining the thermal characteristics of a via array and propose methods by which designers can both account for the effects of microspreading resistance and mitigate its contribution to the overall thermal behavior of such substrate–via systems. Finite element modeling (FEM) of TXV unit cells is performed using commercial simulation software (ansys).

Modeling Thermal Spreading Resistance in Via Arrays

As thermal management techniques for 3D chip stacks and other high power density electronic packages continue to evolve, interest in the thermal pathways across substrates containing a multitude of conductive vias has increased. To facilitate the use of numerical models that can reduce computational costs and time in the thermal analysis of through-layer via (TXV) structures, much research to date has focused on defining effective anisotropic thermal properties for a pseudo-homogeneous TXV medium using isothermal boundary conditions. While such an approach eliminates the need to model heat flow through individual vias, the resulting properties can be shown to depend on the specific boundary conditions applied to a unit TXV cell. More specifically, effective properties based on isothermal boundary conditions fail to capture the local “micro-spreading” resistance associated with more realistic heat flux distributions and local hot spots on the surface of these substrates. This work assesses how the thermal spreading resistance present in arrays of vias in interposers, substrates, and other package components can be properly incorporated into the modeling of these arrays. We present the conditions under which spreading resistance plays a major role in determining the thermal characteristics of a via array and propose methods by which designers can both account for the effects of spreading resistance and mitigate its contribution to the overall thermal behavior of such substrate-via systems. Finite element modeling of TXV unit cells is performed using commercial simulation software (ANSYS). Compactly stated, micro-spreading contributes to the total resistance RT = R1d + (fu + fl)Rsp,max, where 0≤ f ≤ 1 are adjustment factors that depend on the conditions at the upper and lower surfaces of the via array layer and Rsp,max occurs under worst-case conditions.