Electronic packaging cabinets simplified modeling, simulation, and experimental validation for systems engineering

A simplified three-dimensional mathematical model for electronic packaging cabinets was derived from physical laws. Tridimensionality resulted from the domain division in volume elements (VEs) with uniform properties, each with one temperature, and empirical and theoretical correlations allowed for modeling their energetic interaction, thus producing ordinary differential equations (ODEs) temperatures versus time system. The cabinet (2048 mm × 1974 mm × 850 mm) thermal response with one heat source was measured. Data set 1 with a 1.6-kW power source was used for model adjustment by solving an inverse problem of parameter estimation (IPPE) having the cabinet internal average air velocities as adjustment parameters. Data set 2 obtained with a 3-kW power source validated model results. The converged mesh had a total of 7500 VE. The steady-state solution took between 16 and 19 s of CPU time to reach convergence and less than 3 min to obtain the 6500-s cabinet dynamic response under variable loading conditions, in an Intel CORE i7 computer. After validation, the model was used to study the impact of heat source height on system thermal response. Fundamentally, a sharp minimum junction temperature Tjct,min = 98.5 °C was obtained in the system hot spot at an optimal heat source height, which was 25.7 °C less than the highest calculated value within the investigated range (0.1 m < zjct < 1.66 m) for the 1.6-kW power setting, which characterizes the novelty of the research, and is worth to be pursued, no matter how complex the actual cabinet design may be.

Recovering Heat Source from Fourth-Order Inverse Problems by Weighted Gradient Collocation

The weighted gradient reproducing kernel collocation method is introduced to recover the heat source described by Poisson’s equation. As it is commonly known that there is no unique solution to the inverse heat source problem, the weak solution based on a priori assumptions is considered herein. In view of the fourth-order partial differential equation (PDE) in the mathematical model, the high-order gradient reproducing kernel approximation is introduced to efficiently untangle the problem without calculating the high-order derivatives of reproducing kernel shape functions. The weights of the weighted collocation method for high-order inverse analysis are first determined. In the benchmark analysis, the unclear illustration in the literature is clarified, and the correct interpretation of numerical results is given particularly. Two mathematical formulations with four examples are provided to demonstrate the viability of the method, including the extreme cases of the limited accessible boundary.