In order to reduce computational resources and time required for thermal design/analysis of large-scale systems, heat transfer processes in complex electronics packages need to be represented by suitably formulated simple models instead of conducting CFD (Computational Fluid Dynamics)-based analysis using detailed models. Relative to a detailed model, a simplified mathematical model for a complex electronics package offers many orders of reduction in computational resources. When used in a system-level environment, it is necessary that the simplified model accurately predict the thermal behavior for various local boundary conditions on the package. Therefore, it is important that these reduced-order models be boundary-condition-independent.
An immediate need for accurate boundary-condition-independent (BCI) reduced-order models (ROM) exists in the area of thermal design and analysis of communication systems such as routers and switches. These systems use optical transceivers for data and tele-communication. These transceivers are sensitive to the surrounding temperatures, and their failure due to overheating results in down-time of the communication network. Heat transfer analysis of detailed models of these transceivers results in consumption of a large amount of computational resources, while analysis with geometrically-simplified models leads to inaccurate results.
The current work identifies two methodologies for developing BCI ROMs for opto-electronic transceiver packages. The first methodology is the well-established DELPHI (DEvelopment of Libraries of PHysical models for an Integrated design) Methodology. In this method, the package is represented by a network of optimized thermal resistances. In the present study, the DELPHI Methodology is extended to develop BCI ROMs for an optical transceiver called Small Form-factor Pluggable package (SFP) which contains four heat-generating sources. A detailed CFD model of the SFP is developed and validated using natural-convection experiments. Using the DELPHI method, a BCI ROM is generated for the SFP, which is represented by 9 nodes and 16 resistors. When used in practical applications, this reduced-order model predicted results with a maximum relative error of 7% in comparison with the detailed CFD model. It is not possible to obtain temperature gradient information using the DELPHI method, and this information is critical during analysis of thermo-mechanical stresses in packages.
The second methodology identified in the current study is the Proper Orthogonal Decomposition (POD)-Galerkin methodology, and it overcomes the limitations of the DELPHI methodology. The POD-Galerkin technique works by capturing the major characteristics of the solution with a relatively few number of orthogonal vectors called POD-basis vectors. Projection of the governing equations in the discretized form on to the compilation of the POD-basis vectors results in the generation of a ROM. BCI ROMs can be generated for simple 1-D objects as well as complex 2-D objects that are made of multiple materials and have multiple heat-generating sources. The model development procedure is studied with isoflux and isothermal boundary conditions. By including the appropriate number of POD-basis vectors, the ROM results show excellent agreement with the CFD solution for both these types of boundary conditions. The study thus demonstrates that POD-Galerkin methodology is a viable approach for generating high-accuracy boundary-condition-independent reduced-order models for complex electronics packages.