• Modeled 2D steady-state heat conduction using finite difference nodal analysis across 60 nodes

• Solved a symbolic system of 60 equations using MATLAB’s solve() and equationsToMatrix() functions

• Leveraged thermal symmetry to reduce computational overhead by mirroring nodal temperatures

• Performed parametric sweeps to study effects of:

  • Heat transfer coefficient ℎ

  • Ambient air temperature 𝑇∞

  • Thermal conductivity of heat spreader 𝑘𝑠 and board 𝑘𝑏

• Evaluated how each parameter impacts temperature distribution and compliance with the 85 °C safety limit

• Programmed full symbolic system of 60 nodal equations in MATLAB, covering:

  • Corner, edge, and interior nodes

  • Nodes with and without internal heat generation

  • Material discontinuities (e.g., chip-to-board interface)

• Performed parametric sweeps on thermal inputs:

  • Heat transfer coefficient ℎ

  • Ambient temperature 𝑇∞

  • Thermal conductivities 𝑘𝑠 , 𝑘𝑏

• Evaluated how these variations impact temperature profiles and safety margins

• Observed key thermal behaviors:

  • Inversion trends when increasing 𝑘𝑠 or decreasing 𝑘𝑏

  • Plot amplitude shifts under changing 𝑇∞ or ℎ

  • Identified edge cases where chip exceeded 85°C limit

• Verified that under baseline conditions, the system remained within industrial thermal safety limits

• Manually constructing and debugging 60 symbolic equations

• Managing boundary conditions and property changes across node groups

• Validating thermal symmetry logic across all six rows

• Ensuring convergence across all parameter variations without numerical errors

• Manually constructed and validated 60 symbolic nodal equations across mixed boundary and material conditions

• Debugged edge, corner, and interior node logic to ensure correct convection and conduction modeling

• Verified thermal symmetry implementation across all six rows to reduce computational workload

• Iteratively tested parameter sweeps (e.g., h, 𝑇∞ , 𝑘𝑠 , 𝑘𝑏) to ensure stability and convergence without symbolic solver failures

• Ensured final temperature distributions remained physically consistent and within industrial limits (or flagged critical cases when they did not)

These iterations improved my ability to translate complex boundary value problems into programmable logic and reinforced the importance of error checking in large symbolic systems. 

Thermal System Modeling · Nodal Heat Transfer Analysis · Symbolic Math Toolbox (MATLAB) · Parametric Study & Plotting · Chip Packaging & Cooling Design · Engineering Documentation & Communication

This project gave me hands-on experience in modeling temperature distributions using nodal heat transfer and symbolic programming in MATLAB. By varying realistic thermal parameters, I gained insight into how material properties and boundary conditions impact passive cooling behavior and chip safety. I developed a deeper understanding of thermal constraints in electronic packaging, where overheating can lead to performance degradation or failure. This experience strengthened my ability to approach thermal design challenges using both analytical and simulation-based techniques.