MEC 3130 004 Heat Transfer

Milwaukee School of Engineering

Chad Clogston Ryan Cox Nathan Wilde

This project analyzes the heat transfer in a tubular light bulb by modeling a longitudinal 2-D cross-section of the bulb and its surroundings. The physical system includes resistive filament embedded within a gas-filled interior and enclosed by the glass envelope, which is exposed to the surrounding air and thermal radiation from the environment. The objective is to predict how heat generated in the filament is distributed though theses different regions and how it ultimately leaves the bulb.

The model this system, the bulb is idealized as a 2-D grid of nodes that approximate the geometry and material layers. Within the model, the volumetric heat generation occurs in the filament region, while conduction carries the energy though the gas and glass. At the outer surface, boundary conditions include convection to the ambient air and radiation exchange with its surroundings. And a constant temperature boundary condition is applied at the base to represent heat sinking into the electrical socket connection. These assumptions allow for the complex 3-D physics to approximated with a traceable 2-D finite-difference method.

Using this nodal model, the team first computes the steady‑state temperature distribution by assembling and solving a matrix of energy balance equations with MATLAB. Contour plots of the resulting temperatures provide insight into hot spots, temperature gradients, and the relative roles of conduction, convection, and radiation in the bulb’s operation. Building on the steady‑state solution, the project then extends to transient heat conduction, where explicit and implicit time‑stepping schemes are used to simulate how the temperature field evolves from initial conditions toward steady operation. These results are used to compare numerical methods, assess model limitations, and suggest how design or operating conditions could be modified for improved thermal performance