Overview

This project investigates heat transfer in a long tubular light bulb. The bulb was selected because it naturally includes several important heat‑transfer mechanisms: internal heat generation in the filament, conduction through the gas and glass envelope, and combined convection and radiation from the outer surface to the surroundings. To make the analysis tractable, the real three‑dimensional geometry is idealized as a two‑dimensional longitudinal half‑section of the bulb and base.

The simplified bulb cross‑section is modeled using a 15‑node finite‑difference mesh with equal spacing in both coordinate directions. This nodal network provides a representative sample of the filament, air gap, and glass regions, and allows the governing energy balance equations to be written in finite‑difference form and assembled into a matrix system for solution in MATLAB.

Nodal Model and Regions

The finite‑difference mesh is shown in Figure 1. Nodes are grouped into regions that represent the main physical parts of the bulb:

  • Filament region (red nodes): uniform volumetric heat generation

  • Air gap region (green nodes): conduction through the gas surrounding the filament

  • Glass region (black nodes): conduction through the glass envelope and support structure

Boundary conditions are applied to represent how the bulb interacts with its surroundings:

  • Left/base boundary: constant temperature to represent the bulb base and socket

  • Bottom boundary: symmetry along the horizontal centerline of the bulb

  • Exterior boundary: combined convection to ambient air and radiation to the environment

  • Source region: uniform internal heat generation applied to the filament nodes

Figure 1 - 15 Node Finite-Difference Model of a Tubular Light-Bulb

Modeling Assumptions and Properties

To keep the model manageable and consistent with course objectives, the following assumptions are used:

  • Two‑dimensional longitudinal half‑section of the bulb

  • Constant material properties within each region

  • Uniform volumetric heat generation in the filament region

  • Conduction‑only model in the air gap

  • Equal node spacing in the dx and dy directions

  • Steady‑state conditions for the Part II 2‑D analysis

Material thermal conductivities k (W/m·K) are specified for each region (filament, air, and glass) and are used consistently in the finite‑difference energy balance equations and in the MATLAB implementation.