Engineering-Design-Labs

A collection of PHYS 222 engineering design labs by Eric Chen and Ethan Yang, featuring Arduino-based signal processing, high-speed data acquisition, and heat transfer simulations using finite difference approximations.

Lab 1: Transient Heat Conduction in a Fin

• Objective: Simulate transient heat conduction by cooling a steel nail in ice water and recording temperature decay at the top.
• Hardware: Arduino, temperature sensor, and a steel nail.
• Calculations: * Determined convective heat transfer coefficient ($\overline{h}$) as $59.84 \text{ W/m}^2\text{K}$.
  • Calculated thermal diffusivity ($\alpha$) as $1.008 \cdot 10^{-5} \text{ m}^2/\text{s}$.
• Results: Experimental values matched published ranges for steel ($4.2 \cdot 10^{-6}$ to $1.88 \cdot 10^{-5} \text{ m}^2/\text{s}$).

Lab 2: Finite Difference Approximation (Heat Equation)

• Objective: Use Excel to solve steady-state and transient heat equations for a square column.
• Steady-State: Modeled a column with one $100^\circ\text{C}$ face and three $0^\circ\text{C}$ faces until stability was reached.
• Transient State: Simulated the temperature profile of a $100^\circ\text{C}$ column submerged in $0^\circ\text{C}$ water over time.
• Constraint: Applied $\Delta x=1$, $\Delta y=1$, $\Delta t=1$, and $\alpha=0.062$ to satisfy the stability criteria.

Lab 3: Arduino Oscilloscope

• Objective: Transform an Arduino into a dual-channel oscilloscope to record $1000\text{ Hz}$ signals.
• Key Feature: Modified the ADC prescaler (ADCSRA) to maximize sampling speed for high-frequency capture.
• Data: Collected 100 samples per channel at a 115200 baud rate using micros() for precise timing.
• Findings: Successfully visualized signal periods of $\approx 1000\text{ }\mu\text{s}$.

Lab 4: Arduino Function Generator

• Objective: Generate Square, Triangle, and Sine waves using Arduino and analog circuitry.
• Circuit Design: Utilized TL081 Op-Amps in an integrator configuration to convert square waves into triangle and sine waves.
• Analysis: * Triangle Wave: Measured amplitude $\approx 2.17\text{V}$ (Theoretical: $2.1\text{V}$).
  • Sine Wave: Measured amplitude $\approx 1.00\text{V}$ (Theoretical: $0.90\text{V}$).
• Theory: Theoretical values were approximated using Fourier series expansions.

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