Question 4:

A heated 6-cm-thick Pyroceram plate (ρ = 2600 kg/m3 , cp = 808 J/kg·K, k = 3.98 W/m·K, and α = 1.89 × 10−6 m2 /s) is at an initial temperature of 500°C. The side walls of the plate are at a temperature of 25°C. Find the non-dimensional temperature at x/L = 0, 0.25, 0.5, 0.75 for Fourier numbers of 0.05, 0.1, 0.15, 0.2, 0.3. Use 10-terms, 5-terms, 3-terms, 2-terms and 1-term to get the solutions at each location and at each Fourier Number. How much is the error in using the one-term approximation at each location and at each Fourier Number. What can you conclude from your analysis?

You can use any software you are comfortable with to solve this question.