Nondimensionalizing Length and Temp data from 2-D Ansys Transient thermal in Matlab

I have a text file that has dimensionalized data from Ansys (in micron and Kelvin). The first column is length and the second column is temperature. I am trying to nondimensionalize these data points and then put them in a graph where the x-axis represents nondimensionalized length and the y-axis represends nondimensionalized temperature.

xs = 100µm

Tf = 500K

Ti = 300K

How do I nondimensionalize this properly?

Answer 1

[Athanasios Paraskevopoulos]

The characteristic length scale is 100 µm (or 100 × 10⁻⁶ m). The nondimensional length can be calculated as:

where x is the dimensional length from your data.

The characteristic temperature scale is derived from the temperature difference, where is 500 K and is 300 K. The nondimensional temperature can be calculated as:

whereT is the dimensional temperature from your data.

Here, we'll create a simulated temperature distribution over the length of 0 to 100 µm.

% Simulate data points
x = linspace(0, 100, 50); % Length from 0 to 100 microns, with 50 points
T = linspace(300, 500, 50); % Temperature from 300K to 500K, linear distribution

% Given reference scales
L_s = 100e-6;   % Reference length scale in meters (100 µm)
T_f = 500;      % Final temperature in Kelvin
T_i = 300;      % Initial temperature in Kelvin

% Nondimensionalize length and temperature
x_tilde = x * 1e-6 / L_s;             % Convert µm to meters and then nondimensionalize
T_tilde = (T - T_i) / (T_f - T_i);    % Nondimensionalize temperature

% Plot the nondimensionalized data
figure;
plot(x_tilde, T_tilde, 'o-', 'LineWidth', 2);
xlabel('Nondimensional Length \(\tilde{x}\)', 'Interpreter', 'latex');
ylabel('Nondimensional Temperature \(\tilde{T}\)', 'Interpreter', 'latex');
title('Nondimensionalized Temperature Profile');
grid on;

[Whitney]

Thank you very much for your help. Your code gave the same results as mine so I think there might be something wrong with my actual data. I appreciate the assistance!