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