Perhaps the most intuitive heat transfer problem is . The activity “How Fast Does Your Coffee Cool?” introduces students to Newton’s Law of Cooling using MATLAB’s ode45 solver. Students:

If the internal thermal resistance of the solid is negligible compared to the external fluid thermal resistance (indicated by a

. Suddenly, both ends are plunged into ice water, fixing the boundary temperatures at . We will track the temperature decay over using an explicit numerical scheme. MATLAB Solution Implementation

The 1D transient heat conduction equation without generation is governed by:

). A MATLAB script can use an iterative solver to find the temperature distribution: www.mchip.net Key Parameters : Length ( ), spatial points ( ), and boundary conditions.

% Lesson 4: Radiation Exchange Between Two Black Surfaces clear; clc; % Input Parameters T1 = 800; % Temperature of Plate 1 (Kelvin) T2 = 400; % Temperature of Plate 2 (Kelvin) sigma = 5.67e-8; % Stefan-Boltzmann constant (W/m^2*K^4) % View factor variation array F12 = linspace(0.1, 1.0, 50); % Net radiation heat flux calculation (q/A1) % Note: Temperatures must be in Kelvin q_flux = F12 .* sigma .* (T1^4 - T2^4); % Plotting the results figure; plot(F12, q_flux, 'm-', 'LineWidth', 2); grid on; title('Radiation Heat Flux vs. Geometric View Factor'); xlabel('View Factor (F_12)'); ylabel('Net Heat Flux (W/m^2)'); Use code with caution. Summary of Core Engineering Principles Heat Transfer Mode Key Driving Parameter Primary Dimensionless Metric MATLAB Approach Used Temperature Gradient ( Biot Number ( Spatial discretization vectors Convection Fluid Velocity ( Reynolds ( ), Nusselt ( Functional matrix element evaluations Radiation Absolute Temperature ( T4cap T to the fourth power View Factor ( F12cap F sub 12 Non-linear geometric arrays

to combine equations, code, and visualizations for teaching the transient solution of the heat equation. Heat Transfer with MATLAB Curriculum Materials Courseware

MATLAB is an excellent tool for solving complex heat transfer problems, particularly those involving numerical methods like Finite Difference Method (FDM) for 2D or 3D systems. MATLAB Simulation: 1D Transient Conduction This script solves the 1D heat equation using FDM.

Beyond simple scripts, complex industrial problems are solved using dedicated MATLAB tools: PDE Toolbox

Q = epsilon * sigma * A * (T_s^4 - T_sur^4); fprintf('Heat transfer rate: %f W\n', Q);

with constant thermal conductivity, the temperature distribution is linear, and the equation simplifies to:

Review (concise)

h = 10; % convective heat transfer coefficient (W/m^2-K) A = 1; % surface area (m^2) T_s = 100; % surface temperature (°C) T_f = 50; % fluid temperature (°C)