Chapter 5 Transient Heat Conduction Analysis

This chapter explores transient heat conduction, where temperature changes over time. It begins with the lumped capacitance method, which simplifies heat transfer to an exponential decay equation under the assumption of uniform temperature, valid when the Biot number is less than 0.1. The Biot number compares internal conduction to surface convection, and its value determines the validity of different models. The time constant and Fourier number are introduced to quantify the rate of temperature change and the depth of heat penetration. When the Biot number is greater than 0.1 and the Fourier number exceeds 0.2, the one term approximation is used, representing temperature with a single exponential and cosine term. For more precise solutions, exact series methods are introduced using Fourier series and eigenvalue problems, with Bessel functions applied for cylindrical and spherical objects. A structured problem solving approach is included to select the correct method based on Biot and Fourier number calculations. The chapter also provides a mathematical review covering exponential decay, Fourier series, eigenvalue problems, and dimensionless analysis. A final cheat sheet summarizes the key equations and criteria for selecting lumped capacitance, one term, or exact solutions based on object shape, time, and thermal properties.