Heat transfer

Why does a powered device become hotter inside than at its cooled surface? How long does warming take? How would you know whether a computed temperature is credible? This book follows those questions from a small energy account to a spatial model you can run and inspect.

You can begin here. We introduce the needed conservation law, gradients, and boundary conditions as they become useful. Familiarity with derivatives and integrals is enough; the mathematical modeling book offers longer explanations when you want them.

The investigation

Imagine a solid cross-section with uniform internal heating and a surface held at a fixed temperature. First predict the direction of heat flow and how the interior temperature changes with conductivity. Solve a simpler slab by hand. Then express the two-dimensional problem in .eqi, calculate a small finite element problem independently, and run the heated-body example. Finally, add heat storage and distinguish physical warming from the error introduced by time stepping.

Chapter	Question to answer
1. Conservation and Fourier’s law	What is stored, what crosses a surface, and what creates energy?
2. Steady conduction	Why is one profile straight and another curved?
3. Boundaries and interfaces	What does a temperature, flux, or exchange condition mean?
4. A heated body in Eqiora	How do the equations become a reusable model and a calculation?
5. Transient storage	What determines the warming time?
6. Assessing a thermal calculation	Which comparison diagnoses which error?

The slab and composite-wall calculations are pencil-and-paper investigations. The computational thread uses a square cross-section, constant conductivity, uniform generation, and prescribed exterior temperature. Keeping those assumptions visible makes comparisons meaningful.

How to use the chapters

Make each prediction before running a calculation. Read the equations in the maintained component before using its package entry. Then change one physical parameter, predict its effect, and explain the result. The package saves you from repeating a model you already understand.

For installation, use Get started. For the next step after this book, Numerical simulation develops the methods behind the mesh and time-step comparisons. The energy account also connects to circuits and dynamics, where storage and exchange can be represented by a small number of states.