Intermediate module

Heat Transfer

Model conduction, convection, radiation, transient heating, heat exchangers, and thermal resistance networks.

Course outline only for now. Full chapter-level lessons are still in progress. Use this page for readiness, concepts, worked-example format, practice, review, and portfolio direction. Complete course contents are live today for Math, Physics, and Statics.

01

Readiness check

Before starting, confirm the prerequisite habits.

  • Understand temperature difference.
  • Use W, J/s, and thermal conductivity units.
  • Draw heat flow direction.
  • Know when steady state is reasonable.
0 or 1 weak itemContinue, but slow down at the worked example.
2 weak itemsReview the foundation page linked in the roadmap before solving practice problems.
3 or more weak itemsStep back to prerequisites; this module depends on them.
02

The core idea

Estimate heat flow and temperatures from a physical thermal model.

Heat transfer is about identifying which of the three modes (conduction, convection, radiation) controls the path, then building a thermal-resistance network so the dominant resistance is obvious.

q = k A Delta T / L
Works when: the geometry is reduced to a resistance network and the controlling mode (largest resistance) is identified before you compute a single q.
Breaks down when: you add a convection coefficient and a conduction term without checking which resistance actually limits the heat flow.
Figure 1. Concept model for Heat Transfer. The figure names inputs, computed variables, geometry, and result.
input/load result/constraint computed variable dimension/model geometry
03

The method

1Model

Make the physical situation visible.

2Relate

Translate the model into symbols.

3Solve

Calculate only after the model is clear.

4Check

Use units, scale, and limiting cases.

04

Worked example

Figure 2. Worked problem setup: A flat wall has area 2 m^2, thickness 0.08 m, and conductivity 0.7 W/m-K. The inside surface is 80 C and the outside surface is 20
Figure 3. Calculation model. The result follows from the model, units, and reasonableness check.

A flat wall has area 2 m^2, thickness 0.08 m, and conductivity 0.7 W/m-K. The inside surface is 80 C and the outside surface is 20 C. Find heat transfer rate.

  1. Problem A flat wall has area 2 m^2, thickness 0.08 m, and conductivity 0.7 W/m-K. The inside surface is 80 C and the outside surface is 20 C. Find heat transfer rate.
  2. Given and find A = 2 m^2, L = 0.08 m, k = 0.7 W/m-K, Delta T = 60 K. Find: Heat rate q.
  3. Assumptions Idealized model, consistent units, and no hidden effects outside the stated scope.
  4. Step Use one-dimensional steady conduction.
  5. Step q = k A Delta T / L.
  6. Step q = 0.7 * 2 * 60 / 0.08 = 1050 W.
  7. Step Check: doubling insulation thickness would halve heat loss.
  8. Conclusion q = 1050 W. Carry this result into the design decision, not just into the answer box.
05

Misconceptions and diagnostics

MistakeSymptomDiagnostic questionCorrection
Series vs. parallel resistancesAdds resistances that actually act in parallelDoes the heat have one path or several?Draw the resistance network; add in series, combine in parallel.
Forgetting surface convectionUses only k A Delta T / L and ignores the filmIs the surface exposed to a fluid?Add 1/(h A) convective resistances at every fluid boundary.
Steady vs. transientUses steady q while the body is still warmingIs temperature still changing in time?Use the lumped-capacitance or transient method when time matters.
06

Practice ladder

Level 1: direct skill

Redo the worked example with one changed input. Predict the trend before calculating.

Check yourself

The trend must match the governing relation: q = k A Delta T / L.

Level 2: mixed concept

Draw the model from memory, label knowns and unknowns, then write the first equation without looking.

Check yourself

Your first equation should connect the model to q.

Level 3: independent problem

Create a similar problem from a real object near you. State assumptions, solve it, and include a reasonableness check.

Check yourself

A valid solution has a sketch, given/find list, governing relation, units, and a conclusion.

Level 4: transfer task

Turn the result into a design decision: what would you change if the output missed its target by 25 percent?

Check yourself

Name the design variable with the strongest influence and justify it from the equation.

07

Working with AI, and proving it yourself

Useful AI role

Ask for a critique of assumptions, units, diagram labels, and missing checks after you have attempted the solution.

Do not outsource

Do not paste the problem and accept a final answer. Your evidence is the model, the checks, and the explanation.

08

Retrieval and spaced review

Closed-notes prompts: sketch the geometry, identify the dominant heat-transfer mode, draw the thermal-resistance network, and write q in terms of the controlling resistance.

TodayRedo the worked example from a blank page.
+1 daySolve Level 1 without notes.
+3 daysSolve Level 2 with changed numbers.
+7 daysConnect this module to another course.
+30 daysAdd a portfolio artifact.
09

Mapping and portfolio task

Course mapping

Heat transfer turns thermodynamics' energy balances into rates: it sits between thermo (how much energy) and design (how big the heat sink, how thick the insulation).

First-pass focus: definitions, model setup, units, and worked examples. Save edge cases for the second pass.

Portfolio task

Create a one-page thermal-resistance note for a wall, heat sink, or insulated pipe: sketch, assumptions, equations, result, reasonableness check, limitation, and recommendation.