Thermal Resistances Cheat Sheet

This cheat sheet covers the concept of thermal resistance, its application in modeling heat flow using electrical analogies, and its calculation for plane walls, composite walls (series and parallel), and cylindrical geometries. It also touches upon convection and provides worked examples.

Core Principles

Thermal resistance is analogous to electrical resistance, used to model heat flow.
Heat flow can be modeled using thermal circuits, similar to electrical circuits.
Thermal resistance depends on material properties, geometry, and mode of heat transfer.
Conduction, convection, and radiation are the primary modes of heat transfer.
Steady-state conditions simplify heat transfer analysis.
One-dimensional heat flow is a common simplifying assumption.
Composite materials and geometries require summing resistances in series or parallel.
The electric-thermo-hydraulic analogy provides a framework for understanding heat transfer.

Action Steps

Identify the geometry and mode(s) of heat transfer.
Determine the relevant thermal resistances for each component.
Construct an equivalent thermal circuit.
Calculate the total thermal resistance (series/parallel combination).
Apply the heat flow formula ($q = \frac{\Delta T}{R}$) to find heat transfer rate.
Calculate temperature at intermediate points using individual resistances.

Formulas

For plane wall conduction: $R = \frac{L}{kA}$
For convection: $R = \frac{1}{hA}$
For cylindrical conduction: $R = \frac{\ln(\frac{r_2}{r_1})}{2\pi kL}$
For series resistances: $R_{total} = R_1 + R_2 + ...$
For parallel resistances: $\\frac{1}{R_{total}} = \\frac{1}{R_1} + \\frac{1}{R_2} + ...$
Heat flow: $q = \frac{\Delta T}{R}$
Heat flux: $q" = \frac{q}{A}$

Key Terms

Thermal Resistance: A measure of a material's or object's opposition to heat flow.
Heat Flux: The rate of heat transfer per unit area.
Thermal Conductivity (k): A material property indicating its ability to conduct heat.
Convection Heat Transfer Coefficient (h): A measure of the effectiveness of heat transfer by convection.
Steady-State: A condition where temperatures at all points in a system do not change with time.
One-Dimensional Heat Flow: Heat transfer occurring only along a single spatial dimension.

Pro Tips

Always check units for consistency.
Draw the thermal circuit clearly, labeling all nodes and resistances.
For composite walls, ensure layers are in series or parallel correctly.
Remember the assumptions (1-D, steady-state, no internal generation) when applying formulas.
The electric-thermo-hydraulic analogy is a powerful tool for conceptualizing problems.

Pitfalls to Avoid

Confusing series and parallel resistance calculations.
Incorrectly applying formulas for different geometries (plane vs. cylinder).
Forgetting to include convection resistances at boundaries.
Errors in unit conversions.
Assuming constant properties when they vary significantly.

Real World Examples

Insulating a house wall: Calculating the thermal resistance of wall materials (e.g., brick, insulation, drywall) to minimize heat loss/gain.
Cooling electronic components: Using heat sinks with fins (increasing surface area) and thermal paste to reduce thermal resistance between the component and the air.
Heat exchangers: Designing systems where heat is transferred between fluids through a separating wall, considering conduction and convection resistances.

People

Frank P. Incropera: Author of 'Fundamentals of Heat and Mass Transfer'
David P. Dewitt: Author of 'Fundamentals of Heat and Mass Transfer'
C.P. Kothandaraman: Author of 'Fundamentals of Heat and Mass Transfer'
Dr Marco Bernagozzi: Instructor