Process Engineering Reference Sheets by MyEngineeringTools.com
THE CALCULATORS

Fourier's Second Law (Unsteady State Heat)

Calculates the temperature at a specific position and time within a plane wall using the one-term approximation for unsteady-state heat conduction.

📖 Need the theory? Read the methodology, assumptions, and equations in the full reference guide.
Read Fourier's Second Law (Unsteady State Heat) Guide →

1. Define Input Parameters

2. Engineering Output

Fourier Number (Fo)
- dimensionless
First Eigenvalue (zeta1)
- rad
First Coefficient (C1)
- dimensionless
Dimensionless Temperature (theta)
- dimensionless
Absolute Temperature (Tz)
- K
Temperature in Celsius (TzC)
- °C

Need this calculation offline?

Download Offline Excel Calculation

Context & Assumptions

Fourier's Second Law is essential for analyzing transient temperature distributions in materials where thermal equilibrium has not yet been reached. This model utilizes the one-term approximation, which is valid for Fourier numbers greater than 0.2, to predict temperature profiles in industrial applications like curing and quenching.

Understand the Engineering Principles

Review the step-by-step derivations, typical industrial limits, and scale-up rules.

Looking for more tools?

Explore our full library of interactive Process Engineering calculators.

View the Calculator Index