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Here’s how a real formula entry appears in the workspace. Every card breaks down the core equation, its variables, units, assumptions, and a quick example—so you understand the “why”, not just the “what”.

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Preview • Heat Transfer Formula workspace

\( q_x = -k A \dfrac{dT}{dx} \)

Heat flows from hot to cold: define conductivity \(k\), area \(A\), and gradient \(dT/dx\).

Variable setup

k = 45 W/m·K A = 0.50 m² ΔT = -80 K Δx = 0.008 m

Result: \( q_x = 225{,}000 \,\text{W} \)

FormuLab surfaces the sign convention, units, and key notes automatically.

Heat Transfer • Fourier’s Law

Fourier’s Law of Conduction

q_x = -k A \frac{dT}{dx}

Fourier’s Law of Conduction quantifies the heat rate \( q_x \) flowing through a material due to a temperature gradient. The negative sign shows that heat travels from hot regions to cold regions.

Variables & Units

q_x — heat transfer rate [W]
k — thermal conductivity of the material [W/m·K]
A — cross-sectional area normal to heat flow [m²]
dT/dx — temperature gradient along the x-direction [K/m]

Assumptions

Steady-state, one-dimensional heat conduction
Constant thermal conductivity
No internal heat generation within the slab

Worked Example

A steel plate with \( k = 45 \,\text{W/m·K} \) is 8 mm thick. The hot side is at 120 °C and the cool side at 40 °C. The plate area is 0.5 m².

q_x = -k A \dfrac{\Delta T}{\Delta x}

\Delta T = 40 - 120 = -80\,\text{K}, \qquad \Delta x = 0.008\,\text{m}

q_x = -45 \times 0.5 \times \dfrac{-80}{0.008} = 225{,}000 \,\text{W}

FormuLab highlights the sign convention, unit conversions, and final answer. You can attach notes, link related formulas like thermal resistance, or run an AI explainer to see what happens if thickness halves.

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Workspace tools

Each formula card includes quick exports, AI questions, and slider controls to visualize parameter sensitivity. Save it to your Thermodynamics workspace and sync annotations across devices.