Thermal–electrical analogy: in lumped-parameter modeling, which thermal quantity is analogous to electrical current in a circuit representation?

Introduction / Context:
Analogies map thermal systems to electrical circuits to leverage well-developed analysis methods. Correct mapping of variables is essential for building equivalent RC networks for heat transfer problems.

Given Data / Assumptions:

• Resistive conduction or convection modeled as a thermal resistance.
• Thermal capacitance models stored heat (mass * specific heat).
• One-dimensional lumped-parameter representation.

Concept / Approach:
In the most common analogy (temperature ↔ voltage), temperature difference ΔT corresponds to voltage difference ΔV. The time rate of heat flow q̇ (W) corresponds to electrical current i (A). Thermal resistance R_th corresponds to electrical resistance R, and thermal capacitance C_th corresponds to electrical capacitance C. Using this mapping, Fourier/Newton laws mirror Ohm’s law: q̇ = ΔT / R_th just as i = ΔV / R.

Step-by-Step Solution:

Verification / Alternative check:
Energy storage equations align: C_th * dT/dt ↔ C * dV/dt, reinforcing the mapping consistency.

Why Other Options Are Wrong:

Common Pitfalls:
Mixing the less common analogy (current ↔ temperature difference) used in some texts; the voltage–temperature mapping is more widely taught in process control.

Final Answer:
Heat flow rate