Analogy Between Heat and Electricity

Definition

The analogy between heat and electricity is a conceptual framework used in physics and engineering to explain the flow of thermal energy by comparing it to the flow of electric current. In this model, the parameters of heat transfer (temperature difference, thermal resistance, and heat flow) are mapped onto the parameters of electrical circuits (voltage, resistance, and current) to simplify complex thermal calculations.

Main Content

1. Thermal Potential vs. Electric Potential

• Heat flows due to a temperature difference ($\Delta T$), just as electricity flows due to an electric potential difference or voltage ($V$).
• Temperature is the "driving force" for heat transfer, whereas voltage is the "driving force" for the movement of electrons.

2. Thermal Resistance vs. Electrical Resistance

• Just as materials resist the flow of electric current, materials also resist the flow of heat. This is known as thermal resistance ($R_{th}$).
• The degree of resistance depends on the material's properties (thermal conductivity vs. electrical conductivity) and the geometry of the medium.

3. Rate of Flow

• Heat transfer rate ($Q$) is the quantity of thermal energy flowing per unit of time (Watts), analogous to electric current ($I$), which is the quantity of charge flowing per unit of time (Amperes).
• The relationship is defined by Ohm’s Law for both fields: $I = V/R$ for electricity and $Q = \Delta T / R_{th}$ for heat.

Electrical Circuit:          Thermal Circuit:
      I                          Q
  ----[R]----                ----[R_th]----
  |         |                |            |
( V1 )    ( V2 )           ( T1 )       ( T2 )
  |         |                |            |
  ----------                 --------------

Working / Process

1. Identifying the System

• Define the thermal system, such as a composite wall or a heat sink, and identify the hot and cold boundary temperatures.
• Convert the physical dimensions and material properties (thermal conductivity $k$, thickness $L$, and area $A$) into a thermal resistance value ($R_{th} = L / kA$).

2. Constructing the Equivalent Circuit

• Represent the thermal paths as circuit elements connected in series or parallel, depending on the physical arrangement of the materials.
• Place temperature nodes at the junctions of different materials, similar to how voltage nodes are placed in electrical schematics.

3. Solving the Equations

• Use Kirchhoff’s laws (modified for heat) to solve for the unknown temperature at any node or the total heat flow through the system.
• Perform calculations using the simple algebraic formula $Q = (T_{hot} - T_{cold}) / \sum R_{th}$.

Advantages / Applications

• It allows engineers to solve complex steady-state heat conduction problems using simple circuit analysis tools like Ohm’s law.
• It is highly effective for designing electronic cooling systems, where heat generated by a chip must flow through multiple layers (like thermal grease, heat spreaders, and fins).
• It simplifies the visualization of heat flow in multi-layer walls, making it easier to identify where the "bottleneck" (highest resistance) occurs.

Summary

The analogy between heat and electricity treats thermal energy transfer as an electrical circuit where temperature difference acts as voltage, thermal resistance as electrical resistance, and heat flow as electric current. This method provides an intuitive, mathematical bridge to solve thermal resistance networks efficiently. Important terms to remember include thermal conductivity, thermal resistance, heat flow rate, and temperature gradient.