Conduction analogy – Meaning of x/(kA) In one-dimensional steady conduction through a plane wall of thickness x, area A, and thermal conductivity k, Fourier’s law can be written as q = (ΔT) / (x/(kA)). The term x/(kA) is called:

Introduction / Context:Heat transfer by conduction is often analyzed using an electrical analogy. The temperature difference plays the role of voltage, heat rate the role of current, and x/(kA) the role of resistance.

Given Data / Assumptions:

• One-dimensional, steady-state conduction through a uniform slab.
• Constant material properties.

Concept / Approach:Fourier’s law in slab form: q = kA * (ΔT/x). Rearranged: q = (ΔT) / (x/(kA)). Thus x/(kA) impedes heat flow just as electrical resistance R impedes current I in Ohm’s law, I = V/R.

Step-by-Step Solution:Start with q = kA * ΔT / x.Define thermal resistance R_cond = x/(kA).Write q = ΔT / R_cond, highlighting the analogy.

Verification / Alternative check:Units: x in m, k in W/m·K, A in m^2 → x/(kA) has units K/W, the correct unit for thermal resistance.

Why Other Options Are Wrong:

• Thermal conductivity k is already in numerator of Fourier’s law.
• “Thermal coefficient” is vague; not a standard term here.
• Heat capacity and Biot number relate to transient response and internal/external resistance ratio, respectively.

Common Pitfalls:Forgetting area in the resistance; mixing up contact resistance (additional) with conduction resistance.

Final Answer:thermal resistance