In refractory materials engineering, the thermal diffusivity (α) of a brick is defined as α = k / (ρ * cp). For a given refractory brick, thermal diffusivity will be high when which property is high?

Introduction / Context:
Thermal diffusivity tells us how quickly a temperature disturbance travels through a solid. In refractory selection for furnaces, kilns, and ladles, knowing which material property most increases thermal diffusivity helps engineers balance heat storage against heat flow. The classic definition used in heat transfer is α = k / (ρ * cp).

Given Data / Assumptions:

• Thermal diffusivity α relates to thermal conductivity k, density ρ, and specific heat cp.
• We compare the effect of increasing k, ρ, and cp on α, assuming the other two remain constant.
• Brick behavior is considered under steady, single-phase, homogeneous conditions relevant to refractories.

Concept / Approach:
From α = k / (ρ * cp), thermal diffusivity rises with larger k and falls with larger ρ or cp. Physically, k measures how effectively heat is conducted, while ρ * cp measures the material’s thermal inertia (how much heat it stores per unit volume per degree).

Step-by-Step Solution:

Verification / Alternative check:
Dimensional analysis confirms α has units of m^2/s. Increasing k (W/m·K) while keeping volumetric heat capacity (ρ * cp) constant raises α, meaning faster heat penetration—consistent with observed transient heating of high-k refractory inserts.

Why Other Options Are Wrong:

• Density: Increasing ρ raises heat storage per volume, reducing α.
• Specific heat: Increasing cp also increases thermal inertia, lowering α.
• None of these: Incorrect because k clearly increases α.

Common Pitfalls:
Confusing thermal conductivity (steady-state property) with thermal diffusivity (transient response). A material can have high k yet lower α if its ρ * cp is also very high.

Final Answer:
thermal conductivity