Thermal diffusivity definition: Given h = thermal diffusivity, rho = density, S = specific heat, and k = thermal conductivity, which expression is correct for thermal diffusivity?

Introduction / Context:Thermal diffusivity indicates how quickly a material's temperature field responds to thermal disturbances. It combines conductivity with thermal storage capacity (density and specific heat).

Given Data / Assumptions:

• Symbols: h for thermal diffusivity (often denoted alpha), k for conductivity, rho for density, S for specific heat.
• Homogeneous, isotropic material.

Concept / Approach:Thermal diffusivity is defined as the ratio of the ability to conduct heat to the ability to store heat: h = k / (rho * S)This has units of m^2/s and appears in the transient heat conduction equation, controlling the rate of temperature equalization.

Step-by-Step Solution:Start from energy balance in a control volume and Fourier's law.Group terms to obtain the transient diffusion equation: dT/dt = h * (d^2T/dx^2 + ...).Identify h as k / (rho * S) with dimensions m^2/s.

Verification / Alternative check:Dimensional analysis: k has W/(mK) = J/(smK); rhoS has J/(m^3K); dividing gives m^2/s, confirming the expression.

Why Other Options Are Wrong:

• rhoS/k or krhoS: have incorrect units.
• (rho + S)/k: dimensionally inconsistent.
• k/rho: ignores specific heat, wrong units.

Common Pitfalls:Confusing thermal diffusivity with thermal conductivity; high conductivity does not guarantee high diffusivity if heat capacity is also high.

Final Answer:h = k / (rho * S)