Both Fourier's law of heat conduction and Fick's law of mass diffusion can be expressed as \(\dot{Q}=-k A(d T / d x)\). What do the quantities \(\dot{Q}, k, A\), and \(T\) represent in \((a)\) heat conduction and \((b)\) mass diffusion?

Fourier's Law of heat conduction is given by: \(\dot{Q} = -kA \frac{dT}{dx}\) Here, \(\dot{Q}\) represents the heat flow rate, which is the amount of heat transferred through the material per unit time (in watts). \(k\) represents the thermal conductivity of the material (in watts per meter-kelvin, W/(m·K)). It denotes the ability of the material to conduct heat. \(A\) represents the cross-sectional area through which heat is being transferred (in square meters). \(T\) is the temperature of the material at a given position x (in kelvin). \(\frac{dT}{dx}\) represents the temperature gradient in the material (in temperature units per distance unit, like K/m). It demonstrates how the temperature changes with respect to distance.

Fick's Law of mass diffusion can also be represented by the same equation: \(\dot{Q} = -k A\frac{dT}{dx}\) In this context, \(\dot{Q}\) represents the mass flow rate, which is the amount of mass transferred through the material per unit time (in kg/s). The variable \(k\) represents the mass diffusion coefficient of the substance (in square meters per second, m²/s) that determines the ability of the substance to diffuse through another material. \(A\) represents the cross-sectional area through which mass is being transferred (in square meters). For Fick's law of mass diffusion, \(T\) represents the concentration of the substance being diffused at a given position x (in kg/m³ or other concentration units). \(\frac{dT}{dx}\), in this case, represents the concentration gradient in the substance (in concentration units per distance unit, like kg/(m⁴)). It demonstrates how the concentration changes with respect to distance.