Question $2$

Conductive heat transfer is one example of a larger family of physical phenomena that involve diffusion of a measurable entity. For stationary diffusion, the concentration gradient $gra{d}_C{?}_x$ and the flux $q_{{?}_{?}}(x)$ are related by the equation

$q_{{?}_{?}}(x)=-D_{x}gra{d}_C{?}_x$

where $D_x$ is the diffusion coefficient for entity $x.$ Diffusion coefficients always have dimension of area per time; examples include kinematic viscosity, mass $($chemical$)$ diffusion coefficient, and thermal diffusivity.

$2\mathrm{.}1)$ Chemical diffusion describes the process in which a chemical concentration gradient results in a mass flux. If concentration has unit $kg*m^{-3},$ and flux has unit of $kg*m^{-2}*s^{-1},$ show that the unit of $D_x$ is $m^2*s^{-1}.$

$2\mathrm{.}2)$ Thermal diffusivity $$ can be computed from the thermal conductivity $$ via

$=\frac{}{c_p}$

where $c_p$ is the volumetric heat capacity $($unit $($:$J*m^{-3}*K^{-1}\}.$

Show that $$ has units of $m^2*s^{-1}.$

$2\mathrm{.}3)$ Rewrite Fourier's law of stationary heat conduction

$q_{?}=-gra{d}_u$

in terms of the thermal diffusivity. What entity is it describing the diffusion of$?$