Can anyone tell me what these two equations represent?

What is the source?

Broadly, the first is an Arrhenius equation, which provides the rate of a thermally activated process, i.e., one with an activation energy.

$Q_r$: a rate (based on the second equation, likely a heat flux)
$C^n$: some type of pre-exponential factor, where n may be the reaction order; problem specific
$-Delta H_r$: H often stands for enthalpy and r for reaction
$Z$: typically a collision frequency
$E$: the activation energy
$R$: the gas constant
$T$: the temperature

The second equation is a heat capacity equation describing how an object heats up from a net heat flux.

$C_p$: specific heat capacity at constant pressure
$rho$: density
$t$: time
$Q_r$: likely an input heat flux, with units of J/m³s
$Q_c$: likely an output heat flux, perhaps to a cold sink (c)

Put together, the equations provide an energy balance: the thermal energy generated from a reaction minus any output thermal energy goes into heating the system.