Q$1/(20$ pts$)$

The equation which describes the change of temperature of the fluid system $($no reaction$)$ is given as follows:

$\frac{C}{b}ar(DT)\frac{DT}{Dt}=-(grad*q)-($:gradv$)-(\frac{delln}{dellnT}{)}_p\frac{Dp}{Dt}$

$($ : fluid density, T: temperature, $t$ : time, $Cp$ : heat capacity per unit mass, $q$ : heat flux vector, $$ : viscous momentum flux tensor, $v$ : fluid velocity vector, $p$ : pressure$)$

The above equation can be simplified into the following form $(k$ : heat conductivity$)$:

$\frac{}{b}ar(Cp)\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{t}}=k\frac{\text{d}\text{e}\text{l}\text{T}}{del{x}^2}$

Write down all the assumptions or conditions for the simplification.