Stream $A$ with specific heat capacity $C_{PA}=2000\:J/\left ( kg\:K \right )$ is cooled from $90^{\circ}C$ to $45^{\circ}C$ in a concentric double pipe counter current heat exchanger having a heat transfer area of $8$ $m^{2}$. The cold stream $B$ of specific heat capacity $C_{PB}=1000\:J/\left ( kg\:K \right )$ enters the exchanger at a flow rate $1$ $kg/s$ and $40^{\circ}C$. The overall heat transfer coefficient $U=250\:W/\left ( m^{2}\:K \right )$. Assume that the mean driving force is based on the arithmetic mean temperature difference, that is,

$\left [ \Delta T \right ]_{AMTD}=\left [ \frac{T_{A,in}+T_{A,out}}{2} \right ]-\left [ \frac{T_{B,in}+T_{B,out}}{2} \right ]$ where $T_{i,in}$ and $T_{i,out}$ refer to the temperature of the $i^{th}$ stream $\left ( i=A,B \right )$ at the inlet and exit, respectively. The mass flow rate of stream $A$ (in $kg/s$), is _____________________ (rounded off to two decimal places).