$1.$ A cross flow type air heater with both fluids unmixed has an area of $50$ m$2$ and the overall heat transfer coefficient is $45$ W$/$m$2-$K$.$ The flow rate of both hot and cold air are $1$ kg$/$s$.$ Hot air enters at $600$C and cold air enters at $200$C$.$ Determine the exit temperatures of both streams. Also determine the exit temperature if $($i$)$ the flow rate of both fluids is halved and $($ii$)$ the flow rates are doubled. Compare the heat flow rates.