The temperature distribution across a wall $1$ m thick at a certain instant of time is given as $T(x)=a+bx+c{x}^2,$ where T is in $C$ and x is in meters, while $a=900C,b=-300\frac{C}{m},$ and $c=-50\frac{C}{m^2}.$ A uniform heat generation $q^{}=1000\frac{W}{m^3},$ is present in the wall of area $10m^2$ having the properties $=1600k\frac{g}{m^3},k=40\frac{W}{m}.K$ and $c_p=4k\frac{J}{k}g.K.$ Determine:

a$)$ the rate of heat transfer entering the wall