$(15$ pts$)$ A horizontal flat plate is maintained at a constant temperature $T_s=95C.$ The temperature gradient in the vertical direction at a certain location on the plate surface is $(\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{y}}{)}_y=0=-20,000\frac{K}{m}$ when water at $25C$ flows over it$.$ Determine the local heat transfer coefficient $h_x$ at the location.