$1.$ A drill string in a wellbore is initially at $150\backslash$deg C due to geothermal heat. It is then cooled by drilling mud circulating at $40\backslash$deg C$.$ The surface area of the drill string in contact with the mud is $10$ m$\text{'},$ and the convective heat transfer coefficient between the mud and the drill string is $50$ W$/$m$\text{'}.$K$.$ Calculate the rate of heat loss from the drill string at the moment its surface temperature is $100\backslash$deg C$.$