7. Derive an expression for the rate of conduction through a cylindrical pipe wall. A long carbon steel pipe which has an internal diameter of 2m and a wall thickness of 5cm is be used to house an exothermic chemical reaction flowing at a rate of 3kg/s and a temperature of 210C (Figure 8). The pipe will be exposed to surrounding air temperatures of between 5C and 35C. The heat transfer coefficient in the pipe has been found to be equal to 1790W/m2K while the heat transfer coefficient of the wind flowing over the pipe is 380W/m2K. (i) Assuming that the heat from the chemical reaction ensures that the temperature of the reacting mixture remains constant at 210C as it flows down the pipe, present the temperature profile through the steel pipe wall graphically as a function of the outside temperature. (ii) Comment on the results obtained in part (i) and sketch a plot of what you would expect to happen if you were to add insulation to the pipe (this sketch is meant to be illustrative of what you think will happen - so make sure to explain your reasoning)