4) A 20cm long open-ended, horizontal pipe stub on the sample port of a flare line is initially filled with methane when sampling is completed and the sample system is removed. Assume the pipe tube can be modeled as a horizontal tube that is initially completely filled with methane up to the exit plane, beyond which is pure air. Assume the diffusivity of methane in air is 0.000021m2/s. a) Write a governing differential equation describing the diffusion of air into the pipe stub. b) Solve the equation to derive an expression for mole fraction of methane in the pipe as a function of time (Hint: This is a solvable equation analytically but you might want to consult a heat transfer or math text for help finding a solution) c) How long would it take until the mixture half-way into the pipe reaches stoichiometric