Question text1. The one-dimensional heat conduction equation for a cooling dyke with no internal heating can be written: [math: ∂T∂t=κ∂2T∂x2]Where [math: T] is temperature, [math: t] is time, [math: x] is horizontal distance, and [math: κ] is the thermal diffusivity, and has a solution of the form: [math: T(x,t)=T02[erf(w−x2(κt))+erf(w+x2(κt))]] At t=0, T=T0 for –[math: w] < x < [math: w], and at t=0, T=0 for |x| > [math: w]. If the half-width of the dyke is [math: w=2.7m], centred on x = 0, and if T0 = 1500 oC and [math: κ] = 10-6 m2s-1 a) calculate the temperature at the centre of the dyke after one week and after one year (365 days) in degrees Celsius to three significant figures. HINT: Use a calculator, an online tool or MATLAB to calculate the error function (in MATLAB simply use erf(your value) ). After one week: [math: T=] Answer 1 Question 1[input] degrees Celsius [3]After one year: [math: T=] Answer 2 Question 1[input] degrees Celsius [3]b) Calculate the temperature of the dyke at the edges after 1 year in degrees Celsius to three significant figures.[math: T=] Answer 3 Question 1[input] degrees Celsius [4]