Reference no: EM132455111

Question (1)  Create a user-defined m-file function frho_m that calculates ρ m using equation (2) from the concentration of the paramagnetic salt, c (M), and temperature, T (°C), as the arguments.

Question (2) Plot the dependence of 0t (min) and R (µm) obtained experimentally (data from the table) on log-log scale.

Question (3) Obtain the dependence of 0t (min) on R (µm) numerically, and plot the numerical solutions on the
same figure (log-log scale).
a. [10 points] Re-write equation (3) as dt 1 dz z α β = + and solve it using an ODE solver (note that i 0 z zz ≤ ≤ , ( ) 0 i t z = and tz t ( 0 0 ) = ) for every R

b. [10 points] Re-write equation (3) as dz dt α β z = + and solve it by integrating the left-hand side from 0 to 0t and the right-hand side from i z to 0 z numerically (that is,001

• izz t dz  α β z = + ∫ ) for every R

Question (4) On the same figure, plot the analytical solution given by equation (4). Make the numerical and the analytical solutions look distinct on the graph (yes, all three of them).

Question (5) Fit the experimental data with a power-law function m y bx = . In a new figure, plot the data and the fitted curve. Find 0t (min) for R = 87 (µm) (using the power-law fit).

Question (6) Interpolate the experimental data with the ‘cubic' method. In a new figure, plot the data and the interpolant. Find 0t (min) for R = 70 (µm) (using cubic interpolation).
Attachment:- user defined.rar