The mercury thermometer in Chap. 4 was considered to have all its resistance in the convective film surrounding the bulb and all its capacitance in the mercury. A more detailed analysis would consider both the convective resistance surrounding the bulb and that between the bulb and the mercury. In addition, the capacitance of the glass bulb would be included. Let Ai = inside area of bulb, for heat transfer to mercury Ao = outside area of bulb, for heat transfer from surrounding fluid m = mass of mercury in bulb mb = mass of glass bulb C = heat capacity of mercury Cb = heat capacity of glass bulb hi = convective coeffi cient between bulb and mercury ho = convective coefficient between bulb and surrounding fluid T = temperature of mercury Tb = temperature of glass bulb Tf = temperature of surrounding fluid Determine the transfer function between Tf and T. What is the effect of the bulb resistance and capacitance on the thermometer response? Note that the inclusion of the bulb results in a pair of interacting systems, which give an overall transfer function. Solve this problem with the help of Matlab. Grading: - Finding an appropriate heat transfer problem and writing down the reference (2p) - Solving the problem by hand till the point you need a software (Explain all the steps with reasons) (3p) - Solving the rest with a suitable software (Matlab) (Explain all the steps with reasons) (3p) - Commenting on the results (2p)