代写CHEN 4010 - Exam 2 2024代写数据结构语言

CHEN 4010 - Exam 2

Nov 6, 2024

Time: 60 minutes

Total Points: 100

State your assumptions and demonstrate your reasoning and analysis clearly. No points will be given for just writing down the result.

1. Use the method ofFrobenius to find the solution of the following equation:

(35 points)

2. Consider a pipe through which a fluid is flowing carrying a solute A. The solute balance for species A is given as:

where v0  is the constant, uniform. (plug) fluid velocity profile, DA  is solute diffusivity in the fluid, and CA  is the solute molar composition. There is radial diffusion but no axial diffusion of A. The solute flux at the fluid-wall interface is given as:

where KOLis the overall transport coefficient. The inlet solute composition is C0  at the axial position z=0.

Show that the average composition CA  obeys the analytical solution at position z=L:

where Bi = K0LR/DA and the eigenvalues are obtained from

λnJ1 (λn ) = BiJ0 (λn )

(30 points)

3. Consider is an electric wire of circular cross section with radius R and electrical conductivity ke, ohm-1 cm-1. Through this wire there is an electric current with current density I amp/cm2. The transmission of an electric current is an irreversible process, and some electrical energy is

converted into heat (thermal energy). The rate of heat production per unit volume is given by the expression The quantity Se is the heat source resulting from electrical dissipation.

We assume here that the temperature rise in the wire is not so large that the temperature dependence of either the thermal or electrical conductivity need be considered. The surface of the wire is maintained at temperature T0. Please determine (i) the radial temperature distribution within the wire, (ii) maximum temperature rise, and (iii) heat outflow at the surface.

(35 points)