Question 1: Consider a fluid flowing in turbulent flow at velocity (v), inside a pipe diameter (D) and undergoing heat transfer to the wall. Find the dimensionless groups relating the heat transfer coefficient (h), to the variables diameter (D), density (, viscosity (, heat capacity (c), thermal conductivity (k) and velocity (v). (a) Use four variables D, k, and v as the core variables common to all the dimensionless groups and identify some of them by known names of Nusselt number (Nu), Reynolds number (Re) and Prandtl number (Pr). That is, show that Nusselt Number = f (Reynolds Number, Prandtl Number). (b) State without proof, a similar dimensionless numbers expression (equation) for mass transfer process involving the diffusivity (D) of A and B components terms of the Sherwood number (Sh) and Schmidt number (Sc) to estimate the mass transfer coefficient as Nu = 2.0 + 0.60 (NR)°³ (Npr)" for a flow past a single sphere for the estimation of the mass transfer coefficient. Hint: See section 4-14-1 of the fourth edition or section 15.1C of the fifth edition of the class text on using Buckingham theorem for finding dimensionless groups that relate to variables involve. Question 2: Consider a sphere shaped naphthalene (CH) having a radius of 20 mm suspended into a large volume of still air at 50 °C and 1 atm absolute pressure. At 50 °C, the vapor pressure of naphthalene is 0.9 mm Hg, its density is about 1.1 g/cm' and its diffusivity in air is 7.02 X10 m/s. (a) Calculate the rate of evaporation of naphthalene into the still air in kgmol/s.m (b) Calculate the time for the complete evaporation of the naphthalene into the still air. Hint: See example 6.2-4 of the 4* edition or example 19.1-4 of the 5th edition of the class text. Question 3: Water flowing at the rate of 1.1 kg/s in a 2-4 shell-and-tube heat exchanger is heated from 50 °C to 75 °C by an oil having a heat capacity of 1.9 kJ/kg.K. The oil enters the heat exchanger at 125 °C and leaves at 90 °C. Calculate the area of the heat exchanger if the overall heat-transfer coefficient is 250 W/m²K. Question 4: A well stirred storage vessel is originally filled with 500 kg of 20 wt % ethanol solution. The operator decided to dilute the solution in the vessel by flowing a 10 wt % ethanol solution at a rate of 1000 kg/h into the vessel and withdrawing the well stirred solution from the vessel at a rate of 500 kg/h. (a) Calculate the time it takes the solution in the vessel to reach a concentration of 15 wt % ethanol. (b) If the vessel can only hold 1500 kg of the solution, calculate the ethanol concentration when the vessel is completely filled. Assume that the density of ethanol solution during the operation remains essentially constant within the ethanol concentration range of operation.