Fluid X is flowing in a circular pipe with a constant velocity ν (m/s). The fluid is cooled by a jacket kept at constant temperature, Tj. Fluid velocity is plug shaped , in other words uniform at radial positions. Assume that temperature is uniform in radial positions because of turbulent flow conditions; ρ and Cp of the fluid are constants. The inlet temperature (at z=0) is constant and uniform at To (To>Tj). Assume that thermal conduction of heat along the z axis is small relative to convection. Heat transfer film coeffiecient h is given as 40 (J/m2.°C.s).

Δz

Cooling jacket, Tj

v, To, ρ, Cp
R

z z=0

a. Perform an unsteady state energy balance using shell balance technique and obtain a PDE model. Do not solve.

b. Perform a steady state energy balance using shell balance technique to obtain an ODE model . Solve the model to find the steady state temperature distribution as a function of axial position z. Take Tref=0.

c. Given that; at t=0, To=90°C; ν=0.5 m/s; h=40 J/(m2.°C.s); R=0.1m; ρ=100 kg/m3; Tj=10 °C and Cp=10J/(kg°C); find the temperature value at z=1 m? (Ans.= 26 °C)

Predict trends in glass transition and melting temperatures. Why are these properties considered in the design of consumer products like plastic cups and ice trays?

explain population growth in terms of ode

Change in concentration of salt in a reactor can be modeled
by the following equation y’ = ty+y1/2
Initial concentration of salt at time (t= 0 hours) is 1g/l, y(0)=
1, find the concentration of salt after 0.2 hour y(0.2)= ? by
using Euler, Heun and RK4 methods. Use h= 0.1

4. (20) A stoichiometric mixture of CO and O₂ enters a reactor at 100 ^oC. CO₂, CO and O₂ leave the reactor in chemical equilibrium at 1527 ^oC and 2 atm. Calculate the partial pressures of CO₂, CO and O₂ in the products.

CO + ½ O₂ = CO₂:                  ΔG^o_373K = -250.8 kJ

CO + ½ O₂ = CO₂:                  ΔG^o_1800K = -127.4 kJ

The reaction rate constants for an investigation of ascorbic acid deterioration in a multivitamin mix during storage at different temperatures were:

(i) Determine the activation energy at 70 oC

(ii) Determine the rate constant at 80 oC

(iii) Suppose the temperature increased from 20 oC to 70 oC, determine the sensitivity of the reaction rate to this rise is temperature.

(iv) At what time would the ascorbic acid deteriorate by 50%?

A binary mixture of benzene and toluene will be separated by continuous distillation. The mixture consists of 20% mol of benzene and 80% mol of toluene at the bubble point of 91ºC. The binary mixture is available at 100 mol h-1 and the separation should deliver a distillate product that has a concentration of 90% mol of benzene and that contains half of the benzene in the feed stream. a) Plot the equilibrium line for benzene. b) Determine the minimum reflux ratio. b) Determine the minimum number of stages required to achieve this separation. Note: You may require looking for properties of components◢

volatilities of components need to looked up

Continue

• A pub opens its door for business at 6:00 PM. From 6:00 P.M. to 8:00 P.M. 50 smokers in the pub smoke 2 cigarettes per hour and each cigarette emits 4mg formaldehyde. Fresh air is introduced into the pub @ 1,000 m3/hr. At 8:00 P.M. the number of smokers in the pub increases from 50 to 75 and as a result, the fresh air flow rate is increased from 1,000 m3/hr to 1,500 m3/hr to flush out the stale air. Assume that all smokers in the pub still smoke 2 cigarettes per hour, what is the formaldehyde concentration (ppmv) in the air inside the pub @ 9:00 P.M.?
• The air volume inside the pub is 1,000 m³,
• the air temperature inside the pub is 25^oC,
• the air pressure inside the pub is 1 atm,
• and formaldehyde is converted to carbon monoxide following a first-order reaction pathway with k = 0.4 1/hr.

Thermodynamics problem:

An engine operates on an air-standard Otto cycle. The pressure and temperature of the isentropic compression 100 kPa and 40 °C, respectively. The pressure at the end of compression is 2.0 MPa and the net work is 87,000 J/mol. Assume ideal air-standard cycle. Determine the following:

1. pressure, volume, and temperature at end of each step.
2. compression ratio.
3. heat input and heat rejected per mol of working fluid.
4. thermal efficiency of the cycle.

A cylinder contains 200 kg of carbon dioxide at 5 MPa and 25°C (TC=304.2K, Pc=72.8atm, w=0.225, M=44.10 kg/kmol). A second cylinder contains nitrogen at 7 MPa and 25° C (Tc=126.2K, Pc=33.5atm, w=0.040, M=28 kg/kmol). A third cylinder contains oxygen at 6 MPa and 25°C (Tc=154.6K, Pc=49.8atm, w=0.021, M=32 kg/kmol). All 3 cylinders are the same size. When the contents of all the cylinders are moved into a reactor at a temperature of 75°C, the pressure is 12 MPa. Using the law of corresponding states and the generalized compressibility chart, determine the volume (m³) of the reactor.

Despite hydrophobic recovery shortcomings, surface activation methods are widely used for rendering PDMS hydrophilic. Why?