Heat Transfer: Practical Problems

1.      An insulation tip mean k = 0; or dT/dx=0

2.      How can we find the direction of fluid flow in a metal pipe by the concept of heat transfer?

     Ans: if we heat the pipe, and measure temperature at two point in different sides, then fluid will be flowing in the direction of high temperature.

3.      Mineral oil is filled in between the narrow gap of 2 horizontal smooth plates which are maintained at constant temperature. The heat flux in 2^nd case will be more than/less than or equal to 39 W/m², explain.

Ans: in second case. heat flux will be less because it will have only conduction while in 1st we have both conduction and convection.

4. What will be more effective way of heating a room 1 kW heater or refrigerator having power consumption of 1 kW?
Ans: 1 kW heater will give 1 kW heat while 1 kW power refrigerator will give more heat to the room.

5.      In a process at steady state, an ideal fin is at a base temperature of 100 °C, the temperature at the base for the real fin will be less, more or same, explain?

Ans: the ideal fin transfers more heat than a real fin, in order to transfer same heat the base temperature should be more for a real fin.

6.      If we open the refrigerator and its radiator portion outside the room, will it work as air conditioner? Explain

7.      In air cooler, if water and air are at same temperature, then also will there be cooling? Explain.

8.      In an oil water finned tube heat exchanger, which fluid should be passed through fin side and why?

9.      Can we transfer heat from low temperature to high temperature, explain?

10.         LMTD profile for i) 1, 2 shells & tube heat exchanger and ii) steam condensation in double pipe HE.

     

Chemical Engineering Thermodynamics: Questions and solutions

   1.  An electrical battery fully insulated discharges at constant volume. During one hour test, it is found that a current of 20 amps at 10 volts flows, while the temperature increases from 20 °C to 35°C. The battery is used to heat the heating element which in turn heats water. The temperature of heating element and water is raised by 20 °C. The heating element has heat capacity equivalent of ¼ kg of water. Determine the change in internal energy, work done and heat transfer when, 

a)   Only battery is treated as a system

b)   Only heating element is treated as a system.

c)   Water and heating element are treated as a system.

d)  Battery, container, water and heating element are treated as a system.  
 Ans: here we have electric work =VI=200 W
a) W =-200, Q=0 (insulated), ΔU = -200W

b) W =200, Q=-200+5.815=-194.185, ΔU = mcpΔT = 1.05*20=21kJ/hr=5.815Watt

c)  W = 200; ΔU=200; Q = 0 (assume insulated) 

d)  W =0; Q=0; ΔU = 0

                                   

    2.  In a certain process a vapour is condensed at 500 °C by transferring energy to water, which in turn is vaporized at 250 °C. The resulting water vapour is used in a Carnot engine with the ambient atmosphere at 25 °C as its sink. Determine the fraction of the availability lost due to the irreversible energy transfer.        max efficiency = (1-298.15/773.15)=0.614
      Carnot engine efficiency = (1-298.15/523.15)=0.43
      fraction of availability lost = (0.614-0.43)/0.614=0.3
                                                                                                       

    3.   A rigid vessel contains 0.014 m³ of saturated vapor steam in equilibrium with 0.021 m³ of saturated liquid water at 100 °C. Heat is transferred to the vessel until one phase just disappears, and a single phase remains. Which phase (liquid or vapor) remains, and what are its temperature and pressure? How much heat is transferred in the process? 

                                                     

   4.      Dry methane is burned with dry air. Both are at 298 K initially. The flame temperature is 1600 K. if complete combustion is assumed, how much excess air is being used? The reaction is

CH₄ + 2O₂ → CO₂ + 2H₂O

The standard heat of reaction is -8.028×10⁵ J/mol of methane reacted. Mean molal specific heats of gases between 298 K and 1600 K are in J/mol K:

CO₂ = 51.66; H₂O = 40.45; O₂ = 34.01; and N₂ = 32.21.                                                             

   5.  It is required to prepare 1 litre of an antifreeze solution of 30 mole % methanol and 70 mole % water. Determine the volumes of pure methanol and pure water which must be mixed to prepare the solution at 25 °C. The partial molar volumes of methanol and water at 25 °C. The partial molar volumes of methanol and water at 25 °C and the given composition are:                      

Methanol (1)  = 38.632 litre/kmol;  Water (2)  = 17.765 litre/kmol;

Molar volumes of pure methanol and water at 25 °C are:

Methanol (1)  = 40.727 litre/kmol;  Water (2)  = 18.068 litre/kmol                             

   6.     a) How the boiling phenomenon is different for immiscible liquids than miscible liquids? How it can be beneficial in separation?
      Ans: miscible liquids have the contribution in the total pressure in accordance with their mole fraction. the boiling point of miscible liquids is in between the boiling temperature of both components. the immiscible liquids have the boiling points lesser than both the components as the contribution of each component is equal to its vapor pressure. therefore, boiling point reaches before the boiling point of more component itself. e.g. steam distillation             
                                                                                         

b) Explain the process and draw it on T - x, y diagram, used to get a solution having 90 mol % more volatile component (1) from an equi-molar solution, shown as points B and A in the T-x, y diagram respectively.  Ans: As in the vapor phase the concentration of more volatile component is more than that of liquid phase, we will heat it to 2 phase region, collect the vapor and condense it, further heat it to 2 phase region, collect the vapor, condense and so on till we get the desired concentration i.e. distillation                                               
          

7.      Calculate the fugacity and fugacity coefficient for butadiene at 40 °C for the pressure 2 bar and 5 bar. At 40 °C the vapour pressure of butadiene is 4.287 bar. The molar volume of the saturated liquid butadiene at 40 °C is 90.45 cm³/mol. For butadiene: T_c = 425.0 K, P_c = 43.3 bar, ω = 0.195                                     

                                                                                             

8.      Water (1) - hydrazine system forms an azeotrope containing 58.5 mol % hydrazine at 393 K and

    101.3 kPa. Calculate the equilibrium vapour composition for a solution containing 20 mol % hydrazine.The relative volatility (relative vapor pressure) of water with reference to hydrazine is 1.6 and may be assumed to remain constant in the temperature range involved. The vapor pressure of hydrazine at 393 K is 124.76 kPa.

9.      a) The standard Gibbs energy of reaction for the decomposition H₂O → H₂ (g) + O₂ (g) is +118.08 kJ/mol at 2300 K. Is the reaction possible? If yes, then how?                                                              

b) Estimate the maximum conversion of ethylene to ethanol by vapor-phase hydration at 250 °C and 35 bar for an initial steam to ethylene ratio of 5. The equilibrium constant at 250 °C is 10.02 × 10^-3.

C₂H₄ (g) + H₂O (g) →C₂H₅OH (g)

The fugacity coefficient of C₂H₄, H₂O and C₂H₅OH are 0.977, 0.887 and 0.827 respectively.         

Chemical Engineering Thermodynamics: Boiling

The binary solution of miscible liquids, when heated from liquid state at a fixed pressure, a stage comes when we have first bubble formation, this temperature is bubble point of the solution. At this stage the total pressure is equal to the summation of its partial pressure and for an ideal system in vapor-liquid equilibrium:

P = x1P1 + x2P2

at bubble point the liquid phase has the same composition as original solution, since there is only a single bubble formation. As we increase the temperature above bubble point, the boiling continues leads to decrease in concentration of more volatile component in liquid phase as well as in vapor phase. The vapor pressure increases as temperature increases but the composition decreases so as to maintain the constant pressure. At a point all the liquid has been vaporized and we are left with last drop of liquid in equilibrium with vapor phase called Dew point. at this point, the vapor phase composition is same as original liquid mixture composition. 

The solution start boiling at its bubble point and stops at its dew point. The boiling temperature of the solution is between the boiling temperature of two components.

The im-miscible liquids start boiling at a temperature lower than the boiling point of either component. because each component contribute to the total pressure as it is pure. Therefore, when the sum of vapor pressure becomes equal to total pressure, the solution start boiling. This is used in steam distillation, where we use steam to distill heat sensitive components.