Heat Exchanger: LMTD

In heat exchanger, we calculate log mean temperature difference (LMTD). LMTD gives the logarithmic mean of temperature difference between  hot streams and cold streams. there are other types of mean also like arithmetic mean, geometric mean, harmonic mean. In heat exchanger we use log mean because the temperature profile is logarithmic in a heat exchanger. in case of same temperature difference at the two ends of a heat exchanger which can be in counter current flow, arithmetic mean temperature difference is used.

Practical Aspects: can we increase the heat transfer rate by attaching fins to the tubes? 

Fluid Flow: Bernoulli theorem applicability

Bernoulli theorem is based on the principle of conservation of total energy with fluid. When the flow is divided into 2 or more streams, then how can we apply the Bernoulli theorem?

we can apply continuity equation, if density remains constant then Q1= Q2 + Q3. for same area velocity will be in relation v1=v2+v3. but will v2 be equal to v3? 

The relation between v2 and v3 will be found out by applying Bernoulli theorem. The total energy in will be equal to sum of the total energy out with two streams, but the energy per unit mass/weight will be same at any point in the fluid. So Bernoulli theorem can be applied between any two points.  

Mechanical Operation: Filtration and Fluidization Questions

1.      A constant pressure filtration test gave data that can fit an expression dt/dV = 9.3 V + 8.5; (t in seconds, V in liters). If the resistance of the filter medium is assumed unaffected with pressure drop and the compressibility coefficient of the cake is 0.3, what will be the time taken for the collection of 3.5 liters of filtrate at a filtration pressure twice that used in the test.     

2.      A pressure filter is operated in the constant rate mode to yield 10 m³ in the first ten minute, as the pressure increases from zero. In the next 20 minutes the filtration was continued at constant pressure, after which it was stopped. Assume filter medium resistance is negligible and the cake is incompressible.

a) Estimate the total volume of filtration obtained.

           b) Determine washing time if the volume of wash liquid equals the volume of filtrate obtained.

3.      Solid particles having a size of 0.12 mm, sphericity 0.88 and a density of 1000 kg/m³ are to be fluidized using air at 2 atm abs and 25°C. The voidage at minimum fluidizing conditions is 0.42. The cross section of the empty bed is 0.3 m² and the bed contains 300 kg of solid. Take viscosity of air 0.0185 cP.

a) Calculate the pressure drop across the bed.

b) Calculate the minimum fluidization velocity using Ergun’s equation for calculating pressure drop.                                  

   4.    A packed bed is composed of cylinders having a diameter of 0.02 m and height = 1.5 Diameter.           The density of the packed bed is 980 kg/m³ and the density of the solid cylinder is 1500 kg/m³.           Calculate the porosity of the bed, effective diameter and sphericity of the particle.

Chemical Reaction Engineering: CSTR vs PFR

To carry out reaction, there are two kinds of continuous reactors used: CSTR and PFR. In CSTR the concentration remains constant throughout the reactor which is equal to outlet concentration, while in PFR the concentration changes along the length of reactor. The rate of reaction depends on the concentration of the reactant for a non zero order reaction. Therefore,  the rate of reaction in CSTR remains constant corresponding to out concentration of the reactant, but the rate of reaction decreases along the length of reactor in PFR.

The shaded area corresponds to the volume of reactor required to carry out reaction. So, if the rate of reaction decreases as the concentration decreases, that means (1/-rA) increases, the rate of reaction in PFR is high intially and decreases along the length of reactor. So it can be seen that volume in case of PFR is less than that required for CSTR.
The volume required to achieve a specified conversion for a positive order reaction is less when we connect CSTRs in series than a single CSTR of volume equal to the sum of the volume of CSTRs connected in series. this is because of the increased rate of reaction in small CSTR. while in PFR the volume reamains same whether we use a single PFR or PFRs connected in series.

Mechanical Operation: Agitation and Mixing

Agitation is used to maintain homogeneity in the system while mixing is used to mix two of more phases in one phase. if we have calcium carbonate and water, initially we have 2 phases, as we start mixing it after some time it will form slurry and this slurry has to be agitated to make its concentration uniform. One more example of agitation is related to curd, when we agitate curd, ghee will come over and the rest yogurt (lassi) will remain below.

For agitation we can use Impellers which are categories in 3: Propeller, Turbine and High efficiency impellers.

Propellers produce axial flow like marine propeller, turbine produce generally radial but also axial like mixture grinder in home and improved of turbine is high efficiency impeller which reduces the power consumption.