Help please, need to understand!! Bacteria are initially held within a bioreacto

Question

Help please, need to understand!!

Bacteria are initially held within a bioreactor of volume V and a concentration C0 (bacteria per unit volume). The bacteria metabolically generate heat at a volumetric rate of qgen = khearC, where kheat is a constant (heat generation rate per bacterium) and C is the bacteria concentration in the reactor. The bioreactor has one inlet and one outlet, and a mass flow rate m of clean water flows in, while an identical mass flow rate flows out (laden with bacteria), (a.) Obtain an expression for the concentration of bacteria in the reactor as a function of time, (b.) Assuming the reactor is well insulated from its surroundings and no work is done in the reactor, develop a differential equation to describe the rate of change of the temperature in the bioreactor as a function of time, assuming it has a specific heat of cp and density rho.

Explanation / Answer

Given :

initial Concentration of bacteria = C0 (bacteria/volume);

volume flow rate of water = d / m' where d is the density of water;

sol for vol V a concentration of bacteria C is removed ;

at C0 volume = V

at any C volume = d/m'

C0/C = V/(d/m');

C0/C = m' * V/d

C = C0 * d * dt /( m * V)

m = d*v ;

C = C0 dt/V2;

b. Let dT be the change in temperature of the bio reactor

the

m' Cp dT = k C;

m' Cp dT = k C0 dT/V2;

from the above expression;

so we get

dT/dt = k C0/(m' Cp V2);

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.