please answer this question in 35 minutes, please just to the point , i will surely upvote your efforts it is a transpor
Posted: Mon May 09, 2022 1:48 pm
please answer this question in 35 minutes, please just to the
point , i will surely upvote your efforts
it is a transport phenomenon task , there are
eight steps in it , just write these eight steps
for this problem
8-STEP METHOD: Step 1. Title the Problem Step 2. Drom the diagram step 3: State assumptions Step 4. state initial conditions & boundry Conditions step 5. Set up enery balance equations) Step & Math Step 5: Check Unit must be canceled boundary Check Step 8: Implications
A packed bed of hot spherical particles is to be cooled by passing a cooling fluid with known entering temperature Toz through the bed. We will assume steady state behavior and take the known temperature of the spheres, To, to be maintained constant throughout the bed of particles. S4 To, hot particles Toi cooling 2=0 Si fluid Az SzZ=L You are to solve the integral energy balance equation, as given in the attached sheet, to obtain the bulk fluid temperature To as a function of z, on the fluid side for beginning with a Az segment of this system as shown above. You must follow steps 1-7 of the 8-step method. There is no 8th step for this part of the exam. We will neglect macro kinetic and macro potential energy terms, assume constant physical properties, and neglect shaft work. You should combine the internal energy and pressure terms into an enthalpy term as we did in the energy exchanger problem [H(hat)=U(hat) + P/p]. Then express the convective enthalpy change with z in terms of the heat capacity at constant pressure and bulk fluid temperature change as we did in the energy exchanger problem (dH(hat)/dz = Cp(hat) dTb/dz). In addition, the fluid velocity or mass flow rate will be constant throughout the tube. (You do not have to prove this.) Note that the surfaces Si and S2 are equal and represent the constant, void area as in the packed bed reactor problem. For this problem, we will neglect any energy transfer along the walls (S3) and only consider energy transfer at the spherical particle surfaces, S4. On S4 we will define an energy transfer coefficient according to Sq.nds along S4 = a S az hoc (To-T.) where To(z) is the bulk fluid temperature at any z and, again, To is the constant (known) uniform particle temperature in the bed. The constant "a" is the interfacial area per empty bed volume
from some correlating equation. ned known. hier is the local energy transfer coefficient that is also assumed known Hint: This problem is nearly identical and simpler than the integral energy balance in tube flow - only the surfaces for energy flux are different and we are not considering any conduction problem in the solid phase. You should obtain a simple exponential increase of bulk fluid temperature with respect to z. This is a relatively simple problem - don't make it hard! 2. (20%) use a pseudo steady state approximation. In this approach, we can use the solid phase Now, in actual application the temperature of the particles will diminish with time, but we can the average particle temperature in the bed as a function of time To(t). This is similar to what unsteady state integral energy balance over the entire bed of particles to get an equation for we did for the home diffusion experiment and, thus, for the surface energy flux on the solid side we would use the same flux expression as part 1. but integrate it over the entire bed: q.na S dz along S4 = ſas a S hloc [To - Tb(z)] dz 0 Note that n points into the fluid for this solid side balance. Write the simple ordinary differential equation for To(t) that would need to be solved; since the solid phase is stationary there are only two terms in the integral energy balance for this phase: the unsteady state term involving Utot and the energy flux term along S4. Express the total internal energy of the particles as a function of time in terms of the heat capacity at constant volume and temperature: dUtot/dt = C, dTo/dt to obtain your final equation. You do not have to use the 8-step method here; just write down the two relevant terms from the integral summary sheet and cast these into an ordinary differential equation for To(t); you will need your Tb(z) solution from Part 1 and your math integral tables. There is no 8-step method required for this part of the exam! Do not solve the equation or check units, no assumptions box, etc.; just show me the ordinary differential equation that you would solve! 3. (10%) It is proposed to use water as the cooling fluid in the above process, and simply discard the outlet water stream into a nearby river. What potential environmental hazards exist for this proposal? What alternatives to environmental release would you propose?
point , i will surely upvote your efforts
it is a transport phenomenon task , there are
eight steps in it , just write these eight steps
for this problem
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A packed bed of hot spherical particles is to be cooled by passing a cooling fluid with known entering temperature Toz through the bed. We will assume steady state behavior and take the known temperature of the spheres, To, to be maintained constant throughout the bed of particles. S4 To, hot particles Toi cooling 2=0 Si fluid Az SzZ=L You are to solve the integral energy balance equation, as given in the attached sheet, to obtain the bulk fluid temperature To as a function of z, on the fluid side for beginning with a Az segment of this system as shown above. You must follow steps 1-7 of the 8-step method. There is no 8th step for this part of the exam. We will neglect macro kinetic and macro potential energy terms, assume constant physical properties, and neglect shaft work. You should combine the internal energy and pressure terms into an enthalpy term as we did in the energy exchanger problem [H(hat)=U(hat) + P/p]. Then express the convective enthalpy change with z in terms of the heat capacity at constant pressure and bulk fluid temperature change as we did in the energy exchanger problem (dH(hat)/dz = Cp(hat) dTb/dz). In addition, the fluid velocity or mass flow rate will be constant throughout the tube. (You do not have to prove this.) Note that the surfaces Si and S2 are equal and represent the constant, void area as in the packed bed reactor problem. For this problem, we will neglect any energy transfer along the walls (S3) and only consider energy transfer at the spherical particle surfaces, S4. On S4 we will define an energy transfer coefficient according to Sq.nds along S4 = a S az hoc (To-T.) where To(z) is the bulk fluid temperature at any z and, again, To is the constant (known) uniform particle temperature in the bed. The constant "a" is the interfacial area per empty bed volume
from some correlating equation. ned known. hier is the local energy transfer coefficient that is also assumed known Hint: This problem is nearly identical and simpler than the integral energy balance in tube flow - only the surfaces for energy flux are different and we are not considering any conduction problem in the solid phase. You should obtain a simple exponential increase of bulk fluid temperature with respect to z. This is a relatively simple problem - don't make it hard! 2. (20%) use a pseudo steady state approximation. In this approach, we can use the solid phase Now, in actual application the temperature of the particles will diminish with time, but we can the average particle temperature in the bed as a function of time To(t). This is similar to what unsteady state integral energy balance over the entire bed of particles to get an equation for we did for the home diffusion experiment and, thus, for the surface energy flux on the solid side we would use the same flux expression as part 1. but integrate it over the entire bed: q.na S dz along S4 = ſas a S hloc [To - Tb(z)] dz 0 Note that n points into the fluid for this solid side balance. Write the simple ordinary differential equation for To(t) that would need to be solved; since the solid phase is stationary there are only two terms in the integral energy balance for this phase: the unsteady state term involving Utot and the energy flux term along S4. Express the total internal energy of the particles as a function of time in terms of the heat capacity at constant volume and temperature: dUtot/dt = C, dTo/dt to obtain your final equation. You do not have to use the 8-step method here; just write down the two relevant terms from the integral summary sheet and cast these into an ordinary differential equation for To(t); you will need your Tb(z) solution from Part 1 and your math integral tables. There is no 8-step method required for this part of the exam! Do not solve the equation or check units, no assumptions box, etc.; just show me the ordinary differential equation that you would solve! 3. (10%) It is proposed to use water as the cooling fluid in the above process, and simply discard the outlet water stream into a nearby river. What potential environmental hazards exist for this proposal? What alternatives to environmental release would you propose?