Can you help with this project for Heat and Mass Transfer?
Microsoft Word - Project 1 Corporate Headquarters Process Engineering Group One Algae Way Somewhereville, NJ 08000 MEMORANDUM To: From: Dr. Donald Sebastian, VP R&D Date: March 24, 2022 RE: Scale to Market Project Welcome to the process engineering team. I hope you are ready to hit the ground running. The R&D team has completed the lab work for our new zero-carbon footprint, regenerative power plant that uses waste heat from condensed turbine steam and CO2 recovered from the combustion stack gases to feed a biomass reactor. The reactor grows algae that is later converted to biodiesel to fuel the power plant generation units. Now it is time to scale from batch glassware to continuous pilot plant operations. The heart of the system is a tubular photo-bioreactor (PBR). Solar energy drives growth of an algae inoculant that metabolizes the sequestrated CO2 during photosynthesis to grow a critical biomass for biodiesel production. The R&D scientists have determined that the algae must be maintained between 25C and 12C to ensure adequate growth rates, and the plant must operate under average worst-case winter conditions listed in the accompanying documentation. The flow in the PBR cannot be laminar or the tube walls will foul and block sunlight to the core, while radial temperature gradients in the PBR could reduce efficiency. All relevant supporting documents are on the corporate CANVAS server. The suggested outline for your work follows: 1. Use your knowledge of heat transfer fundamentals to develop a design equation for the axial profile of cup average temperature in the PBR tube as a function of a single dimensionless group, St(L/l). 2. Select a PBR diameter from one of the standard sizes. 3. Use the required residence time to find the length of the PBR. 4. Use your knowledge of fluid dynamics to establish the flow regime internal to the PBR– laminar, transitional, turbulent. If ReD is laminar, reject and go back to step 2 and repeat with a new diameter. 5. Use your knowledge of heat transfer fundamentals to select an appropriate Nu correlation to determine the tube side heat transfer coefficient. 6. Use your knowledge of fluid dynamics to establish the flow regime external to the PBR– laminar, transitional, turbulent. 7. Use your knowledge of heat transfer fundamentals to select an appropriate Nu correlation to determine the shell side (external) heat transfer coefficient. 8. Use your relationship from (1) to compute the exit, cup average temperature. 9. If the cup average is less than 12C, reject and go back to step 2. 10. Compute the cost of the PBR using cost data in the tables. If this is not the lowest cost design, reject and go back to step 2. 11. Use your knowledge of scaling and similarity to size a PBR for the scale up to the production facility operating at 10 time the throughput of the pilot plant. Prepare a report that details all assumptions and calculations supporting your recommendation. We need this done before the investor meeting on April 15, so please complete all tasks and submit your report to me by April 13. Corporate R&D Process Research Laboratories One Algae Way Somewhereville, NJ 08000 Process Flow Sheet Photo Bioreactor PBR Feed Mix Algae Innoculant Power Plant Steam Condensate Power Plant Stack Gas To Biodeisel Reactor Corporate R&D Materials Characterization Laboratories One Progress Way Somewhereville, NJ 08000 Material Property and Operating Data Algae Feedstream Density, {kg/m3} 1000 Viscosity, {Pa s} 0.001 Heat Capacity, Cp {J/kgK} 4184 Thermal Conductivity, k {W/mK} 0.598 Feed rate, �̇� {kg/s} 0.275 Batch Reactor Holding Time, ? {s} 5400 Feed temperature, TF {C} 25 Pilot Plant Ambient Air Density, {kg/m3} 1.225 Viscosity, {Pa s} 0.000018 Heat Capacity, Cp {J/kgK} 700 Thermal Conductivity, k {W/mK} 0.025 Avg. Wind Velocity, v {m/s} 2 Avg. Winter Low temperature, TA {C} 0 PMMA Acrylic Tubing Spec Sheet OD {mm} t {mm} L {mm} 50 2 2000 75 2 2000 100 3.3 2000 110 3.3 2000 120 3.3 2000 130 3.3 2000 140 3.3 2000 150 3.3 2000 160 3.5 2000 170 3.5 2000 180 3.5 2000 190 3.5 2000 200 3.5 2000 220 3.7 2000 240 3.7 2000 250 3.7 2000 Technical Data PMMA Tubing Color Transparent Density 1.2 {g/cm3} Thermal Conductivity 0.214 {W/mK} Heat Defelection Temp 70 {C} Glass Trans Temp 100 {C} Coeff. Expan. 7x10-5 {m/m/K} Cost 1.20 {$/kg} 999B Hillock Ave. Middlesex, NJ 08846 Phone: 800-555-1212 www.polytrude.com Heat Transfer Characteristics of PMMA Tubing Axial Flow In smooth PMMA Tubing Nu = 3.66 Re <2000 =="" 3.66="" +="" 0.065="" 1="" +="" 0.40="">< 0.05="">< 2000="" nu="1.25" (="" 0.79="" ln(re)-="" 1.64)-2="" repr1/3="" 2000="">< re="">< 10,000="" nu="0.023" re4/5pr1/3="" re=""> 10,000 0.70 < pr=""><160 longitudinal="" flow="" over="" pmma="" tubing="" =="" 0.664??="" .="">< 5?10=""> 0.5 ?? = 0.037?? . ?? / 5?10 <>< 10="" 0.5=""><>< 60="" cross="" flow="" over="" pmma="" tubing="" nu="0.911" re0.385="" pr1/3="">< re=""><40 nu="0.683" re0.466="" pr1/3="">< re=""><4000 =="" 0.30="" +="" 0.62??="" [1="" +="" 0.4/??="" ]="" 1="" +="" (="" 282000="" )="" 4000=""><>< 40000 999b hillock ave. middlesex, nj 08846 phone: 800-555-1212 www.polytrude.com 40000="" 999b="" hillock="" ave.="" middlesex,="" nj="" 08846="" phone:="" 800-555-1212="">