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Q1: Module Code: MECH267001 SECTION A (50%) ● : Section A and Section B. 1. The final treatment of a novel polymer material requires holding the material above a temperature of 100°C for 5 minutes. This is achieved by suspending the polymer rod in a moving airstream that has a free air temperature of 150°C. The rod is held vertically, with the air stream moving horizontally. There are two sections The air velocity is 10m/s. The polymer rod has a diameter of 5cm and a length of 2m. Physical properties are shown in the table below. Material Air Air Property Density Specific heat capacity Polymer Thermal conductivity Polymer Specific heat capacity Polymer Density a) Sketch a suitable arrangement including a heating element. Value 1.16 kg/m³ 1006 J/kgK 11.0 W/mK 1200 J/kgK 1500 kg/m³ [3 marks] b) Using a value of the heat transfer coefficient of 80 W/m°K, and taking care to justify the approach you adopt, calculate the total time required to heat- treat the sample. i. ii. [6 marks] c) Further study of the novel polymer suggests that the polymer should remain below a temperature of 135°C to minimise reduction in the structural strength of the polymer. Demonstrate whether this criterion is met or not. [6 marks] d) One of the engineering team working with you on this project proposes a reduction in the heated free air temperature to 110°C to save energy. Assess this proposal in terms of: Page 2 of 15 The total cycle time for treatment of one rod The relative energy cost when compared to the original condition of using heated air at 150°C. Note that the air is heated from an ambient temperature of 20°C and assume all properties of the gas (except the free air temperature) remain constant. Consequently, provide an informed response to the engineer's suggestion. [10 marks] Ref: ME20214G74-2 Turn the page over Module Code: MECH267001 2. Biogas is produced through anaerobic digestion of waste food. It has a composition of 80% methane and 20% carbon dioxide (by volume). The biogas is burned stoichiometrically in air (of composition 21% oxygen and 79% nitrogen by volume) with the flame used to heat a tube containing flowing water. The biogas has an initial temperature of 25°C and the combustion gases exit from the burner at 102°C. a) Write a stoichiometric equation for the combustion of methane in air, and then adapt it for burning the biogas in air, assuming products are carbon dioxide, water, nitrogen only. [5 marks] b) Calculate the mass flowrate of air for the complete combustion of 1 kg/s of biogas. Molecular weights of appropriate elements and compounds can be found on page 9. [5 marks] c) From considering the combustion of the biogas, show that an energy transfer takes place of 35.5 kJ per kg of biogas that is burned. [5 marks] d) After heating, in the burner, the hot water passes through a shell and tube heat exchanger and is used to heat an oil flow. The water from the shell and tube heat exchanger passes directly back to the burner at 20°C. The flowrate of biogas into the combustor is 50 kg/s. Water enters the burner with a flow rate of 7kg/s at a temperature of 20˚C. Oil enters the shell and tube heat exchanger at a flow rate of 37.5 kg/s at a temperature of -5°C. i. ii. Sketch the arrangement Calculate the surface area of the heat exchanger, given an overall heat transfer coefficient of 750 W/m² K Take heat capacities as water 4.2 kJ/kgK oil 1.6 kJ/kgK Page 3 of 15 [10 marks] Ref: ME20214G74-2 Turn the page over Module Code: MECH267001 SECTION B (50%) Water with a density of 1000 kg/m³ and dynamic viscosity of 1.0 x 10-³ Pa.s flows under gravity from a reservoir through a galvanized iron pipe with an equivalent roughness of 0.15mm at a flow rate of 600 litres per minute into the local atmosphere. The flow path comprises a sharp edged entrance from the reservoir into the pipe (loss factor (K₁) of 0.5, based on average outlet velocity), a 4m horizontal length of the galvanized pipe of 80mm internal diameter, a fully open gate valve (KL = 0.15, based on average inlet velocity) and a 6m horizontal length of the galvanised pipe of 40mm internal diameter. There is no fitting or restriction at the outlet of the pipe into the local atmosphere and so no additional minor head loss. The liquid surface of the reservoir is exposed to the local atmosphere. a) 3. Sketch the system and calculate the mean velocity and the Reynolds number of the flow in the two different pipe sections and state whether the flow is laminar or turbulent in each. [6 marks] Determine the height of water in the reservoir required above the sharp edged entrance into the pipe to achieve the required flow rate. Note, the major and minor head losses can be summed in this flow path, like resistors in series, and the general equation for energy conservation in pipes compares the pressures at the inlet and outlet of the system only. [10 marks] c) The gate valve is replaced by a fully open globe valve (K₁ = 10, based on average inlet velocity). Determine the change in the height of water in the reservoir required above the sharp edged entrance into the pipe to achieve the required flow rate. b) d) Provide an explanation for the result obtained in part c). Page 4 of 15 [4 marks] [5 marks] Ref: ME20214G74-2 Turn the page over Module Code: MECH267001 4. A new design of telecommunications tower is modelled as a 5m diameter perfectly smooth sphere on top of a vertical perfectly smooth cylinder, 30m high and 2m diameter. It has to withstand an aerodynamic force imposed by a 100 km/h wind. For air take the density to be 1.20 kg/m³ and the kinematic viscosity to be 1.5 x 10-5 m²/s. a) b) c) d) Estimate at 100km/h the aerodynamic drag force acting on the sphere. [7 marks] Estimate at 100km/h the aerodynamic drag force acting on the cylinder. [7 marks] Estimate the bending moment at the base of the tower. [5 marks] Discuss why these results should only be regarded as an estimate of the influence of drag on the real tower. Page 5 of 15 [6 marks] Ref: ME20214G74-2 Turn the page over Module Code: MECH267001 Biot number, Bi = Nusselt number, Nux Prandtl number, Pr = Composite cylinders α where v is kinematic viscosity Stefan-Boltzmann constant, o= 56.7 x 10 kWm -12 n-² K-4 Newton's Law of Cooling Composite plain walls One dimensional heat transfer Fourier's Law Tt - To To - Too hv KA = = exp V Rex hx k Rex ReL Page 6 of 15 FORMULA SHEET Heat Transfer A - [ht] = exp Forced Convection over a flat plate ≤500 000 Nux > 500 000 Nux = 500 000 NUL Thermal diffusivity, a = Transient heat transfer: Lumped heat capacity system (Bi < 0.1) Stanton number, = = Grashof number, G₁ where t = is the time constant of the system. cpV hA Q = ġA = −kA Heat diffusion equation in cartesian coordinates k ə 1/2 (²017) = ( ² ( ² ) + 2, (^²7) (二)={ (x + ²₁ (^ ²) + ²/₂ (^²} + a₂ (KZT) k k ġg ду ду, дz дz. St = where v is kinematic viscosity No. of transfer units, NTU dT dx • (-/-) Q = -hA(T∞ - Tw) (Tb - Ta) {Σ (A) + Σ (4)} = 0.332 Pr0.333 Re0.5 0.0296 Pr0.333 Re0.8 0.037 Pr0.333 Re8 k pcp h pcpu gβ∆Td3 v² (Tb - Ta) (In(ro/ri)` {Σ (²n (7/²)) + Σ (1/²/A)} 2πlk = = UA Cmin Nu Re Pr Turn the page overSee Answer
Q2:Q2 (20 pts): A smooth transition section connects two rectangular flat channels. The upstream channel has a width of 5.0 ft and a water depth of 2 ft. If the flow rate in the channel is 30 cfs: a) Determine the minimum width the channel can have in section 2 so that conditions upstream remain unchanged. Neglect head losses. b) If the channel width in the downstream conditions is 2 ft, show the change in upstream conditions graphically. Neglect head losses.See Answer
Q3:PROBLEM 1 Problem 6.5. Water at room temperature flows through a 5 cm-diameter smooth tube at Re, = 20,000. a) Calculate C,,U, and R. b) Using van Driest's expression for mixing length, calculate the eddy diffusivity E at y = 10 and y = R/3, where y is the distance from the wall.See Answer
Q4:PROBLEM 3 Problem 7.9. The fuel rods in an experimental nuclear reactor are arranged in a rectangular pattern, as shown in the Fig. P7.9. The fuel rod diameter is 1.14 cm, and the pitch is Pitch=1.65 cm. The rod bundle is 3.66 m tall. Assume that the core operates at 6.9 MPa, and the water temperature at inlet is 544 K. Heat flux on the fuel rod surface is uniform and equal to 6.31×10¹ W/m². The flow is assumed to be 1-D, and the mass flow rate through a unit cell is 0.15 kg/s. Estimate the fuel rod surface temperature at x = 10 cm, x= 25 cm, and x = 50 cm locations. Flow -|| - Channel Fuel Rods PitchSee Answer
Q5:PROBLEM 4 Problem 7.21. Atmospheric water at 300 K flows through a 0.5 cm inner diameter tube that is 12 cm long. The velocity at inlet can be assumed to be uniform, and equal to 2.5 m/s. The surface temperature is 350 K. a) Find the heat transfer coefficient at the exit. b) Suppose that the mean surface roughness was 46 um. Estimate the heat transfer coefficient at the exit. c) For part a, calculate the time-average water temperature at exit on the centerline of the tube. Hint: The Fanning friction factor C, can be found from the correlation of Churchill (1977a) for the transition flow regime.See Answer
Q6:PROBLEM S Problem 7.27. Liquefied petroleum gas (LPG) (assumed to be pure propane, for simplicity) in a partially insulated horizontal tube at a pressure of 7 bars. The tube diameter is 4 cm. The mixture mass flux is 197 kg/m³.s. Assume fully- developed flow, and thermally-developed conditions. At a location where the propane bulk temperature is equal to 120 K, the wall surface temperature is equal to 135 K. a) Find the frictional pressure gradient and convection heat transfer coefficient, using appropriate correlations of your own choice. Assume that the tube is hydraulically smooth. b) Repeat the calculations in Part a, this time assuming that the tube is coiled into a vertically-oriented helical configuration with R=25 cm and 1=10 cm. In part a, repeat the calculations this time assuming that the surface has a characteristic roughness of 50 μm.See Answer
Q7:Problem 1: Thermodynamic Derivations Expand the following terms into expressions with variables that can be measured experimentally such as pressure, temperature, volume, Cv, and Cp. Two of the below expressions will result with S in the final expression: A) (@A/OS)P B) (@A/OS)T C) (@G/OP)sSee Answer
Q8:Problem 2: Pump calculations A liquid has a molar volume of 0.2 L/mol at 400 K and 4 bar. This liquid is compressed with a pump that operates at steady-state and adiabatically. The liquid enters the pump at a rate of 3 mol/s, at a temperature of 400 K and pressure of 4 bar and exits at a pressure of 20 bar. The liquid has the following properties which can be used (if needed) in the solution: Coefficient of thermal expansion, ay = 2 x 10³ K-¹ • Isothermal compressibility factor, K7= 4 x 10¹5 bar¹ Cp = C₁ = 30 J/mol-K Find the following: A) Work done by the pump B) Temperature of the liquid leaving the pump C) Molar volume of the liquid leaving the pumpSee Answer
Q9:Question 2 You are to design a finned heat sink for a computer mother board, which comprises of vertically mounted rectangular parallel plates on a porous base, as shown in figure 2. The height of each fin is 40 mm, and the temperature of the fins are constant at 80 °C. The heat from the fins induces an air flow (due to free convection) from the surroundings through the porous base and through the parallel plates, where they exit at the top. The surrounding temperature is constant at 80 °C. The base is square, with a width of 50 mm. Neglect heat transfer Air flow (via free convection) Fins Neglect heat transfer 50 mm Porous base Neglect heat transfer Figure 2: Free convection in between parallel plates. 40 mm Neglecting the heat transfer from the bottom of the base, and through the extreme left and right side of the fins, i.e., the only heat transfer is due to the convection in between the parallel plates (as shown in figure 2), calculate the minimum number of fins (plates) required if the required heat transfer rate is 18 W. [10 marks] You may assume that the thickness of the fins is negligible.See Answer
Q10:Question 3 A large horizontal brass plate is used to boil water at atmospheric pressure. What is the maximum permitted temperature of the plate so that it does not exceed the critical heat flux? [8 marks]See Answer
Q11:The chocolate peanut factory One worldwide-recognised brand in the field of agroindustry manufactures the industrial chocolate peanut snack W&W's in three steps. Initially, the peanuts are sieved in order to remove broken grains (B); then, the unbroken peanuts (P) are driven to the next unit where are first roasted and then covered with chocolate (C). Following, the third step consists of a crusting operation, where each piece is covered with a layer of a sugar (S) - water (W) mixture and then is dried. The scheme below shows the process. Qkg/h 0.590 kg P/kg 0.410 kg B/kg Sieving Qkg Bih Qkg P/h Qkg C/h Roasting & Coating Qkg/h w.kg C/kg w kg P/kg Qkg/h w.kg Cikg wkg P/kg Qkg/h 0.660 kg S/kg 0.340 kg W/kg Crusting Qkg W/h Qkg/h 0.290 kg C/kg 0.430 kg P/kg 0.280 kg S/kg The stream Qe is made of low quality pieces that cannot be commercialised so it keeps the same composition as the product sent to crusting unit. In average, there are 10 kg of satisfactorily coated peanuts per each kg of rejected peanuts. If the production of commercial W&W's is stated to be 1000.0 kg/h, find the mass flowrate and compositions of the rest of streams, this is, all feeds (Q₁, Q4 and Q₂) and exits (Q3, Q6, Qs and Q9). Assume that the process operates in steady state.See Answer
Q12:EML 4706 - Two water tanks, A and B, are 1.5km apart and you have been tasked with connecting the two reservoirs together so you can transfer water from one reservoir to another. The two reservoirs are open to atmosphere and the surface of the two reservoirs is at the same level. Your goal is to achieve a volumetric flow rate of at least 1 m³/s using a pump that outputs 20kW of power. Select a pipe material and size that would be appropriate for this application. You might have to research how to include power in a conservation of energy equation (covered in previous courses). Make any assumptions you feel are necessary. You do not need to consider minor losses if you choose not to. 1 PUMP BSee Answer
Q13:#Question 2 (20%) Construct the Cp vs. T graphs for hydrogen and ammonia, then compare the quantities of heat obtained in an isobaric process that operates between 300 and 600 K. Which gas has a larger quantity of heat? Comment on the difference. The Excel data template for H₂ is provided in "Q2-Cp_vs_T".See Answer
Q14: Experiment 2 - Energy Balance and Overall Efficiency Objective To perform an energy balance across a Shell and Tube Heat Exchanger and calculate the Overall Efficiency at different fluid flowrates. MCE 431 - Thermal Science Lab Method By measuring the changes in temperature of the two separate fluid streams in a shell and tube heat exchanger and calculating the heat energy transferred to/from each stream to determine the Overall Efficiency. Equipment Required As Exercise A. Equipment set-up If using the results from Exercise A then the equipment is not required. If previous results are not available refer to the Set-up and Procedure sections of Exercise A. Theory/Background Note: For this demonstration the heat exchanger is configured for countercurrent flow (the two fluid streams flowing in opposite directions). Therefore: ahot Mass flowrate (qm)= Volume flowrate (qv) x Density of fluid (p) (kg/s) Heat power (Q) = Mass flowrate (qm) x specific heat (Cp) x change in temperature (AT) (W) Overall Efficiency T41 Heat power emitted from hot fluid Qe = qmn. Cph (T1 - T2) (W) Heat power absorbed by cold fluid Qa = qmc. Cpc (T4 - T3) (W) Heat power lost (or gained) Q₁ = Qe - Qa (W) M = T3 ↑ a cold x 100 (%) 4 MCE 431- Thermal Science Lab Theoretically Qe and Qa should be equal. In practice these differ due to heat losses or gains to/from the environment. Note: In this exercise the cold fluid is circulated through the outer shell, if the average cold fluid temperature is above the ambient air temperature then heat will be lost to the surroundings resulting in n<100%. If the average cold fluid temperature is below the ambient temperature, then heat will be gained resulting in n>100%. Procedure Use the results obtained from Exercise A. Results and Calculations The software records all sensor outputs and also calculates several derived figures, and presents the recorded data in tabular form. The following columns are relevant to this exercise, and are suggested as suitable column headings if recording values manually: Hot fluid volume flowrate Hot fluid inlet temperature Hot fluid outlet temperature Cold fluid volume flowrate qVhot (m³/s) Multiply Fhot (litres/min) by 1.667x10-5 T1 Specific heat of hot fluid Specific heat of cold fluid Density of hot fluid Density of cold fluid T2 qVcold Cold fluid inlet temperature T3 Cold fluid outlet temperature T4 You should also estimate and record the experimental errors for these measurements. For each set of readings, the software calculates the average hot fluid temperature (from T1 and T2) and the average cold fluid temperature (from T3 and T4) and then automatically provides values for the following variables. If recording data manually, calculate these values and obtain the variables from the Reference Tables section 14.3: Cph Cpc Ph Po (°C) (°C) (m³/s) Multiply Foold (litres/min) by 1.667x10-5 5 (°C) (°C) kJ/kg°K (From table 1) kJ/kg°K (From table 1) kg/m³ (From table 2) kg/m³ (From table 2) MCE 431 - Thermal Science Lab For each set of readings, the relevant derived results are calculated and presented with the following headings: Mass flowrate (hot fluid) Mass flowrate (cold fluid) Heat power emitted Heat power absorbed Heat power lost Overall Efficiency qmn qmc Qa 6 Q4 M (kg/s) (kg/s) These values should be calculated manually if not using the software. A graph may be plotted of the results. The software graph facility may be used for this. Estimate the cumulative influence of the experimental errors on your calculated values for Qe, Qa, Qf and n. Conclusions Explain any difference between Qe and Qa in your results. Comment on the effects of the increase in the cold fluid flowrate. Exercise C should be carried out on completion of this exercise. (W) (W) (%) Compare the heat power emitted from/absorbed by the two fluid streams at the different flowrates.See Answer
Q15:Let us consider a fully-developed laminar flow between infinitely-large parallel plates with the stream wise pressure gradient (laminar Poiseuille flow). The pressure gradient in the stream wise (x) direction is given by dp/dx and constant. The gap between the top and bottom walls is H. The bottom and top walls are fixed. For simplicity, the momentum accommodation factor can be assumed to be v1.0. Choose the origin of the coordinate system at the bottom wall (y-H corresponds to the top wall). Answer the following questions. 1) Derive the velocity profile u-u(y) for the wall boundary condition with the non-slip flow. 2) Compute the volume flow rate for the non-slip flow QNs. 3) Determine the optimum parameter b in the second-order slip flow boundary condition proposed by Karniadakis & Beskok. 4) Derive the velocity profile u-u(y) for the second-order slip flow boundary condition proposed by Karniadakis & Beskok with the optimum parameter b determined in 3). 5) For large Knudsen numbers, the fluid viscosity u can be modeled as μ = μ o/(1+9.658Kn1-159), where pois the viscosity in the ordinary scale. Under this assumption, plot a graph for QSL2/QNs at 0<Kn<10, where QSL2 is the volume flow rate with the 2nd-order slip flow boundary condition. Ref.: A. Beskok, and G. Karniadakis, "REPORT: A MODEL FOR FLOWS IN CHANNELS, PIPES, AND DUCTS AT MICRO AND NANO SCALES," Microscale Thermophysical Engineering, Vol. 3, pp. 43-77 (1999).See Answer
Q16:8) If the pressure, Px, is 75 kPa, find the pressure, Py, in the adjoining water pipe.See Answer
Q17:9) Determine the required property for water. Interpolate as needed.See Answer
Q18:10) A 2500 L rigid tank contains 50 kg of air at a temperature of 50°C. Heat is added until the pressure is doubled. What is the final temperature inside the tank?See Answer
Q19:11) 3 kg or steam initially at 375 kPa and 141.3°C is contained in a piston-cylinder with a diameter of 88 cm. A spring, that is attached to the piston cylinder and initially at equilibrium at a piston height of 160 cm from the bottom, has a spring constant of 128,450N/m. If the piston raises to double its initial height, find the heat input into the steam.See Answer
Q20:The interior space of a building in winter is to be heated by a heat pump to maintain the internal temperature at 22.0°C. The 55.0 kW building heat load is to be provided by a heat pump that absorbs heat from a geothermal water source at 18.0°C. The water from the geothermal water source enters the evaporator heat exchanger at 18.0°C and exits at 11.00°C. The heat pump utilises refrigerant R-134a as the working fluid and operates with a discharge pressure of 1.40 MPa and a suction pressure of 320 kPa. Modelling the heat pump cycle as an actual vapour compression cycle (AVCC), with an evaporator exit temperature of 10.00°C and condenser entry and exit temperatures of 80°C and 30°C respectively, determine: What is the COP of this AVCC system? b. Determine mass flowrate of refrigerant (in kg/s). Find the required volumetric flowrate of water from the geothermal source (in L/min) d. Determine the isentropic efficiency of the compressor (assume the compressor to be adiabatic). e. If the heat pump were replaced by an ideal Carnot heat pump what would be the required power input to the heat pump? (Assume the heat load is still 55.0 kW).See Answer

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