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Q1: 1. A 2-D, transient heat conduction problem in a rectangular body, illustrated by the figurebelow, is to be investigated using a numerical solution. There is no heat generation presentin this dimensionless constant property problem with = 1.0. The plate has a width W = 2.0and a height H = 1.0. It is insulated on all sides except over one-half of the top side whichhas a constant heat addition flux q₁ = 1.0. The initial condition is T(x,y,0) = 0. a. Show the describing PDE and the boundary conditions for the problem analytically. b. The body is to be divided into a number of elements. Construct a figure for the problem showing a set of elements with a finite number of ºx's and ºy's (but °x need not equalºy) and label the nodes. Place nodes on the sides and corners. Specify the actual number of nodes and the resulting number of algebraic equations that you recommend for the numerical solution. c. Use appropriate finite-difference approximations (i.e., central, forward, or backward differences) for the spatial derivatives to derive finite-difference equations for: i.a typical interior node. ii. an edge node that includes heating. d. Employ a forward-difference approximation for the time derivative. Chose an explicitor implicit scheme for the solution; note any stability restriction(s).See Answer
Q2:3D Model The scope includes making a 3D model as per the below sketch and heat exchanger inlet nozzle along with cavity before the heat exchanger tubes shall be modelled. 881mm 10" Pipe Effect of position & Inclination angle of chemical injection quill Outlet 10 Elbow 10" X 8" Reducer 1/4" Quill Injection Ethyl Acetate 3363mm Injection Quill shall be as below; 8" Pipe Nozzle of heat exchanger and cavity inside heat exchanger before the tube shall be modelled Styrene Inlet Note: Dimensions are from Center of elbow to edge of nice Ethyl Acetate Inlet with 3 options 1. Quill dispersion Angle at 45deg. 2. Quill dispersion Angle at 60deg. 3. Quill dispersion Angle at 30deg. The Objective is to check which angle has maximum coverage of ethyl acetate at outlet/n3D Model The scope includes making a 3D model as per the below sketch and heat exchanger inlet nozzle along with cavity before the heat exchanger tubes shall be modelled. 881mm 10" Pipe Effect of position & Inclination angle of chemical injection quill Outlet 10 Elbow 10" X 8" Reducer 1/4" Quill Injection Ethyl Acetate 3363mm Injection Quill shall be as below; 8" Pipe Nozzle of heat exchanger and cavity inside heat exchanger before the tube shall be modelled Styrene Inlet Note: Dimensions are from Center of elbow to edge of nice Ethyl Acetate Inlet with 3 options 1. Quill dispersion Angle at 45deg. 2. Quill dispersion Angle at 60deg. 3. Quill dispersion Angle at 30deg. The Objective is to check which angle has maximum coverage of ethyl acetate at outlet/n3D Model The scope includes making a 3D model as per the below sketch and heat exchanger inlet nozzle along with cavity before the heat exchanger tubes shall be modelled. 881mm 10" Pipe Effect of position & Inclination angle of chemical injection quill Outlet 10 Elbow 10" X 8" Reducer 1/4" Quill Injection Ethyl Acetate 3363mm Injection Quill shall be as below; 8" Pipe Nozzle of heat exchanger and cavity inside heat exchanger before the tube shall be modelled Styrene Inlet Note: Dimensions are from Center of elbow to edge of nice Ethyl Acetate Inlet with 3 options 1. Quill dispersion Angle at 45deg. 2. Quill dispersion Angle at 60deg. 3. Quill dispersion Angle at 30deg. The Objective is to check which angle has maximum coverage of ethyl acetate at outlet/n3D Model The scope includes making a 3D model as per the below sketch and heat exchanger inlet nozzle along with cavity before the heat exchanger tubes shall be modelled. 881mm 10" Pipe Effect of position & Inclination angle of chemical injection quill Outlet 10 Elbow 10" X 8" Reducer 1/4" Quill Injection Ethyl Acetate 3363mm Injection Quill shall be as below; 8" Pipe Nozzle of heat exchanger and cavity inside heat exchanger before the tube shall be modelled Styrene Inlet Note: Dimensions are from Center of elbow to edge of nice Ethyl Acetate Inlet with 3 options 1. Quill dispersion Angle at 45deg. 2. Quill dispersion Angle at 60deg. 3. Quill dispersion Angle at 30deg. The Objective is to check which angle has maximum coverage of ethyl acetate at outletSee Answer
Q3:Project 2 Heat Transfer The glass in a single-glazed window of a house is to be replaced with a double-glazed unit. | Page 4 of 8 Figure 2. Example of double window (KLG Rutland) The air fills the gap between the double-glazed unit's panes, which offers negligible resistance to heat transfer resistances at interior glass surfaces. If the room temperature in the house is maintained at 20 °C and the outside air temperature is 0 °C, the rate of heat loss per unit area is 32.8 W m-². Design a double window for this room by determining the thickness of each glass and the area of the window and draw your window design in Solidworksor similar CAD software. You should provide the correct assumptions for your design. Please take all the air and glass properties from an online database (e.g https://www.engineeringtoolbox.com/).See Answer
Q4:General Presentation Report should include section headings, tables, figures, captions and referencing. Figures must be clear, all text readable (not too small) with a white background. The report requires a logical layout and flow. Each section should lead to the next in a logical fashion. Grammar, spelling, and engineering and mathematical notation should be used correctly. [Marks 10]See Answer
Q5:/n3-D Results: 3.1 3.2 3-D CED velocity and pressure fields: Describe the 3-D fields that the CER produces. Which flow phenomena can you observe in them. Link your observations to the graphs with Fig no, stating clearly where exactly the figure shows what. Qualitatively describe the flow behaviour, why is the flow in the simulation doing what you observe? Is this correct? Or should we see a different behaviour? If you spot any discrepancy, explain what you think causes it. Analysis of 3-D pressure drop data: Quantify the pressure drop predicted by the 3-D simulations. Compare to at least two of the experimental/heuristic formulae from the literature and the 2-D results. Use more for higher credit. Explain any discrepancies. Summary: Summarise the methods you have used to arrive at your results. What are the main results? Give a concise but complete summary of the main points of your discussion in 2.2 and 3.2. If you designed a pipe network, which method would you be propose to use to determine the pressure drop?See Answer
Q6: Prove that the 1-D heat conduction equation \frac{\partial T}{\partial t}=\alpha \frac{\partial^{2} T}{\partial x} is a parabolic equation.See Answer
Q7: Q3: Increase the inlet speed used in the previous question so that the Reynolds number becomes 5000, solve the problem again and provide new results. Before solving the problem initialize it,i.e. do not continue over the previous solution. Is there any unexpected behavior in this solution?If there is any, what is the cause of it? Provide the residual plot and discuss its behavior.See Answer
Q8: Q2: Grid convergence is required for all CFD analysis. When grid size is reduced gradually, certain critical parameter gradually reaches convergence. In the present study, the drag coefficient can betaken as the critical parameter. Reduce the mesh size and solve the problem again, until grid convergence is achieved. Before solving the problem initialize it, i.e. do not continue over the previous solution.See Answer
Q9: Q2 Consider the non-staggered tube bank arrangement as shown below. All the conditions are the same as that from periodic tube bank heat transfer tutorial except the geometry. The tube diameter's 1cm, You need: 1) identify a small region for the CFD simulation; 2) generate the appropriate geometry using ANSYS 3) generate the necessary mesh 4) follow the steps in the tutorial to perform CFD simulation of the heat transfer in a non-stagger tube bank 5) compare you results with that from the staggered tube bank and explain the difference in terms of heat transfer and pressure distribution around the cylinder. 6) show the pressure contours (show at least 3 rows and four columns of tube banks), 7) show the temperature contours 8) plot the streamlines 9) temperature and pressure variations along the vertical lines A-A and B-B See Answer
Q10: [10 pts.]Derive the second-order central difference approximation for the term du/ dy using Taylor's series.See Answer
Q11: Q4: run the case of Re=5000 using transient solver. Monitor the lift force or lift coefficient of the cylinder. Estimate the oscillation frequency of the flow from the profile of life force/coefficient and compare it with the data in literature. Experiments show that the frequency, f, of this periodic flow (in Hz) can be expressed in terms of a non-dimensional parameter known as the Strouhal number, defined as: S t=\frac{f D}{U_{\infty}} See Answer
Q12: a)Describe why departure functions are used to calculate changes in thermodynamic properties(4)under non-ideal conditions. (b)Butane gas undergoes a change of state from an initial condition of 2 MPa and 160°C to 3.5MPa and 227°C. Using departure functions and the thermodynamic data below calculate thechange in enthalpy and entropy.(12) \text { The heat capacity at constant pressure is } c_{\mathrm{p}}=9.487+0.3313 T-1.108 \times 10^{-4} T^{2}-2.822 \times 10^{-9} T^{3} \text { in } units of J kg1 K, where T is the temperature in kelvin. The enthalpic and entropicdeparture functions for butane are given by: \text { At } 2 \mathrm{MPa} \text { and } 160^{\circ} \mathrm{C}, h-h^{\mathrm{ig}}=-2.4263 \mathrm{~kJ} / \mathrm{mol} \text { and } s-s^{\mathrm{i} 8}=-3.9507 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \text { At } 3.5 \mathrm{MPa} \text { and } 227^{\circ} \mathrm{C}, h-h^{i 8}=-3.2693 \mathrm{~kJ} / \mathrm{mol} \text { and } s-s^{\mathrm{i} 8}=-4.7567 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} Using the Peng-Robinson equation of state, what is h- h for 56.11 g of 1-butene at 2 MPa and160°C?(c)(4) You might find the PREOS spreadsheet useful to answering part (c), but you are welcome to useother sources of information if you wish. You must describe how you went out about answeringthis question, which is simply assessing your ability to obtain information.See Answer
Q13: Specific energy is given below for a range of depths in a trapezoidal channel with a base width of 6 ft and a 2:1 side slope a) Calculate flow rate (cfs) in channel b) Calculate critical depth in channel c) Briefly explain how critical depth is used to measure flow rate in an open channelSee Answer
Q14: [10 pts.]2. Consider steady one-dimensional heat conduction in a pin fin of constant diameter D, like the one shown below, with constant thermal conductivity k. The fin is losing heat by convection to the ambient air at T with a heat transfer coefficient of h. The nodal network of the fin consists of nodes 0 (at the base), 1 (in the middle), and 2 (at the fin tip) with a uniform nodal spacing of Ax. Using the energy balance approach, obtain the finite difference formulation of this problem to determine T₁ and T₂ for the case of specified temperature at the fin base and negligible heat transfer at the fin tip. Temperatures are in °C. See Answer
Q15: What is the significance of Burger's equation? Elaborate briefly.See Answer
Q16:Problem Description: Three simple heat exchanger designs are shown below. Cold water flows in the 2-direction over heated tubes. The water comes at 2m/s and at a temperature of 15 C. The water tubes are kept at 60 C. (a) Inline design Compare the three designs in terms of: (b) Staggered design I (c) Staggered design II Figure 1: proposed heat exchanger designs 1. Pressure drop: pressure difference between the inlet and the outlet on the water side 2. Water temperature rise: difference between average exit temperature and the inlet temperature 3. Exit water temperature uniformity: a. Choose your own way of defining how uniform the exit water temperature is 4. In each design, which tube is working the hardest in heating the water? Why? Deliverables 1. A workbench archive (file should have the extension *.wbpz) that contains all three simulations [30 % of the final project grade] a. Each simulation should have its own geometry, mesh, and converged solution. 2. A professional report that describes your geometry, mesh, problems set up and solution explaining how you achieved your answers to the questions above. Each slide should contain at least a brief paragraph explaining what the slide describes. [20% of the final project grade]See Answer

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