# engineering equation discussion

Help me do a two files of assignments of Engineering equation solverPlease bid on it when only you are familiar with these……………………..

Page 1/5 Homework Set Module 4 Problem 4.1 The following set of differential equations models the system of predator and prey 𝑑𝑥 𝑑𝑡 = 𝛼𝑥 − 𝛽𝑥𝑦 𝑑𝑦 𝑑𝑡 = 𝛿𝑥𝑦 − 𝛾𝑦 Where x represents prey and y represents predator. Where x(0) = 8 and y(0) = 4 The constants are given below α = 1.5 : β = 1.0 : 𝛿 = 1.0 : 𝛾 = 3.0 Deliverables a) Use EES’ built in integration function to solve this system of ODE’s. b) Make a plot of x and y as a function of time for 0 < t < 10. c) Hand in your EES code showing the equations window and a sample solution. Page 2/5 Problem 4.2 A 1 kg mass is attached to a spring with a spring constant of 10 N/m. The mass is pushed up and released from rest at a point 0.5 m above the equilibrium position. The damping provided by the surrounding medium is equal 0.1 times the instantaneous velocity. Neglect gravity. The force balance is Solve this ODE using EES’s built in Integral function over a time from 0 to 10 s. Deliverables a) Make a plot of x vs t. b) Make a plot of 𝑑𝑥 𝑑𝑡 vs t c) Hand in your EES code (Equation Window and Solution Window) 𝑘 = 10 𝑁 𝑚 𝑚 = 1 𝑘𝑔 𝛽 = 0.1 𝑁 − 𝑠 𝑚 +𝑥 Page 3/5 Problem 4.3 Consider a 1 m by 1 m aluminum block with the following temperature conditions on the surfaces as shown below. Compute the steady state temperature in the system. That is, solve the 2-D steady-state heat equation for the system above: Deliverables a) Find the temperature distribution for 𝑑𝑥 = 𝑑𝑦 = 0.1 m. Make a colored contour plot of temperature with a legend ranging from 100 K to 500 K. b) Find the temperature distribution for 𝑑𝑥 = 𝑑𝑦 = 0.05 m. Make a colored contour plot of temperature with a legend ranging from 100 K to 500 K. c) Hand in your EES code and solution window T=400 K T=200 K +y +x Page 4/5 Problem 4.4 You are an engineer working for an automotive engine manufacturer. The figure below shows a spark plug for an internal combustion engine. You are interested in estimating the temperature distribution in the center wire within the spark plug during an engine cycle. After some analysis you have found that you can model the center wire as a 3 cm long iron rod with a time varying boundary condition on the bottom and a constant temperature boundary condition of 100°C on the top. Assume 1-D conduction. The time varying boundary condition was found by measuring the surface temperature. The temperature measurement as a function of time can be found in “CenterWireTemp.lkt”. The initial temperature is 100°C. Spark Plug Model of Center Wire Assume 1-D transient conduction (i.e., solve the equation below). Use EES’s integration for time and a 𝛿𝑥 value of 0.25 mm. where , c is specific heat of the material, 𝜌 = density of the rod, and k is the thermal conductivity of the rod. For parts a and b you can evaluate 𝜌, 𝑐, 𝑎𝑛𝑑 𝑘 at 𝑇 = 100°𝐶. T=100°C T=T(t) See CenterWireTemp.lkt Page 5/5 Deliverables a) Make a plot showing the temperature at 0 mm (bottom boundary), 0.25 mm, 0.5 mm, 10 mm, and 29.75, 30 mm (top boundary) as a function of time from 0 to 0.25 seconds. Clearly label each line. b) Make a plot showing the temperature distribution at 0.05, 0.15, and 0.25 seconds. Clearly label each line. c) Hand in your EES code and a solution window.

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