Write a design by c++include understanding the programflowchart test

Problem Statement You will apply your knowledge of arrays to gain an understanding of a heat transfer model over one- and two-dimensional objects. To do this, you will implement the explicit method for solving finite difference approximations. Your program will simulate the diffusion of heat through a 1-D or 2-D object, such as a wire or plate, using the explicit method to solve for new time instances. Since diffusion is the rate of change, then derivatives are needed to calculate this rate of change in heat over time. This following equation is how you calculate the diffusion of heat in a 1-D object over time: 2 lul ox2 Ot To solve this, it would require techniques from calculus, but we can't do calculus/take a derivative on the computer like we would do by hand. Instead, we need to approximate the derivative, and one approximation method is the explicit method for finite difference approximations to solve this equation. At Where the inputs are as follows Thermal conductivit Material densit Specific heat capacity of materia 1-D object Location on u Time rho Note, the symbol represents the change in a variable. For example, is the change in x, and t is the change in time. The change in x, Ax, is calculated by knowing the length of the 1-D object and how many sections you want to calculate the diffusion of the heat for. For example, a wire that is 5 inches divided into 5 sections have 1-inch sections, ie. is 1. Similarly, the change in time, , is calculated by knowing how long to run the simulation and for how many time instances to calculate the diffusion. For example, we want to simulate the heat diffusion for 10 minutes at 5 time instances is of 2 minutes. Below shows a picture of the first two time instances for a 1-D object broken into 5 sections tl XIL t+At Now, we want to solve for Lastly, we want to make sure that our simulation is stable. Use this equation k At Any value below 0.5 is stable, otherwise it is unstable Start by using the material properties of Nickel 52.4 0.321 0.12 10 10 rho Wire length Sections Time interval Time of Simulation 0.01675 Right temp xIn 100 Left temp x[0] Initial temp (t0 0 Example Output: 2. ENGR Re-attach Fullscreen Stay on top Duplicate 3.58786 7.97197 13.9748 22.1366 33.0024 46.5734 62.747 80.8305 100 3.95072 8.70962 14.9587 23.3688 34.2352 47.7594 63.6173 81.3254 100 4.31902 9.3887 15.9435 24.4882 35.4464 48.8229 64.4605 81.7659 100 4.66111 10.0655 16.8503 25.5881 36.5484 49.8533 65.2205 82.1891 100 4.99983 10.6946 17.7403 26.6009 37.6168 50.7931 65.9503 82.573 100 5.31651 11.3102 18.5674 27.5831 38.6013 51.6958 66.6181 82.9395 100 5.62512 11.886 19.3688 28.4957 39.5475 52.5288 67.2557 83.2763 106 5.91483 12.4428 20.118 29.3729 40.4268 53.3243 67.8453 83.5967 100 6.19426 12.9656 20.8379 30.1927 41.2669 54.0641 68.406 83.8938 100 6.45725 13.4673 21.5135 30.9763 42.0521 54.7681 68.9282 84.1756 100 6.70918 13.9395 22.1591 31.7114 42.7995 55.4262 69.4237 84.4385 100 6.94666 14.3903 22.7664 32.4113 43.5006 56.0509 69.8873 84.6876 100 7.17314 14.8152 23.3446 33.0695 44.1664 56.637 70.3266 84.921 10 7.38685 15.2196 23.8894 33.6947 44.7924 57.1925 70.7389 85.1418 100 7.59004 15.6011 24.4069 34.2837 45.3859 57.7149 71.1292 85.3493 100 7.78189 15.9633 24.8949 34.8421 45.945 58.2095 71.4964 85.5455 100 7.96393 16.3052 25.3577 35.3688 46,4744 58.6754 71.8438 85.7303 100 8.13588 16.6293 25.7945 35.8676 46.9736 59.1162 72.171 85.9049 100 8.29883 16.9355 26.2082 36.3383 47.446 59.5319 72.4805 86.0695 106 8.45277 17.2254 26.5989 36.7838 47.8918 59.925 72.7723 86.2251 100 8.59851 17.4992 26.9687 37.2045 48.3134 60.296 73.0483 86.3719 100 8.73623 17.7584 27.3179 37.6024 48.7116 60.6468 73.3087 86.5107 100 8.86653 18.0033 27.6483 37.9782 49,088 60.9779 73.5548 86.6416 100 8.98967 18.2349 27.9604 38.3336 49.4435 61.291 73.7872 86.7654 100 9.1613 18.4538 28.2556 38.6693 49.7796 61.5866 74.0068 86.8822 166 9.21619 18.6607 28.5344 38.9867 50.0971 61.8661 74.2143 86.9927 100 9.32025 18.8563 28.7981 39.2866 50.3972 62.13 74.4103 87.097 100 9.4186 19.0412 29.0473 39.5701 50.6808 62.3795 74.5955 87.1956 100 9.51157 19.2159 29.2828 39.838 50.9488 62.6152 74.7705 87.2887 100 9.59943 19.3811 29.5053 40.0912 51.202 62.838 74.9359 87.3767 100 9.68249 19.5372 29.7157 40.3304 51.4413 63.0485 75.0922 87.4599 160 9.76098 19.6848 29.9145 40.5565 51.6675 63.2474 75.2398 87.5385 100 flipl -/cs161/privateew 212 Next, you can implement the two-dimensional model Ou (Ar) (Ay) Here, each point in your material is influenced by the points above and beside it. ij+I ij lu i-1j i+I,j ij-1 Use the properties of nickel again 52.4 0.321 0.12 10 10 50 0.01675 100 100 0 rho Plate height and width Sections across height/width Time intervals Time of simulation Left/Right column tem Bottom/Top row tem Initial temp Step 1: Understanding the Problem/Problem Analysis. (15 pts) Do you understand everything in the problem? List anything you do not fully understand, and make sure to ask a TA or instructor about anything you do not understand . What are the user inputs/requirements, program outputs, etc.? (5 pts) . What assumptions are you are making? (5 pts) . What are all the tasks and subtasks in this problem? (5 pts) Step 2: Program Design. (25 pts) . What does the overall big picture of this program look like? (flowchart or pseudocode) (15 pts) o What data do you need to create, when do you read input from the user, what is the dealer strategy going to be? o What are the decisions that need to be made in this program? o What tasks are repeated? . What kind of bad input are you going to handle? (5 pts) . Provide a drawing/diagram of what the initial plate and wire will look like (5 pts). Based on your answers above, list the specific steps or provide a flowchart of what is needed to create this program Step 4: Program Testing. (10 pts) Create a test plan with the test cases (bad, good, and edge cases). What do you hope to be the expected results? o What are the good, bad, and edge cases for ALL input in the program? Make sure to provide enough of each and for all different inputs you get from the user Problem Statement You will apply your knowledge of arrays to gain an understanding of a heat transfer model over one- and two-dimensional objects. To do this, you will implement the explicit method for solving finite difference approximations. Your program will simulate the diffusion of heat through a 1-D or 2-D object, such as a wire or plate, using the explicit method to solve for new time instances. Since diffusion is the rate of change, then derivatives are needed to calculate this rate of change in heat over time. This following equation is how you calculate the diffusion of heat in a 1-D object over time: 2 lul ox2 Ot To solve this, it would require techniques from calculus, but we can't do calculus/take a derivative on the computer like we would do by hand. Instead, we need to approximate the derivative, and one approximation method is the explicit method for finite difference approximations to solve this equation. At Where the inputs are as follows Thermal conductivit Material densit Specific heat capacity of materia 1-D object Location on u Time rho Note, the symbol represents the change in a variable. For example, is the change in x, and t is the change in time. The change in x, Ax, is calculated by knowing the length of the 1-D object and how many sections you want to calculate the diffusion of the heat for. For example, a wire that is 5 inches divided into 5 sections have 1-inch sections, ie. is 1. Similarly, the change in time, , is calculated by knowing how long to run the simulation and for how many time instances to calculate the diffusion. For example, we want to simulate the heat diffusion for 10 minutes at 5 time instances is of 2 minutes. Below shows a picture of the first two time instances for a 1-D object broken into 5 sections tl XIL t+At Now, we want to solve for Lastly, we want to make sure that our simulation is stable. Use this equation k At Any value below 0.5 is stable, otherwise it is unstable Start by using the material properties of Nickel 52.4 0.321 0.12 10 10 rho Wire length Sections Time interval Time of Simulation 0.01675 Right temp xIn 100 Left temp x[0] Initial temp (t0 0 Example Output: 2. ENGR Re-attach Fullscreen Stay on top Duplicate 3.58786 7.97197 13.9748 22.1366 33.0024 46.5734 62.747 80.8305 100 3.95072 8.70962 14.9587 23.3688 34.2352 47.7594 63.6173 81.3254 100 4.31902 9.3887 15.9435 24.4882 35.4464 48.8229 64.4605 81.7659 100 4.66111 10.0655 16.8503 25.5881 36.5484 49.8533 65.2205 82.1891 100 4.99983 10.6946 17.7403 26.6009 37.6168 50.7931 65.9503 82.573 100 5.31651 11.3102 18.5674 27.5831 38.6013 51.6958 66.6181 82.9395 100 5.62512 11.886 19.3688 28.4957 39.5475 52.5288 67.2557 83.2763 106 5.91483 12.4428 20.118 29.3729 40.4268 53.3243 67.8453 83.5967 100 6.19426 12.9656 20.8379 30.1927 41.2669 54.0641 68.406 83.8938 100 6.45725 13.4673 21.5135 30.9763 42.0521 54.7681 68.9282 84.1756 100 6.70918 13.9395 22.1591 31.7114 42.7995 55.4262 69.4237 84.4385 100 6.94666 14.3903 22.7664 32.4113 43.5006 56.0509 69.8873 84.6876 100 7.17314 14.8152 23.3446 33.0695 44.1664 56.637 70.3266 84.921 10 7.38685 15.2196 23.8894 33.6947 44.7924 57.1925 70.7389 85.1418 100 7.59004 15.6011 24.4069 34.2837 45.3859 57.7149 71.1292 85.3493 100 7.78189 15.9633 24.8949 34.8421 45.945 58.2095 71.4964 85.5455 100 7.96393 16.3052 25.3577 35.3688 46,4744 58.6754 71.8438 85.7303 100 8.13588 16.6293 25.7945 35.8676 46.9736 59.1162 72.171 85.9049 100 8.29883 16.9355 26.2082 36.3383 47.446 59.5319 72.4805 86.0695 106 8.45277 17.2254 26.5989 36.7838 47.8918 59.925 72.7723 86.2251 100 8.59851 17.4992 26.9687 37.2045 48.3134 60.296 73.0483 86.3719 100 8.73623 17.7584 27.3179 37.6024 48.7116 60.6468 73.3087 86.5107 100 8.86653 18.0033 27.6483 37.9782 49,088 60.9779 73.5548 86.6416 100 8.98967 18.2349 27.9604 38.3336 49.4435 61.291 73.7872 86.7654 100 9.1613 18.4538 28.2556 38.6693 49.7796 61.5866 74.0068 86.8822 166 9.21619 18.6607 28.5344 38.9867 50.0971 61.8661 74.2143 86.9927 100 9.32025 18.8563 28.7981 39.2866 50.3972 62.13 74.4103 87.097 100 9.4186 19.0412 29.0473 39.5701 50.6808 62.3795 74.5955 87.1956 100 9.51157 19.2159 29.2828 39.838 50.9488 62.6152 74.7705 87.2887 100 9.59943 19.3811 29.5053 40.0912 51.202 62.838 74.9359 87.3767 100 9.68249 19.5372 29.7157 40.3304 51.4413 63.0485 75.0922 87.4599 160 9.76098 19.6848 29.9145 40.5565 51.6675 63.2474 75.2398 87.5385 100 flipl -/cs161/privateew 212 Next, you can implement the two-dimensional model Ou (Ar) (Ay) Here, each point in your material is influenced by the points above and beside it. ij+I ij lu i-1j i+I,j ij-1 Use the properties of nickel again 52.4 0.321 0.12 10 10 50 0.01675 100 100 0 rho Plate height and width Sections across height/width Time intervals Time of simulation Left/Right column tem Bottom/Top row tem Initial temp Step 1: Understanding the Problem/Problem Analysis. (15 pts) Do you understand everything in the problem? List anything you do not fully understand, and make sure to ask a TA or instructor about anything you do not understand . What are the user inputs/requirements, program outputs, etc.? (5 pts) . What assumptions are you are making? (5 pts) . What are all the tasks and subtasks in this problem? (5 pts) Step 2: Program Design. (25 pts) . What does the overall big picture of this program look like? (flowchart or pseudocode) (15 pts) o What data do you need to create, when do you read input from the user, what is the dealer strategy going to be? o What are the decisions that need to be made in this program? o What tasks are repeated? . What kind of bad input are you going to handle? (5 pts) . Provide a drawing/diagram of what the initial plate and wire will look like (5 pts). Based on your answers above, list the specific steps or provide a flowchart of what is needed to create this program Step 4: Program Testing. (10 pts) Create a test plan with the test cases (bad, good, and edge cases). What do you hope to be the expected results? o What are the good, bad, and edge cases for ALL input in the program? Make sure to provide enough of each and for all different inputs you get from the user