Challenge: Solving ODE for pendulum swing for the given inputs Code for plotting and animation: %Code for solving Second Order ODE clear all close all clc %Inputs b = 0.05; %Damping Co-efft g = 9.81; %Accleration due to gravity l = 1; %Lenght of Pendulum m = 1; %Mass %Initial Conditions theta_0 = [0 ; 3]; %Initial Displacement…

Write a code in MATLAB to optimise the stalagmite function and find the global maxima of the function. Code clear all, close all, clc x = linspace(0,0.6,150); y = linspace(0,0.6,150); num_cases = 50; [xx yy] = meshgrid(x,y); for i = 1:length(xx) for j = 1:length(yy) input_vector(1) = xx(i, j); input_vector(2) = yy(i,j);…

OBJECTIVES: 1. Write a function that extracts the 14 co-efficients and calculates the enthalpy, entropy and specific heats for all the species in the data file. You will be reading this file NASA thermodynamic data. The formulae are shown below. `(Cp)/R = a1 + a2.T + a3.T^2 + a4.T^3 + a5.T^4` `(H)/(RT) = a1 + a2.T/2…

OBJECTIVES Create a Rankine Cycle Simulator. Your code should calculate the state points of the Rankine Cycle based on user inputs.  Then, plot the corresponding T-s and h-s plots for the given set of inputs.   RANKINE CYCLE The Rankine cycle is an idealized thermodynamic cycle describing the process by which…

CHALLENGE OBJECTIVE: I. Derive the following 4th order approximations of the second-order derivative.    1. Central difference    2. Skewed right-sided difference    3. Skewed left-sided difference    Prove these skewed schemes are fourth-order accurate. II. Write a program in Matlab…

Objective: Solve the 2D heat conduction equation by using the point iterative techniques for both Steady State and Transient State Analysis. Following method should be implemented for solving Implicit Equations Jacobi Gauss-Seidel Successive over-relaxation   Input: Boundary conditions: Top Boundary = 600 K Bottom…

Objective: To compare the effect of Time Step variations on both Explicit and Implicit methods on the stability of the solution. Also evaluate the value at which the CFL becomes unstable. Input: Boundary conditions: Top Boundary = 600 K Bottom Boundary = 900 K Left Boundary = 400 K Right Boundary = 800 K Error Criteria…

Objective: Compare the convergence rate [Number of iterations] of the steady state and transient [explicit and implicit] simulations and justify the numerics. Input: Boundary conditions: Top Boundary = 600 K Bottom Boundary = 900 K Left Boundary = 400 K Right Boundary = 800 K Error Criteria = 1e-4   STEADY STATE:…

Objective: Solve the 2D heat conduction equation by using the point iterative techniques for both Steady State and Transient State Analysis. Following method should be implemented for solving Implicit Equations Jacobi Gauss-Seidel Successive over-relaxation   Input: Boundary conditions: Top Boundary = 600 K Bottom…

Objective: Find Numerical Solution to the One-Dimensional Linear Convection equation. Compare the original and final velocity profiles in a single figure window for time steps, dt = 1e-4, 1e-3, 1e-2, and 1e-1 Explain the CFL criteria that govern the linear convection equation. Does this criterion apply to an implicit solution…

Objective: Find Numerical Solution to the One-Dimensional Linear Convection equation. Compare the original and final velocity profiles in a single figure window for Number of nodes, n = 20, 40, 80 and 160. Explain the following phenomena observed from the solutions- numerical diffusion and instability and how they relate…