From the Taylor Table method, the fourth-order approximation of second-order derivative has been derived.  Central Difference: `(d^2 f)/(dx^2 )=(-0.0833*f(i-2)+1.3333*f(i-1)-2.500*f(i)+1.3333*f(i+1)-0.0833*f(i+2))/dx^2` Skewed Right Side Difference: `(d^2 f)/(dx^2 )=(0.6753*f(i)-0.5977*f(i+1)-1.2586*f(i+2)+1.6092*f(i+3)-0.4282*f(i+4))/dx^2`…

Non-Conservative Function: function [rho,v,T,a,x,mach,q,mass_flow,rho_throat,Temp_throat, mach_throat, Pr_throat, m_throat,k] = non_conservative(L,n,nt) x = linspace (0,L,n); dx = x(2)-x(1); gamma = 1.4; %% Initial profiles rho = 1-0.3146*x; %rho =density T = 1- 0.2314*x; %T = temperature v = (0.1 +1.09*x).*T.^0.5; %v…

STEADY STATE: Matlab Code: clear all close all clc %% Initial and Boundary conditions L = 1; nx = 81; ny = nx; dx = L/(nx-1); dy = dx; %w = 1.1; T = 298* ones(nx,ny); T(1,:) = 900; % Bottom (1st row is being counted from bottom) T(:,1) = 400; % Left T(:,end) = 800; % Right T(end,:) = 600; % Top % Corner points T (1,1)…

BlockMesh Coding: /*--------------------------------*- C++ -*----------------------------------*\\ ========= | \\\\ / F ield | OpenFOAM: The Open Source CFD Toolbox \\\\ / O peration | Website: https://openfoam.org \\\\ / A nd | Version: 7 \\\\/ M anipulation | \\*---------------------------------------------------------------------------*/…

All the inputs have been discussed in the exercise of the week - 11. For 10 degree angle in symmetry boundary condition, all the samples have been given here. For the rest, these will be almost same.  MATLAB Programme to generate block mesh file for 10 degree: clear all close all clc %% Inputs L = 1.5; theta = 10;…

Density of water = 998 kg/m3 Dynamic viscosity of water = 8.90 *10-4 Pa. s Reynolds no = 2100 Let the Diameter = 0.01 m Inlet velocity = 0.1874 m/s Entry length for a laminar pipe is = L = 0.05*Re*D = 1.05 m Therefore for the simulation, a length of 1.5 m has been taken which is greater than the entry length. According…