Solving the steady and unsteady 2D heat conduction problem

1. popt and pcov popt = This will retrun the optimal values for the coefficients of expression for which curve is to be plotted. pcov = This will return the covariance which shows how the values or corealated. Covariance is proportional to slope of line. 2. np.array This function is used to convert the temperature list…

Below is the program for the data visualizer which can plot the graph and perform the required calculations. In the following program you can select the desired input file for which the plots are required. Compablity Check. Tk inter library is used to create the dialog box for the file selction. After selection of the…

In the following project, program is written to solve the ordinary differential equation of simple pendulum and plotting the results are various time steps to generate the animation at the end.   The motion of simple pendulum is represented using following ODE:   `(d^2theta)/dt^2 + b/m (d theta)/dt + g/l(sin…

\'\'\' Simulating Otto cycle By Devdatta \'\'\' import math import matplotlib.pyplot as plt import numpy as np def engine_kinematics(bore, stroke, conn_rod, cr, start_crank, end_crank): # Geomtric Paramters a = stroke/2 R = conn_rod/a # Volume Computation v_s = (math.pi/4)*pow(bore,2)*stroke v_c = v_s/(cr-1) sc = math.radians(start_crank)…

Possible types of combustion simulation in ansys fluent. Non premixed Combustion Premixed Combustion Partially Mixed Combustion Fluid Phase (voumetric reactions) Wall (Surface Reactions) Particles (Surface reactions) Porous Regions. In the following project, a 2D steady-state combustion simulation is performed. SETUP:…

In the following project parametric study on the gate valve is performed. The following conditions are considered. Inlet boundary condition is set to pressure set with a value of 10 Pa. Outlet boundary condition is set to pressure outlet. Mesh size selected is 8mm with 250K elements. Steady- state simulation is performed…

In the following project 2D simulation of rotating gear with water and oil is performed. To study the gearbox sloshing effect.   CASE SETUP Fluid Volume is extracted from the provided 3D model and 2D representation of the same extracted fluid volume is used to perform simulation. For meshing the mesh size selected…

The four efficiciency models used for the cyclone seprator are as follows: A.Iozia and Leith Model.1.This model is based on the force balancing and it is the modified form of the model given by the Barth.2.The model makes the assumption that due to the formation of the vortex two forces act on the particle namely, centrifugal…

  In the following project conjugate heat transfer analysis over graphics card was performed using 2 mesh variations. One baseline mesh and another more refined mesh.   The aim of the project was to calculate maximum temperature attained by the processor, find out heat transfer coefficients and potential hotspots…

Conjugate Heat transfer Analysis: Conjugate heat transfer analysis is generally used when there is temperature variation during heating or cooling in the material due to interaction between solid and fluid phases. It is the combination of heat transfer in solids to heat transfer in fluids. Examples of Conjugate Heat transfer…

In the following project a script was written in MATALB to generate the blockMeshDict file according to wedge angle, diameter and length of a pipe. Analytical calculations are done and compared with the simulation results. With some trials grid size 400 cells around X-direction and 40 cells around Y-direction is used keeping…

Practical Model CFD Models based on Rayleigh Taylor waves. 1. K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities. K-epsilon (k-ε) turbulence model is the most common model used in Computational Fluid Dynamics (CFD) to simulate mean flow characteristics for…

Ahmed Body: Ahmed body is standard model first created by S. R. Ahmed in 1984. It has similar features like car and it is widely used for validation of new codes in automotive industry.As results for experimental data are availabe which can be compared with simulation results. It helps to capture the various aspects of…

FLOW OVER A CYLINDER In the following challenge steady and unsteady flow over s cylinder is carried out to observe von Karnman effect and calculate the Strouhal Number. Von Karman effect  is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady…

In the following project a script was written in MATALB to generate the blockMeshDict file according to wedge angle, diameter and length of a pipe using symmetry boundary condition.   Simulation results obtained for 10, 25 and 45 degree of angle (Symmetry boundary condition) are compared with wedge boundary condition…

In the following project 3 different variations of the mixing tee are simulated and compared. Ansys spaceclaim utility was used to clean up the geometry. And ansys fluent to process the simulation. Following are the conditions used for the simulation. Element size is 0.002mm Hot inlet temperature is 300K and cold inlet…

Interpolation Schemes : Interpolation is the process of using points with known values or sample points to estimate values at other unknown points. In FVM interpolation schmes are used to find the values of volume intergrals required at the points other than nodes. Some of the used methods are the central differencing…

 In this project the 1D super sonic nozzle flow equation was solved. Seprate functions for conservative and non-conservative part are written. And Grid dependency test with grid size of 31,61 and 91 is performedThe governing equations were referred from the book "COMPUTATIONAL FLUID DYNAMICS" By John D Anderson.Following…

 In this project the 1D super sonic nozzle flow equation was solved. Seprate functions for conservative and non-conservative part are written. And Grid dependency test with grid size of 31,61 and 91 is performed The governing equations were referred from the book \"COMPUTATIONAL FLUID DYNAMICS\" By John D Anderson.…

 The objective of this project is to set up greate a geometry by editing blockMeshdict file and simulate a flow through backward-facing step. For different mesh grading factors. To set up geometry. The figure was divided into 5 parts, total number of cells along X direction is 200 which is divided as 80 number of…

Stability analysis for transient state simulation was done as follows. For the implicit method, the solution is stable for varying time steps. And reducing or increasing the time step does not affect the stablity of solution. For explicit methods the stability of the solution depends on the CFL number which is calculated…

The fastest steady-state simulation was obtained with the SOR method. Following are the results obtained by the SOR method.     The number of iterations is 142. The time required for solving was 0.090692 The error value = 0.000097   Whereas for the transient state method the fastest simulation was obtained…

A. Solving Steady State 2D heat conduction equation.Driver script for program. %Script for solving 2d steady state heat conduction equation clear all close all clc nx= 50; ny = nx; x=linspace(0,1,nx); y=linspace(0,1,ny); dx= x(2)-x(1); dy= y(2)-y(1); u = 400*ones(nx,ny); u(2:end-1,1)=400; u(1,2:end-1)=600; u(2:end-1,ny)=800;…

To calculate the eigenvalues, Spectral raidius and solving the system using Jacobi, Gauss Sidel and SOR method follow is the program. clear all close all clc method = 1; % USE 1 for jacobi , 2 for gauss-sidel and 3 for SOR ) A = [5 1 2; -3 9 4; 1 2 -7]; % Matrix A is given. D = diag(diag(A)); % Decomposing in diagonal…

Numerical solution to wave equation varying time steps.   Following is the function for varying time steps.   function [x,u,nt]=simple_linear_convection_timestep(dt,color,DisplayName,name) % Inputs for the linear convention L=1; c=1; t_end = 0.4; nt = (0.01:dt:t_end); n = 80; %calculation x = linspace(0,L,n);…

Basic quantities with units Kinematic viscosity (ν) - Kinematic viscosity is defined as ratio of dynamic viscosity per unit density. ν = μ/ρ Unit of Kinematic viscosity is m2/s. As μ = dynamic viscosity (N-s/m2) ρ = density (kg/m3)   Dynamic viscosity (µ) -  Dynamic viscosity is the…

Numerical Solution to the wave equation.   Below is the function for the plot % function for numerical solution function out=simple_linear_convection(n,h) %clear all %close all %clc % Inputs for the linear convention L=1; c=1; dt =1e-2; t_end = 0.4; nt = (0.01:dt:t_end); %n =20; %calculation x = linspace(0,L,n); dx…

Numerical Solution to the wave equation.   Below is the function for the plot % function for numerical solution function out=simple_linear_convection(n,h) %clear all %close all %clc % Inputs for the linear convention L=1; c=1; dt =1e-2; t_end = 0.4; nt = (0.01:dt:t_end); %n =20; %calculation x = linspace(0,L,n); dx…

Using the Taylor table method to derive the coefficients a b c d and e for skewed right side difference, skewed left side difference and central difference scheme. Table for skewed forward difference scheme is as follows-   f(i) f’(i) f’’(i) f’’’(i) f’’’’(i)…

Basic quantities with units Kinematic viscosity (ν) - Kinematic viscosity is defined as ratio of dynamic viscosity per unit density. ν = μ/ρ Unit of Kinematic viscosity is m2/s. As μ = dynamic viscosity (N-s/m2) ρ = density (kg/m3)   Dynamic viscosity (µ) -  Dynamic viscosity is the…

Code is as follows   clear all close all clc x = pi /3; % given value of x dx = pi/25 %grid spacing %given function f(x) =sin(x)/x^3 = sin_x is saved as function in another %file analytical_derivative = (x^3*cos(x)-sin(x)*3*x^2)/x^6; %First order approximation using forward differencing scheme % forward_differincing…

Function for first order approximation   function out = first_order_approximation(x,dx) % Analytical function = sin(x)/x^3; % analytical derivative % f\'(x) =(x^3(cos(x)) -sin(x)*3*x^2)/x^6; analytical_derivative =(x^3*(cos(x)) -sin(x)*3*x^2)/x^6; %numerical derivative %forward differincing % forward_differincing…

Code is as follows   clear all close all clc x = pi /3; % given value of x dx = pi/25 %grid spacing %given function f(x) =sin(x)/x^3 = sin_x is saved as function in another %file analytical_derivative = (x^3*cos(x)-sin(x)*3*x^2)/x^6; %First order approximation using forward differencing scheme % forward_differincing…

Function for pendulum is as follows function [zdot] = odefun_second_order_pendulum(t,z) % let z = angle %given data L=1; m=1; b=0.5; g=9.81; z1=z(1); z2=z(2); zdot(1)=z(2); zdot(2) =(-b/m)*z2-(g/L)*sin(z1); zdot = [zdot(1),zdot(2)]\'; end   Below is the program for solving second order ODE.   clear all close…

General for hydrocarbons is given as follows   alkane = CnH2n+2. alkene = CnH2n. alkyne = CnH2n.   The standard balanced equation for combustion hydrocarbon is given as   CxHy+(x+y/4)O2→xCO2+(y/2)H2O   Therefore using above equation we calculate \"ar\" stochiometric ratio for alkane, alkene, alkyne.…

Consider ∇ = nabla operator     1. DivergenceDivergence is the dot product between ∇ and vector. if V = vector then V.∇ = Divergence   2. Gradient Gradient is ∇ multiplied by scalar quantity if F= scalar quantity ∇F = Gradient 3. Curl Curl is cross product between ∇ and…

A PDE is a differential equation containing two or more independent variables and partial derivatives of functions of those variables. PDEs are used to create various mathematical models in FEM and FVM.Initial Conditions-The initial conditions are the starting points where the function begins.   Boundry Conditions-…

1. A=[1,2,3,4,5]The above command creates a matrix \'A\' with 1 row and 5 columns containing values 1,2,3,4,5 in each column respectivelySo the output will be A = 1 2 3 4 5 2. B=[1;2;3;4;5] The above command creates a matrix \'B\' with 1 column and 5 rows containing values 1 2 3 4 5 in each row respectively.So the output…