2D Steady state Unsteady state heat conduction equation solve using implicit and explicit methods

1.A=[1,2,3,4,5] - A is a variable and A is having collection of values and its called as array.each value separated by a comma(,),by executing this command my understanding is normal array.  //make sure to observe correctly it is a row matrix 2.B=[1;2;3;4;5]-B is a variable and B is having collection of values…

  Objective: The objective of this project is to write code solve the 1D supersonic nozzle flow equations using the Macormack Method. To implementing both the conservative and non-conservative forms of the governing equations To perform grid dependence test MacCormack method: MacCormack's technique is used, which…

Function of non - conservative form of 1D supersonic nozzle flow %%%%%%%Function of non - conservative form%%%%%%%% --------------------------------------------------- function[K,rho,t,v,m_n,M_n,p_n,p_th_n,rho_th_n,t_th_n,rho_exact_n,t_exact_n,M_exact_n,rho_res_n,t_res_n,v_res_n]=Non_conservative_f(x,n,gamma,nt,a,dx,dt)…

Understanding linear systems to write computer programs to manually determine the Eigen Value and Spectral Radius of the given system of equations   ## Matlab code (main code with functions code)  clear all; close all; clc; n=10; method =input('Enter the method no.') %% %%solving linear system and solving using…

Stability analysis in unsteady state heat conduction equation solve using implicit and explicit method. CFL Number - Courant Friedrich Lewy,it is a dimensionless number.It must be less than 1 to maintain the solution stability. A physical explanation, for a CFD simulation, of the Courant number could be that it tells you…

Comparision of Fastest steady state vs fastest transient (unsteady) unsteady state simulation time  2D-Heat conduction equation solve using implicit & explicit methods   Transient state : ∂T/∂t = ∂²T/∂x² + ∂²T/∂y²   Steady state: ∂²T/∂x²…

Objective: 1.To write a MatLab code to solve numerically 1D Linear convection equation. 2.Generate and plot the velocity profile of 1D Linear convection equation. 3.Compare the effect of the grid spacing on velocity profile by plotting the velocity profile for a varying number of nodes. Assumption: Numerical solution to…

Obejective: To write a function that accepts time step as an argument & compare the effect of time step on the numerical solution.   Two Dimensional momentum equation:   Effect of different time step Time steps were used.dt=1e-4,1e-3,1e-2,1e-1 When time step, dt = 1e-4, time n=80, The velocity profile comes…

Objective: In this project, we are going to simulate the pipe flow using previous results of wedge boundary conditions. Instead of using wedge Boundary Condition, Symmetry Boundary Condition is used & blockMeshDict generate using the Matlab program for angle 10, 25 & 45 degrees. Matlab code to generate blockMesh…

Simulation of flow through the pipe using OpenFoam Objective: The main objective of this project is to simulate flow through the pipe using OpenFOAM software. For that, Write a program in Matlab that can generate the computational mesh automatically for any wedge angle and grading scheme. Calculate the length of the pipe…

Finite Volume Method Literature review Finite Volume Method Finite Volume method provides a robust way of discretization the equations to solve for the certain class of heat transfer & fluid flow problem .Similar to the FDM technique wherein derivatives are replaced/discretized in form of differences that is been applied…

Objective:  In this project we are going  to  Simulate a flow through backward facing step in 2D. Analyse the result of velocity profile after 0.085m in this geometry. The main objective of this project is to understand how the flow field properties (velocity,pressure etc.,) changing due to the sudden step. …

Stoichiometric equation is theoritical calculation of AF mixture(Air Fuel) Genrally formula of stoichiometric equation,Cx Hy + (x + y/4)O2 into xCO2 + (y/2) H2O with some quantity of heat it produces.By using mole method in the above equation for both reactant and product,we will get the co-efficient of stoichiometric.from…

Youtube link: https://youtu.be/YVHlv_63OcQ %simple pendulumclear allclose allclcl=1;b=0.05;m=5;g=9.81;%Time t = [0 20];%initial conditiontheta_0=[0 3];%solving ode using ode45[t,theta] = ode45('odefun_second_orders',t,theta_0);%plottingfigure(1)%subplot(2,1,1)plot(t,theta(:,1),'color','r','linewidth', 3)%xlabel('time');%ylabel('Displacement');hold…

#commentThere is not explanation on the background Youtube link:https://youtu.be/YVHlv_63OcQ%simple pendulumclear allclose allclcl=1;b=0.05;m=5;g=9.81;%Time t = [0 20];%initial conditiontheta_0=[0 3];%solving ode using ode45[t,theta] = ode45('odefun_second_orders',t,theta_0);%plottingfigure(1)%subplot(2,1,1)plot(t,theta(:,1),'color','r','linewidth',…

MAT LAB CODE Function of skewed right hand side: function [right_error]=skewed_right_side(x,dx) %Analytical derivative analytical_derivative = -2*exp(x)*sin(x); %Numerical solution skewed_right = (35*(exp(x)*cos(x))-104*(exp(x+dx).*cos(x+dx))+114*(exp(x+2*dx).*cos(x+2*dx))-56*(exp(x+3*dx).*cos(x+3*dx))+11*(exp(x+4*dx).*cos(x+4*dx)))./(12*dx.^2)…

1.A=[1,2,3,4,5] - A is a variable and A is having collection of values and its called as array.each value separated by a comma(,),by executing this command my understanding is normal array.  //make sure to observe correctly it is a row matrix2.B=[1;2;3;4;5]-B is a variable and B is having collection of values…

Stoichimetric equation is theoritical calculation of AF mixture(Air Fuel).Genrally formula of stoichiometric equation,Cx Hy + (x + y/4)O2 into xCO2 + (y/2) H2O with some quantity of heat it produces.By using mole method in the above equation for both reactant and product,we will get the co-efficient of stoichiometric.from…

#commentThere is not explanation on the background Youtube link:https://youtu.be/YVHlv_63OcQ%simple pendulumclear allclose allclcl=1;b=0.05;m=5;g=9.81;%Time t = [0 20];%initial conditiontheta_0=[0 3];%solving ode using ode45[t,theta] = ode45('odefun_second_orders',t,theta_0);%plottingfigure(1)%subplot(2,1,1)plot(t,theta(:,1),'color','r','linewidth',…

Steady state & unsteady state 2D - heat conduction equation solve using implicit & explicit method Diffusion – It’s the process of moving from higher concentration to lower concentration.   Heat diffusion – If the temperature increases the diffusion process will starts, Then the heat diffuses…

The main prospective of this numerical discretization is to give approximate solution to analytical derivative. Numerical discretization  is very simple method used to convert analytical derivative(PDE) in to algebric from and then we can able to get the solution approximately. In order to do this we need to be familiar…

Objective: The objective is to derive fourth order approximation of skewed right side , left side & central scheme with the help of taylor's table & numerical stencil.   The equation one will be  `del^2f`/`delx^2` -------- (1)   Stencil that we are using for this fourth order approximation is  …

  %computation of derivative both numerically and analytically% In first order approximation the value of dx is increases the error decreases.%In second order approximation the value of dx is increases the error increases.%In fourth order approximatiion the value od dx is increases the error will remains zero.the…