To derive the following 4th order approximations of the second-order derivative.  1. Central difference 2. Skewed right-sided difference 3. Skewed left-sided difference Central diffrence scheme To derive the fourth order approximate central difference scheme for the second order derivative, we use the following formula:…

Week 5 Assignment 1. Steady state analysis & Transient State Analysis for  2D heat conduction equation . Steady state analysis & Transient State Analysis What is steady and unsteady State Heat Transfer? Heat transfer is the transfer of thermal energy from a body, at a high temperature, to another at a…

Simulation of a 1D Super-sonic nozzle flow simulation using Macormack Method. AIM: To simulate the 1-D super sonic nozzle flow using Macormack Method  A comparison is made between conservative and non conservative form of governing equation to check which one is faster and how the parameters changes along the…

To simulate the flow through a backward facing step & compare the flow obtained at diffrent mesh values.   Mesh specification:- Number of cells along the x direction (longer dimension) = 200 Number of cells along the y direction = 10 Use a graded mesh. Grading factor near all walls should be 0.2 Question. Follow…

Study of various interpolation schemes and flux limiters in FVM.  Finite volume method : The finite volume method (FVM) is a method for representing and evaluating partial diffrential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential…

Simulation of Flow through a pipe in OpenFoam. In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar…

Symmetry vs Wedge vs HP equation This is the continuation of the previous challenge simulation, Tasks to be completed in this challenge. You should have results obtained from solving the Hagen Poisuelle's equation You should have results obtained from simulating the pipe flow with the wedge BC You should obtain results…

To write a program in Python to plot an otto cycle and calculate its thermal efficiency. Theory An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.…

Python code to describe the transient behavior of a Simple pendulum with a damping constant of 'b'. Theory In Engineering, ODE is used to describe the transient behavior of a system.  A simple example is a pendulum   The way the pendulum moves depends on Newton's second law. When this law is written down, we…

Curve fitting Using Python AIM To write code to fit a linear and cubic polynomial for the Cp data and explain the following Questions 1. What do popt and pcov mean?  2. What does np.array(temperature) do? 3. What does the * in *popt mean?  4. What needs to be done in order to make the curve fit perfectly?…

Data analysis using Python. AIM: To create a data visualizer tool.  Data visualizer: Your script should take column numbers as the input and plot the respective columns as separate images Each file should be saved by the name of the column The plot labels should be extracted from the file. If I request a plot…

   Adiabatic Flame Temperature Calculation using Python and Cantera. Aim : To study the effect of equivalence ratio on Adiabatic Flame Temperature using the Newton Raphson method and Cantera. To calculate the Adiabatic Flame Temperature for the constant pressure with heat loss. To calculate the Adiabatic…

Week 4 - Handling Mixtures with Cantera Theory Mixtures are substances composed of two or more forms of matter. We can separate them by physical methods. Examples include a solution of salt and water, a mixture of sugar and water, different gasses, air, ...etc. In any mixtures, the various components do not combine through…

 Aim: 1.What is the effect of preheating on the adiabatic flame temperature? Change pre-heating from 298 to 600K Explain your results 2. Does preheat help with fuel-saving? If yes, how does combustion efficiency go up as a function of pre-heating temperature? Assume that the furnace exit temperature is 1700K Write…

Objective: To review the literature about ODE and to write the python program to substantiate our results.               When does an ODE become unstable? When we writing code for explicit form solution goes unstable because if the time step is really large, nos. of grid points…

Multivariate Newton Rapshon Method :-In numerical analysis, Newton's Method also known as the Newton-Raphson method is a root.Finding algorithms that produce a successively better approximation to the root or zeros of a real values function.The most basic version starts with a single variable function defined for a real…

OBJECTIVES:-  To solve the challenge of Auto-ignition by using Python with Cantera.   PROBLEM STATEMENTS:-  PART-A Use the same reactor network code as shown in the video to simulate the auto-ignition Time for methane under the following conditions, (Simulation time = 10 Secs). Plot the variation of auto-ignition…

 Week 9 - Sensitivity Analysis Assignment Aim: Sensitivity analysis of GRI-3.0 mechanism Objectives: Determine 10 most sensitive reactions from the GRI-3.0 mechanism Determine sensitivity with respect to temperature Output the reactions in decreasing order of sensitivity Theory: In any reaction mechanism, multiple…