Aim: To write code to fit linear and cubic polynomial curve fit with a comparison of the original data in Matlab and to plot the linear and cubic fit with raw data. Curvefit: The curve fit is the process of constructing the curve or mathematical function which posses the closet proximity to the real series of data points. …

Objective: The objective of this challenge is to write a code to solve stiff ODE system by using the multivariant Newton  Rhapson method.  Since these are the stiff system, we are using an implicit method to find out the solution. The general formula for backward differentiation is  `f^' (x_i )= (f(x_i )-f(x_(i-1)))/∆x`…

Objective: The project aims to stimulate the movement of the simple pendulum(0-20s) which moves according to the below second order differential equation(ODE) and to create an animation of its movement using Python.  `(d^2 θ)/(dt^2 )+b/m*(dθ/dt)+g/l (sin⁡θ )=0` where: b - damping coefficient l -…

Objective: The objective of this challenge is to mesh the cylinder model using ANSA. Procedure: Open the file of the cylinder by clicking the \'File\' option on the top of the taskbar. Make sure that the file is supported by the ANSA. Select the shadow mode. This mode helps to see the 3D part of the cylinder. Change the…

Objective: The objective of this project is to write code to extract the data from the \'engine_data.out\' and calculate the work done, power output and fuel consumption of the engine. Definitions and Formulas: Power Output: Engine power or horsepower is the maximum power that an engine can put out. It can be expressed…

Objective: To write a code solve the 1D linear convection equation for the various grid points and to generate the plot for the velocity profile using the Matlab. Convection: The flow that combines diffusion and the advection is called convection. Advection: The bulk transport of mass, heat or momentum of the molecules.…

Objective: The aim of this project is to write the code to stimulate an Otto cycle i.e to calculate the state variables at four different states, plot the PV diagram for the given condition and to calculate the thermal efficiency of the Otto cycle for a specified engine parameter. Theory and Formula: The air-standard Otto…

Objective: To stimulate the forward kinematics of a 2R robotic arm by using Matlab. Formula:  Equations used to calculate the positions of two links for different angles. `x_1=l_1*cos⁡(θ_1); y_1=l_1*sin⁡(θ_1 ); x_2=x_1+l_2*cos⁡(θ_2 ); y_2=y_1+l_2*sin⁡(θ_2)`. Workflow: The study and stimulation…

Objective: To derive the central differentiation scheme, skewed right-sided difference, the skewed left-sided difference and write code for 3 numerical approximations in Matlab. The whole idea of the numerical discretization is to convert continues equation into algebraic form. so that we can solve it using computers …

Objective: To write code to extract the different coefficients of the species and calculate the enthalpy-entropy and specific heat of the given NASA THERMODYNAMIC DATA and calculate the molecular weights for all species in the given data file. Plot the graph between entropy, enthalpy and specific heat for local temperature…

Objective:  To write code and optimize stalagmite function and to figure out global maxima of the function. Genetic Algorithm(GA): Genetic algorithm is a search algorithm which is based on natural selection and natural genetics. It basically based on the concept of \"survival of fittest\"(Darwinian Theory), i.e the…

Adiabatic flame temperature (AFT): The final temperature obtained after fuel is completely burned is called adiabatic flame temperature. This gives an idea of the maximum amount of energy produced by burning a particular fluid. The combustion takes places adiabatically (i.e Q = 0) Generally, we define the adiabatic flame…

Objective: The purpose of this challenge is to write code for calculation of auto-ignition time for methane under various conditions using cantera. Ignition delay is the lowest temperature at which ignition takes place. It is the property of the fuel. Generally, auto ignition time is given by  `Time_(ignition delay)=Time_(initial…

Aim: To derive the reaction rate ODEs of a simple reaction mechanism by compact notation. why compact notation? The compact notation is used to simulate the chemical kinematics which can be understood by the computers. compact notations help to describe any size notation to a computer.   Reaction Mechanism: Here,…

Recuperator: It is the type of heat exchanger, in which two fluids are separated all time by the solid barrier (metallic or ceramic walls). The special purpose is to counter flow the energy. These are often used in the burner portion. The flue gases or exhaust gases from the burner portion helps the inlet gases to heat…

Aim: To perform a literature review on stability analysis for ODE systems. The computed solution get close to the fixed points or equilibrium solution as x or t gets large is called stability   When do ODEs become unstable? When we use the explicit schemes the solution becomes unstable. These are not usable.…

Objective: To write a code solve the 1D linear convection equation for the various time step and to generate the plot for the velocity profile using the Matlab. Convection: The flow that combines diffusion and the advection is called convection. Advection: The bulk transport of mass, heat or momentum of the molecules.…

Aim: To write code to fit linear and cubic polynomial curve fit with a comparison of the original data and to plot the linear and cubic fit with raw data.   Curvefit: The curve fit is the process of constructing the curve or mathematical function which posses the closet proximity to the real series of data points. …

Objective: To solve the given equation and find the minimum pressure required to break a given thickness of the ice by using \'Newton Raphson\' iterative technique in python. The formula used to determine the minimum pressure required to break a given thickness of the ice is given by  where p denotes the cushion pressure,…

  Objective: The aim of this project is to write the code to stimulate an Otto cycle i.e to calculate the state variables at four different states, plot the PV diagram for the given condition and to calculate the thermal efficiency of the Otto cycle for a specified engine parameter using Matlab.    Theory…

Objective: To perform 1D flame speed analysis for a methane and hydrogen mechanism using python and cantera. 1D Laminar Premixed Flame Speed Analysis(Deflagration) Premixed Flame: A premixed flame is a flame formed under certain conditions during the combustion of a premixed charge (also called pre-mixture) of fuel and…

Sensitivity Analysis: Ignition delay is sensitive to the reaction mechanism, i.e some reaction is more sensitive to ignition delay and some are less sensitive. Hence, \'sensitivity analysis\' plays a vital role in tune the reaction mechanism. What is the sensitivity analysis and why?  Sensitivity analysis is the process…

Objective: To write a code solve the 1D linear convection equation for the various grid points and to generate the plot for the velocity profile using the Matlab. Convection: The flow that combines diffusion and the advection is called convection. Advection: The bulk transport of mass, heat or momentum of the molecules.…

The stoichiometric chemical equation of methane is  \"CH4 + 2(O2 + 3.76N2) = CO2 + 2H2O + 7.52N2\" In, TPX - T, P are the temperature, pressure and X- is the dictionary which gives the information about the mole fraction. The summation of the all mole fraction should be equal to 1. \"mole fraction = no.of moles of…

Objective: The aim of this project is to write the code to stimulate a Rankine cycle i.e to calculate the state variables at four different states, plot the T-S and H-s diagram for the given condition and to calculate the thermal efficiency of the Rankine cycle.  Introduction: Rankine cycle is the ideal thermal powerplant…

Objective: The aim of the project is to stimulate the movement of the simple pendulum(0-20s) which moves according to the below second order differential equation(ODE) and to create an animation of its movement.  `(d^2 θ)/(dt^2 )+b/m*(dθ/dt)+g/l (sin⁡θ )=0` where: b - damping coefficient l - length…