1D Heat conduction Equation - FVM

Objective: - Simulation of Conjugate Heat Transfer in a solid pipe ------------------------------------------------------------------------------------------------------------------- Case setup: Solid: Aluminium Fluid: Air start Time: 0 s End Time: 0.5 s Inlet velocity: 3.64 m/s Outlet Pressure: 1 bar Super-cycle Modelling:…

Problem Description: - To simulate the flow in the shock tube. ------------------------------------------------------------------------------------------------------------------- Shock Tube: A shock tube is a device in which a shock is produced in a long tube by rupturing of the diaphragm. The shock tube is a long tube…

Project Description: - To run a transient simulation on the throttle body with the rotation of the throttle --------------------------------------------------------------------------------------------------------------- The throttle is a mechanism which controls the fluid flow by obstruction. The application of throttle…

Problem Definition:      - To derive the Compact Notation for the chemical reaction ------------------------------------------------------------------------------------------------------------------ Reaction: `CO + O_2 overset(kf_1)underset(kr_1)(=)CO_2 + O` `O+H_2O overset(kf_2)underset(kr_2)(=)OH+OH` `CO+OH…

Problem Description: 1) Simulate the flow through Backward-facing Step with three Base Mesh. ---------------------------------------------------------------------------------------------------------------- Backward Facing Step Backward step flow is the representative separation model used in the industry to validate the…

Problem Description: 1) To run the simulation for 3 Base Mesh sizes in the Channel flow and analyze the Plots -----------------------------------------------------------------------------------------------------------------  Channel FLow: The channel flow has been simulated with 3 different Mesh sizes, 2e-4m, 1.5e-4m,…

  Shock wave: As the object moves through the gas, the gas molecules deflected around the object. when an object moves faster than the speed of sound, and there is an abrupt decrease in the flow area, shock waves generated in the flow. Shock waves are very small regions in the gas where the gas properties by…

In this, the simulation is carried out for the flow through the throttle body. The main objective of the simulation is that the simulation is carried out by steady state condition.  The throttle is a mechanism which controls the fluid flow by obstruction. The application of throttle is widespread from domestic usage…

Problem Description: 1) To compare the Analytical and Numerical Method of 1D Heat Conduction Equation using C++ ------------------------------------------------------------------------------------------------------------------- Solving Analytically:   The equation is linear, so y = mx + b m = slope b = constant or…

  Problem Definition:  To Solve the set of Ordinary Differential Equation Implement the Multivariate Newton Raphson Solver using Python Run the Simulation for 10 Minutes -------------------------------------------------------------------------------------------------------- ODE system `dy_1/dt = -0.04y_1 + 10^4y_3y_3`…

Introduction: Stability is one of the significant issues in the numerical solution of the differential equation. Stability requires a time step that is small, and the numerical error is damped, and not amplified. This type of problem is called stiff. A stiff system is one involving rapidly changing components together…

Problem Description: 1) Plot the variation of Auto Ignition time of Methane with a constant temperature of 1250K and pressure varying from 1 to 5 atm. 2)Plot the variation of Auto Ignition time of Methane with a constant pressure of 5 atm and temperature varying from 950K to 1450K. 3) rate of change of molar…

Problem definition:  1) Calculation of Adiabatic Flame Temperature for various pre-heating temperature ranging    from 298k to 600k 2) Calculation of Percentage of fuel savings to the change in pre-heating temperature  ---------------------------------------------------------------------------------------------------------------…

Objectives: 1) Analyze the flame speed of Methane and Hydrogen Mechanism files. ---------------------------------------------------------------------------------------------------------------- The Conservation equation for the Combustion process: Mass Conservation: `(partialrho)/(partialt) + del/(delx_i) rhou = 0`…

Problem Description:   - To calculate the Top sensitive reaction in GRI 3.0 Mechanism ------------------------------------------------------------------------------------------------------------------- An essential tool that is used to analyze the effect of the input parameters is Sensitivity analysis. It is needed…

1.1 Introduction:             Conduction is a fundamental transport phenomenon of Heat. In this study, the 2D steady state and Unsteady state Heat conduction equation was analyzed. For steady state, the primary iterative solvers have been implemented to study the rate of convergence. The iterative…

Problem Definition: 1) Effect of equivalence ratio on Adiabatic Flame temperature (AFT) and comparing with Cantera for methane 2) Constant pressure chamber with Heat loss        - Calculation of AFT for Alkane, Alkene, Alkyne with the Heat loss of 35 percent        - Comparison…

Matlab code for the 1D Linear Convection equation `(du)/(dt) + c*(du)/(dx) = 0` Assumption: Numerical solution to the wave equation 1. Assume that the domain length is L = 1m 2. The initial velocity profile is a step function. It is equal to 2m/s between x= 0.1 and 0.3 and 1m/s everywhere else 3. Use first order forward…

A robot with two links with length l1 and l2, and having an angle between them are `theta1` and `theta2`with respect to X-axis: In this simulation, the various angle for the robotic link had been calculated using Python The module used in the python is: 1)"matplotlib" for plotting 2)"math" for mathematical operation…

Function `5 - (x-2)^2-2(y-1)^2` Constraint: `x+4y = 3`   `5 - (x-2)^2-2(y-1)^2` `5-(x^2-4x+4)-2(y^2-2y+1)` `f(x) = 5-x^2+4x-2y^2+4y-6` `g(x) = x+4y-3`    `f =f(x) + lambdag(x)`   `f = 5-x^2+4x-2y^2+4y-6 + lambda(x+4y-3)`   `(delf)/(delx) => -2x + 4 +lambda = 0 to A` `(delf)/(dely) => -4y+4+4lambda…