Numerical Solution of 2D Heat equation using Matlab.

Adiabatic flame temperature:       The temperature of the products in adiabatic combustion of fuel without applying for any shaft work is defined as the “Adiabatic Flame Temperature”.        In a combustion process, the heat produced during the exothermic chemical reaction…

The heat equation is a second order partial differential equation that describes how the distribution of some quantity (such as heat) evolves over time in a solid medium, as it spontaneously flows from places where it is higher towards places where it is lower. It is a special case of the diffusion equation. …

The first step to computing the Navier-Stokes’ equation is a wave propagation equation in 1D. The 1 dimensional linear convection equation: `(del u)/(del t) + c (del u)/(del x) = 0` 'u' is a quantity that is transported at a constant velocity. The constant velocity makes the equation linear in nature contrary to…

Problem Statement: The comparative error analysis of different order of approximations for the function sin(x)/x^3 is presented below using Finite Difference Method.  The matlab is used to code and plot the results.     The error and slope analysis are presented for 20 values of dx. The range is mentioned…

Problem Statement: Code to compare the effect of number of moles of carbon: clear all close all clc % Effect of number of moles of carbon on the stoichiometric co-efficient "ar". % Fuel - Alkane % Stoichiometric Combustion relation. % [(n*C)*((2*n+2)*H)] + ar[(2*O)*(3.76*2*N)] = a*(2*O)*C + b*(2*H)*O + % c*(2*N) n = 1:10;…

Matlab Code to evaluate the second order derivative of the analytical function exp(x)*cos(x) by Central and Skewed Scheme.  Taylor's Table: Taylor's series expansion of functions about a fixed point provides a means for constructing finite-difference operator of any order. A simple and straight forward way to carry…

Comparative Analysis of Symmetry and wedge Boundary condition and its validation with Hagon-Poiseuille Equations.  The matlab code for all the above conditions remains the same except changing angle theta. The simulation is first performed with wedge boundary condition replacing symmetry boundary conditions. The simulation…

For any pipe, calculation of velocity and pressure distribution is very important for designing any piping system. Flow inside the pipe could be laminar or turbulent. The principle parameter used to specify this flow regime is Reynold's number.                    …

BlockMesh drill down by OpenFoam. The geometry dimesions provided above are critically followed, but mesh is slightly modified. In the y direction 3 blocks has been created in blockmeshDict and for each block 10 cells has been created. So, in total there are 30 cells created in the y direction. In the x direction for first…

Flame Speed Analysis:- The flame is a self-sustaining propagation of a localized combustion zone at subsonic velocities. The flame occupies a small portion of the combustible mixture at any one time and it is propagating towards the unburned gases. The velocity at which reactants enter the flame will be the same as flame…

Objective: - In this assignment, we will be writing a Python/Cantera Code to find the 10 most sensitive reactions out of all the reactions in the GRI3.0 mechanism. The main parameters of this assignment are given below: - Write a code that takes all the reactions from the GRI mechanism and calculates 10 most sensitive…

Title:- Autoignition using Cantera Problem Statement:- Using the inbuilt reactor network code in Cantera, the following objectives to be attained. 1. Variation of Auto Ignition time of Methane with a constant temperature of 1250 K and pressure to be varied from 1 to 5 atm. 2. Variation of Auto Ignition time of Methane…

The equations given in the challenge to solve are:                         `dy_1/dt = -0.04*y_1 + 10^4*y_2*y_3`                         `dy_2/dt = 0.04*y_1 -10^4*y_2*y_3 - 3*10^7*y^2`      …

Suppose we have an ordinary differential equation,                                 `dx /dt = f(x)` equillibria will be reached when, `dx/dt = 0` i.e `f(x) = 0` If `f(x_e) = 0`, then `x(t) = x_e` is a solution. The initial…

Steady State Simulation.       The geometry is created in DesignModeler and meshing is done with tri mesh and inflation layer around the cylinder wall. The total number of elements is 41638, which gives pretty fine mesh. Reynold's number maintained at 100, by giving velocity input 1 m/s, density 1 kg/m3…

Three cases are presented here one by one and comparative observations are written in the end. For all the cases the number of mesh elements is kept almost the same and hot and cold temperature is taken as 25 0C and 10 0C resp. For all the cases hot inlet is maintained in x-direction and cold inlet in a y-direction. …

          A recuperator is a heat exchanger in which energy from the exhaust of hot combustion products, i.e flue gases, is transferred to the inlet air for increasing its temperature. The effect of such preheating of air can be seen in improving combustion efficiency as well as Adiabatic Flame…

Four reactions Given are: Compact Notation: j        Species                  i           Reactions 1        `CO`     …

Gearbox Sloshing Effect          Sloshing refers to the movement of liquid which has a free surface inside the object or container(which is, typically, also undergoing motion). Sloshing dynamics or effect significantly alters the system dynamics. Like in a moving tank, sloshing is a violent resonant…

CFD analysis of Conjugate Heat Transfer on a graphics card.              The conjugate heat transfer is the study when heat transfer is taking place from solid to fluid or vice versa. In this case, the heat transfer will take place from an electronics component to air through conduction…

          The parametric study allows the user to reduce the repeated task and saves time in defining the same physics which contain variations. Ansys workbench allows a user to set such variations as an input parameter and get the desired output as an output parameter. Such parameters can be set…

Cyclone Separator:                 Cyclone separators are gas cleaning devices that utilize a centrifugal force created by a spinning gas stream to separate particulate matter from the gas. The difference in specific gravity allows centrifugal force to separate out the particulate…

 Rayleigh–Taylor instability:-                       Rayleigh–Taylor instability (RTI) occurs whenever fluids of different density are subjected to acceleration in a direction opposite that of the density gradient. It is a dynamic process whereby…

The Conjugate Heat Transfer(CHT):-                     Heat transfer in solids and heat transfer in fluids are combined in the majority of applications. This is because fluids flow around solids or between solid walls and because solids are usually immersed in a fluid.…

Ahmed body and its importance:-          The Ahmed body is a benchmark model widely used in the automotive industry for validating the simulation codes or results.           The Ahmed body represents a simplified, ground vehicle geometry of a bluff body type. Its shape…