The 2D temperature distribution equation is  developed from Fourier\'s law of heat conduction. The temperature distribution equation we are dealing is for a 2D rectangular slab. The right hand term of which represents heat generation (as it has the differential with respect to time). In case of steady state, wherein…

Introduction: In this challenge, Navier Stoke's equations along a convergent divergent nozzle is to be solved, and find the variation of different significant parameters. The equations will be solved using MacCormack method, in both conservative form and non conservative form.  As we know that, a flow is possible…

Introduction: In the geometry shown in the figure below, the area of intrest is the step which is 0.08 metres from the inlet. As there is sudden change in cross section, fluid particles rotate and eddy formation happens. When the fluid has low enough viscosity, eddies form right after the fluid crosses the step. This occurs…

Introduction: Fluid is a substance which deforms (shear strain) continuously under the application of shear stress. The shear stress is applied by each layer on the adjacent layers above and beneath it. Due to this there exists a velocity gradient along the transverse length of fluid flow from a surface. The shear stress…

Introduction: In this project, the simulation of laminar flow of water through a pipe is done using 'symmetry' patch type (unlike in the previous project, where 'wedge' patch type is used). The inputs used are same, Reynold's number is 1000 and the fluid is water. When a plane is defined as a symmetry patch, it just means…

Aim:  To calculate Adiabatic Flame Temperature (AFT) for constant volume system and constant pressure system under varying conditions. The varying conditions and the analysis to be made are, When the process is of constant volume, the effect of equivalene ratio on AFT should be studied and plot the results (methane…

Objectives: To find the total number of moles of object A, which takes the inputs temperature (K), pressure (Pa) and a dictionary of reactant species, with their mole fractions To find the mole fraction and mass fraction of A using the function mass_fraction_dict() To explain the mole fraction input given to the object…

Objectives: To study the effect of preheating on Adiabatic Flame Temperature of the recuperator system To study the effect of preheating on combustion efficiency and fuel saving   Theory: In a gas turbine, to increase the overall efficiency, the exhaust gases coming out of the turbine are utilised to heat up the incoming…

Objective: To derive the reaction rate Ordinary Differential Equations (ODE) for the reaction mechanism below, `CO + O_2 rightarrow CO_2 + O` `O + H_2O rightarrow OH + OH` `CO +OH rightarrow CO_2 + H` `H + O_2 rightarrow OH + O`   Theory: A simple chemical reaction contains several elementary intermediate reactions,…

Introduction:  In mathematics, when a certain small amount of disturbance is inserted into the system, if the system tend to minimize it, it is called as a stable system. If the disturbance amplifies as the system progresses in time and does not decrease in value, it is called as an unstable system.  In Numerical…

Objectives: Solve the given set of coupled Ordinary Differential Equations (ODEs), implicitly, using multivariate Newton Rhapson technique Find the effect of time step on stability of the system The given ODEs are, `(dy_1)/(dt) = -0.04y_1 + 10^4y_2_y3` `(dy_2)/(dt) = 0.04y_1 - 10^4y_2y_3 - 3*10^7y_2^2` `(dy_3)/(dt) = 3*10^7y_2^2` …

Objectives: Plot the effect of pressure on auto ignition time, with constant inlet temperature Plot the effect of inlet temperature on auto ignition time, with constant pressure Plot the rate of change of molar concentrations of given species with time when inlet temperature is 500K, 1000K and pressure - 5 bar   Theory:…

Objective: To write a code that calculates ten top most sensitivity values of temperature, and plot the results with respect to corresponding reactions, of a GRI30 mechanism file   Theory: Sensitivity analysis in general is the study of change of dependent variable with respect to the independent variable i.e. the…

Objectives: Write a reaction mechanism reduction code in python starting from 40 to 325 most temperature sensitive reactions and calculate maximum temperature and ignition delay time for the reduced mechanism at varying values of temperature, pressure and equivalence ratio   Theory: Reaction mechanism is a sequence…

Objectives: Set up steady state simulations to compare the mixing effectiveness, in the two given tee - joints, at given conditions   Theory: The Reynold's Averaged Navier Stokes equations, which are used to describe turbulent fluid flows contain a term called 'Reynold's stress', which arises due to 'averaging' of…

Objectives: Simulate a steady and unsteady flow over a cylinder for a Reynold's number 100 and find the Strouhal Number in the latter case Simulate the flow over a cylinder for different values of Reynold's number and calculate the coefficient of Drag and Lift Analyze and discuss the effect of Reynold's Number on coefficient…