#ODE of the motion of a pendulam #Inputs b=0.05; g=9.81; l=1; m=1; Here, 'b' is the damping coefficient, 'g' is the tacceleration due to gravity, 'l' is the length of string by which ball is attached, 'm' is the mass of ball. #Initial condition theta_0 = [0;3]; This array saves the initial values of theta i.e. angle made…

Aim: To undertand the concept of genetic algorithm, stalagmite function and ways to optimise the stalagmite function. Also, to write a code in MATLAB that will optimise the stalagmite function using 'ga' command and its attributes. Governing equations: Stalagmite function, `f(x,y)=f_(1,x)*f_(2,x)*f_(1,y)*f_(2,y)` where,…

Aim: To analyse the data from NASA thermodynaic data file and to evaluate molecular weights of species and it's thermodynamic properties such as Cp, H and S with respect to temperature range, by using MATLAB Program. Governing Equations: NASA came up with polynomials that can be used to evaluate thermodynamic properties…

Aim: To create a Rankine Cycle Simulator using MATLAB Theory: Rankine cycle is the theoretical cycle on which the steam turbine (or engine) works. The schematic diagram and T-s diagram of Rankine Cycle, are given as follows,                     It comprises of…

Aim: To derive equations for 4th order approximations of the second-order derivative by using methods i.e. Central difference, Skewed right-sided difference, Skewed left-sided difference and to evaluate the results from MATLAB program for the given methods with the help of Taylor's table. Theory: Central difference method…

Aim: To solve steady as well as unsteady(transient) 2D heat conduction equation by using the point iterative techniques. Theory: The 2D heat conduction equation, eqn.1, is stated as follows, `(delT)/(delt)+alpha((del^2T)/(delx^2)+(del^2T)/(dely^2))=0` This equation can be solved by either steady state approach…

Aim: To investigate steady-state flow-field variables of both the conservative and non-conservative forms of the governing equations viz. continuity, momentum and energy equation, and to compare these two forms by comparing their solutions. Theory: We consider the steady, isentropic flow through a convergent-divergent…

Aim: To simulate flow over a backward facing step in OpenFoam and to evaluate velocity profile at entry and step regions with/without grading factor. Theory: Here, we have considered an incompressible-laminar-viscous flow. The transient simulation has to be performed. OpenFoam has built-in tutorials which are categorized…

Finite Volume Method: The Finite Volume Method (FVM) is a numerical technique that transforms the partial differential equations representing conservation laws over differential volumes into discrete algebraic equations over finite volumes (or elements or cells). Major differences between FDM & FVM: On structured grids,…

Aim: To simulate a flow through mixing tee and understand the mixing effectiveness based on length of the mixing tee and the momentum ratio given that the hot inlet temperature is `36^0`C and the cold inlet is at `19^0`C. Theory: Mixing Tees utilizes a specifically engineered internal geometry to efficiently…