Result Discussion of Curve Fitting MATLAB Program

  Flux  Limiters:  We can study the shocks and discontinuity that arises in the Engineering problems,particularly Fluid Dynamics problems by applying numerical schemes. It can be said that Low Order Schemes are usually stable but quite dissipative around the points of discontinuity. On the other side, High…

Given, `A = [[5,1,2],[-3,9,4],[1,2,-7]], x=[(x_1),(x_2),(x_3)]`  and  `B = [(10),(-14),(33)]`   by Jacobi method:      `x = -D^(−1) .(L + U).x_(old)+D^(−1).B` by Gauss Siedal method:      `x = -(D + L)^(−1).U.x_(old)+(D + L)^(−1).B` by…

TAKEN INPUTS: Diameter = 0.04 m Length = 0.1 m Density of Air = 1.225 kg/m3 Dynamic Viscosity = 18.6e-6 Pa.sec at 20 Degree Celsius Reynold No. = 20, 40, 100 We know that, Reynold No. = (Density x Velocity x Diameter)/Dynamic Viscosity By applying above inputs in the Formula, we obtained: Velocity for (Re = 20) is 0.007592…

  Formulae involved: a) Entry Length of a Pipe for Laminar Flow, L = 0.07*Re*D b) Velocity = (Re*mu)/(rho*Diameter) c) Hagen-Poiseuille\'s Pressure Drop, dP = -(32*mu*u_avg*L)/(D*D) Here, u_avg = u_max/2 d) Hagen-Poiseuille\'s Velocity Distribution, u(r) = -[1/(4*mu)]*(dP/dX)*[(R*R)-(r*r)] Here, r = Radius at which…

Genetic Algorithm (GA)s are Optimization Algorithms based on Darwin's theory of Natural Evolution. It is dependent on natural selection in natural genetics.                  GA is based on an analogy with the genetic behaviour within a population of indivduals: There are…

Consider a large Uranium Plate of thickness, L=4 cm and thermal conductivity, k=28 W/m.Degree Cel in which Heat is generated uniformly at constant rate of Hg=5x10^6 W/m^3. One side of the plate is maintained at 0 Degree Cel by iced water while the other side is subjeted to convection…

  OBTAINED PLOTS: (A) Linear Polynomial Fits:             Comparison for Best Fit between the above 2 Curve Fits:         (B) Cubic Polynomial Fits:             Comparison for Best Fit between the above 2 Curve Fits:    …

  (a) Symmetrically Simulated for Wedge Angle = 10 Degree, 25 Degree and 45 Degree (b) Axi-Symmetrically Simulated for Wedge Angle = 4 Degree   SCREENSHOT  of  the  25  Degree  Wedged  Pipe'  Inlet  in  ParaView:   Plots  Obtained: Comparison  of …

  PV Diagram obtained:   RESULT obtained for PV plot:                                Area under the P-V diagram: 456.064 m²                   Power Output of the engine: 11.402 kW…

Governing Equations for Non-Conservative form: (A) Continuity Equation: `(delrho)/(delt) = -rho(delV)/(delx)-rhoV((del(lnA))/(delx)) - V((delrho)/(delx))` (B) Momentum Equation: `(delV)/(delt) = -V(delV)/(delx) - 1/gamma((delT)/(delx) + T/rho(delrho)/(delx))` (C) Energy Equation: `(delT)/(delt) = -V(delT)/(delx) - (gamma-1)T[(delV)/(delx)…

To create PV diagram of Otto Cycle, a Function of engine Kinematics must be called. And the file name of created Function Program must be same as that of the Function   i.e. Otto_engine_kinematics % Otto cycle engine kinematics Function % function [v]=Otto_engine_kinematics(bore, con_rod, stroke,…

 % Function program % function [dtheta_dt]=ode_pendulum(t,theta,m,g,L) theta1=theta(1); theta2=theta(2); omega=g/(L*m); dtheta1_dt=theta2; dtheta2_dt=-(omega^2)*sin(theta1); dtheta_dt=[dtheta1_dt;dtheta2_dt]; end   % Main program % close all clear all clc %Inputs% m=0.8; %Mass of the Pendulum in Kg g=9.81; %Acc…

Given Combustion Process for Alkane fuels is, `C_nH_(2n+2)+ar(O_2+3.76 N_2)=aCO_2+bH_2O+cN_2` Now here `n=a` ,  `2n+2=2bimpliesb=n+1`   and   `ar=a+b/2=n+(n+1)/2=(3timesn+1)/2` Again Combustion Process for Alkene fuels will be, `C_nH_(2n)+ar(O_2+3.76 N_2)=aCO_2+bH_2O+cN_2` Here `n=a`…

  First Order Error Function: function Error_First_order_der=frst_order(x,dx) Analytical_der=((cos(x))/x^3)-((3*sin(x))/x^4); Numerical_First_order_der= ((sin(x+dx)/(x+dx)^3)-(sin(x)/x^3))/dx; Error_First_order_der=abs(Numerical_First_order_der-Analytical_der); end   Second Order Error Function: function Error_Second_order_der=scnd_order(x,dx)…

Consider a large Uranium Plate of thickness, L=4 cm and thermal conductivity, k=28 W/m.Degree Cel in which Heat is generated uniformly at constant rate of Hg=5x10^6 W/m^3. One side of the plate is maintained at 0 Degree Cel by iced water while the other side is subjeted to convection to an environmet at 30 Degree Cel with…

  import matplotlib.pyplot as plt # Inputs # # Air density in Kg/m^3 density = 1.2 # Constant Frontal Area of Cyclist in m^2 area = 0.4 # (1) For "Drag Force vs Vel" for a constant Drag Coeff # # Velocities of the cycle in m/sec V = [1,2,3,4,5,6] # Constant Drag Coefficient cd_const = 0.47 fD = [] for v in V: fD.append(0.5*density*area*v*v*cd_const)…

  close all clear all clc % Inputs % l1 = 1; l2 = 0.5; theta1 = linspace(0,90,10); theta2 = linspace(0,90,10); %Origin x0 = 0; y0 = 0; ct = 1; for i = 1:length(theta1) THETA1 = theta1(i); for j = 1:length(theta1) THETA2 = theta2(j); %Connector of Link1 and Link2 x1 = l1*cosd(THETA1); y1 = l1*sind(THETA1); %Coordinates…

  Grid  Dependency  Test:  The Test is done at Valve Lift  =  0.001 m for three different Mesh SetUp.   Mesh SetUp:           (1)  Number of cells in X Axis  =  16                      …

  Total  Number of Iterations  taken  for  Simulation  =  500   CUT  PLOTs  Obtained  for  Velocity: (A)  Outlet  Velocity =  10 m/sec:     (B)  Outlet  Velocity =  20 m/sec:     (C)  Outlet …

  Problem  SetUp: Velocity  =  0.05  m/sec Start  Time  =  0  sec End  Time  =  1  sec delta  Time  for  0.2  Graded  Mesh  =  0.00001  sec delta  Time  for  0.5  Graded  Mesh  = …

  Assembled  Machine  Vice:       Drafting: (1)  Clamping  Plate:     (2)  Handle  Cap:     (3)  Handle:     (4)  Jaw:     (5)  Lock  Nut:     (6)  Moveable  Jaw:     (7) …

  (1)  Pipe  Vice:   (2)  Knuckle  Joint:   (3)  Screw  Jack:   (4)  Toy  Train  Model:   (5)  Socket  Spigot  Joint:   (6)  AirCraft  Model:      

  Sheet Metal Designs:       Surface Models:          

  RESULTS Obtained:   (A) Angle of Attack = 0 Degree:     (B) Angle of Attack = 2 Degree:     (C) Angle of Attack = 4 Degree:     (D) Angle of Attack = 6 Degree:     (E) Angle of Attack = 8 Degree:     (F) Angle of Attack = 10 Degree:       Lift…

STEADY STATE HEAT EQUATION: 2D Steady State Heat Conduction Equation is, `(del^2T)/(delx^2) + (del^2T)/(dely^2) = 0`   by  EXPLICIT METHOD: Now Discretizing the Equation, `=> (T_(i-1,j) - 2T_(i,j) + T_(i+1,j))/(Deltax^2) + (T_(i,j-1) - 2T_(i,j) + T_(i,j+1))/(Deltay^2) = 0` `=>(2T_(i,j)) /(Deltax^2) + (2T_(i,j))…