Solving 1D Linear Convection Equation for Different Grid Poins

REPORT: AIM: To perform a conjucate heat transfer(CHT) analysis for an exhaust manifold of an I.C Engine. OBJECTIVES: To simulate the exhaust air in exhaust manifold. To find out the area where is the maximun heat transfer. Effect of coarse and fine mesh. Adding inflation layer to the boundary to get the accurate heat…

REPORT: AIM: To simulate for the case of ahmed body and check the drag and lift values and also check the grid independence of the solution. OBJECTIVES To Describe Ahmed's body and its importance.  Explain the reason for the negative pressure in the wake region.   Explain the significance of the point of…

REPORT: AIM: To find out the mixing efficiency of the short and long tee with different momentum ratio of 2 and 4, When the hot inlet temperature is 360C & the Cold inlet is at 190C with the hot inlet velocity of 3m/s. To Use the k-epsilon and k-omega SST model for the first case and based on your judgment use…

REPORT: AIM: To write code to solve the 1D supersonic nozzle flow equations using the Macormack Method. OBJECTIVES: Write separate functions for conservative and non-conservative forms Figure out the minimum number of cycles for which the simulation should be run in order for convergence Compare the normalized mass flow…

REPORT: AIM: To observe the effect of time step on stability of the solution for both implicit and explicit methods. To show how an unstable solution looks like. At what CFL number does the solution becomes unstable. TRANSIENT CASE: There two methods used in the transient case, Implicit method Explicit method In the explicit…

REPORT: AIM: To compare the fastest steady state simulation and the fastest transient simulation and also to write a detailed report of the results. TRANSIENT CASE: In the transient case the program is solved by two methods, Explicit method  Implicit method The explicit method is solved directly since all the values…

REPORT: AIM: To see the effect of time step size in the 1D Linear wave equation,by using time marching method of finite difference method. EXPLANATION: The governing equation of 1D linear wave equation is given as, `frac{delu}{delt} = c.frac{delu}{delx}`.............(1) Here, c is the constant `frac{delu}{delt}` = Time…

REPORT: AIM: To solve the 1D Linear convection equation. 1D Linear Convection Equation: `frac{delu }{delt} + cfrac{delu}{delx} = 0` where, `frac{delu}{delt} =`Time derivative `frac{delu}{delx}` = Convective term 'u' is a quantity that is transported in a constant velocity.The constant velocity makes the equation linear…

REPORT: AIM: The aim of this project is to observe the effect of dx in error for first,second and third order approximations using matlab. PROCEDURE: The analytical function we consider is f(x) = `frac{sin(x)}{x^3}`,then the analytical derivative is calculated for it. The forward difference,central difference and…

REPORT: DISCRETIZATION BASICS OBJECTIVE: In this project the first order derivative is discretized to obtain the desired order of accuracy. It is then discretized with forward differencing scheme to compare the results. FORMULA FOR THE FOURTH ORDER APPROXIMATION USING FIRST DERIVATIVE:  GIVEN: function f(x) = sinx/x^3…

REPORT: OBJECTIVES: Obtain temperature distribution for a thin square plate by 2D heat conduction solution. Solve both steady and unsteady 2D heat conduction equation. The transient state is solved using both implicit and explicit methods. The implicit method requires iterative solvers such as jacobi method,gauss-seidal…

REPORT: AIM: The aim of the project is to plot the comparison of effect of number of mole of carbon on the stiochiometric co-efficient "ar"using MATLAB.Also, observe this comparison wih respect to different fuel types(Alkane, alkene and alkyne).  EQUATION: Where, n = No.of moles of C ar = Stoichiometric co-efficient…