[Solved]Consider Fully Developed Flow Rectangular Duct Constant Streamwise Pressure Gradient Cross Q37269311
Consider a fully developed flow in a rectangular duct with a constant streamwise pressure gradient. The cross-section of the duct, along with its dimension and the coordinate system used, is illustrated in below. The x-momentum equation is reduced to lu lu It is required to numerically solve the above equation using Matlab by Point Gauss-Seidel scheme (30 points) and Line Gauss-Seidel scheme (30 points) and subject to following set of data JM-61 (Maximum number of grid points in y) KM-41 (Maximum number of grid points in z) L-1.5 m and h-1.0 m (duct is 3m x 2m) The fluid is oil with a viscosity of 0.4 N.s/m2. The value of pressure gradient to be considered is: P–25 N/m2/m op ox Use a convergence criterion of 0.00001 over the entire domain. The analytical solution is given by cosh(m T 1 / 2L) -1,3,5 Where ua represents the velocity obtained by the analytical solution. Compute the error distribution within the domain determined by the following relation ua 1 * 100.0 ER = ABS uadj.k) ua(i,k) Plot the numerical solution (u), analytical solution (ua), and the error within the domain for all the z locations and at each y locations at increments of 0.5 m for both cases. Show transcribed image text Consider a fully developed flow in a rectangular duct with a constant streamwise pressure gradient. The cross-section of the duct, along with its dimension and the coordinate system used, is illustrated in below. The x-momentum equation is reduced to lu lu It is required to numerically solve the above equation using Matlab by Point Gauss-Seidel scheme (30 points) and Line Gauss-Seidel scheme (30 points) and subject to following set of data JM-61 (Maximum number of grid points in y) KM-41 (Maximum number of grid points in z) L-1.5 m and h-1.0 m (duct is 3m x 2m) The fluid is oil with a viscosity of 0.4 N.s/m2. The value of pressure gradient to be considered is: P–25 N/m2/m op ox Use a convergence criterion of 0.00001 over the entire domain. The analytical solution is given by
cosh(m T 1 / 2L) -1,3,5 Where ua represents the velocity obtained by the analytical solution. Compute the error distribution within the domain determined by the following relation ua 1 * 100.0 ER = ABS uadj.k) ua(i,k) Plot the numerical solution (u), analytical solution (ua), and the error within the domain for all the z locations and at each y locations at increments of 0.5 m for both cases.
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