Fig 1.
Plastic injection manufacturing.
Fig 2.
The schema of framework for the manuscript.
Table 1.
Obtained outcomes of DSC relies on suggested method with diverse bandwidth (2S+1), regulation parameter γ, grid size αx= αy = βx = βy = 1, x0 = y0 =0.5, t = 0.0006, x = y = 0.5.
Table 2.
Variation of the results by RDK with different parameters (T), RSK methods using SSP-RK54 scheme and optimal ones in [0,1]2 with various grid sizes Mx X My with Mx = My .
Table 3.
L∞ error norms in [0, 1]2 with and different grid points Mx × My with Mx = My. αx =0.1, αy = 0.01, βx = βy = 0.5, x0 = y0 =0.5, t = 0.0025,(2S+1) = 5, γ = (5*gx).
Table 4.
L2 error norms in [0, 1]2 with and different grid points Mx × My with Mx = My. αx =0.1, αy = 0.01, βx = βy = 0.5, x0 = y0 =0.5, t = 0.0025,(2S+1) = 5, γ = (5*gx).
Table 5.
ROC in [0, 1]2 with and various grid sizes Mx × My with Mx = My αx =0.1, αy = 0.01, βx = βy = 0.5, x0 = y0 =0.5, t = 0.005,(2S+1) = 5, γ = (5*gx).
Table 6.
Comparisons between DSC kernels and optimal solution in [0, 1]2 with various with Mx = My = 5. αy = 1, βx = βy = 1, x0 = y0 =0, t = 0.0004,(2S+1) = 5, γ = (5*gx), x = y = 0.5.
Table 7.
Comparisons between DSC kernels and optimal solution in [0, 1]2 with various with Mx = My = 5. αx = αy, βy = 1, x0 = y0 =0, t = 0.004,(2S+1) = 5, γ = (5*gx), x = y = 0.5.
Fig 3.
Numerical solution using RSK-SSPRK54 at for several times.
Fig 4.
Numerical solution using RDK-SSP-RK54 at for several locations.
Fig 5.
Physical behavior of proposed techniques compared to optimal solution at a) Optimal b) DLK-SSPRK54 c) RSK-SSPRK54 d) RDK-SSPRK54.
Fig 6.
Contour plots of absolute errors of DLK-SSP-RK54 technique compared to optimal solution atαx = αy= βx = βy = 1, x0 = y0 = 0.5, t = 0.6msec a) Mx × My = 5 X 5 b) Mx × My = 9 X 9.
Fig 7.
Influence ofαx, αy, βx, βy on the results using RDK-SSP-RK54 at x0 = y0 = 0.5. a) b) c).
Fig 8.
Distribution of 2- dimensional convection-diffusion equation using RD K-SS P-RK54 withax = ay = 0.5, βx = βy = 0.8, x0 = y0 = 0.5 at different times a) Time = 0.4 b) Time = 4.
Fig 9.
RDK-RK54 solution withax = ay = 1, x0 = y0 = 0.5 at time = 2 a) βx = βy = -1 b) βx = βy = 0 c c) βx = βy = 1 d). βx = βy = 10.
Table 8.
The pseudocode of Mat-PYS controlling system.
Fig 10.
Moving on the meshes suggested via mathematical phase [77].
Fig 11.
Impact of Fractional parametersα, β on concentration field at t = 0.4 at.
Fig 12.
Influence of fractional on Fluid velocity (m/s) of conversion behaviour [] at Peclet number = 3.5, Heat and mass Grashof number = 2.6 and 4.5, when t = 0.4 and 0.02.
Fig 13.
The topology optimization zone effect.
Fig 14.
The significant variables effect the quality of product.
Fig 15.
The suggested flow of convection-diffusion under control of DSC-DQM–(RSK or RDK).
Table 9.
The position of air inlet to and
.
Table 10.
The defect per million opportunity occurrences for most defective types .
Table 11.
OEE without and with using the proposed mathematical model and improve injection process.
Fig 16.
Experimental moist and Temperature data predicted by a suggested mathematical model as a function of time through digital twin simulation.
Table 12.
Comparison before and after programing digital Mat-PYS with proposed convection-diffusion mathematically behaviour.
Fig 17.
The Optimisation of the injection controller.
Table 13.
The comparison of fifteen mechanisms with the proposed digital Mat-PYS simulator [95].
Table 14.