On the nondimensionalization of coupled, nonlinear ordinary differential equations

Conesa, Manuel; Pérez, Joaquín; Alhama, Iván; Alhama, F.

doi:10.1007/s11071-015-2233-8

Cited by 20 publications

(16 citation statements)

References 6 publications

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“…Non-dimensional analysis is known as a dramatically important method used to extract the dimensionless groups that affect the solution of a number of complex problems [37]. In order to further clarify the characteristics of the pressure oscillations, a preliminary non-dimensional analysis was performed.…”

Section: Non-dimensional Analysis Of the Pressure Oscillationsmentioning

confidence: 99%

The Effects of the Downstream Contraction Ratio of Organ-Pipe Nozzle on the Pressure Oscillations of Self-Resonating Waterjets

et al. 2018

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Self-resonating waterjets (SRWJs) are being widely used in the fields of energy exploitation, due to the significantly increased penetration rate of roller bits in deep-hole drilling. To further improve the impact and erosion abilities of SRWJs, the effects of the downstream contraction ratio of organ-pipe nozzle on the axial pressure oscillations were experimentally studied. The axial pressure oscillation peak and amplitude were used to evaluate the effects under two inlet pressures and various standoff distances. The results show that the downstream contraction ratio can affect the development trends of the pressure oscillations and determines the values of the peaks and amplitudes. Under the experimental conditions, 2.5 is the ratio that leads to the maximum peaks and amplitudes at almost all the testing standoff distances, while the ratio of 2 always results in the minimum ones. The development trend of the pressure oscillation peak for the ratio of 3.5 has a great change at an inlet pressure of 20 MPa. Generally, the relative pressure oscillations are more violent at an inlet pressure of 10 MPa, which is regardless of the contraction ratio. This study helps provide a guideline for determining the physical parameters required in the fabrication of organ-pipe nozzles used for deep-hole drilling.

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Section: Non-dimensional Analysis Of the Pressure Oscillationsmentioning

confidence: 99%

The Effects of the Downstream Contraction Ratio of Organ-Pipe Nozzle on the Pressure Oscillations of Self-Resonating Waterjets

et al. 2018

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“…The physical and geometrical characteristics that change are: It is worth mentioning here the emergence of m , an averaged value of the effective pressure, in the two dimensionless groups. Undoubtedly, the existence of m in the monomials can be explained not only by the nonlinearity of the problem but also by the kind of dependences in the constitutive relations (there are other nonlinear problems in which averaged variables do not emerge [18]). How do we choose m ?…”

Section: Verification Of the Results By Numerical Simulationsmentioning

confidence: 99%

“…The technique applied in this paper, which we call nondimensionalization of governing equations [16,17], starts from the governing equation in order to deduce the dimensionless groups. In this, after normalizing the variables, these and their changes are averaged -in fact, the equation itself is averaged -and assumed to be of the order of unity, a valid hypothesis in problems with relatively smooth nonlinearities, thus allowing the coefficients of the equations to be of the same order of magnitude and unequivocally providing the most precise solution as demonstrated in many studies [18]. Based on this methodology, Manteca et al [19] study the nonlinear consolidation problem with constitutive dependencies of logarithmic type, providing as a solution the universal curves and the dimensionless groups that govern the process.…”

Section: Introductionmentioning

confidence: 99%

Derivation of Universal Curves for Nonlinear Soil Consolidation with Potential Constitutive Dependences

García‐Ros

Alhama

Cánovas

et al. 2018

Mathematical Problems in Engineering

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Nonlinear consolidation scenarios, based on potential type constitutive dependences—like those proposed by Juárez-Badillo—and eliminating the more restrictive hypothesis of 1+e and dz constant, were characterized by the nondimensionalization process of the governing equations, providing the independent dimensionless groups that rule the main unknowns of interest. From these, universal curves have been depicted for both the characteristic time and the average degree of consolidation. The solutions were verified by numerical simulations and successfully compared in a case study, showing the simplicity of use of the curves and the high reliability of the solutions they provide.

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“…(1)- (4). The advantages of nondimensionalizations can be found in Al Kalbani et al [46] and Conesa et al [47]. The succeeding nondimensional variables are used to make the nondimensionalization:…”

Section: Physical and Mathematical Modelingmentioning

confidence: 99%

Heat Transportation in Copper Oxide-Water Nanofluid Filled Triangular Cavities

Uddin

Rahman²

2020

IJHT

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This paper performs a comparative analysis of two-dimensional transient water-copper oxide nanofluid flow and heat transportation inside a right-, acute-and obtuse-angled triangular cavity in the presence of a magnetic field. The vertical and inclined walls of the enclosure are maintained at a constant low temperature whereas the base wall is heated by a uniform thermal condition. The finite element method is used to solve the principal equations of nanofluid within the cavities along with the wall conditions. The outcomes of the present problem for a specific case are verified by the standard published numerical results. For comparative analysis, the isotherms, streamlines, the heat transfer distribution, the average heat transfer rate on the heated wall and within the cavities for the several pertinent parameters of the problem are demonstrated. The result shows that the nanofluid filled obtuse-angled triangular cavity exhibits a higher heat transfer rate for the lower and moderate values of the thermal Rayleigh number whereas for the higher thermal Rayleigh number acute-angled triangular cavity shows better heat transfer performance than that of the other two cases analyzed in the present study. The presence of a magnetic field lessens the heat transfer rate in nanofluid applications. The magnetic field inclination angle controls the flow and heat transfer of nanofluid. Nanofluid flow shows insignificant effects of the friction in cavities compared to that of the base fluid.

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On the nondimensionalization of coupled, nonlinear ordinary differential equations

Cited by 20 publications

References 6 publications

The Effects of the Downstream Contraction Ratio of Organ-Pipe Nozzle on the Pressure Oscillations of Self-Resonating Waterjets

The Effects of the Downstream Contraction Ratio of Organ-Pipe Nozzle on the Pressure Oscillations of Self-Resonating Waterjets

Derivation of Universal Curves for Nonlinear Soil Consolidation with Potential Constitutive Dependences

Heat Transportation in Copper Oxide-Water Nanofluid Filled Triangular Cavities

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