Thermal behavior of fluid within pipes based on discriminated dimensional analysis. An improved approach to universal curves

Seco-Nicolás, Manuel; Alarcón, Mariano López; Alhama, F.

doi:10.1016/j.applthermaleng.2017.11.091

Cited by 10 publications

(7 citation statements)

References 27 publications

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“…For the deduction of the dimensionless groups that rule the solutions of the problems described, the technique of discriminated and normalized non‐dimensionalization of the governing equations will be used (Manteca Jr et al 2012; Seco‐Nicolás et al 2018). This protocol, formal from the physical–mathematical point of view, leads to the least number of independent dimensionless groups and to the most precise solution in terms of the pi theorem (Buckingham 1914).…”

Section: Methodsmentioning

confidence: 99%

“…Thus, for both scenarios and from the mathematical model, these groups are deduced using the technique of discriminated and normalized non‐dimensionalization of the governing equations. This protocol has always been shown to be efficient in a large number of coupled problems of similar or greater complexity (Alhama et al 2012; Cánovas et al 2015; Cánovas et al 2016; Seco‐Nicolás et al 2018). Discrimination is particularly necessary to deduce the most accurate groups in anisotropic media.…”

Section: Introductionmentioning

confidence: 99%

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Dimensional Characterization of Groundwater Oblique Flow Problems with Heat Transport

Jiménez-Valera¹,

Alhama

2023

Groundwater

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A dimensional study of two problems in which groundwater flow is oblique has been carried out in order to characterize the vertical profiles of temperature along the domain affected by the flow, determining an input region in which the profiles depend on the horizontal position followed by a region in which profiles only depend on the vertical component of the flow. In the first problem, the horizontal and vertical components of velocity are constant. In the second scenario, the oblique flow of groundwater is generated because in the boundary conditions, the hydraulic potentials present a constant value. From the discriminated dimensional analysis of the mathematical model (governing equations and boundary conditions), the dependencies of the unknowns of greatest interest, characteristic lengths for the development of temperature‐depth profiles, velocity profiles and the temperature field, with the dimensionless groups deduced are established. Once these dependencies have been verified, they are graphically represented by means of curves and surfaces as universal solutions to these problems. Based on these universal solutions an inverse problem protocol for estimating water flows from temperature measurements is proposed. The use of universal graphs of the two proposed scenarios avoids the large number of numerical simulations that this type of problem required.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dimensional Characterization of Groundwater Oblique Flow Problems with Heat Transport

Jiménez-Valera¹,

Alhama

2023

Groundwater

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“…About the length of the pipe, it has been used the concept of characteristic length, l*, defined as the length needed for the fluid to fully develop the thermal process [26], in…”

Section: The Network Modelmentioning

confidence: 99%

“…Other researchers have studied the flow with periodically varying inlet temperature in pipes of different shapes [23], pipes subjected to a sudden [24] or periodical change [25] in external heat or ambient temperature, etc. Also significant is the formulation of the concept of characteristic length of the process, carried out by discriminated dimensional analysis by Seco-Nicolás et al [26]. All these studies, based on radial symmetry, assume the 2D hypothesis.…”

Section: Introductionmentioning

confidence: 99%

Alarcón¹,

Seco-Nicolás²,

Luna-Abad³

et al. 2023

Pipeline Engineering - Design, Failure, and Management

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This chapter studies the fluid flow within pipes subjected to thermal asymmetrical boundary conditions. The phenomenon at hand takes place in many real-world industrial situations, such as solar thermal devices, aerial pipelines. A steady-state analysis of laminar forced-convection heat transfer for an incompressible Newtonian fluid is studied. The fluid is considered to flow through a straight round pipe provided with straight fins. For the case studied, axial heat conduction in the fluid has been considered and the effects of the forced convection have been considered to be dominant. A known uniform temperature field is applied at the upper external surface of the assembly. The 3D assembly has been created combining cylindrical and Cartesian coordinates. The governing differential equation system is solved numerically through suitable discretization in a set of different finite volume elements. The results are shown through the thermal profiles in respect of longitudinal and radial-azimuthal coordinates and the problem characteristic length. To facilitate the resolution of this phenomenon, an open computing platform called HEATT©, based on this model, has been developed, and it is also shown here. The platform is now being built and is expected to be freely available at the end of year 2022.

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“…In each case, the value of one or more of the parameters involved has been significantly altered, but the numerical value of the dimensionless groups has been retained so that it is verified that the same pattern of solutions is obtained for the whole set of cases; or the value of the groups has been modified appropriately to confirm that the form of the solutions changes. As a deduction technique for these groups, the nondimensionalization of governing equations [8][9][10] has been used, a form of application of the pi theorem [11], thus allowing the dimensionless parameters involved in the problem (void ratio and compression index), and that they would form independent dimensionless groups, to be included in the inferred groups. In the nondimensionalization process, which has been carried out in terms of both excess pore pressure dissipation and settlement, the characteristic time of consolidation is introduced as a reference, an unknown that is incorporated into one of the resulting monomials and whose dependency with the rest of the groups is established by the pi theorem.…”

Section: Introductionmentioning

confidence: 99%

Dimensionless characterization of the non-linear soil consolidation problem of Davis and Raymond. Extended models and universal curves

García‐Ros

Alhama

2019

Applied Mathematics and Nonlinear Sciences

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The dimensionless groups that govern the Davis and Raymond non-linear consolidation model, and its extended versions resulting from eliminating several restrictive hypotheses, were deduced. By means of the governing equations nondimensionalization technique and introducing the characteristic time concept, both in terms of settlement and pressures, was obtained (for the most general model) that the average degree of settlement only depends on the dimensionless time while the average degree of pressure dissipation does it, additionally, on the loading ratio. These results allowed the construction of universal curves expressing the solutions of the unknowns of interest in a direct and simple way.

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Thermal behavior of fluid within pipes based on discriminated dimensional analysis. An improved approach to universal curves

Cited by 10 publications

References 27 publications

Dimensional Characterization of Groundwater Oblique Flow Problems with Heat Transport

Dimensional Characterization of Groundwater Oblique Flow Problems with Heat Transport

Forced Laminar Flow in Pipes Subjected to Asymmetric External Conditions: The HEATT© Platform for Online Simulations

Dimensionless characterization of the non-linear soil consolidation problem of Davis and Raymond. Extended models and universal curves

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