Fabio Andrade Pontes, Emanuel Negrão Macêdo, Clauderino da Silva Batista, João Alves de Lima and João Nazareno Nonato Quaresma
The purpose of this study is to show the procedure, application and main features of the hybrid numerical-analytical approach known as generalized integral transform technique by…
Abstract
Purpose
The purpose of this study is to show the procedure, application and main features of the hybrid numerical-analytical approach known as generalized integral transform technique by using it to study magnetohydrodynamic flow of electrically conductive Newtonian fluids inside flat parallel-plate channels subjected to a uniform and constant external magnetic field.
Design/methodology/approach
The mathematical formulation of the analyzed problem is given in terms of a streamfunction, obtained from the Navier–Stokes and energy equations, by considering steady state laminar and incompressible flow and constant physical properties.
Findings
Convergence analyses are performed and presented to illustrate the consistency of the integral transformation technique. The results for the velocity and temperature fields are generated and compared with those in the literature as a function of the main governing parameters.
Originality/value
A detailed analysis of the parametric sensibility of the main dimensionless parameters, such as the Reynolds number, Hartmann number, Eckert number, Prandtl number and electrical parameter, for some typical situations is performed.
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Nielson Veloso Medeiros, Emanuel Negrão Macêdo, Rui Nelson Otoni Magno, Claudio José Cavalcante Blanco and João Nazareno Nonato Quaresma
The aim of this paper is related to an analysis of hydrodynamic lubrication of circular thrust bearings.
Abstract
Purpose
The aim of this paper is related to an analysis of hydrodynamic lubrication of circular thrust bearings.
Design/methodology/approach
The modified Reynolds equation was treated to obtain a hybrid numerical-analytical solution through the generalized integral transform technique (GITT) for the problem.
Findings
Numerical results for the engineering parameters such as pressure field, load capacity and power consumption were thus produced as functions of the radial and circumferential directions. These parameters depend on the geometry of sector-shaped used: Rayleigh pad with 4, 8 and 16 steps. Comparing among them, on the numerical point of view, the Rayleigh pad geometry with N = 16 steps has a better satisfactory performance because it has a lower power consumption.
Originality/value
The present GITT results and those obtained by the finite volume method (FVM) from previous works in the literature were confronted to verify whether the results are consistent and to demonstrate the capacity of the GITT approach in handling thrust bearing problems.
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R.R. Gondim, E.N. Macedo and R.M. Cotta
This paper seeks to analyze transient convection‐diffusion by employing the generalized integral transform technique (GITT) combined with an arbitrary transient filtering…
Abstract
Purpose
This paper seeks to analyze transient convection‐diffusion by employing the generalized integral transform technique (GITT) combined with an arbitrary transient filtering solution, aimed at enhancing the convergence behavior of the associated eigenfunction expansions. The idea is to consider analytical approximations of the original problem as filtering solutions, defined within specific ranges of the time variable, which act diminishing the importance of the source terms in the original formulation and yielding a filtered problem for which the integral transformation procedure results in faster converging eigenfunction expansions. An analytical local instantaneous filtering is then more closely considered to offer a hybrid numerical‐analytical solution scheme for linear or nonlinear convection‐diffusion problems.
Design/methodology/approach
The approach is illustrated for a test‐case related to transient laminar convection within a parallel‐plates channel with axial diffusion effects.
Findings
The developing thermal problem is solved for the fully developed flow situation and a step change in inlet temperature. An analysis is performed on the variation of Peclet number, so as to investigate the importance of the axial heat or mass diffusion on convergence rates.
Originality/value
This paper succeeds in analyzing transient convection‐diffusion via GITT, combined with an arbitrary transient filtering solution, aimed at enhancing the convergence behaviour of the associated eigenfunction expansions.
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Debarati Mahanty, Reeba Babu and B. Mahanthesh
In heat transfer problems, if the temperature difference is not sufficiently so small then the linear Boussinesq approximation is not adequate to describe thermal analysis. Also…
Abstract
Purpose
In heat transfer problems, if the temperature difference is not sufficiently so small then the linear Boussinesq approximation is not adequate to describe thermal analysis. Also, nonlinear density variation with respect to temperature/concentration has a significant impact on heat and fluid flow characteristics. Because of this reason, the impact of nonlinear density variation in the buoyancy force term cannot be neglected. Therefore in this paper, the unsteady flow and heat transfer of radiating magneto-micropolar fluid by considering nonlinear Boussinesq approximation is investigated analytically.
Design/methodology/approach
The flow is fully developed and time-dependent. Heat and mass flux boundary conditions are also accounted in the analysis. The governing equations of transport phenomena are treated analytically using regular perturbation method. To analyze the tendency of the obtained solutions, a parametric study is performed.
Findings
It is established that the velocity field is directly proportional to the nonlinear convection parameter and the same trend is observed with the increase of the value of Grashof number. The micro-rotational velocity profile decreases with increase in the nonlinear convection parameter. Further, the temperature profile increases due to the presence of radiative heat aspect.
Originality/value
The effectiveness of nonlinear Boussinesq approximation in the flow of micropolar fluid past a vertical plate in the presence of thermal radiation and magnetic dipole is investigated for the first time.
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Guangming Fu, Chen An and Jian Su
The purpose of this study is to propose the generalised integral transform technique to investigate the natural convection behaviour in a vertical cylinder under different…
Abstract
Purpose
The purpose of this study is to propose the generalised integral transform technique to investigate the natural convection behaviour in a vertical cylinder under different boundary conditions, adiabatic and isothermal walls and various aspect ratios.
Design/methodology/approach
GITT was used to investigate the steady-state natural convection behaviour in a vertical cylinder with internal uniformed heat generation. The governing equations of natural convection were transferred to a set of ordinary differential equations by using the GITT methodology. The coefficients of the ODEs were determined by the integration of the eigenfunction of the auxiliary eigenvalue problems in the present natural convection problem. The ordinary differential equations were solved numerically by using the DBVPFD subroutine from the IMSL numerical library. The convergence was achieved reasonably by using low truncation orders.
Findings
GITT is a powerful computational tool to explain the convection phenomena in the cylindrical cavity. The convergence analysis shows that the hybrid analytical–numerical technique (GITT) has a good convergence performance in relatively low truncation orders in the stream-function and temperature fields. The effect of the Rayleigh number and aspect ratio on the natural convection behaviour under adiabatic and isothermal boundary conditions has been discussed in detail.
Originality/value
The present hybrid analytical–numerical methodology can be extended to solve various convection problems with more involved nonlinearities. It exhibits potential application to solve the convection problem in the nuclear, oil and gas industries.
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Kleber Marques Lisboa, Jian Su and Renato M. Cotta
The purpose of this work is to revisit the integral transform solution of transient natural convection in differentially heated cavities considering a novel vector eigenfunction…
Abstract
Purpose
The purpose of this work is to revisit the integral transform solution of transient natural convection in differentially heated cavities considering a novel vector eigenfunction expansion for handling the Navier-Stokes equations on the primitive variables formulation.
Design/methodology/approach
The proposed expansion base automatically satisfies the continuity equation and, upon integral transformation, eliminates the pressure field and reduces the momentum conservation equations to a single set of ordinary differential equations for the transformed time-variable potentials. The resulting eigenvalue problem for the velocity field expansion is readily solved by the integral transform method itself, while a traditional Sturm–Liouville base is chosen for expanding the temperature field. The coupled transformed initial value problem is numerically solved with a well-established solver based on a backward differentiation scheme.
Findings
A thorough convergence analysis is undertaken, in terms of truncation orders of the expansions for the vector eigenfunction and for the velocity and temperature fields. Finally, numerical results for selected quantities are critically compared to available benchmarks in both steady and transient states, and the overall physical behavior of the transient solution is examined for further verification.
Originality/value
A novel vector eigenfunction expansion is proposed for the integral transform solution of the Navier–Stokes equations in transient regime. The new physically inspired eigenvalue problem with the associated integmaral transformation fully shares the advantages of the previously obtained integral transform solutions based on the streamfunction-only formulation of the Navier–Stokes equations, while offering a direct and formal extension to three-dimensional flows.
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Renato M Cotta, Carolina Palma Naveira-Cotta and Diego C. Knupp
The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary conditions by…
Abstract
Purpose
The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary conditions by employing the corresponding nonlinear eigenvalue problem in the construction of the expansion basis.
Design/methodology/approach
The original nonlinear boundary condition coefficients in the problem formulation are all incorporated into the adopted eigenvalue problem, which may be itself integral transformed through a representative linear auxiliary problem, yielding a nonlinear algebraic eigenvalue problem for the associated eigenvalues and eigenvectors, to be solved along with the transformed ordinary differential system. The nonlinear eigenvalues computation may also be accomplished by rewriting the corresponding transcendental equation as an ordinary differential system for the eigenvalues, which is then simultaneously solved with the transformed potentials.
Findings
An application on one-dimensional transient diffusion with nonlinear boundary condition coefficients is selected for illustrating some important computational aspects and the convergence behavior of the proposed eigenfunction expansions. For comparison purposes, an alternative solution with a linear eigenvalue problem basis is also presented and implemented.
Originality/value
This novel approach can be further extended to various classes of nonlinear convection-diffusion problems, either already solved by the GITT with a linear coefficients basis, or new challenging applications with more involved nonlinearities.
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Zefeng Jing, Shuzhong Wang and Zhende Zhai
The purpose of this paper is to investigate the combined effects of slip and rheological parameters on the flow and heat transfer of the Herschel-Bulkley fluid.
Abstract
Purpose
The purpose of this paper is to investigate the combined effects of slip and rheological parameters on the flow and heat transfer of the Herschel-Bulkley fluid.
Design/methodology/approach
The combinative dimensionless parameter method is introduced into the equations of the slip flow and heat transfer to make the discussion more comprehensive. More specifically, the slip and rheological parameters are transformed into the dimensionless slip number as well as Herschel-Bulkley number. We solve the dimensionless equations and then focus on the effects of these parameters on the slip flow and heat transfer.
Findings
The results show that, for a given value of Herschel-Bulkley number, there is a finite critical value of slip number at which the pressure gradient reaches the lowest value and both the dimensionless yield radius and slip velocity become 1. Meanwhile, the Nusselt number tends to be infinite at this critical value of slip number. For the case of slip, the Nusselt number also approaches infinity at a finite critical value of Herschel-Bulkley number. Furthermore, the dimensionless velocity as well as temperature of the yield pseudoplastic fluid with higher slip number is lower within a small radius but becomes higher near the wall. Meanwhile, from the velocity and temperature profiles, the effect of Herschel-Bulkley number on these two parameters of the Bingham fluid at the smaller radius is opposite.
Originality/value
These associated expressions can be generalized to the flow and heat transfer of a Herschel-Bulkley fluid under slip boundary condition. It can provide a reference for the engineering application relating to the heat transfer and flow of a Herschel-Bulkley fluid. Meanwhile, it also suggests some revelations for dealing with this similar problem.
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Roseane L. Silva, João N.N. Quaresma, Carlos A.C. Santos and Renato M. Cotta
The purpose of this paper is to provide an analysis of two‐dimensional laminar flow in the entrance region of wavy wall ducts as obtained from the solution of the steady…
Abstract
Purpose
The purpose of this paper is to provide an analysis of two‐dimensional laminar flow in the entrance region of wavy wall ducts as obtained from the solution of the steady Navier‐Stokes equations for incompressible flow.
Design/methodology/approach
The study is undertaken by application of the generalized integral transform technique in the solution of the steady Navier‐Stokes equations for incompressible flow. The streamfunction‐only formulation is adopted, and a general filtering solution that adapts to the irregular contour is proposed to enhance the convergence behavior of the eigenfunction expansion.
Findings
A few representative cases are considered more closely in order to report some numerical results illustrating the eigenfunction expansions convergence behavior. The product friction factor‐Reynolds number is also computed and compared against results from discrete methods available in the literature for different Reynolds numbers and amplitudes of the wavy channel.
Research limitations/implications
The proposed methodology is fairly general in the analysis of different channel profiles, though the reported results are limited to the wavy channel configuration. Future work should also extend the analysis to geometries represented in the cylindrical coordinates with longitudinally variable radius.
Practical implications
The error‐controlled converged results provide reliable benchmark results for the validation of numerical results from computational codes that address the solution of the Navier‐Stokes equations in irregular geometries.
Originality/value
Although the hybrid methodology is already known in the literature, the results here presented are original and further challenges application of the integral transform method in the solution of the Navier‐Stokes equations.
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Concetta Russo, Alessandra Decataldo and Brunella Fiore
Introduction: The birth of a preterm child requires hospitalization in a neonatal intensive care unit (NICU), which is a very stressful experience for parents. Aim: To determine…
Abstract
Purpose
Introduction: The birth of a preterm child requires hospitalization in a neonatal intensive care unit (NICU), which is a very stressful experience for parents. Aim: To determine the stress level of parents of preterm babies admitted to intensive and sub-intensive units in two hospitals in Northern Italy and its association with their sociodemographic variables and the clinical conditions of their newborns.
Design/methodology/approach
The sampling was non-probabilistic and included parents of preterm babies admitted to intensive and/or sub-intensive care for at least 10 days. Instruments: (1) information deduced from the clinical record of preterm newborns; (2) sociodemographic determinants of parents' well-being deduced from a questionnaire; (3) parental stress scale: neonatal intensive care unit (PSS:NICU), which measures the perception of parents about stressors from the physical and psychological environment of the NICU.
Findings
Results: A total of 104 parents of 59 hospitalized preterm babies participated in the study. The average parental stress level was 1.87 ± 0.837. The subscale score that got higher was parent-infant relationship subscale. Concerning the infant characteristics, the birth weight of the babies and the length of their hospitalization affected the parents' stress level. Looking at parents' sociodemographic characteristics instead, the greater predictors were gender, age and occupational social class.
Originality/value
The parental role alteration caused by infant premature birth and consequent hospitalization is a major stressor for parents and in particular for mothers. The variables that resulted positively associated with higher stress in parents of preterm infants hospitalized are specific parental characteristics, including not adequately or previously studied ones, and infant characteristics.