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Under the conditions of high speed and density flow, the windage loss in the gap behind an impeller has an important influence on its thermal power conversion efficiency. Daily and Nece took the relative gap and Reynolds number as the characteristic parameters and divided the flow of a rotating disk in a closed chamber into four flow regions through laminar flow, turbulent flow and state of boundary layers. In this paper, the skin-friction coefficient model of Regio III and IV was verified by a numerical method under conditions corresponding to the typical Reynolds number range for a radial impeller. The results show that when the relative gap increases, the relative deviation between the numerical calculation and the model prediction results decreases, and the maximum deviation is −12.4%. With the increase of Reynolds number, the Region IV model is more accurate. Region III has the flow state of boundary layers merging and separation at the same time. Both models have good prediction accuracy with different mediums of air, water-liquid and critical CO2. The deviation in Region III is larger and shows a decreasing trend with respect to Region IV, Based on the two models, a method for predicting the optimal gap is proposed. The method is verified to be reliable and can minimize windage loss. [ABSTRACT FROM AUTHOR]

Under the conditions of high speed and density flow, the windage loss in the gap behind an impeller has an important influence on its thermal power conversion efficiency. Daily and Nece took the relative gap and Reynolds number as the characteristic parameters and divided the flow of a rotating disk in a closed chamber into four flow regions through laminar flow, turbulent flow and state of boundary layers. In this paper, the skin-friction coefficient model of Regio III and IV was verified by a numerical method under conditions corresponding to the typical Reynolds number range for a radial impeller. The results show that when the relative gap increases, the relative deviation between the numerical calculation and the model prediction results decreases, and the maximum deviation is −12.4%. With the increase of Reynolds number, the Region IV model is more accurate. Region III has the flow state of boundary layers merging and separation at the same time. Both models have good prediction accuracy with different mediums of air, water-liquid and critical CO2. The deviation in Region III is larger and shows a decreasing trend with respect to Region IV, Based on the two models, a method for predicting the optimal gap is proposed. The method is verified to be reliable and can minimize windage loss.

This paper investigates the heat transfer of two-phase nanofluid flow between horizontal plates in a rotating system with a magnetic field and external forces. The basic continuity and momentum equations are considered to formulate the governing mathematical model of the problem. Furthermore, certain similarity transformations are used to reduce a governing system of non-linear partial differential equations (PDEs) into a non-linear system of ordinary differential equations. Moreover, an efficient stochastic technique based on feed-forward neural networks (FFNNs) with a back-propagated Levenberg–Marquardt (BLM) algorithm is developed to examine the effect of variations in various parameters on velocity, gravitational acceleration, temperature, and concentration profiles of the nanofluid. To validate the accuracy, efficiency, and computational complexity of the FFNN–BLM algorithm, different performance functions are defined based on mean absolute deviations (MAD), error in Nash–Sutcliffe efficiency (ENSE), and Theil's inequality coefficient (TIC). The approximate solutions achieved by the proposed technique are validated by comparing with the least square method (LSM), machine learning algorithms such as NARX-LM, and numerical solutions by the Runge–Kutta–Fehlberg method (RKFM). The results demonstrate that the mean percentage error in our solutions and values of ENSE, TIC, and MAD is almost zero, showing the design algorithm's robustness and correctness. [ABSTRACT FROM AUTHOR]

This paper investigates the heat transfer of two-phase nanofluid flow between horizontal plates in a rotating system with a magnetic field and external forces. The basic continuity and momentum equations are considered to formulate the governing mathematical model of the problem. Furthermore, certain similarity transformations are used to reduce a governing system of non-linear partial differential equations (PDEs) into a non-linear system of ordinary differential equations. Moreover, an efficient stochastic technique based on feed-forward neural networks (FFNNs) with a back-propagated Levenberg–Marquardt (BLM) algorithm is developed to examine the effect of variations in various parameters on velocity, gravitational acceleration, temperature, and concentration profiles of the nanofluid. To validate the accuracy, efficiency, and computational complexity of the FFNN–BLM algorithm, different performance functions are defined based on mean absolute deviations (MAD), error in Nash–Sutcliffe efficiency (ENSE), and Theil’s inequality coefficient (TIC). The approximate solutions achieved by the proposed technique are validated by comparing with the least square method (LSM), machine learning algorithms such as NARX-LM, and numerical solutions by the Runge–Kutta–Fehlberg method (RKFM). The results demonstrate that the mean percentage error in our solutions and values of ENSE, TIC, and MAD is almost zero, showing the design algorithm’s robustness and correctness.

The present study investigates the impacts of thermal radiation and inclined magnetic field on the Sutterby fluid by capitalizing Cattaneo-Christov heat flux system. The suitable transformations from PDE into ODE are achieved by capitalizing the strength of similarity conversion system. Well known numerical shooting technique is used along with integrated strength Runge-Kutta method of fourth order. The proposed results are compared with Lobatto 111A method which strengthen the convergence and accuracy of present fluidic system. The skin friction coefficients and Nusselt number are numerically exhibited in tabular form, while the parameter of interests in terms of velocity ratio parameter, power law index, the thermal radiation parameter, Prandtl number, Deborah number, and magnetic parameter. Here in this contemporary investigation, the phenomenon of thermal radiation on an inclined magnetic field using Sutterby capitalizing Cattaneo-Christov heat flux model has been discussed. The resulting complex non-linear ODE are tackled numerically by utilizing a famous shooting technique with the integrated strength of the Runge-Kutta method of fourth order. The obtained numerical results are compared with the MATLAB built-in solver bvp4c. The numerical values of the skin friction coefficient and reduced Nusselt number are narrated in tabular form, while some proficient parameters like velocity ratio parameter, power-law index, Deborah number, magnetic parameter, inclined magnetic angle, the thermal radiation parameter, Reynolds number, and Prandtl number on the velocity and temperature profiles have been discussed numerically as well as graphically. Outcomes of the proposed research show that by increasing the inclined angle, enhancement is seen in the skin-friction coefficient and reduces the Nusselt number. Moreover, by increasing the Reynolds number, the temperature profile declines initially and then moves upward in the channel. The stability and convergence of the proposed methodolgy in validated through residual errors based different tolerances. [ABSTRACT FROM AUTHOR]

The nonlinear differential equations governing the inherent irreversibility in a steady hydromagnetic permeable channel flow of a conducting fluid with variable electrical conductivity and asymmetric Navier slip at the channel walls in the presence of induced electrical field is solved. An approximate analytical solution for dimensionless velocity and dimensionless temperature are derived using Homotopy Analysis Method. The current density, the entropy generation number and the Bejan number are also derived analytically. The results obtained are discussed graphically and analytically. [ABSTRACT FROM AUTHOR]

This paper studies the mathematical implications of the two dimensional viscous steady laminar combined free-forced convective flow of an incompressible fluid over a semi infinite fixed vertical porous plate embedded in a porous medium. It is assumed that the left surface of the plate is heated by convection from a hot fluid which is at a temperature higher than the temperature of the fluid on the right surface of the vertical plate. To achieve numerical consistency for the problem under consideration, the governing non linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity variable and then solved numerically under conditions admitting similarity solutions. The effects of the physical parameters of both the incompressible fluid and the vertical plate on the dimensionless velocity and temperature profiles are studied and analysed and the results are depicted both graphically and in a tabular form. Finally, algebraic expressions and the numerical values are obtained for the local skin-friction coefficient and the local Nusselt number.

Direct numerical simulation of a spatially developing turbulent boundary layer over a compliant wall with anisotropic wall material properties is performed. The Reynolds number varies from 300 to approximately 860 along the streamwise direction, based on the external flow velocity and the momentum thickness. Eight typical cases are selected for numerical investigation under the guidance of monoharmonic analysis. The instantaneous flow fields exhibit a traveling wavy motion of the compliant wall, and the frequency-wavenumber power spectrum of wall pressure fluctuation is computed to quantify the mutual influence of the wall compliance and the turbulent flow at different wave numbers. It is shown that the Reynolds shear stress and the pressure fluctuation are generally enhanced by the wall compliance with the parameters considered in the present study. A dynamical decomposition of the skin-friction coefficient is derived, and a new term (CW) appears due to the wall-induced Reynolds shear stress. The influence of the anisotropic compliant wall motion on the turbulent boundary layer through the wall-induced negative Reynolds shear stress is discussed. To elucidate the underlying mechanism, the budget analysis of the Reynolds stress transportation is further carried out. The impact of the wall compliance on the turbulent flow is disclosed by examining the variations of the diffusion and velocity–pressure correlation terms. It is shown that an increase of the Reynolds stress inside the flow domain is caused by enhancement of the velocity–pressure correlation term, possibly through the long-range influence of the wall compliance on the pressure field, rather than diffusion of the wall-induced Reynolds shear stress into the fluid flow. [ABSTRACT FROM AUTHOR]

Aim of the paper is to investigate the effects of linearly varying viscosity and thermal conductivity on steady free convective flow of a viscous incompressible fluid along an isothermal vertical plate in the presence of heat sink. The governing equations of continuity, momentum and energy are transformed into coupled and nonlinear ordinary differential equations using similarity transformation and then solved using Runge-Kutta fourth order method with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and Nusselt number at the plate are derived, discussed numerically and their numerical values for various values of physical parameters are presented through Tables.

Similarity solution of the boundary layer flow and heat transfer of a viscous incompressible fluid along a vertical unsteady stretching sheet in quiescent fluid is presented in case when temperature difference between sheet and ambient fluid satisfies a specific relation. The governing equations are subjected to similarity transformation and converted to a system of nonlinear ordinary differential equations and solved numerically. The effects of different parameters on velocity and temperature profiles are discussed through graphs. The variations in skin-friction coefficient and the Nusselt number at the sheet are presented through table and discussed. [ABSTRACT FROM AUTHOR]

Natural convection laminar flow from an isothermal sphere immersed in a viscous incompressible optically dense fluid in the presence of radiation effects has been investigated. The governing boundary layer equations are transformed into a non dimensional form and the resulting nonlinear systems of partial differential equations are reduced to local non-similarity boundary layer equations, which are solved numerically by two distinct, efficient methods, namely, (i) implicit finite difference method together with the Keller box scheme and (ii) local non-similarity method. Numerical results of the velocity and temperature profiles of the fluid are presented. The results of the shearing stress and the heat transfer rate in terms of skin-friction coefficient and Nusselt number respectively are also presented for a wide range of the radiation-conduction parameter or Planck number Rd (=0.0, 1.0, 2.0, 3.0), the surface heating parameter θw (=1.1, 1.2, 1.4), and Prandtl number Pr (=7.0, 10.0, 15.0, 20.0). [ABSTRACT FROM AUTHOR]

Based on fine measurement of time-averaged data of hot-wire anemometer we have developed the method determining local values of skin-friction coefficient in the vicinity of the wall on the planar porous surface at the flow past which the noncanonical turbulent boundary layer is formed. The method may be applied at investigation of the efficiency of various effects on the incompressible boundary layer, in particular, with microblowing of air where usage of direct methods of friction determination is complicated. [ABSTRACT FROM AUTHOR]

Aim of the paper is to investigate the effects of linearly varying viscosity and thermal conductivity on steady free convective flow of a viscous incompressible fluid along an isothermal vertical plate in the presence of heat sink. The governing equations of continuity, momentum and energy are transformed into coupled and nonlinear ordinary differential equations using similarity transformation and then solved using Runge-Kutta fourth order method with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and Nusselt number at the plate are derived, discussed numerically and their numerical values for various values of physical parameters are presented through Tables. [ABSTRACT FROM AUTHOR]

Abstract: Skin-friction coefficient of turbulent boundary layer flow over a smooth-wall with transverse square grooves was investigated. Four grooved-wall cases were investigated. The four grooved-wall configurations are single 5mm square grooved-wall, and 5mm square grooves spaced 10, 20 and 40 element widths apart in the streamwise direction. Laser-Doppler Anemometer (LDA) was used for the mean velocity and turbulence intensity measurements. The skin-friction coefficient determined from the velocity profile increases sharply just downstream of the groove. This overshoot is followed by an undershoot and then relaxation back to the smooth-wall value. This behavior is observed in most grooved-wall cases. Integrating the skin-friction coefficient in the streamwise direction indicates that there is an increase in the overall drag in all the grooved-wall cases. [Copyright &y& Elsevier]

Similar solutions for the boundary layer equations of a second-order fluid flow over a stretching sheet are presented to obtain the coefficients of skin-friction and heat transfer. [ABSTRACT FROM AUTHOR]