Journal of Applied Fluid Mechanics1735-35727420140901An Accurate Taylors Series Solution with High Radius of Convergence for the Blasius Function and Parameters of Asymptotic Variation557564146810.36884/jafm.7.04.21339ENS.Anil LalDepartment of Mechanical Engineering, College of Engineering Trivandrum, Kerala, India0000-0001-8597-9905M.Neeraj PaulDepartment of Mechanical Engineering, College of Engineering Trivandrum, Kerala, IndiaJournal Article19700101This paper reports a high accurate solution of the Blasius function f (h) in the form of a converging Taylor’s series for a higher range of h 2 [0;9]. The method used consists of conversion of the boundary value problem into an initial value problem and solution by differential transform method. The initial value of the second derivative of the Blasius function is determined from the final value of first derivative of another function. The final value of first derivative of the latter function is determined by the Taylor’s series expansions with center at h = 15. The series expansion for the Blasius function is obtained with center of expansion at h = 4, is alternating and is accurately converging for higher values of h, with the number of used for summation equal to 2000. The present expansion is obtained without resorting to approximations and has a higher radius of convergence. The first 200 coefficients of the series, the second derivative of the function at h = 0, the parameters of the asymptotic solution are reported with 21 decimal places accuracy. The level of accuracy of the results presented is higher than any other results reported so far. This note also reports the mathematical steps involved in the derivation of the similarity variable of Blasius problem.https://www.jafmonline.net/article_1468_47008f322a8ea084e76c5b6e1babcc0d.pdfJournal of Applied Fluid Mechanics1735-35727420140901Active Flow Control at the Rear End of a Generic Car Model Using Steady Blowing565571146910.36884/jafm.7.04.21752ENR.MestiriLESTE, Ecole Nationale d’Ing´enieurs de Monastir, TunisieA.Ahmed-BensoltaneEcole Sup´erieure des Techniques de l’A´eronautique, Alger, AlgerieL.KeirsbulckTEMPO, EA 4542, 59313 Valenciennes, Universit´e Lille Nord de FranceF.AlouiTEMPO, EA 4542, 59313 Valenciennes, Universit´e Lille Nord de France0000-0003-2157-9528L.LabragaTEMPO, EA 4542, 59313 Valenciennes, Universit´e Lille Nord de FranceJournal Article19700101Numerous aerodynamic designs of automotive vehicle have been made to reduce aerodynamic drag for lower fuel consumption. Indeed, automotive industry was primarily interested in the passive control based on the shape changes. But, as shape modifications are limited by several factors, this industry is recently more focused on active flow control. In this experimental investigation, the influence of continuous blowing along the sharp edge between the roof and the rear window is addressed. This actuation represents a new configuration based on a steady blowing tangentially to the surface of the rear window of the 25 slanted Ahmed body model. The study was carried out in a wind tunnel at Reynolds numbers based on the model length up to 2:78106. The actuation leads to a maximum drag reduction slightly upper than 10% obtained with a Reynolds number of 1:74 106 and a blowing velocity of 0:65V0, where V0 is the freestream velocity. Reductions between 6% and 7% were obtained for the other studied cases. These aerodynamic drag measurements were used to evaluate the actuator efficiency which reveals a maximum efficiency of 9. Visualizations show that tangential steady blowing increase the separated region on the rear window and consequently disrupt the development of the counter-rotating longitudinal vortices appearing on the lateral edges of the rear window. It is also noted that the flow is reattached to the upper half of the rear window. As the actuation occurred directly on the recirculation region at the top of the rear window wall, the flow control was seen very effective.https://www.jafmonline.net/article_1469_ff9904b62175eb396b3032a86b9235f3.pdfJournal of Applied Fluid Mechanics1735-35727420140901Rayleigh-Taylor Instability at the Interface of Superposed Couple-Stress Casson Fluids Flow in Porous Medium under the Effect of a Magnetic Field573580147010.36884/jafm.7.04.19356ENM. Agoor.BothainaFaculty of Science El-Fayoum University, Fayoum, Egypt.N. T.EldabeDepartment of Mathematics Faculty of Education, Ain Shams University, Cairo, Egypt.Journal Article19700101The Rayleigh-Taylor instability (RIT) at the interface of two superposed Couple-stress Casson fluids flowing in porous medium and in the presence of a uniform normal magnetic field is studied. The fluids have different densities. For mathematical simplicity, the stability analysis based on fully developed approximations is used. The maximum wave numbers and the corresponding maximum frequency are obtained. The Growth rate of Rayleigh-Taylor instability in the case of non-Newtonian Casson fluid with couple-stress through porous medium is discussed. The effects of physical parameters of the problem such as the permeability parameter, magnetic parameter, non-Newtonian Parameter and couple-stress parameter on the regions of stability are discussed numerically and illustrated graphically through a set of figures.https://www.jafmonline.net/article_1470_6b0bee8e8365c1f45ce454ad1c555794.pdfJournal of Applied Fluid Mechanics1735-35727420140901Effects of Through-Flow and Internal Heat Generation on a Thermo Convective Instability in an Anisotropic Porous Medium581590147110.36884/jafm.7.04.19410ENR. K.VanishreeMaharani’s Science college for Women, Bangalore – 560 001, IndiaJournal Article19700101A linear stability analysis is performed to study the effects of through-flow and internal heat generation on the preferred mode of stationary thermal convection in a variable viscosity liquid saturating an anisotropic porous medium. The Rayleigh-Ritz technique is used to obtain the eigenvalue of the problem. The influence of porous parameter, mechanical anisotropy parameter, Peclet number, thermal anisotropy parameter, Brinkman number and variable viscosity parameter on the stability of the system is analyzed. The problem suggests another method of controlling convection by externally controlling porous media damping and shear. This is in addition to the through-flow mechanism of regulating convection.https://www.jafmonline.net/article_1471_dd7099f4f30ab1f4db9acac0f0b93e63.pdfJournal of Applied Fluid Mechanics1735-35727420140901On the Cooling Process of Nanofluid in a Square Enclosure with Linear Temperature Distribution on Left Wall591601147210.36884/jafm.7.04.20239ENA. A.Abbasian AraniDepartment of Mechanical Engineering, University of Kashan, Kashan, IranM.MahmoodiDepartment of Mechanical Engineering, Amirkabir University of Technology, Tehran, IranS.Mazrouei SebdaniDepartment of Mechanical Engineering, University of Kashan, Kashan, IranJournal Article19700101In the present paper the problem of natural convection of Al2O3-water nanofluid with consideration of variable properties inside a square cavity with different linear temperature distribution on the left wall is investigated numerically. Effects of variations of Rayleigh number, temperature distributions, and volume fraction of nanoparticles on flow and temperature field and rate of heat transfer are studied. The obtained results show that as the temperature distribution on the left wall varies, the flow and temperature patterns inside the cavity vary too. Moreover the existence of the nanoparticles in the base fluid enhances or reduces the average Nusselt number depending on the Rayleigh number and value of the nanoparticles concentration. It is found that at convection dominated regime (Ra=105 and 106), high values of nanoparticles volume fraction motivated the rate of heat transfer to decreases. When the lower end of left wall is cooled and its temperature increases by moving toward the top, a higher Nusselt number is obtained.https://www.jafmonline.net/article_1472_cfca7f2155642bf2996678f0ba2a92b5.pdfJournal of Applied Fluid Mechanics1735-35727420140901Visco-Elastic MHD Free Convective Flow through Porous Media in Presence of Radiation and Chemical Reaction with Heat and Mass Transfer603609147310.36884/jafm.7.04.20307ENR.ChoudhuryDepartment of Mathematics, Gauhati University, Guwahati-781 014, Assam, IndiaS.Kumar DasDepartment of Mathematics, Bajali College, Pathsala, Barpeta, Assam, India.Journal Article19700101An analysis of visco-elastic free convective transient MHD flow over a vertical porous plate through porous media in presence of radiation and chemical reaction with heat and mass transfer is presented. A transverse variable suction velocity is applied on the porous plate. The equations governing the fluid flow, heat and mass transfer are solved by applying multiple perturbation technique. The expressions for transient velocity, temperature, species concentration and non-dimensional skin friction at the plate are obtained and the expressions for transient velocity and non-dimensional skin friction at the plate are illustrated graphically to observe the visco-elastic effect in combination of other flow parameters involved in the solution.https://www.jafmonline.net/article_1473_d9ec9dce7be691aa0f388e8fdf16d163.pdfJournal of Applied Fluid Mechanics1735-35727420140901Experimental Study of the Scour Regimes Downstream of an Apron for Intermediate Tailwater Depth Conditions611624147410.36884/jafm.7.04.21238ENP.EspaDipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, via G.B. Vico, 46, Varese, 21100, ItalyS.SibillaDipartimento di Ingegneria Civile e Architettura, Università di Pavia, via Ferrata, 3, Pavia, 27100, ItalyJournal Article19700101The local scour of a non-cohesive bed due to a 2-D submerged horizontal jet is investigated experimentally in presence of a protection apron. Previous researches conducted without protection apron demonstrate that, when the tailwater depth is either deep or shallow, the equilibrium state characteristics of the scoured bed profile are mainly a function of the densimetric Froude number. However, when the submergence is between these two extremes, at fixed Froude number, three different scour regimes are possible. For relatively shallow tailwater depths, the jet mainstream directs towards the free surface (surface jet scouring regime), determining shallow and elongated scour profiles. For relatively large tailwater depths, the jet remains attached to the channel bottom (bed jet scouring regime), leading to deeper and shorter scour profiles. For intermediate conditions, the flicking of the jet between the erodible bed and the water free-surface is possible. When this instability occurs, the shape of the scour hole rapidly changes as a response of the jet mainstream position (bed-surface jet scouring regime). This paper aims to give an experimental description of the three mentioned regimes when a protection apron partly reduces the action of the flow on the loose bed. Scour hole profile evolution and velocity profile measurements obtained by LDA and ADV velocimetry are discussed.https://www.jafmonline.net/article_1474_0000ea00b01102be56cd116cf75fc320.pdfJournal of Applied Fluid Mechanics1735-35727420140901Morphological Considerations of Fish Fin Shape on Thrust Generation625632147510.36884/jafm.7.04.21358ENK.KikuchiFaculty of Science and Engineering, Toyo University, 2100 Kujirai, Kawagoe, 350-8585 JapanY.UeharaDepartment of Biomedical Engineering, Toyo University, 2100 Kujirai, Kawagoe, 350-8585 JapanY.KubotaFaculty of Science and Engineering, Toyo University, 2100 Kujirai, Kawagoe, 350-8585 JapanO.MochizukiDepartment of Biomedical Engineering, Toyo University, 2100 Kujirai, Kawagoe, 350-8585 JapanJournal Article19700101In this study, we aimed to determine the relationship between thrust generation and fish fin shape. To compare the effect fin shape had on thrust generation, we categorized the morphological shapes of fish fins into equilateral polygonal shapes. Polygonal fins were used to generate thrust that depended only on shape. These fins were constructed of a hard elastic material to eliminate any influence of shape deformation. A servomotor with a reciprocal rotation moved a fin cyclically, and thrust was experimentally measured using a strain gage system. Thrust tended to be proportional to the inertia moment of a fin, which indicated difficulty with rotation. Moreover, this trend for thrust generation was directly related to the number of apexes of a polygonal fin. The force translated ratio, which was thrust divided by the force required for fin rotation, was evaluated to determine the hydrodynamic characteristics of fins. This finding showed that the force translated ratio of a fin increased with increased movable perimeter length. The greatest thrust was generated by a triangular fin rotated at its apex, which is often seen in general fish tail fins, whereas the hydrodynamic characteristics were the worst in polygonal fins.https://www.jafmonline.net/article_1475_46bfe65d32a04eb5fb91b300d619bacf.pdfJournal of Applied Fluid Mechanics1735-35727420140901Heat Transfer in Hydromagnetic Fluid Flow: Study of Temperature Dependence of Fluid Viscosity633640147610.36884/jafm.7.04.21385ENS. K.GhoshDepartment of Mathematics, Garhbeta College, Paschim Medinipore-721127, W.B., IndiaG. C.ShitDepartment of Mathematics, Jadavpur University, Kolkata-700032, IndiaJ. C.MisraInstitute of Technical Education & Research, Siksha O Anusandhan University, Bhubaneswar – 751030, IndiaJournal Article19700101Flow of a viscoelastic fluid through a channel with stretching walls in the presence of a magnetic field has been investigated. The viscosity of the fluid is assumed to vary with temperature. Convective heat transfer is considered along with viscous dissipation and Ohmic dissipation. The equations that govern the motion of the fluid and heat transfer are coupled and non-linear. The governing partial differential equations are reduced to a set of ordinary differential equations by using similarity transformation. The transformed equations subject to the boundary conditions are solved by developing a suitable finite difference scheme. Numerical estimates of the flow and heat transfer variables are obtained by considering blood as the working fluid. The computational values are found to be in good agreement with those of previous studies.https://www.jafmonline.net/article_1476_9110d75658b550c47de12655ea27d9c2.pdfJournal of Applied Fluid Mechanics1735-35727420140901Radiation Effect on Mhd Heat and Mass Transfer Flow over a Shrinking Sheet with Mass Suction641650147710.36884/jafm.7.04.21389ENP. R.BabuDept. of Mathematics, Sri Kottam Tulasi Reddy Memorial College of Engineering, Kondair(village), Itikyala(Mandal), Mahabubnagar(Dist), A.P., India.J. A.RaoDept. of Mathematics, OsmaniaUniversity, Hyderabad, A.P., IndiaS.SheriDept. of Mathematics, Githam University, Hyd, A.P., India.Journal Article19700101A numerical analysis has been carried out to study the effects radiation and heat source/sink on the steady two dimensional magnetohydrodynamic (MHD) boundary layer flow of heat and mass transfer past a shrinking sheet with wall mass suction. In the dynamic system, a uniform magnetic field acts normal to the plane of flow. The governing partial differential equations are transformed into self-similar equations are solved by employing finite difference using the quasilinearization technique. From the analysis it is found that the velocity inside the boundary layer increases with increase of wall mass suction and magnetic field and accordingly the thickness of the momentum boundary layer decreases. The temperature decreases with Hartmann number, Prandtl number, and heat sink parameter and the temperature increases with heat source parameter, radiation parameter. The concentration decreases with an increase of Hartmann number, mass suction parameter, Schmidt number, chemical reaction parameter.https://www.jafmonline.net/article_1477_8fd47b2cb1b30f728bc41e5e12e497d3.pdfJournal of Applied Fluid Mechanics1735-35727420140901Applications of 2-D Moiré Deflectometry to Atmospheric Turbulence651657147810.36884/jafm.7.04.21420ENS.RasouliDepartment of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, IranM. D.NiryDepartment of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, IranY.RajabiDepartment of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, IranA. A.PanahiDepartment of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, IranJ.NiemelaThe Abdus Salam ICTP, Strada Costiera 11, 34151 Trieste, ItalyJournal Article19700101We report on applications of a moiré deflectometry to observations of anisotropy in the statistical properties of atmospheric turbulence. Specifically, combining the use of a telescope with moiré deflectometry allows enhanced sensitivity to fluctuations in the wave-front phase, which reflect fluctuations in the fluid density. Such phase fluctuations in the aperture of the telescope are imaged on the first grating of the moiré deflectometer, giving high spatial resolution. In particular, we have measured the covariance of the angle of arrival (AA) between pairs of points displaced spatially on the telescope aperture which allows a quantitative measure of anisotropy in the atmospheric surface layer. Importantly, the telescope-based moiré deflectometry measures directly in the spatial domain and, besides being a non-intrusive method for studying turbulent flows, has the advantage of being relatively simple and inexpensive.https://www.jafmonline.net/article_1478_ce5b066743ac23354cae0f3616495ea6.pdfJournal of Applied Fluid Mechanics1735-35727420140901Numerical and Experimental Investigations on the Aerodynamic Characteristic of Three Typical Passenger Vehicles659671147910.36884/jafm.7.04.21460ENY.WangHubei Key Laboratory of Advanced Technology of Automotive Parts, Wuhan University of Technology, Wuhan 430070, ChinaY.XinHubei Key Laboratory of Advanced Technology of Automotive Parts, Wuhan University of Technology, Wuhan 430070, ChinaZh.GuState Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Changsha 430082, ChinaSh.WangState Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Changsha 430082, ChinaY.DengHubei Key Laboratory of Advanced Technology of Automotive Parts, Wuhan University of Technology, Wuhan 430070, ChinaX.YangWuhan Ordnance Noncommissioned officers School, Wuhan 430075, ChinaJournal Article19700101The numerical simulation and wind tunnel experiment were employed to investigate the aerodynamic characteristics of three typical rear shapes: fastback, notchback and squareback. The object was to investigate the sensibility of aerodynamic characteristic to the rear shape, and provide more comprehensive experimental data as a reference to validate the numerical simulation. In the wind tunnel experiments, the aerodynamic six components of the three models with the yaw angles range from -15 and 15 were measured. The realizable k-ε model was employed to compute the aerodynamic drag, lift and surface pressure distribution at a zero yaw angle. In order to improve the calculation efficiency and accuracy, a hybrid Tetrahedron-Hexahedron-Pentahedral-Prism mesh strategy was used to discretize the computational domain. The computational results showed a good agreement with the experimental data and the results revealed that different rear shapes would induce very different aerodynamic characteristic, and it was difficult to determine the best shape. For example, the fastback would obtain very low aerodynamic drag, but it would induce positive lift which was not conducive to stability at high speed, and it also would induce bad crosswind stability. In order to reveal the internal connection between the aerodynamic drag and wake vortices, the turbulent kinetic, recirculation length, position of vortex core and velocity profile in the wake were investigated by numerical simulation and PIV experiment.https://www.jafmonline.net/article_1479_d499397b28eaa97805d9d5fa85bddc38.pdfJournal of Applied Fluid Mechanics1735-35727420140901Development of a Segregated Compressible Flow Solver for Turbomachinery Simulations673682148010.36884/jafm.7.04.21482ENJ.BenajesCMT - Motores Térmicos, Universitat Politècnica de València, Camino de Vera S/N, Valencia, 46022, SpainJ.GalindoCMT - Motores Térmicos, Universitat Politècnica de València, Camino de Vera S/N, Valencia, 46022, SpainP.FajardoBioingeniería e Ingeniería Aeroespacial, Universidad Carlos III de Madrid, Leganés, 28911, SpainR.NavarroCMT - Motores Térmicos, Universitat Politècnica de València, Camino de Vera S/N, Valencia, 46022, SpainJournal Article19700101A steady multiple reference frame segregated compressible solver and an unsteady sliding mesh one are developed using OpenFOAM® to simulate turbomachinery. For each of the two solvers, governing equations, numerical approach and solver structure are explained. Pressure and energy equation are implemented so as to obtain the best numerical properties, such as the ability to use large time-steps. Sod shock tube test case is used to assess the prediction of compressible phenomena by the transient scheme, which shows proper resolution of compressible waves. Both solvers are used to simulate a turbocharger turbine, comparing their solutions to corresponding ones using ANSYS® Fluent® as a means of validation. The multiple reference frame solver global results quantitatively differ from those computed using ANSYS Fluent, although predicted flow features match. The solution obtained by the sliding mesh solver presents better agreement compared to ANSYS Fluent one.https://www.jafmonline.net/article_1480_277f6068711153c78f53d5a7ba200559.pdfJournal of Applied Fluid Mechanics1735-35727420140901Effects of Hall Currents and Radiation on Unsteady MHD Flow Past a Heated Moving Vertical Plate683692148110.36884/jafm.7.04.21486ENS.DasDepartment of Mathematics, University of Gour Bnaga, Malda 732 103, West Bengal, IndiaS. K.GuchhaitDepartment of Applied Mathematics, Vidyasagar University, Midnapore 721 102, West Bengal, IndiaR. N.JanaDepartment of Applied Mathematics, Vidyasagar University, Midnapore 721 102, West Bengal, IndiaJournal Article19700101The effects of Hall currents and radiation on MHD flow of a viscous incompressible electrically conducting fluid past a moving vertical plate with variable temperature in the presence of a uniform transverse magnetic field have been studied. The governing equations are solved analytically using the Laplace transform technique. Effects of the physical parameters on the velocity (both primary and secondary) profiles and temperature distribution are shown graphically and the results are discussed.https://www.jafmonline.net/article_1481_877a492eaa85faf249edb7783094baec.pdfJournal of Applied Fluid Mechanics1735-35727420140901A Framework for Curved Boundary Representation in 2D Discontinuous Galerkin Euler Solvers693702148210.36884/jafm.7.04.21550ENB.BaghapourSchool of Mechanical Engineering, College of Engineering, University of Tehran, North Kargar Ave., P. O. Box 14395-1335, Tehran, IranV.EsfahanianSchool of Mechanical Engineering, College of Engineering, University of Tehran, North Kargar Ave., P. O. Box 14395-1335, Tehran, IranA.NejatSchool of Mechanical Engineering, College of Engineering, University of Tehran, North Kargar Ave., P. O. Box 14395-1335, Tehran, IranJournal Article19700101Finite-element based CFD solvers like the family of Discontinuous Galerkin (DG) solvers suffer severely from inaccurate boundary reconstruction. In this matter, developing an accurate and flexible strategy is highly demanded to provide high-order curved boundary representation in DG simulations. In this paper, a general framework is introduced to design the curved elements in discontinuous Galerkin finite-element (DGFEM) simulations. The aim is to connect the boundary to the surrounding mesh by defining an appropriate set of basis functions which deliver the curvature information inside the mesh region adjacent to the boundary. This information is then used in flux integral calculations. The proposed framework is applied in Lagragian and Hermitian boundary representations. The efficiency of the method is analyzed for compressible inviscid flow test cases using the discontinuous Galerkin scheme. It is illustrated that using the curved-side elements in the present approach, is adequate to reduce the artificial entropy generation near the boundaries. This leads to the simulations with the desired order of accuracy. The results show a well consistency in h/p-refinement which advocates the use of the proposed approach in high-order CFD simulations.https://www.jafmonline.net/article_1482_638f6531c791a5d61b7f05e0dea19b00.pdfJournal of Applied Fluid Mechanics1735-35727420140901Steady Stagnation Point Flow and Heat Transfer Over a Shrinking Sheet with Induced Magnetic Field703710148310.36884/jafm.7.04.21822ENA.SinhaDepartment of Mathematics Jadavpur University, Jadavpur-700032, IndiaJournal Article19700101The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a shrinking sheet is studied. The effects of an induced magnetic field and thermal radiation are taken into account. Velocity and thermal slip conditions have also been incorporated in the study. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using Newton’s linearization method. Computational results for the variation in velocity, temperature, skin-friction co-efficient and Nusselt number are presented graphically and in tabular form. Study reveals that the surface velocity gradient and heat transfer are enhanced by decreasing magnetic parameter.https://www.jafmonline.net/article_1483_18a6042926ed79dbc21828c049d1332a.pdfJournal of Applied Fluid Mechanics1735-35727420140901Spectral Homotopy Analysis Method for PDEs That Model the Unsteady Von Kàrmàn Swirling Flow711718148410.36884/jafm.7.04.21996ENZ. G.MakukulaSchool of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South AfricaS. S.MotsaSchool of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South AfricaJournal Article19700101A spectral homotopy analysis method (SHAM) is used to find numerical solutions for the unsteady viscous flow problem due to an infinite rotating disk. The problem is governed by a set of two fully coupled nonlinear partial differential equations. The method was originally introduced for solutions of nonlinear ordinary differential equations. In this study, its application is extended to a system of nonlinear partial differential equations (PDEs) that model the unsteady von Kàrmàn swirling flow. Numerical values of the pertinent flow properties were generated and validated against results obtained using the Keller-box numerical scheme. The results indicate that the present method is very accurate and can be used as an efficient tool for solving nonlinear PDEs of the type discussed in this paper.https://www.jafmonline.net/article_1484_3272f43b1bfb7ede718be72234054bf5.pdf