Magnetic Field Angle Research Articles

The Solar Wind Parker Spiral Angle Distributions and Variations at 1 au

Using the data from the Advanced Composition Explorer (ACE) and Wind spacecraft, we statistically studied the Parker spiral angle (PSA) of the solar wind magnetic field from 1998 to 2019 at 1 au. The PSA occurrences over both a Carrington rotation (CR) and a year can be well fitted by a Gaussian distribution. However, large-scale magnetic structures, such as interplanetary coronal mass ejections (ICMEs), can significantly deviate the PSA distribution of a CR from the Gaussian distribution. The PSA distributions of each CR and each year are affected by the solar activity: They are more concentrated at a relatively higher average PSA at solar maximum. There is also a weak anticorrelation between the yearly solar wind speed (v sw) and the average PSA. MESSENGER, Venus Express, and ACE observations at different heliocentric distances within 1 au show that the dominating polarities of the heliospheric magnetic field change greatly from year to year even when the solar activity is on the same level. Our results suggest that the PSA distribution in addition to the sunspot number can provide some new information on the magnetic field variation of the Sun.

Effect of site disorder on the resonant microwave absorption in Co2Fe0.5Ti0.5Si Heusler alloy thin films

100 nm Co2Fe0.5Ti0.5Si (CFTS) thin films were grown on Si (100) substrate at different substrate temperatures TS to study the effect of site disorder on the magnetization relaxation processes and magnetic anisotropy in them. To this end, two different ferromagnetic resonance (FMR) techniques have been employed: broad-band (3 – 17 GHz) FMR at a fixed static magnetic field angle in the ‘in-plane’ (IP) sample geometry, and X-band (9.45 GHz) FMR at different polar field-angles, θH, in the ‘out-of-plane’ (OP) sample configuration. Increase in TS reduces the degree of disorder and improves crystalline order. Improvement in crystallinity, in turn, results in the decrease in the strength of magnetocrystalline anisotropy. Irrespective of the degree of disorder present, the OP anisotropy field, Hk⊥, is an order of magnitude higher than the IP counterpart, Hk‖. Out of the CFTS thin films studied, the film (TS500), deposited at TS = 500 °C, has the maximum L21 crystalline order, maximum saturation magnetization (MS = 779 G), and the least values for Hk‖ (5.3 Oe), Hk⊥ (17 Oe), Landé splitting factor, g = 2.02, and the Gilbert damping constant, α=5.5×10-3. These optimum values of MS, g and α, at room temperature, are conducive for spintronics applications. In the OP configuration, the FMR linewidth, ΔH⊥, mainly arises from the intrinsic Landau-Lifshitz-Gilbert damping and extrinsic angular spread of crystallite misorientation. However, the extrinsic two-magnon scattering contribution to ΔH⊥, is appreciable only in the angular range 70° ≤ θH ≤ 110° .

Solar Cycle and Seasonal Variability of Martian Ionospheric Irregularities from Mars Atmosphere and Volatile Evolution Observations

Spacecraft observations around Mars show that ionospheric irregularities occur frequently in the Martian ionosphere. In this study, Mars Atmosphere and Volatile Evolution data (the region is below ∼200 km) during 2015 January to 2021 March were used to revisit the statistical characteristics of ionospheric irregularities and the comparison of irregularities in Martian years with higher or lower solar activity phase of solar cycle. Results show that the characteristics of the irregularities with a larger length scale associated with the magnetic field and solar zenith angle are similar to the previous studies. Moreover, our results show that the occurrence rate of irregularities exhibits dawn and dusk asymmetry, and the occurrence rate at dusk is higher than that at dawn. In addition, results demonstrate that the occurrence rate of irregularities is higher in Martian years with higher solar activity than Martian years with lower solar activity, which means that the solar cycle might play an important role in the formation of irregularity events. Further studies show that the solar zenith angle (SZA) and altitude at the maximum occurrence rate depend on the level of solar activity. The SZA and altitude of the maximum occurrence rate are smaller in the Martian year with higher solar activity than the lower. We also found that the rate of events is lower during the day than the terminator in the ionospheric dynamo region. By contrast, in the regions where both electrons and ions are magnetized, events have a higher rate during the day than the terminator. Furthermore, the seasonal variation of the irregularity events was also presented in this study. Results show that the occurrence rate in the dynamo region with 80° < SZA < 150° in MY34 and MY35 show an incremental trend from spring to winter, but this trend is not obvious in MY33.

Electromagnetic field/hypersonic flow field coupled algorithm and its application in the magnetic controlled inlet design

A novel magnetic controlled inlet design method is proposed for the airbreathing hypersonic vehicles cruising at an extremely high Mach number. By introducing the electromagnetic source terms to the Euler equations, an electromagnetic field/hypersonic flow field coupled algorithm is developed as the numerical design tool. A quasi-one-dimensional simplified model of the magnetic controlled inlet is constructed to analyze the compression performance under the different combinations of magnetic field and leading-edge shock angle. The results show that the combination of weak leading-edge shock and strong magnetic field can obtain a better compression effect. Three inlets are designed under the magnetic field with the induction intensity of 0.05 T, 0.08 T, and 0.1 T, respectively. The designed inlets have a contraction ratio of nearly 1.5 and the wall shape is not sensitive to the variation of magnetic induction intensity. With an inflow Mach number of 10, the exit Mach number can be reduced from 5 to 2.5 when the magnetic induction intensity is adjusted from 0.05 T to 0.1 T. In addition, there is no reflected shock in the inner channel of the inlet and therefore the complex shock/boundary layer interaction in the conventional inlet has been greatly relieved. Although the total pressure recovery is significantly reduced, part of the energy loss can be transformed to electric energy by the MHD energy extraction equipment and used to accelerate the nozzle flow.

MHD Mixed Convective Heat Transfer of Cu-Al2O3 Water Hybrid Nanofluid over a Stretching Wedge with Ohmic Heating

The main purpose of the current article is present exploration scrutinizes a numerical simulation for the magneto-mixed convection flows of hybrid nanofluid over a stretching wedge with Ohmic heating applying Tiwari and Das model. Proper dimensionless variables are applied the governing PDEs which are solved numerically using Matlab program. The obtained results of velocity and temperature profiles for several key parameters are portrayed and construed in detail. It has been observed that the amount of skin friction coefficient and the Nusselt number of the hybrid liquid nano improve and increase with the increase of the nanoparticle size fraction, magnetic field, mixed load, and wedge angle while it decreases when we increase the velocity ratio and increases with the increase of the Nusselt number.

Numerical analysis of a time-dependent aligned MHD boundary layer flow of a hybrid nanofluid over a porous radiated stretching/shrinking surface

This work explores the two-dimensional time-dependent hydromagnetic flow of a hybrid nanofluid across a permeablestretching/shrinking sheet. Moreover, the current study includes the combined effect of heat generation, velocity slip, thermalradiations, and convective conditions. Using the similarity transformations, the governing nonlinear PDEs have been converted toordinary differential equations (ODEs). Finally, the MATLAB solver bvp4c has been used to get the numerical solutions. The variousgraphical results of temperature, heat transport, velocity, and friction drag have been plotted for the diverse values of parametersassociated with the current effects of the problem. These outcomes state that the higher values of nanoparticles concentration causeto reduce the velocity and enhance the fluid temperature. The rising values of nanoparticles concentration, slip parameter,unsteadiness parameter, and the inclination angle of magnetic field intensify the skin friction, however, it decreases with the growth ofHartmann and Darcy number. Additionally, the rate of heat transport intensifies with the rising values of concentration and alignedmagnetic field angle, although the growth of the Hartmann number and slip parameter reduces the rate of heat transport. Moreover,the skin friction and the local Nusselt number respectively decline and enhances for the increasing values of the stretching parameter.

Mixed bioconvection flow of Ag-MgO/water in the presence of oxytactic bacteria and inclined periodic magnetic field

In this paper, a numerical investigation on mixed bioconvection flow of silver(Ag)-magnesium oxide(MgO)-water hybrid nanofluid in a trapezoidal porous cavity under the effect of inclined periodic magnetic field is carried out. Brinkman–Forchheimer-extended Darcy model for the porous medium is adopted. Galerkin weighted residual finite element method is implemented to simulate the governing steady dimensionless equations. The resulting discrete nonlinear algebraic systems are treated using the adaptive Newton's method. The fluid flow, heat and mass transfer behavior are examined in variation of parameters as Hartmann number (Ha=0−100), angle of periodic magnetic field (θ=0∘−90∘), period of periodic magnetic field (Λ=0.1−1), bioconvection Rayleigh number (Rb=10−100), Richardson number (Ri=0.1−5), Lewis number (Le=1−10) and Peclet number (Pe=0.1−1). The rise in Hartmann number has a weakening effect on both transfer of heat and mass. When θ=0∘, convective heat and mass transfer is the smallest at Λ=1 where the most reduction in the average Nusselt and Sherwood numbers is 9.14% and 6.98% as Λ is raised from 0.1 to 1, respectively, and occurs at Ha=100. The significant decrement in the average Nusselt number is 42.57% at Ha=75 and in the Sherwood number is 10.4% at Ha=50 when θ is changed from 0∘ to 90∘.

Lattice Boltzmann-based numerical analysis of nanofluid natural convection in an inclined cavity subject to multiphysics fields

This research conducts a study of natural convection heat transfer (NCHT) in a nanofluid under a magnetic field (MF). The nanofluid is in a cavity inclined at an angle of 45°. The MF can take different angles between 0° and 90°. Radiative heat transfer is present in the cavity in volumetric form. There are two hot semicircles, similar to two half-pipes, on the bottom wall. The top wall is kept cold. The side walls and parts of the bottom wall, except the pipes, have been insulated. The lattice Boltzmann method has been used for the simulation. The studied parameters are the Rayleigh number (in the range 103–106), magnetic field angle, radiation parameter (in the range 0–2), and nanoparticle volume fraction (in the range 0–5%). The generated entropy has been studied as the NCHT. The results indicate that adding nanoparticles improves heat transfer rate (HTR). Moreover, the addition of volumetric radiation to the cavity enhances the Nusselt number by 54% and the generated entropy by 12.5%. With an augmentation in the MF angle from 0° to 90°, HTR decreases and this decrease is observed mostly at higher Rayleigh numbers. An augmentation in the Ra increases NCHT and entropy generation. Indeed, a rise in the Ra from 103 to 106 increases HTR by almost sixfold.

Tunable photonic bandgap and reflection phase shift properties of 1D binary photonic crystal consisting of double negative and magnetic cold plasma materials

In this manuscript, by using alternate layers of double negative and magnetic cold plasma materials, we have studied the reflection and reflection phase shift properties of 1D binary photonic crystals. The simulations of the proposed work have been carried out by using the transfer matrix method with the help of MATLAB software. It has been found that the combination of the angle of incidence and external magnetic field under both right hand polarized and left handed polarized configurations can be used for right and left tuning of photonic bandgap (PBG) of the proposed structure under consideration. Under the aforementioned circumstances, the reflection phase shift corresponding to TE and TM waves can be smoothly switched between 0 to π and –π to 0, respectively, across PBGs of the proposed structure. The variation in external magnetic field values from 0 to 6 T and angle of incidence from 0° to 80° can be used for precise tuning of PBG and reflection phase shift between –π and π depending upon TM and TE polarization cases, respectively. This study may open a new gateway for designing externally tunable microwave devices like single to multichannel band-stop filters, buffers that can hold data temporarily, tunable wave plates, and tunable phase retarders.

Persistent horizontal and vertical, MR-induced nystagmus in resting state Human Connectome Project data

ObjectiveStrong magnetic fields from magnetic resonance (MR) scanners induce a Lorentz force that contributes to vertigo and persistent nystagmus. Prior studies have reported a predominantly horizontal direction for healthy subjects in a 7 Tesla (T) MR scanner, with slow phase velocity (SPV) dependent on head orientation. Less is known about vestibular signal behavior for subjects in a weaker, 3T magnetic field, the standard strength used in the Human Connectome Project (HCP). The purpose of this study is to characterize the form and magnitude of nystagmus induced at 3T. MethodsForty-two subjects were studied after being introduced head-first, supine into a Siemens Prisma 3T scanner. Eye movements were recorded in four separate acquisitions over 20 min. A biometric eye model was fitted to the recordings to derive rotational eye position and then SPV. An anatomical template of the semi-circular canals was fitted to the T2 anatomical image from each subject, and used to derive the angle of the B0 magnetic field with respect to the vestibular apparatus. ResultsRecordings from 37 subjects yielded valid measures of eye movements. The population-mean SPV ± SD for the horizontal component was -1.38 ± 1.27 deg/sec, and vertical component was -0.93 ± 1.44 deg/sec, corresponding to drift movement in the rightward and downward direction. Although there was substantial inter-subject variability, persistent nystagmus was present in half of subjects with no significant adaptation over the 20 min scanning period. The amplitude of vertical drift was correlated with the roll angle of the vestibular system, with a non-zero vertical SPV present at a 0 degree roll. InterpretationNon-habituating vestibular signals of varying amplitude are present in resting state data collected at 3T.

The angular dependence of magnetization dynamics induced by a GHz range strain pulse

The dynamics of magnetization is important in spintronics, where the coupling between phonon and magnon attracts much attention. In this work, we study the angular dependence of the coupling between longitudinal-wave phonon and magnon. We investigated the magnetization dynamics using the time-resolved magneto-optical Kerr effect, which allows measuring spin-wave resonances and the magnetic echo signal. The frequency, mode number, and amplitude of the spin-wave resonance change with the out-of-plane angle of the external magnetic field. The amplitude of the magnetic echo signal caused by the strain pulse also changes with the angle. We calculate these angular dependences based on the Landau–Lifshitz–Gilbert equation and find that the angles of the external field and magnetic moment are important factors for the phonon–magnon coupling when phonon propagates in the thickness direction under the out-of-plane magnetic field.

Aligned Magnetohydrodynamics (MHD) Flow of Hybrid Nanofluid Over a Vertical Plate Through Porous Medium

The future research on hybrid nanofluids need to be done as there are many applications of hybrid nanofluids. Some of them are electro-mechanical, renewable energy and manufacturing process application and also the application in automotive cooling. Therefore, this numerical study is conducted to investigate the aligned magnetohydrodynamics (MHD) flow of hybrid nanofluid over a vertical plate through a porous medium. The base fluid (water), silver and copper oxide flowed over a vertical plate in the presence of MHD and porous medium with boundary conditions of constant wall temperature by taking a few types of parameters into consideration. By using similarity transformation, the governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. Keller Box method is applied to solve numerically the nonlinear ordinary differential equations and the system is solved by using Fortran programming. The results of the study are illustrated graphically to show the behavior of velocity and temperature also skin friction and Nusselt number of hybrids nanofluid affected by the parameters. It is found that the velocity profiles increase, and temperature profiles decrease when the angle of aligned magnetic field, the interaction of magnetic parameter and local Grashof number increase while the velocity profiles decrease, and temperature profiles increase when the porous parameter and volume fraction of nanoparticles parameter increase. Besides, the skin friction of Ag-CuO-water is less than CuO-water and Nusselt number of Ag-CuO-water is higher than CuO-water.

Magnetohydrodynamic shock refraction at an inclined density interface

Shock wave refraction at a sharp density interface is a classical problem in hydrodynamics. Presently, we investigate the strongly planar refraction of a magnetohydrodynamic (MHD) shock wave at an inclined density interface. A magnetic field is applied that is initially oriented either perpendicular or parallel to the motion of incident shock. We explore flow structure by varying the magnitude of the magnetic field governed by the non-dimensional parameter β∈(0.5,106) and the inclination angle of density interface α∈(0.30,1.52). The regular MHD shock refraction process results in a pair of outer fast shocks (reflected and transmitted) and a set of inner nonlinear magneto-sonic waves. By varying magnetic field (strength and direction) and inclination interface angle, the latter waves can be slow shocks, slow expansion fans, intermediate shocks, or slow-mode compound waves. For a chosen incident shock strength and density ratio, the MHD shock refraction transitions from regular (all nonlinear waves meeting at a single point) into irregular when the inclined density interface angle is less than a critical value. Irregular refraction patterns are not amenable to an analytical solution, and hence, we have obtained irregular refraction solutions by numerical simulations. Since the MHD shock refraction is self-similar, we further explore by converting the initial value problem into a boundary value problem (BVP) by a self-similar coordinate transformation. The self-similar solution to the BVP is numerically solved using an iterative method and implemented using the p4est adaptive mesh framework. The simulation shows that a Mach stem occurs in an irregular MHD shock refraction, and the flow structure can be an MHD equivalent to a single Mach reflection irregular refraction and convex-forwards irregular refraction that occur in hydrodynamic case. For Mach number M = 2, both analytical and numerical results show that perpendicular magnetics fields suppress the regular to irregular transition compared to the corresponding hydrodynamic case. As Mach number decreased, it is possible that strong perpendicular magnetics promote the regular to irregular transition, while moderate perpendicular magnetics suppress this transition compared to the corresponding hydrodynamic case.

Impact of nanoparticle shape on thermo-solutal buoyancy induced lid-driven-cavity with inclined magnetic-field

The aim of this paper is to numerically investigate the influence of nanoparticles shape on heat and mass transport phenomena in a moving lid cavity under the combined effect of thermo-solutal buoyancy force and magnetic force. The governing equations are transformed into velocity-vorticity form of equations and solved using Galerkin's weighted residual finite-element-technique. The analysis has been carried out with parameters like buoyancy ratio (−5 ≤ N ≤ 5), magnetic field inclination angle (0° ≤ ϕ ≤ 90°) with four shapes of Al2O3 nanoparticle like bricks, blades, platelets and cylinders. The results revealed that the shape factor on Nusselt number is significant depending upon the inclined magnetic field and buoyancy ratio whereas on mass transfer the shape effect is negligible. The diffusion mode of transport process is stronger than the convection mode at higher inclination angle of magnetic field. Based on a given value of N and ϕ, blade and cylinder shows the best performance in Nusselt and Sherwood number respectively except the platelet shape that shows maximum frictional loss in terms of wall shear stress.

MHD mixed convection and entropy generation of CNT-water nanofluid in a wavy lid-driven porous enclosure at different boundary conditions

In this study, Galerkin Finite Element Method or GFEM is used for the modeling of mixed convection with the entropy generation in wavy lid-driven porous enclosure filled by the CNT-water nanofluid under the magnetic field. Two different cases of boundary conditions for hot and cold walls are considered to study the fluid flow (streamlines) and heat transfer (local and average Nusselt numbers) as well as the entropy generation parameters. Richardson (Ri), Darcy (Da), Hartmann angle (γ), Amplitude (A), Number of peaks (N), Volume fraction (φ), Heat generation factor (λ), Hartmann number (Ha) and Reynolds number (Re) are studied parameters in this study which results indicated that at low Richardson numbers (< 1) increasing the inclined angle of magnetic field, decreases the Nu numbers, but at larger Richardson numbers (> 1) it improves the Nu numbers.

MHD mixed convection and irreversibility analysis of hybrid nanofluids in a partially heated lid-driven cavity chamfered from the bottom side

In this research, magneto-convection flow in the cavity problem driven by the lid is examined using computational fluid dynamics (CFD) techniques. To this effect, the cavity considered in this numerical study has two rounded corners and is partially heated from the bottom side and filled with Al2O3-Cu/water hybrid nanofluid (HBNF). Accordingly, a solver based on C++ object-oriented language has been developed under OpenFOAM® libraries to solve the mathematical governing equations. The numerical findings are thoroughly validated with other studies. To this end, different parameters analysis is adopted, which consists of Richardson numbers (0.1 ≤ Ri ≤ 10), Hartmann numbers (0 ≤ Ha ≤ 100), magnetic field angle (0° ≤ γ ≤ 90°), solid volume fraction (0 ≤ ϕ ≤ 0.04), composition ratio (25 % ≤ Cu,Al2O3 ≤ 75%), corners radius (0.01 ≤ R ≤ 0.3). This analysis is achieved by exploring streamlines, isotherms, total entropy generation, local and average Nusselt numbers. After the data analyses, the findings indicated that the magnetic field orientation strongly affects the hybrid nanofluid flow and temperature distribution. In other words, at Ri = 10, Applying a magnetic field perpendicular to the gravity force leads to better heat transfer. Furthermore, decreasing corners radius enhances heat transmission and reduces irreversibility. The composition ratio (Al2O3 75%, Cu 25%) gave the highest values of the mean Nusselt Number (Num) and the total entropy production (Sg). Moreover, the heat transfer rate and irreversibility decrease with increasing Ha and decreasing Ri. Finally, suspending nanoparticles (NPs) in the base fluid improves heat transfer and increases irreversibility except for Ri = 10 at Ha = 100 and Ri = 1 at Ha = 50, where the opposite behavior has been observed.

Temperature-field-angle dependent critical current estimation of commercial second generation high temperature superconducting conductor using double hidden layer Bayesian regularized neural network

We estimated the critical current of the second generation (2G) high-temperature superconducting (HTS) conductor using neural network fitting methods. The critical current of 2G HTS conductors depends on magnetic field strength and angle as well as on temperature, Ic(T, B, θ). Moreover, the critical current values vary for 2G HTS conductors from different manufacturers. In this study, we addressed three challenging issues in critical current assessment by neural network fitting methods, namely 90° asymmetry, a wide range of temperature-field-angle dependence, and different manufacturer conductor differences. Prediction models for three commercial HTS conductors were trained and evaluated by convergence, accuracy, and robustness. The linear regression correlation coefficient R was approximately equal to 1 for the three models. The critical current estimation obtained from the proposed method was compared with the critical current estimation from the interpolation method at different fixed temperatures using a multi-width no-insulation magnet. The model computation speed was also discussed. The proposed model needed only 2.7 s to compute 10 million data sets. Therefore, the convergence, accuracy, reliability, and speed of the proposed method prove that it can be used in a wide range of industrial applications and academic fields.

Identification of a Kitaev quantum spin liquid by magnetic field angle dependence

Quantum spin liquids realize massive entanglement and fractional quasiparticles from localized spins, proposed as an avenue for quantum science and technology. In particular, topological quantum computations are suggested in the non-abelian phase of Kitaev quantum spin liquid with Majorana fermions, and detection of Majorana fermions is one of the most outstanding problems in modern condensed matter physics. Here, we propose a concrete way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence. Topologically protected critical lines exist on a plane of magnetic field angles, and their shapes are determined by microscopic spin interactions. A chirality operator plays a key role in demonstrating microscopic dependences of the critical lines. We also show that the chirality operator can be used to evaluate topological properties of the non-abelian Kitaev quantum spin liquid without relying on Majorana fermion descriptions. Experimental criteria for the non-abelian spin liquid state are provided for future experiments.

Natural convection and entropy generation of non-Newtonian nanofluids with different angles of external magnetic field using GPU accelerated MRT-LBM

In this article, the influence of applied magnetic field on the non-Newtonian power-law nanofluid in a rectangular-shaped enclosure has been studied and investigated by deploying the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). The enclosure is filled with water containing Cu nanoparticles. For the proper investigation, the equation for mass, momentum, and energy has been governed by the lattice Boltzmann method for non-Newtonian power-law nanofluid. The code validation with the previous studies is presented in the paper. The study presented here takes consideration of a wide range of magnetic field angles (γ = 0°, 30°, 45°, 90° and 120°), thermal Rayleigh number (Ra = 104 and 105), power-law index (n = 0.6, 1.0 and 1.4) of non-Newtonian power-law fluid. The study found that the average Nusselt number rises with the increment of magnetic angle up to γ = 90°, then it starts to exacerbate when γ = 120°. The average Nusselt number also increases for the higher values of the power-law index and maximum when n = 1, then it starts to decrease when the fluid becomes shear-thickening. Furthermore, finally, the entropy profile of the study is thoroughly investigated in detail.

MHD Forced Convection Using Ferrofluid Over a Backward Facing Step Containing a Finned Cylinder

Abstract In this paper, a numerical study of forced convection on a backward facing step containing a single-finned fixed cylinder has been performed, using a ferrofluid and external magnetic field with different inclinations. The partial differential equations, which determine the conservation equations for mass, momentum and energy, were solved using the finite element scheme based on Galerkin’s method. The analysis of heat transfer characteristics by forced convection was made by taking different values of the Reynolds number (Re between 10 and 100), Hartmann number (Ha between 0 and 100), nanoparticles concentration (φ between 0 and 0.1) and magnetic field inclination (γ between 0° and 90°); also, several fin positions α [0°–180°] were taken in the counter clockwise direction by a step of 5. After analysing the results, we concluded that Hartmann number, nanoparticles concentration, Reynolds number and magnetic field angles have an influence on the heat transfer rate. However, the fin position on the cylinder has a big impact on the Nusselt number and therefore on heat transfer quality. The best position of the fin is at (α = 150°), which gives the best Nusselt number and therefore the best heat transfer, but the fin position at (α = 0°) remains an unfavourable case that gives the lowest Nusselt values.