Oblate Spheroid Research Articles

On the Calculation of the Magnitude of Induced Charges and the Electrostatic Dipole of an Oblate Spheroid with an Axis of Symmetry Collinear to an External Homogeneous Electrostatic Field

The values of the surface induced charges, the positions of their centers and the value of the equivalent dipole of an oblate conducting spheroid are determined by transition from spheroidal coordinates to a spherical system of coordinates in the analytical asymptotic calculations of the first order of smallness with respect to the squared eccentricity. The characteristics of the equivalent dipole are obtained depending on the value of the electrostatic field strength, squared eccentricity, and the radius of an equal sphere.

Equilibrium points and Lyapunov families in the circular restricted three-body problem with an oblate primary and a synchronous rotating dipole secondary: Application to Luhman-16 binary system

We numerically study a version of the synchronous circular restricted three-body problem, where an infinitesimal mass body is moving under the Newtonian gravitational forces of two massive bodies. The primary body is an oblate spheroid while the secondary is an elongated asteroid of a combination of two equal masses forming a rotating dipole which is synchronous to the rotation of the primaries of the classic circular restricted three-body problem. In this paper, we systematically examine the existence, positions, and linear stability of the equilibrium points for various combinations of the model's parameters. We observe that the perturbing forces have significant effects on the positions and stability of the equilibrium points as well as the regions where the motion of the particle is allowed. The allowed regions of motion as determined by the zero-velocity surface and the corresponding isoenergetic curves as well as the positions of the equilibrium points are given. Finally, we numerically study the binary system Luhman-16 by computing the positions of the equilibria and their stability as well as the allowed regions of motion of the particle. The corresponding families of periodic orbits emanating from the collinear equilibrium points are computed along with their stability properties.

PR-DNS investigation on momentum and heat transfer of two interactive non-spherical particles in a fluid

Particle-resolved direct numerical simulations (PR-DNS) are carried out to investigate the momentum (quantified by the drag coefficient, Cd) and heat (quantified by the average Nusselt number, Nu) transfer of two interactive non-spherical porous particles in a fluid. The leading particle (relevant parameters marked by a subscript ‘L') is a spheroid with different shapes and porosities, and the trailing particle (relevant parameters marked by a subscript ‘T') is a sphere. The numerical model is firstly well validated against previously published data and then the effects of the leading particle aspect ratio (ArL), orientation (θL), porosity (εL), distance (L) and Reynolds number (Re) are stressed, respectively, on the CdT and NuT of the trailing one. New findings from the current numerical results are: CdT increases when increasing θL for a leading oblate spheroid but decreases with θL for a leading prolate spheroid. When θL = 0°, CdT increases with increasing ArL but the opposite trend is found when θL = 90°. When θL = 45° and the distance between the two particles is small, CdT increases with the increase of ArL. However, when the distance between the two interactive particles gets larger, CdT first decreases and then increases with ArL. When the leading particle is a spheroid and the two interactive particles are far away from each other, NuT increases first and then decreases with increasing θL. When the leading particle is a spheroid and the two interactive particles are close to each other, the changing trend of NuT with θL can be more greatly influenced by εL. That is, when εL = 0.9, NuT increases with θL for a leading oblate spheroid but decreases with θL for a leading prolate spheroid. On the contrary, when εL = 0 and εL = 0.5, NuT increases first and then decreases with θL for both leading oblate and prolate spheroids. When θL = 45°and the two interactive particles are close to each other, a large εL of the leading spheroid plays an important role in affecting NuT which makes it drop significantly. When θL = 45°and the two interactive particles are far away from each other, and the effects of a leading inclined spheroid on both CdT and NuT are weaker than that of a leading sphere. Generally speaking, both CdT and NuT decrease with increasing εL. At last, a back propagation neural network (BPNN) model is established in this study for prediction purposes.

A triple emulsion droplet in an extensional flow

In this theoretical report we analytically explore the deformation and breakup of an initially spherical triple emulsion drop undergoing an axisymmetric extensional creeping flow. The triple emulsion, suspended in an external fluid (fluid 1), is originally made from an inner spherical drop (fluid 4), engulfed by a spherical shell (fluid 3), which is subsequently engulfed by another spherical shell (fluid 2). The problem is described by eight dimensionless parameters: the external capillary number (Ca), three viscosity ratios (λ21, λ32, λ43), two radii ratios (K, k), and two surface tensions ratios (M, m). When the triple emulsion is subjected to an external uniaxial extensional flow (Ca > 0), the outer interface (21) and the inner drop interface (43) deform into prolate spheroids, while the interface between them (32) deforms into an oblate spheroid. The reverse occurs for an external biaxial flow (Ca < 0), the outer interface (21) and the inner drop interface (43) deform into oblate spheroids and the middle interface (32) becomes a prolate spheroid. Three types of breakup mechanisms are to be expected: when the outer and the middle interfaces are in contact, when the middle and the inner interfaces are in contact, and when the inner drop breaks while the two shell phases remain continuous. Finally, an analytical expression for the effective viscosity of a dilute emulsion containing spherical triple emulsion droplets is suggested. For a triple emulsion which behaves like a solid: a very viscous or a very thin outer shell (λ21→∞ or K→ 1), the effective viscosity reduces to Einstein’s formula, and when the triple emulsion behaves like a single drop: a very thick outer shell such that the inner shell and the inner drop disappear (K→ 0), Taylor’s expression is recovered.

A novel correlation of bubble aspect ratio through analysis of gas/shear-thinning liquid two-phase flow in a bubble column

Gas/shear-thinning liquid two-phase flow is often involved in the petroleum, chemical, and food industries, with the bubble shape playing a vital role in the theoretical analysis and numerical simulation of the flow. This study investigates the bubble shape variation in a shear-thinning liquid (carboxymethyl cellulose sodium solution) under the bubble swarm condition using high-speed imaging and a bubble recognition algorithm. The results show that trailing bubbles accelerate as they rise along the flow path of leading bubbles. During acceleration, the bubbles are subjected to lateral forces that cause them to deform from an oblate spheroid to a prolate spheroid. The effect of the shear-thinning property is enhanced owing to the increased superficial gas velocity and solution concentration, leading to an increase in the number of prolate spherical bubbles. Considering the significant difference in energy transfer in the flow fields around oblate and prolate particles, new aspect ratio correlations were developed for the two shapes based on the correlations of Re·Eo derived from the Newtonian fluid case. Compared to the previous correlation developed by assuming that the two shapes have the same aspect ratio, the proposed method significantly improves the prediction accuracy of the bubble aspect ratio for a shear-thinning fluid case.

Pollen morphology of the Brazilian species of Dyschoriste Nees and Hygrophila R.Br (Ruellieae, Acanthaceae) and its taxonomic significance

Acanthaceae is an eurypalinous and pollen morphology has been used in species delimitation and as a support to new taxa recognition. The aim of the present study is to provide new pollen descriptions for the Brazilian species of Dyschoriste (7 spp.) and Hygrophila (4 spp.). We analysed the pollen under light and scanning electronic microscopy. Pollen grains of D. erythrorhiza, D. eulinae, D. glandulifera, D. vinacea, H. acutangula, and H. paraibana are described here for the first time. Dyschoriste species has pollen grains medium to large, isopolar, prolate spheroidal, subprolate to prolate, circular, subcircular, and subtriangular amb, 3-colporate and 13–20-pseudocolpate and the exine is psilate-microechinate to perforate-microechinate. Hygrophila species has pollen grains small to medium, isopolar, oblate spheroidal, subcircular to subquadrangular amb, 4-colporate and 15–21-pseudocolpate and exine is perforate-reticulate. Palynological characters of high taxonomic relevance were: pollen size; pollen shape; length of colpi; endoaperture shape; sexine and nexine thickness; sexine ornamentation; number of pseudocolpi. From our results, a new combination is proposed, D. glandulifera, based on both pollen and macro morphology traits.

Slow translation of a slightly deformed spherical fluid drop

A drop of one fluid moving in another immiscible fluid causes shear, the flow-induced stress tends to deform the drop, and the interfacial tension between the phases resists this deformation. The present article deals with the analytical treatment of the problem of steady translational motion of a slightly deformed spherical fluid drop suspended in an immiscible viscous fluid under the consideration of vanishing Reynolds number. This is the case when the induced stress is slightly higher than the interfacial tension so that the drop is slightly deformed but does not break. The flow fields in both the interior and exterior of the drop are governed by the steady Stokes equations that are solved asymptotically using a method of perturbed expansions under suitable boundary conditions. The deformation from spherical shape is characterized by a small parameter called the deformation parameter, and the hydrodynamic boundary value problem is solved up to the second order of the deformation parameter by neglecting the higher-order terms. The effect of deformation parameter is observed by means of force expression. The explicit expressions for the hydrodynamic drag force exerted on the drop are obtained for the special cases of prolate and oblate spheroids. In the limiting cases of the drop behaving as a solid particle and a gas bubble, the force expressions agree with the corresponding formulas for the slow translation of a slightly deformed slip sphere in the limiting conditions of no slip and full slip, respectively.

Marangoni instability in oblate droplets suspended on a circular frame

We study theoretically internal flows in a small oblate droplet suspended on the circular frame. Marangoni convection arises due to a vertical temperature gradient across the drop and is driven by the surface tension variations at the free drop interface. Using the analytical basis for the solutions of Stokes equation in coordinates of oblate spheroid, we have derived the linearly independent stationary solutions for Marangoni convection in terms of Stokes stream functions. The numerical simulations of the thermocapillary motion in the drops are used to study the onset of the stationary regime. Both analytical and numerical calculations predict the axially symmetric circulatory convection motion in the drop, the dynamics of which is determined by the magnitude of the temperature gradient across the drop. The analytical solutions for the critical temperature distribution and velocity fields are obtained for the large temperature gradients across the oblate drop. These solutions reveal the lateral separation of the critical and stationary motions within the drops. The critical vortices are localized near the central part of a drop, while the intensive stationary flow is located closer to its butt end. A crossover to the limit of the plane film is studied within the formalism of the stream functions by reducing the droplet ellipticity ratio to zero value. The initial stationary regime for the strongly oblate drops becomes unstable relative to the many-vortex perturbations in analogy with the plane fluid films with free boundaries.

Detachment of inclined spheroidal particles from flat substrates

The detachment of fine particles attached to a solid substrate or rock surface significantly affects colloidal transport in porous media. The work is devoted to quantifying the detachment conditions for inclined oblate spheroids subjected to creeping viscous flow. A numerical and a laboratory study were conducted to systematically evaluate the impact of the orientation (pitch) angle towards the hydrodynamic moment, adhesive DLVO force, contact area, and critical detachment velocity. The methodology developed to produce stretched latex polystyrene particles reduces the geometric uncertainty of nonspherical fines. The geometry of the produced oblate spheroids is fully determined by the semi-major and semi-minor axes. For inclined attached particles, an explicit formula has been derived for the detaching velocity, where the detaching drag torque exceeds the attaching adhesion torque. The probabilistic distribution of the model parameters for the detachment velocity of the inclined particles attached to the plane substrate provides upscaling for fines detachment from the particle to porous media scale.

Activity recovery for differently shaped objects in quantitative SPECT

Objective. The aim was to theoretically and experimentally investigate recovery in SPECT images with objects of different shapes. Furthermore, the accuracy of volume estimation by thresholding was studied for those shapes. Approach. Nine spheres, nine oblate spheroids, and nine prolate spheroids phantom inserts were used, of which the six smaller spheres were part of the NEMA IEC body phantom and the rest of the inserts were 3D-printed. The inserts were filled with 99mTc and 177Lu. When filled with 99mTc, SPECT images were acquired in a Siemens Symbia Intevo Bold gamma camera and when filled with 177Lu in a General Electric NM/CT 870 DR gamma camera. The signal rate per activity (SRPA) was determined for all inserts and represented as a function of the volume-to-surface ratio and of the volume-equivalent radius using VOIs defined according to the sphere dimensions and VOIs defined using thresholding. Experimental values were compared with theoretical curves obtained analytically (spheres) or numerically (spheroids), starting from the convolution of a source distribution with a point-spread function. Validation of the activity estimation strategy was performed using four 3D-printed ellipsoids. Lastly, the threshold values necessary to determine the volume of each insert were obtained. Main results. Results showed that SRPA values for the oblate spheroids diverted from the other inserts, when SRPA were represented as a function of the volume-equivalent radius. However, SRPA values for all inserts followed a similar behaviour when represented as a function of the volume-to-surface ratio. Results for ellipsoids were in agreement with those results. For the three types of inserts the volume could be accurately estimated using a threshold method for volumes larger than 25 ml. Significance. Determination of SRPA independently of lesion or organ shape should decrease uncertainties in estimated activities and thereby, in the long term, be beneficial to patient care.

Noncollinear Equilibrium Points in CRTBP with Yukawa-Like Corrections to Newtonian Potential under an Oblate Primary Model

This study is about the effects of Yukawa-like corrections to Newtonian potential on the existence and stability of noncollinear equilibrium points in a circular restricted three-body problem when bigger primary is an oblate spheroid. It is observed that ∂x0/∂λ = 0 = ∂y0/∂λ at λ0 = 1/2, so we have a critical point λ0 = 1/2 at which the maximum and minimum values of x0 and y0 can be obtained, where λ ∈ (0, ∞) is the range of Yukawa force and (x0, y0) are the coordinates of noncollinear equilibrium points. It is found that x0 and y0 are increasing functions in λ in the interval 0 &lt; λ &lt; λ0 and decreasing functions in λ in the interval λ0 &lt; λ &lt; ∞ for all α ∈ α+. On the other hand, x0 and y0 are decreasing functions in λ in the interval 0 &lt; λ &lt; λ0 and increasing functions in λ in the interval λ0 &lt; λ &lt; ∞ for all α ∈ α−, where α ∈ (−1, 1) is the coupling constant of Yukawa force to gravitational force. The noncollinear equilibrium points are found linearly stable for the critical mass parameter β0, and it is noticed that ∂β0/∂λ = 0 at λ ∗ = 1/3; thus, we got another critical point which gives the maximum and minimum values of β0. Also, ∂β0/∂λ &gt; 0 if 0 &lt; λ &lt; λ ∗ and ∂β0/∂λ &lt; 0 if λ ∗ &lt; λ &lt; ∞ for all α ∈ α−, and ∂β0/∂λ &lt; 0 if 0 &lt; λ &lt; λ ∗ and ∂β0/∂λ &gt; 0 if λ ∗ &lt; λ &lt; ∞ for all α ∈ α+. Thus, the local minima for β0 in the interval 0 &lt; λ &lt; λ ∗ can also be obtained.

Global‐Krigger: A Global Kriging Interpolation Toolbox With Paleoclimatology Examples

AbstractMany applications in Earth sciences require spatial prediction, that is, obtaining a continuous scalar field from a set of discrete scalar data points on the Earth's surface. Such applications include model‐data comparisons and derivation of continuous scalar fields as input for Earth system models. The advantage of kriging as an interpolation method is that it provides predictions with confidence intervals for data sets of irregularly distributed points in space. However, the theory of kriging for non‐Euclidean domains such as oblate spheroids (e.g., the Earth's surface) is poorly developed, and existing kriging algorithms for global interpolation oftentimes cannot guarantee the validity of their predictions. Here, we present Global‐Krigger, a new kriging interpolation algorithm adapted for local to global applications that (a) incorporates a numerical check to guarantee that the necessary conditions for the kriging system of linear equations are met, and (b) derives a combined uncertainty field due both to spatial variations in data density and measurement error. The robustness of the method is demonstrated by cross‐validating predictions against reanalysis fields of traditional climatological scalar variables. We also show an example application in paleoclimatology for Holocene mineral dust deposition fluxes. The toolbox includes a user‐friendly graphical user interface that guides users through a range of choices during data pre‐interpolation analysis, kriging, and post‐processing.

3D Radiation-hydrodynamic Simulations Resolving Interior of Rapidly Accreting Primordial Protostar

Direct collapse of supermassive stars is a possible pathway to form supermassive black hole seeds at high redshifts. Whereas previous three-dimensional (3D) simulations demonstrate that supermassive stars form via rapid mass accretion, those resolving the stellar interior have been limited. Here, we report 3D radiation-hydrodynamic (RHD) simulations following the evolution of rapidly accreting protostars resolving the stellar interior. We use an adaptive mesh refinement code with our newly developed RHD solver employing an explicit M1 closure method. We follow the early evolution until the stellar mass reaches ∼10 M ⊙ from two different initial configurations of spherical and turbulent clouds. We demonstrate that, in both cases, a swollen protostar whose radius is 100–1000 R ⊙ appears, as predicted by the stellar evolution calculations. Its effective temperature remains a few thousand Kelvin, and the radiative feedback by ionizing photons is too weak to disturb the accretion flow up to the epoch examined in this work. In the turbulent case, the protostar rotates rapidly at more than 0.4 times the Keplerian velocity owing to the angular momentum provided by the initial turbulence. The protostar approximates an oblate spheroid, and its equatorial radius is more than twice the polar radius. Our results suggest that we need to consider the rapid stellar rotation to elucidate the realistic 3D protostellar evolution in the supermassive star formation.

On the clustering of low-aspect-ratio oblate spheroids settling in ambient fluid

We have performed particle-resolved direct numerical simulations of many heavy non-spherical particles settling under gravity in the dilute regime. The particles are oblate spheroids of aspect ratio $1.5$ and density ratio $1.5$ . Two Galileo numbers are considered, namely $111$ and $152$ , for which a single oblate spheroid follows a steady vertical and a steady oblique path, respectively. In both cases, a strongly inhomogeneous spatial distribution of the disperse phase in the form of columnar clusters is observed, with a significantly enhanced average settling velocity as a consequence. Thus, in contrast to previous results for spheres, the qualitative difference in the single-particle regime does not result in a qualitatively different behaviour of the many-particle cases. In addition, we have carried out an analysis of pairwise interactions of particles in the well-known drafting–kissing–tumbling set-up, for oblate spheroids of aspect ratio $1.5$ and for spheres. We have varied systematically the relative initial position between the particle pair and we have considered free-to-rotate particles and rotationally locked ones. We have found that the region of attraction for both particle shapes, with and without rotation, is very similar. However, significant differences occur during the drafting and tumbling phases. In particular, free-to-rotate spheres present longer drafting phases and separate quickly after the collision. Spheroids remain close to each other for longer times after the collision, and free-to-rotate ones experience two or more collision events. Therefore, we have observed a shape-induced increase in the interaction time which might explain the increased tendency to cluster of the many-particle cases.

Revisiting Raindrop Axis Ratios Based on 3D Oblate Spheroidal Reconstruction: 2D Video Disdrometer Observations During Tropical Cyclone Passages

AbstractRaindrops are usually parameterized by oblate spheroids with axis ratios (ARs) determined from projected images. However, the adequacy of representing the 3‐Dimensional (3D) nature of raindrops with their 2‐Dimensional (2D) shadows remains an open question. This study reexamines raindrop AR parameterizations by applying a 3D oblate spheroidal reconstruction algorithm to 2D video disdrometer (2DVD) observations during the passages of 14 tropical cyclones. The results reveal an appreciable AR overestimation for large raindrops when retrieved from a single camera and especially for 2DVD raw products. This overestimation propagates into the simulated differential reflectivity (ZDR), resulting in an underestimation of ZDR by up to 0.5 dB at X‐band when large raindrops dominate the raindrop size distribution (RSD), which would introduce an underestimation of more than 20% for heavy rain rate (&gt;60 mm hr−1) estimation by polarimetric radar. In precipitating systems with drastically changing RSDs, the importance of adopting more realistic ARs is warranted.

Shape Evolution of Two-Dimensional Au Hexagonal Nanoplates into Pseudo Three-Dimensional Oblate Spheroids

Herein, we report a seed-mediated synthetic method for pseudo three-dimensional oblate spheroids with structural complexity where concave and convex nanofeatures are formed simultaneously through manipulation of the growth directions. By exploiting hexagonal Au nanoplates as a seed material that consists of two Au(111)-faceted basal planes and side-by-side alternating arrangement of six Au(111) and six Au(100) side facets, we identified three growth patterns via a combination of kinetic and thermodynamic controls, leading to concomitant formation of concavity and convexity of the crystal facets. We denote the respective ellipsoidal nanoplates as convex or concave oblate spheroids. Various types of six-fold oblate spheroids were synthesized with high homogeneity in size, shape, and yield, and their optical responses in the ensemble were investigated. Given the many types of complex seed nanocrystals available, the suggested synthetic scheme using two-dimensional nanoplates as a seed will pave the way for the design of highly complex and sophisticated nanoparticles, especially where surface curvature is the main interest.

Revisiting Long-Time Dynamics of Earth’s Angular Rotation Depending on Quasiperiodic Solar Activity

Having taken into account the nonsymmetric form of Earth’s surface (which is an oblate spheroid as the first approximation, with oblateness of approx. 1/300), we outline in the current research that additional large-scale torques stem from unbalanced (reactive) reradiating heat flows back into outer space. They arise during long-time dynamics of Earth’s angular rotation depending on quasiperiodic solar activity. The key idea of our research supports the mainstream idea of most of the researchers in the scientific community regarding this matter. It stipulates that the activity of earthquakes strongly correlates with changes in the regime of Earth’s spin dynamics during all periods of observation. We have demonstrated here that the long-time dynamics of Earth’s angular rotation depends on the quasiperiodic solar activity by arising additional large-scale torques stemming from unbalanced (reactive) reradiating heat fluxes. The latter carry the momentum outside and at an unpredictable angle to the overall Earth’s surface back into outer space (due to the nonsymmetric form of Earth’s surface).

A New Method of Investigation of the Orientation of Galaxies in Clusters in the Absence of Information on Their Morphological Types

The analysis of the orientation of galaxies is one of the most widely used tools in the fields of extragalactic astronomy and cosmology, enabling the verification of structure formation scenarios in the universe. It is based on the statistical analysis of the distribution of angles, giving the spatial orientation of galaxies in space. In order to obtain the correct analysis results, one is obliged to take into account the Holmberg effect and the fact that galaxies are oblate spheroids, with the real axis ratio depending on the morphological type. However, most of the astronomical data available today do not contain information about the morphological types of galaxies. The analysis of sufficiently numerous observational data allows one to calculate the estimated frequency of the occurrence of given morphological types used in the proposed method. As a part of this, on the basis of these frequencies, simulations were performed, which enabled us to recognize new angle distributions used in orientation studies. These distributions already contain information on the frequency of the appearance of galaxies of particular morphological types in clusters, allowing for more accurate results of the statistical tests carried out during the analysis. The method is an extension of results developed in in our previous investigations.

Canonical steering ellipsoids of pure symmetric multiqubit states with two distinct spinors and volume monogamy of steering

Quantum steering ellipsoid formalism provides a faithful representation of all two-qubit states and helps in obtaining correlation properties of the state through the steering ellipsoid. The steering ellipsoids corresponding to the two-qubit subsystems of permutation symmetric $N$-qubit states is analysed here. The steering ellipsoids of two-qubit states that have undergone local operations on both the qubits so as to bring the state to its canonical form are the so-called canonical steering ellipsoids. We construct and analyze the geometric features of the canonical steering ellipsoids corresponding to pure permutation symmetric $N$-qubit states with two distinct spinors. Depending on the degeneracy of the two spinors in the pure symmetric $N$-qubit state, there arise several families which cannot be converted into one another through Stochastic Local Operations and Classical Communications (SLOCC). The canonical steering ellipsoids of the two-qubit states drawn from the pure symmetric $N$-qubit states with two distinct spinors allow for a geometric visualization of the SLOCC-inequivalent class of states. We show that the states belonging to the W-class correspond to oblate spheroid centered at $(0,0,1/(N-1))$ with fixed semiaxes lengths $1/\sqrt{N-1}$ and $1/(N-1)$. The states belonging to all other SLOCC inequivalent families correspond to ellipsoids centered at the origin of the Bloch sphere. We also explore volume monogamy relations of states belonging to these families, mainly the W-class of states.

Impact of nanoparticle shape on entropy production of nanofluid over permeable MHD stretching sheet at quadratic velocity and viscous dissipation

The goal of this study was to determine the effect that NP shape has on the entropy produced by Al2O3−H2O nanofluid across a permeable MHD stretching sheet under the conditions of quadratic velocity, thermal radiation, and viscous dissipation. H2O is the cold fluid, while Al2O3−H2O nanofluid, which includes five various NP forms (oblate spheroid, platelet, blade, brick, and cylinder), is the hot fluid. Nanofluid containing Al2O3−H2O sees widespread use in industrial production because of its remarkable capacity to boost heat transfer. Via a sequence of similarity transformations, the controlling PDEs are converted into a nonlinear differential system of linked ODEs. An efficient implementation of the Runge-Kutta method for getting numerical solutions may be found in the code, which is written in MATLAB. As the φ grows from 0% to 2% or from 0% to 4%, the wall shear stress rises by roughly 6.3% and 12.6%, respectively, in the area that is behind the stretched sheet. Including the magnetic effect in the boundary layer flow at a rate of around 5%, the rate of convective heat transfer increases by about 16.4%. In comparison to nanofluids containing brick-, blade-, cylinder-, and platelet-shaped NPs, the Os-shaped NP nanofluid experiences a greater increase in thermal entropy on the cold fluid side.