Set Of Equations Research Articles

Analytical study of soliton dynamics in the realm of fractional extended shallow water wave equations

In this study, we use the Khater Method (KM) as an efficient analytical tool to solve (3+1)-dimensional fractional extended shallow water wave equations (FESWWEs) with conformable derivatives. The KM transforms fractional partial differential equations to ordinary differential equations (ODEs) via strategic variable transformation. Then, series-form solutions to these ODEs are proposed, which turn them into nonlinear algebraic systems. The solution to this set of algebraic equations yields shock travelling wave solutions expressed in hyperbolic, trigonometric, exponential, and rational functions. The study’s findings are corroborated by 2D, 3D, and contour graphs that show the changing patterns of the detected shock travelling waves. These findings have important significance for the discipline, offering vital insights into the intricate dynamics of FESWWEs. The effectiveness of KM is demonstrated by its capacity to produce varied solutions and contribute to a thorough knowledge of such complex phenomena.

A geometric variation method to extract rock strength parameters via uniaxial compression testing

Numerical modelling in rock engineering and mechanics often requires inputting multiple sets of strength parameters, such as the commonly encountered tensile strength, cohesion, and friction angle. Usually, obtaining these parameters requires performing different types of rock mechanics experiments on certain rock specimens, such as tension tests and triaxial tests, which are time-consuming and labor-intensive. Uniaxial compression testing is simpler and requires less demanding equipment. This paper proposes a solution that relies solely on uniaxial compression testing to obtain multiple sets of rock strength parameters. The basic idea is to treat the process of acquiring multiple parameters as a problem of solving a set of mathematical equations. The uniaxial tests with different geometric specimens provide known quantities and the corresponding equations that link these known quantities (e.g., peak loads) with unknown quantities (e.g., strength parameters). We established three-dimensional numerical tests to represent the relationship between input strength parameters and the peak load. By transforming it into an optimization problem, numerical modelling is embedded into the objective function of the optimization algorithm, thereby achieving the automatic extraction of strength parameters. This method is verified through uniaxial compression tests using red sandstone specimens with various geometries. The results show that by changing the geometry of the rock specimens, multiple sets of strength parameters can be obtained. These parameters are successfully used to predict (extrapolate) peak loads of other geometric specimens. This method holds promise for achieving the automated extraction of material parameters for the numerical modelling of rock.

Improved slip mechanism and convective heat impact for ternary nanofluidic flowing past a riga surface

This study of electro-magneto-hydrodynamics has great significance due to its numerous applications like chromatography, fluid pumping, micro coolers and fluid stirring thermal reactors and flow regulation in fluidics systems. Subject to upper functions on electrical magnetic field, the consequences of electromagnetic initiation into ternary nanofluids flow through the Riga plate were noticed. Furthermore, this ternary hybrid nanofluid flow was based on the effect on slip condition, uniform heat source, convective energy and thermal radiation. The ternary hybrid nanofluid was built from the scattering of silver, copper and copper oxide nanoparticles by this base fluid blood. This phenomenon had been formed by the model of the system in partial differential equations; it was made easy in the dimensionless nonlinear structure of ordinary differential equations by employing comparison substitutions. This result on the acquired set of the differential equations was simulated over the bvp4c method. It has been discovered that the ternary hybrid nanofluid velocity is essentially lower along the differing numbers of permeable media, although it amplifies along the upshot on the Hartmann number. Moreover, an enhanced heat transport rate of up to 14% was marked for the triple nanoparticle nanofluid by relating it to another nanofluid and establishing an excellent behavior on triple nanoparticle nanofluids.

Reducing the Constrained Multibody Dynamics Problem to the Solution of a System of Ordinary Differential Equations Via Velocity Partitioning and Lie Group Integration

Abstract In multibody dynamics, formulating the equations of motion in absolute Cartesian coordinates results in a set of index-3 differential algebraic equations (DAEs). In this work, we present an approach that bypasses the DAE problem by partitioning the velocities in the system into dependent and independent coordinates, thereby reducing the task of producing the time evolution of the mechanical system to one of solving a set of ordinary differential equations (ODEs). In this approach, the independent coordinates are integrated directly, while the dependent coordinates are recovered through the kinematic constraint equations at the position and velocity levels. Notably, Lie group integration is employed to directly obtain the orientation matrix A at each time-step of the simulation. This eliminates the need to choose generalized coordinates to capture the orientation of a body, as the matrix A is a by-product of the solution algorithm. Herein, we outline the new approach and demonstrate it in conjunction with four mechanisms: a single pendulum, a double pendulum, a four-link mechanism, and a slider crank. We report on the convergence order behavior of the proposed method and compare its performance with an established method that combines coordinate partitioning with an Euler parameter formulation. The Python code developed to generate the reported results is open-source and available in a public repository for reproducibility studies.

Stability of Beam Bridges Under Bridge-Vehicle Interaction

In this paper, we provide an accurate and reliable formulation for simulating the interactions of both train/bridge subsystems and suitable for high-speed railway lines as well as for existing lines worldwide that are being renewed or modernized. We model the train as a series of suspended masses, taking into account the energy dissipation and the suspension system for each train vehicle. On the other hand, the bridge supporting the rails with irregular elevations will be modeled as an Euler-Bernoulli beam. The mathematical formulation of the interaction problem between the two subsystems requires the writing of two sets of equations, which interact with each other through contact forces. Using a one-dimensional finite element formulation, a series of equations are constructed by Modeling the beam structure. In addition, the suspended mass equations are first discretized using Newmark's finite difference formulas, which then reduce the degrees of freedom (DOF) of the vehicle to those of the bridge element. This solves the coupling problem between the two subsystems. The derived component is known as the vehicle/bridge interaction (VBI) element. On the other hand, an iterative procedure will be used subsequently to solve the non-linearity problem of the resulting system of differential equations. MATLAB programs provide results that identify the critical parameters influencing the bridge's dynamic stability.

Discrete Boltzmann model with split collision for nonequilibrium reactive flows

Abstract A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based on a unified set of discrete Boltzmann equations that describes the evolution of each chemical species with adjustable acceleration, specific heat ratio, and Prandtl number. On the righ-hand side of discrete Boltzmann equations, the collision, force, and reaction terms denote the change rates of distribution functions due to self- and cross-collisions, external forces, and chemical reactions, respectively. The source terms can be calculated in three ways, among which the matrix inversion method possesses the highest physical accuracy and computational efficiency. Through Chapman-Enskog analysis, it is proved that the DBM is consistent with the reactive Navier-Stokes equations, Fick's law and Stefan-Maxwell diffusion equation in the hydrodynamic limit. Compared with the one-step-relaxation model, the split collision model offers a detailed and precise description of hydrodynamic, thermodynamic, and chemical nonequilibrium effects. Finally, the model is validated by six benchmarks, including multicomponent diffusion, mixture in the force field, Kelvin-Helmholtz instability, flame at constant pressure, opposing chemical reaction, and steady detonation.

Tangent hyperbolic nanofluid flow through a vertical cone: Unraveling thermal conductivity and Darcy–Forchheimer effects

Purpose: This paper demonstrates the way tangent hyperbolic nanofluid flow through a vertical cone is influenced by varying viscosity and varying thermal conductivity. This study also seeks to illustrate the impact of convective boundary conditions on a fluid. The mathematical modeling also takes the Darcy–Forchheimer effect into account. Methodology: Using the appropriate similarity transformation, the fluid problem is reduced into a set of nonlinear ordinary differential equations. These systems of differential equations are evaluated numerically by applying the Optimal Homotopy Asymptotic Method. Findings: The nature of emergent parameters is examined in relation to the temperature distribution, nanoparticle concentration profile, and velocity profile. An increase in variable viscosity corresponds to a decrease in fluid velocity, while enhanced thermal conductivity results in elevated fluid temperature. The skin friction coefficient, Sherwood, and Nusselt numbers are numerically examined for active concerned parameters. These findings can be put into practice in a variety of fields such as polymer cooling systems and medication. Originality: Existing literature has yet to explore the combination of tangent hyperbolic nanofluids with varying viscosity and thermal conductivity under convective boundary conditions.

Development of a fully implicit ODE-solver for containment analysis code

The thermal–hydraulic dynamics in containment are governed by a system of stiff ordinary differential equations (ODEs). A fully implicit discretization scheme is adopted to discretize these ODEs in order to mitigate the effects of stiffness. In comparison with explicit or semi-implicit discretization schemes that are subject to Courant limits on time steps, the fully implicit discretization scheme is more suitable for a containment analysis code that focuses on predicting both short-term and long-term thermal–hydraulic parameters after an accident. This study introduces a general-purpose ODE solver for the containment analysis code. The outline of the solver is as follows: The fully implicit discrete equations lead to a large set of nonlinear equations that need to be solved using Newton’s iterative method. The partial derivative components in the Jacobi matrix are calculated by the perturbation method using finite difference approximation, which avoids the complicated derivation of partial derivatives. The scaling modification technique is incorporated into this ODE solver to deal with significant differences in unknown variable magnitudes, and the line search method is introduced to address the difficulty of obtaining an accurate root estimate with Newton’s method when the initial guess is far from the actual root. This proposed ODE solver was applied to two typical stiff ODE problems to test its stiffness-suppressed ability and to demonstrate that this proposed solver can perform calculations with a very large time step. Then, the CASSIA code, a containment analysis code developed by China Nuclear Power Technology Research Institute Co., Ltd (CNPRI), equipped with this ODE solver, was applied to the CSNI (Committee on the Safety of Nuclear Installations) benchmark problem and the Carolinas Virginia Tube Reactor (CVTR) test 3 problem to preliminarily demonstrate that the proposed ODE solver can perform containment thermal–hydraulic analysis correctly. This study could provide references for the development of a home-made containment analysis code.

Precision Irrigation Soil Moisture Mapper: A Thermal Inertia Approach to Estimating Volumetric Soil Water Content Using Unmanned Aerial Vehicles and Multispectral Imagery

To address the issue of estimating soil moisture at a hyper-resolution scale, a methodology referred to as Precision Irrigation Soil Moisture Mapper (PrISMM), that includes three key components, is developed: high-resolution remotely sensed optical and thermal data, surface energy balance modeling, and site-specific soil analysis. An Unmanned Aerial Vehicle/System (UAV or UAS) collects high-resolution multispectral imagery in the Dallas–Fort Worth metropolitan study area. Orthomosaics are converted to thermal inertia estimates in a spatially distributed format using the remotely sensed data combined with a set of surface energy balance modeling equations. Using thermal and physical properties of soil gained from site-specific soil analysis, thermal inertia estimates were further converted from thermal inertia to daily volumetric soil water content (VSWC) with a horizonal resolution of 8.6 cm. A ground truthing dataset of measured VSWC values taken from a Time Domain Reflectometer was compared with model results, producing a reasonable correlation with an average coefficient of determination of (R2) = 0.79, an average root mean square error (RMSE) = 0.0408, and mean absolute error (MAE) = 0.0308. This study highlights a practical approach of estimating VSWC for irrigation purposes while providing superior spatio-temporal coverage over in situ methods. The authors envision that PrISMM can be implemented in water usage management by relating VSWC with weather forecasts and evapotranspiration rates to develop time-based spatially distributed irrigation management plans.

Counting \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 black holes as algebraic varieties

We calculate the helicity trace index B14 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 pure D-brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi-variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi-variable polynomial equations modulo gauge symmetries. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. The first three methods rely on a mixture of symbolic and high precision numerics whereas the Hilbert series is symbolic and admit a gauge invariant analysis. Furthermore, exploiting various exchange symmetries, we show that quartic and higher order terms are absent in the potential, which if present would have spoiled the counting. Incorporating recent developments in algebraic geometry focusing on computational algorithms, we have extended the scope of one of the authors previous works [1, 2] and presented a new perspective for the black hole microstate counting problem. This further establishes the pure D-brane system as a consistent model, bringing us a step closer to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2 black hole microstate counting.

A Set of Accurate Dispersive Nonlinear Wave Equations

In this study, a set of accurate dispersive nonlinear wave equations is established, using the wave velocity and free surface elevation as variables. These equations improve upon previous equations in which the velocity potential is used as a variable by considering the rotational wave motion and by adding a second-order bottom slope term that applies to general situations, allowing the equations to consider the influence of rapidly changing, horizontal, two-dimensional bottom topographies. The problem of the inaccuracy of the integral calculations used in previous equations in nearshore areas is solved by approximating the integral calculations into differential calculations, and a set of coupled wave equations is established by keeping the free surface elevation and the horizontal velocity constant, thus allowing the calculation of nearshore wave-generated currents. The benefits of the current model are confirmed through comparisons with corresponding laboratory experimental findings and are illustrated through a comparison with the numerical outcomes of other pertinent models.

An efficient approach for solving a class of fractional anomalous diffusion equation with convergence

Abstract This article presents a study on Fractional Anomalous Diffusion (FAD) and proposes a novel numerical algorithm for solving Cupoto’s type fractional sub-diffusion equations. to convert the fractional model into a set of nonlinear algebraic equations. These equations are efficiently solved using the Levenberg-Marquardt algorithm. The study provides the error analysis to validate the proposed method. The effectiveness and accuracy of the method are demonstrated through several test problems, and its performance and reliability are compared with other existing methods in the literature. The results indicate that the proposed method is a reliable and efficient technique for solving fractional sub-diffusion equations, with better accuracy and computational efficiency than other existing methods. The study’s findings have important implications for researchers working in the field of fractional calculus. They could provide a valuable tool for solving sub-diffusion equations in various applications, including physics, chemistry, biology, and engineering.

Two new user-friendly methods to assess pharmacometric parameter identifiability on categorical and continuous scales.

Parameter identifiability methods assess whether the parameters of a model are uniquely determined by the observations. While the success of a model fit can provide some information on this, it can be valuable to determine identifiability before any fit has been attempted, or to separate identifiability from other issues. Two concepts that lean themselves well for identifiability analysis and have been underutilized are the sensitivity matrix (SM) and the Fisher information matrix (FIM). This paper presents two newly developed methods, one based on the SM and one based on the FIM. Both methods can assess local identifiability for a wide set of models, can be used with limited effort, and are freely available. The methods require the proposed model in the form of a set of differential equations, the parameter values, and the study design as input. They can be used a priori, as they do not need observed values or a successful model fit. Traditional methods provide a single categorical (yes/no) answer to the question of identifiability. In many cases, this is not very informative, and identifiability depends on study design (e.g., dose levels or observation times) and parameter values. Indicators on a continuous scale characterizing the level of identifiability would provide more detailed and relevant information, for example, to guide model development. Our two methods provide both categorical and continuous indicators. Both methods indicate which parameter combinations are difficult to identify by calculating the directions in parameter space that are least identifiable. The methods were validated with an example problem.

Polarization evolution in Brillouin scattering with a partially polarized pump

Polarization sensitivity has been a major issue in Brillouin scattering-based optical fiber sensing systems. Randomization of the polarization state of the pump is one of the ways to circumvent the problem. However, there could exist a residual degree of polarization (DOP) for the pump after polarization randomization, and hence, a model to characterize the polarization evolution in Brillouin scattering with a partially polarized pump is essential for the performance evaluation. In this work, a comprehensive theoretical model to characterize the beam variation with the partially polarized pump wave and Stokes wave is proposed, which is based on a set of stochastic differential equations (SDEs). The polarized part of the pump wave and the Stokes wave, as well as the total powers of the waves, are incorporated in the coupled SDE simultaneously, which enables the comprehensive simulation of the polarization evolution in the fiber. It is revealed in the study that the DOPs of the pump wave and the Stokes wave affect the gain stability and should be reduced simultaneously by polarization scrambling to ensure a fixed Brillouin gain without fluctuations.

Gauge-invariant cosmological perturbations in general teleparallel gravity

We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this geometry around a homogeneous and isotropic background geometry, we derive the irreducible decomposition of the perturbation variables, as well as their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms generated by a vector field. In addition, we also study these properties for the most general set of matter variables and gravitational field equations. We then make use of these result to construct gauge-invariant perturbation variables, using a general approach based on gauge conditions. We further calculate these quantities also in the metric and symmetric teleparallel geometries, where nonmetricity or torsion is imposed to vanish. To illustrate our results, we derive the energy-momentum–hypermomentum conservation equations for both the cosmological background and the linear perturbations. As another example, we study the propagation of tensor perturbations in the f(G), f(T) and f(Q) class of theories.

Mixed Convection Flow of a Casson Fluid Past a Thin Needle

Mixed Convection Flow of a Casson Fluid Past a Thin Needle

Composite continuum robots: Accurate modeling and model reduction

Models of continuum robots often trade off accuracy and speed. The constant curvature assumption model can perform fast calculations but with poor accuracy. Static models can obtain good calculation accuracy but with slower computation speed. In this paper, a precise and efficient method for establishing a non-constant curvature kinematic model for composite continuum robots is proposed. First, an algorithm based on the Beam Constraint Model is proposed to establish the static model of the continuum robot. The situation in which friction changes gradually in continuum robots is considered in the static model. Then, the Kepler elliptic curve is used to simplify the static model to build a non-constant curvature kinematic model of the continuum robot. Then, complex inverse kinematics solutions are transformed into explicit sets of equations by mathematical transformation. Finally, simulations and experiments are designed to demonstrate the algorithm proposed in this paper. The simulation results show that the proposed algorithm is 1572 times faster than the Levenberg–Marquardt algorithm. The experimental results show that the average error of the static model is 0.065 mm, accounting for 0.13% of its length. The maximum error is 0.309 mm, accounting for 0.618% of its length. The positioning accuracy of the non-constant curvature model proposed in this paper is 2.02 times that of the constant curvature model. The results show that the simplified kinematic model algorithm based on the static model has high accuracy and computational efficiency. This research is crucial for the practical application of continuum robots in engineering.

Holographic Ricci dark energy in nonconservative unimodular gravity

The structure of unimodular gravity (UG) is invariant to a subclass of diffeomorphism, the transverse diffeomorphism, due to the unimodular condition -g=ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{-g}=\\epsilon $$\\end{document}. Consequently, there is a freedom to define how the conservation laws of the energy–momentum tensor in unimodular gravity in the cosmological context. One of the main characteristics of the complete system of equations that describe cosmological dynamics in UG is that they form an underdetermined system if the usual conservation law of the energy–momentum tensor is not considered in your structure. In this article, we propose the construction of a background cosmological model based on the description of a holographic dark energy component with a cutoff of the order of Ricci scalar in non-conservative UG. This choice means that the complete set of equations remains underdetermined, however, the new feature of this cosmological model is the appearance of an interaction between matter and dark energy. Indeed, this is a well-known characteristic of cosmological models in which we have holographic dark energy density. Consequently, we propose an ansatz to the interaction term Q=βHρm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q=\\beta H \\rho _{m}$$\\end{document}, and obtain the cosmological parameters of our model. We found a viable universe model with similar characteristics to the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda \ extrm{CDM}$$\\end{document} model. We performed statistical analysis of the background model using the “Cosmic Chronometer” (CC) data for H(z), and obtain as a result using AIC, and the BIC as model selection criteria that ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda \ extrm{CDM}$$\\end{document} prevails as the best model. However, the proposed model is competitive when compared to the cosmological model ωCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega \ extrm{CDM}$$\\end{document}.

Elastomer cholesteric waveguide slab for a transverse elongation

ABSTRACT In this work, electromagnetic propagating modes within a planar waveguide featuring a cholesteric elastomer core whose helical axis is oriented perpendicular to the planar boundaries are analysed. The Maxwell equations and the constitutive equation are used to establish a novel configuration, enabling the tuning of mechanical stress through elastic strain in the perpendicular stretching along the helix axis. The derived set of equations is numerically solved, presuming the waveguide to be surrounded by either air or a vacuum medium. The corresponding band structure and the ratio between electric and magnetic modes have been plotted as a function of angular frequency. The amplitudes of the electromagnetic field profiles are also investigated as functions of position. The ratio of Transverse Electric and Transverse Magnetic modes, along with the cut-off frequencies, is also examined as functions of strain. Finally, the mixing of transverse electric and magnetic modes to generate new eigenmodes, as well as the investigation of their propagation conditions within the waveguide, is examined in this study.

Mixed convective flow of engine oil-based non-Newtonian tri-hybrid nanofluid across a porous rotating disk

Purpose Flow induced by rotating disks is of great practical importance in several engineering applications such as rotating heat exchangers, turbine disks, pumps and many more. The present research has been freshly displayed regarding the implementation of an engine oil-based Casson tri-hybrid nanofluid across a rotating disk in mass and heat transferal developments. The purpose of this study is to contemplate the attributes of the flowing tri-hybrid nanofluid by incorporating porosity effects and magnetization and velocity slip effects, viscous dissipation, radiating flux, temperature slip, chemical reaction and activation energy. Design/methodology/approach The articulated fluid flow is described by a set of partial differential equations which are converted into one set of higher-order ordinary differential equations (ODEs) by using convenient conversions. The numerical solution of this transformed set of ODEs has been spearheaded by using the effectual bvp4c scheme. Findings The acquired results show that the heat transmission rate for the Casson tri-hybrid nanofluid is intensified by, respectively, 9.54% and 11.93% when compared to the Casson hybrid nanofluid and Casson nanofluid. Also, the mass transmission rate for the Casson tri-hybrid nanofluid is augmented by 1.09% and 2.14%, respectively, when compared to the Casson hybrid nanofluid and Casson nanofluid. Originality/value The current investigation presents an educative response on how the flow profiles vary with changes in the inevitable flow parameters. As per authors’ knowledge, no such scrutinization has been carried out previously; therefore, our results are novel and unique.