Radiative Second‐Grade Nanofluid Flow Over a Riga Plate With Variable Heat Generation Effects

Model development of coupled thermal and mass transport in a rheological non-Newtonian nanofluid with motile microorganisms induced by a Riga plate embedded within a Darcy–Forchheimer porous medium

Cattano Christov double diffusion model for third grade nanofluid flow over a stretching Riga plate with entropy generation analysis

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

Present attempt reports the characteristics of nonlinear radiation and induced magnetic field on the forced convective Falkner-Skan flow of Single-Walled Carbon NanoHorn(SWCNH)/diamond-ethylene glycol (EG) and water nanofluid over a wedge, plate, and stagnation point. We consider 40:60 EG and water mixture as base fluid. Similarity transformations are utilized to transform the governing equations into ordinary differential equation and solved numerically using Runge–Kutta (RK) Fehlberg method. To check the accuracy of present model, numerical results for various Prandtl numbers have been compared with the results from the literature which divulges good agreement. Influence of active parameters like magnetic Prandtl number, magnetic parameter, radiation parameter, Biot number, Prandtl number and temperature parameter are graphically presented. Results exhibit that SWCNH nanoparticle has a higher heat transfer compared with diamond nanoparticle. Increasing the nanoparticle volume fraction with the suspensions of SWCNH and diamond nanoparticles enhances the temperature over the wedge, plate and stagnation point.

Combined effects of electrophoresis and thermophoresis in Darcy Forchheimer flow of trihybrid nanofluid over a Riga plate: Yamada-Ota and Xue models

The numerous industrial and engineering applications of Casson nanofluid is due to the superiority of its thermophysical properties. Tomatoes paste, engine oil, soup etc., are examples of Casson fluid and when nanometer-sized particles are suspended in such Casson fluid, it becomes Casson nanofluid. This paper considers a natural convective magnetohydrodynamics flow of Cu-engine oil nanofluid across a convectively heated vertical plate. The effects of self-heating of the fluid (measured by the Eckert number), internal conductive resistance to external convective resistance (measured by the Biot number), magnetic field strength, volume fraction of the nanoparticles on the temperature and velocity of mass and heat transfer of Casson nanofluid is analysed. An appropriate model governing the flow of Casson nanofluid is formulated as a system of nonlinear partial differential equations. The natural convection boundary condition is included. To solve the problem, an appropriate similarity transformation is used to reformulate the system as a system of nonlinear ordinary differential equations. The shooting technique is used to convert the boundary problem to initial value problems before Runge-Kutta method, with the Gills constants, is used to solve the reformulated problem. The results are depicted as graphs. Flow velocity is found to increase as the base fluid becomes more Casson and as nanoparticle volume fraction increases. It is also found that increasing Eckert number, Biot number and magnetic field strength causes an increase in the flow temperature.

A Riga plate is an electromagnetic actuator which comprises permanent magnets and alternating electrodes placed on a plane surface. The present article investigates the influence of viscous and Joule heating (Ohmic dissipation) in the magnetohydrodynamic squeezing flow, heat and mass transfer between two Riga plates. A non-Fourier (Cattaneo–Christov) heat flux model is employed which generalizes the classical Fourier law to incorporate thermal relaxation time. Via suitable transformations, the governing partial differential conservation equations and boundary conditions are non-dimensionalized. The resulting nonlinear ordinary differential boundary value problem is well posed and is solved analytically by the variational parameter method (VPM). Validation of the solutions is included for the special case of non-dissipative flow. Extensive graphical illustrations are presented for the effects of squeeze parameter, magnetic field parameter, modified Hartmann number, radiative parameter, thermal Biot number, concentration Biot number, Eckert number, length parameter, Schmidt number and chemical reaction parameter on the velocity, temperature and concentration distributions. Additionally, the influence of selected parameters on reduced skin friction, Nusselt number and Sherwood number are tabulated. An error analysis is also included for the VPM solutions. Detailed interpretation of the results is provided. The study is relevant to smart lubrication systems in biomechanical engineering and sensor design.

Finite element mechanism and quadratic regression of magnetized mixed convective Burgers' nanofluid flow with applying entropy generation along the riga surface

Nanotechnology has become a transformative field in modern science and engineering, offering innovative approaches to enhance conventional thermal and fluid systems. Heat and mass transfer phenomena, particularly fluid motion across various geometries, play a crucial role in industrial and engineering processes. The inclusion of nanoparticles in base fluids significantly improves thermal conductivity and enables advanced phase-change technologies. The current work examines Powell–Eyring nanofluid’s heat transmission properties on a stretched Riga plate, considering the effects of magnetic fields, porosity, Darcy–Forchheimer flow, thermal radiation, and activation energy. Using the proper similarity transformations, the pertinent governing boundary-layer equations are converted into a set of ordinary differential equations (ODEs), which are then solved using the boundary value problem fourth-order collocation (BVP4C) technique in the MATLAB program. Tables and graphs are used to display the outcomes. Due to their significance in the industrial domain, the Nusselt number and skin friction are also evaluated. The velocity of the nanofluid is shown to decline with a boost in the Hartmann number, porosity, and Darcy–Forchheimer parameter values. Moreover, its energy curves are increased by boosting the values of thermal radiation and the Biot number. A stronger Hartmann number M decelerates the flow (thickening the momentum boundary layer), whereas increasing the Riga forcing parameter Q can locally enhance the near-wall velocity due to wall-parallel Lorentz forcing. Visual comparisons and numerical simulations are used to validate the results, confirming the durability and reliability of the suggested approach. By using a systematic design technique that includes training, testing, and validation, the fluid dynamics problem is solved. The model’s performance and generalization across many circumstances are assessed. In this work, an artificial neural network (ANN) architecture comprising two hidden layers is employed. The model is trained with the Levenberg–Marquardt scheme on reliable numerical datasets, enabling enhanced prediction capability and computational efficiency. The ANN demonstrates exceptional accuracy, with regression coefficients R≈1.0 and the best validation mean squared errors of 8.52×10−10, 7.91×10−9, and 1.59×10−8 for the Powell–Eyring, heat radiation, and thermophoresis models, respectively. The ANN-predicted velocity, temperature, and concentration profiles show good agreement with numerical findings, with only minor differences in insignificant areas, establishing the ANN as a credible surrogate for quick parametric assessment and refinement in magnetohydrodynamic (MHD) nanofluid heat transfer systems.

The behavior of the Darcy–Forchheimer flow of a double-hybrid nanofluid toward a Riga plate with radiation and heat source/sink effects is investigated. The two different hybrid nanofluids, (Al2O3 and Ag) and (Al2O3 and TiO2) with a base fluid (H2O), are considered. The governing flow models with accompanying boundary constraints are reshaped into non-linear ODEs by applying the symmetry variables. The reshaped ODEs are numerically computed using Bvp4c in Matlab and the ND solver in Mathematica. The impact of the emerging parameters on the heat transfer, surface shear stress, temperature and velocity profile is scrutinized and expressed in a tabular and graphical structure. It is noticed that the upsurge of the Hartmann number leads to an improvement in the velocity profile. The velocity declines when enriching the porosity parameter. The radiation and Biot number lead to strengthening the temperature profile. The surface shear stress exalts due to a larger modified Hartman number. The radiation and unsteady parameters are downturns in the heat transfer gradient.

Riga plate is known to create a crossing electric and magnetic field to generate a wall-parallel Lorentz force. The significance of Casson nanofluid flow past a Riga plate is observed in the sphere of engineering, such as polymer extrusion, food manufacturing, plastic films, oil reserves and geothermal manufacturing. Researchers are interested in this model because of its potential use in biological rheological models. As Casson nanofluid flows are of great interest, this study aims to investigate the three-dimensional magnetohydrodynamics (MHD) flow with heat and mass transport of Casson nanofluid over a flat Riga plate. As a novelty, this study also includes the effectiveness of wall velocity slip, activation energy, nonlinear radiation, and temperature and space-dependent heat source/sink. Suitable similarity transformations have been employed to generate the dimensionless ordinary differential equations (ODEs) from the partial differential equations (PDEs) regulating the fluid flow problem. The transformed nonlinear boundary value problem is then solved numerically using the in-built routine “bvp4c” in MATLAB. The visual demonstrations are provided for the effects of various significant physical factors on the flow, heat and mass distributions. On the other hand, wall shear stress and rates of heat and mass transport at the surface are measured and displayed numerically in tabular form. The findings indicate that the fluid velocity in both directions slows as the velocity slip parameter increases. However, the velocity profile is escalated with the boost of modified Hartmann number. An increase in heat source parameters leads to decrease the heat transmission rate at the wall. The higher values of the radiation parameter result in a better wall heat transmission rate. Further, the rate of mass transport drops when the activation energy parameter is hiked.

The present work focuses on analyzing the magnetohydrodynamic (MHD) mixed convective boundary layer (BL) flow of nanofluids, when the impacts of thermal radiation, heat generation, higher-order chemical reaction, and lower-order multiple slips boundary conditions are incorporated into the flow occurrences, comparing the impact of slip and no-slip conditions over an inclined porous stretching plate. The intricacy of PDEs is transformed into non-linear ODEs through the similarity transformation. A numerical solution of the resulting nonlinear momentum, energy, and concentration equations, together with their boundary conditions, was then solved using the Spectral Quasi-Linearization method (SQLM). The novelty of this study is in the comprehensive modeling of MHD nanofluid flow by incorporating multiple physical effects and boundary conditions, employing SQLM for the solution, and presenting quantified comparisons between slip and no-slip cases. Graphs and tables are used to illustrate how concerned parameters affect the velocity, thermal, and mass flow fields with both slip and no-slip effects. The analysis indicates that, relative to the slip case, the shear stress coefficient in the no-slip case exhibits an increase of approximately 1.05% for the magnetic field and 0.69% for suction. Furthermore, the local Nusselt number decreases by about 0.99% under heat generation in the no-slip case, whereas the local Sherwood number increases by nearly 1.35% with the Biot number when compared to the slip case. The findings of this study hold relevance for a wide range of engineering and industrial applications, such as thermal management in energy systems, chemical and polymer processing, biomedical heat and mass transfer, and aerospace thermal protection, particularly in scenarios where magnetic fields, radiation, and reactive nanofluid flows over porous or stretching surfaces are significant.

This article addresses the flow of nanofluid towards a radially stretching sheet with convective boundary conditions. The Brownian motion and thermophoresis effects are taken into consideration. The governing equations are reduced to a system of coupled ordinary differential equations through similarity transformations. Analytic solutions valid for all the values of embedding parameters have been obtained by homotopy analysis method (HAM). In addition numerical solutions are computed through a shooting technique using computational software Mathematica. The behaviors of key parameters such as Brownian motion parameter (Nb), thermophoresis parameter (Nt), Biot number (Bi), Prandtl number (Pr) and Lewis number (Le) have been thoroughly examined. It is observed that increase in the strength of Brownian motion effect rises the temperature significantly. However rate of heat transfer and nanoparticles concentration at the sheet is reduced when Nb is increased. Moreover it is noticed that temperature and nanoparticles concentration are increasing functions of Biot number (Bi). A comparative study between analytic and numerical solution shows an excellent agreement.

The two-dimensional electrically conducting magnetohydrodynamic flow of micropolar nanofluid over an extending surface with chemical reaction and secondary slips conditions is deliberated in this article. The flow of nanofluid is treated with heat source/sink and nonlinear thermal radiation impacts. The system of equations is solved analytically and numerically. Both analytical and numerical approaches are compared with the help of figures and tables. In order to improve the validity of the solutions and the method convergence, a descriptive demonstration of residual errors for various factors is presented. Also the convergence of an analytical approach is shown. The impacts of relevance parameters on velocity, micro-rotation, thermal, and concentration fields for first- and second-order velocity slips are accessible through figures. The velocity field heightens with the rise in micropolar, micro-rotation, and primary order velocity parameters, while other parameters have reducing impact on the velocity field. The micro-rotation field reduces with micro-rotation, secondary order velocity slip, and micropolar parameters but escalates with the primary order velocity slip parameter. The thermal field heightens with escalating non-uniform heat sink/source, Biot number, temperature ratio factor, and thermal radiation factor. The concentration field escalates with the increasing Biot number, while reduces with heightening chemical reaction and Schmidt number. The assessment of skin factor, thermal transfer, and mass transfer are calculated through tables.

Impact of radiation in a stagnation point flow of Walters’ B fluid towards a Riga plate