Transient velocity and temperature field predictions for natural convective nanofluid flows immersed in oscillating magnetic fields with physics informed neural networks

Natural convection flow of Casson hybrid nanofluid through a vertically oriented porous cone: Parametric numerical study

This study investigates the natural convection flow of Williamson fluid between two concentric cylinders while affected by the radiation effect and magnetic field. The inner cylinder remains fixed while the outer cylinder rotates. Additionally, magnetic field is oriented radially, which influences the flow of the fluid. Applying a proper transformation, one transform the non-linear partial differential equations of the Williamson fluid model into ordinary differential equations. Artificial neural networks (ANN) facilitate the computation of solutions to these nonlinear ordinary differential equations. Trial functions employ a multilayer perceptron neural network with tunable parameters, including weights and biases. The governing equations are satisfied by determining the trial solution’s changeable parameters by applying the Adam (adaptive moment estimation algorithm) optimization technique. Compared to the analytical solutions, the ANN’s result demonstrates good accuracy. Moreover, graphs show how pertinent parameters affect the velocity and temperature profiles. The temperature and velocity profiles get smaller as the magnetic parameter value increases. Furthermore, the temperature and velocity profiles increase as the Hall parameter value rises.

Ferrofluids flowing over a hydrophobic surface are important in enhancing heat transfer properties for mechanical devices and reducing friction on the surface for efficient use in lubrication. This effort investigates the motion of water-based ferrofluid on a vertical hydrophobic stretching sheet exposed to a magnetic field. In this flow, natural convection and temperature flow in the system are demonstrated. A non-dimensional transformation is used to change the mathematical model into a set of nonlinear formulations of differential equations. Due to the hydrophobic surface, the slip effects are considered. Finally, the system of nonlinearly coupled equations is simulated using the finite element technique. All the aspects of the numerical solution are validated with the previously published literature. The significance of surface roughness, magnetostatic field, and Prandtl number on the velocity profiles, convective boundary layer, and temperature is explained. The hydrophobic surface, the velocity slip parameter enhances the convective boundary layer and roughness factor plays a crucial role in the heat transfer enhancement and self-cleaning purposes in biomedical applications.

The interplay of free convection with mass transfer on an unsteady, viscous, incompressible fluid flow over an oscillating infinite vertical plate in the presence of radiation has been attempted to be investigated analytically. The fluid is seen as a gray, non-scattering medium that emits and absorbs radiation. The dimensionless governing equations have been solved using the Laplace transform approach. With the aid of various graphs, the expressions for the velocity, temperature, and concentration profiles, as well as for the skin friction, Nusselt number, and Sherwood number are obtained and examined for various physical parameters, such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, radiation parameter, and time.

Effects of the melting phenomenon on combined (natural and forced) convection flow adjacent to a vertical plate within a saturated porous medium filled with hybrid nanoparticles such as copper and aluminum, later serving as base fluid, are investigated in this work. The mathematical modeling of the problem reduced the nonlinear partial differential equations into a set of nonlinear ordinary differential equations through similarity transformation. Solutions to these boundary value problems are obtained using the shooting method in Maple software for various values of the concentration of hybrid nanoparticles, mixed (natural and forced) convection parameter, and melting parameter. Results indicate that the solution has two branches within a specific range of the above parameters. Additionally, findings reveal that the process of solid-liquid phase transition enhances the thermal conductivity of hybrid nanofluids and expedites the expansion of boundary layers.

ABSTRACT A steady state Eulerian smoothed particle hydrodynamics (SPH) solver is proposed by integrating the Semi‐Implicit Method for Pressure‐Linked Equations (SIMPLE) algorithm. By removing time dependent terms from the governing equations, the proposed approach directly solves for steady‐state velocity, pressure, and temperature fields for incompressible flows using a matrix‐based formulation. To efficiently handle the resulting large, sparse linear systems, a matrix‐free Bi‐CGSTAB iterative solver is employed and the overall computational algorithm is fully parallelized on GPUs to accelerate performance. The accuracy and efficiency of the proposed steady solver are validated through several benchmark tests, including pipe flow with and without obstacles, 2D/3D lid‐driven cavity flow with and without heat transfer, and natural convection flow. Compared to conventional transient Eulerian SPH solvers, the proposed method achieves 8.97–17.36 times speedup while maintaining high accuracy, making it a promising tool for steady state CFD analysis and as a precursor to transient simulations.

Natural convective ternary nanofluid flow in a trapezoidal wavy enclosure with multiple cold obstacles

Oscillating piezofan effects on natural and forced convection flow in a vertical channel with protruding heat sources

ABSTRACT The present study investigates the steady incompressible natural convective flow of power law fluid in a squared enclosure having a T‐shaped fin under the magnetic field and thermal radiation effects. The governing partial differential equations (PDEs) are transformed into nondimensional equations by employing dimensionless variables. The resulting system of dimensionless PDEs is solved numerically. The numerical simulations showed that the velocity and temperature profiles increases at higher Rayleigh number. Further, the addition of a magnetic field, quantified by the Hartmann number, decreases the fluid velocity and kinetic energy, reflecting the resistive effects of magnetic forces on the flow dynamics. The local and average Nusselt numbers decreases for higher radiation parameter. The obtained outcomes provide valuable insights for applications used in advanced thermal management systems, requiring fluid flow control and enhancing heat transfer.

This paper presents a comprehensive analysis of the effects of mass and thermal stratification by providing analytical solution for the unsteady, one-dimensional natural convection flow past an infinite vertical circular cylinder in a stably thermally stratified fluid medium, incorporating variable thermal conductivity and diffusion coefficients. The dimensionless coupled linear partial differential equations (PDE) governing the flow are solved using Olayiwola’s Generalized Polynomial Approximation Method (OGPAM) for different sets of physical parameters. The effects of these parameters are illustrated and discussed with the aid of graphs. The results show that mass and thermal stratification significantly influence the velocity, temperature, and concentration profiles of the fluid. Specifically, an increase in thermal stratification leads to a rise in the system’s temperature as Increased thermal stratification traps heat in the upper layers, reduces convective mixing, and suppresses cooling. Furthermore, as thermal diffusivity increases, fluid velocity decreases across the radial distance due to reduced buoyancy forces, producing a flatter and less pronounced velocity profile this is due to the fact that heat spreads faster, temperature gradients shrink, buoyancy forces weaken, and fluid motion slows down. This creates a lower and flatter velocity profile across the radial distance. Similarly, increase in mass stratification generates a concentration gradient which traps solute in dense layers, reduces mixing and dilution, and resists vertical transport. This causes local buildup and a rise in the overall concentration of the system.

This paper presents the structural design and supporting analysis for the Microreactor Applications Research Validation and Evaluation (MARVEL) primary coolant system (PCS) using the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code Section III, Division 5, rules. MARVEL is a liquid metal–cooled microreactor intended to provide experimental capabilities for the rapid testing and development of microreactor technologies. The PCS utilizes high-temperature sodium-potassium liquid metal as the primary coolant and operates at a design temperature of 570°C, necessitating the consideration of creep-related failure mechanisms. The base metal for the PCS is 316H stainless steel, and the weldments are made with a 16-8-2 filler. The design approach incorporates the current base code rules along with ASME code cases N-924, N-861, and N-862 to address primary load, ratcheting, and creep-fatigue evaluations, respectively. The reactor’s operation involves complex thermal and mechanical interactions due to natural convective flow and differential thermal expansion between components. This paper discusses the structural engineering challenges encountered, such as managing thermal stresses in the distribution plenum and guard vessel, and outlines the strategies implemented to meet the code requirements, including design modifications and operational constraints.

The study examines the natural convection flow of viscous electrically conductive fluid between two vertical plates in time-dependent thermal conditions with magnetohydrodynamics effect. A fractional-order model that is a generalization of the classical Fourier law by using the Caputo-Fabrizio fractional integral is developed. The model equations are rewritten in analytical form using a synthesis of the Laplace techniques and sine-based Fourier analysis to get analytical solutions. The latter expressions are modeled in generalized G-functions that are useful in generalizing the impact of fractional dynamics. Mathcad is used to assess the analytical results and contour plots in 2Ds are used to illustrate the temperature distribution of the fluid domain at various levels of time. The influence of critical physical determinants, including the fractional order, the intensity of the magnetic field, the Grashof number, and the term associated with heat source/sink, is analyzed comprehensively. The results suggest that elevated values of the fractional parameter enhance both heat retention and fluid velocity due to the phenomenon known as the memory effect.

Hybrid nanofluid convection over an accelerated vertical plate with unsteady surface heating

Fractional theoretical modeling of natural convection flow of Walter’s B fluid through vertical channel with thermal and mass fluxes

In this paper, the effect of viscous dissipation on the two-dimensional, steady Cu-water nanofluid bioconvection containing oxytactic bacteria of oxytactic bacteria is numerically and statistically investigated. The importance of this study lies in addressing viscous dissipation, a significant factor for thermal and solutal transport in nanoparticle suspensions in nanofluid bioconvection systems. The main aim is to examine how the Eckert number, representing viscous dissipation, modifies flow behavior, convective heat transfer, and bacterial distribution in a square cavity. The governing non-dimensional equations are solved by the radial basis function (RBF) collocation method. It is found that viscous dissipation weakens heat transfer along the hot wall while enhancing bacterial density and mass transfer, and that variations in thermal and bioconvective Rayleigh numbers along-side Peclet and Lewis numbers strongly influence the thermal and microbial transport. In the statistical analysis, both curve and surface fittings are carried out involving the Eckert number. Furthermore, neural network modeling is employed to predict the average Nusselt, Sherwood number, and bacterial density along the side walls. All models are constructed on the basis of numerical data generated from the simulations. For varying values of the Eckert number, both quadratic and cubic polynomial approximations yield satisfactory agreement when evaluated using the mean squared error criterion. Moreover, the neural network model reliably captures the average quantities of interest, showing strong consistency with the data. The results highlight both the physical significance of viscous dissipation and the usefulness of data-driven modeling in complex nanofluid problems.

Thermal efficiency evaluation using hybrid ANN-CFD simulations of natural convective flow in rectangular open-ended cavities filled with nanoencapsulated PCM

This article presents a multiphysics simulation methodology to predict the temperature-dependent demagnetization phenomenon of a 900 W permanent-magnet synchronous generator (PMSG). For the 2D electromagnetic model, a commercial finite element method (FEM) package was used to determine the power loss distribution under steady-state conditions, accounting for temperature-dependent demagnetization. The thermal analysis was carried out on a 3D model using computational fluid dynamics (CFD) software, where a polyhedral mesh, rotor rotation effects, and turbulent modeling were implemented. Two simulation cases were evaluated: Case 1, electromagnetic losses at constant temperature without FEM-CFD coupling; Case 2, bidirectional FEM-CFD coupling under steady-state conditions. The analysis confirms that in Cases 1 and 2, there is no risk of irreversible demagnetization, thus validating the selection of the permanent magnet (PM) and the design of the PMSG. Additionally, the methodology accurately captured the heat transfer effects resulting from natural convection and turbulent flow in the critical regions. The CFD modeling convergence criteria, based on residuals and flow monitors, demonstrated numerical stability and a satisfactory mesh discretization in both the FEM and CFD domains, providing valid feedback on the PM temperatures. The proposed methodology provides a robust and accurate tool for coupled electromagnetic–fluid–thermal analysis of the PMSG at rated operating conditions.

This study involves analysis of turbulent natural convection of heat transfer with localized heating and cooling on opposite surfaces of a vertical cylinder. Numerical simulation of turbulent natural convection has been studied in the past using the k-epsilon (k-ε), k-omega (k-ω) and k-ω-SST turbulence models. Further research showed that the k-ω SST model performed better than the k-ε and k-ω models. The study of natural convections in an enclosure has several applications from natural space, warming of household rooms to sections of engineering and atomic installations. This study involves numerical simulation of natural convection flow in a cylindrical enclosure full of air using the k-ω-SST model with an objective of establishing the best position of the heater and the cooler for better distribution of heat in the enclosure. The transfer of heat due to natural convection inside a cylindrical closed cavity was modeled to include the effect of Rayleigh number. The non-linear terms in averaged momentum and energy equation respectively were modeled using k-ω-SST model to close the governing equations. The sidewalls were adiabatic, while the bottom and top surfaces are maintained at 320 K and 298 K, respectively, to induce natural convection. The governing equations, Reynolds-average Navier-Stokes (RANS), energy and turbulence transport, were discretized using the central finite difference method under the Boussinesq approximation. A low Reynolds number k-ω SST turbulence model was employed to accurately resolve turbulent effects. The study explored a range of aspect ratios (AR = 1, 2, 4, 8) while holding the Rayleigh number constant within the turbulent regime R<sub>a</sub> =10<sup>10 </sup>and assuming Prandtl number of 0.71. Simulations were conducted in ANSYS Fluent to obtain vector plot of velocity magnitude, contours of temperature distribution, streamline distributions, effective thermal conductivity, and intensity of turbulence. Results revealed that increasing AR leads to reduced turbulence, weaker convective strength, more stratified temperature fields, and diminished heat transfer efficiency. The findings highlight the critical role of the geometry of the enclosure in shaping the flow structure and thermal behavior in turbulent natural convection.

ABSTRACT This article introduces a mathematical model describing the behavior of a Casson fluid flowing over an exponentially accelerating inclined surface. The fluid passes through a porous medium subjecting to thermal radiation. The plate’s surface concentration and temperature are subjected to ramped and isothermal conditions. The governing equations describing the flow phenomenon have been formulated, including the effects of magnetic field and heat source. The finite element method is employed using the Galerkin weighted residual approach, and the results are presented quantitatively and graphically. The analysis ensured grid-independent results. Results were found to be matched earlier reports in a limiting case. The study shows that the thermal and momentum boundary layer thicknesses are greater when the surface is isothermal than when it is ramped. The thermal layer gets thicker with the heat source and radiation parameters. This study aids applications in polymers, biomechanics, reactors, and food processing by guiding fluid process optimization.