Radiation Boundary Conditions Research Articles

High-precision spectral inversions: Determining what is important for the accurate definition of incident radiation boundary conditions

Spectral inversions are used to analyse spectroscopic observations with the aim of deriving the physical properties of the observed plasma, such as the kinetic temperature, density, pressure, degree of ionisation, or macroscopic velocities. One of the key factors ensuring the high precision of the derived plasma properties is having accurately defined input parameters of the models on which spectral inversions rely. The illumination, which chromospheric and coronal structures receive from the solar surface (and corona), is one of the most crucial input parameters of these models. We do not perform spectral inversions in this work. Our aim is to study two important factors that contribute to the accurate definition of the incident radiation boundary conditions: the altitude above the solar surface and the dynamics of the illuminated plasma. This investigation takes into account a diverse range of solar structures from the high-rising eruptive prominences to low-lying spicules. To study the influence of the altitude and dynamics of the observed plasma on the incident radiation boundary conditions, we used geometrical principles valid for any spectral line. However, to demonstrate the strong impact of dynamics, we considered the specific case of narrow spectral lines of which are highly sensitive to the presence of velocities. We argue that the altitude of the illuminated plasma strongly influences the way we need to define the incident radiation boundary conditions to achieve the most accurate results. For low-lying structures, generally below 50,000 km, the incident radiation may need to be specified directly from the composition of the portion of the solar disc that illuminates them. For high-altitude structures, generally above 300,000 km, the fraction of the solar disc illuminating the analysed plasma is large enough to be realistically approximated by the composition of the entire disc. We also show that for the narrow spectral lines, such as the lines, the impact of dynamics on the incident radiation intensity and profile shapes starts from radial velocities of 30 km $. Such velocities are even exhibited by the fine structures of quiescent prominences and are easily exceeded in spicules or eruptive prominences. The two aspects of the incident radiation definition studied here are relevant for spectral inversions based on any kind of modelling approach. However, their impact on the precision of the results of spectral inversions is likely less significant than the impact of the choice of the complexity of the model geometry, for example.

Enhancing thermal efficiency in MHD kerosene oil-based ternary hybrid nanofluid flow over a stretching sheet with convective boundary conditions

The increasing demand for thermal management due to the high heat density heat exchangers for different technological and industrial processes draw the attention of researchers in heat transfer analysis to investigate the simultaneous solution to this problem. Keeping this in mind, the current work addressed the utilization of ternary hybrid nanofluid, a mixture of graphene oxide with silver and copper, to examine the heat and mass transfer enhancement of MHD Maxwell fluid. In the current model, the author discussed heat and mass transfer analysis of Maxwell MHD ternary hybrid nanofluid flow across a porous medium over an extending sheet. The energy and concentration equations are expressed to include the effects of Brownian motion and thermophoretic diffusion. Additionally, the effects of thermal radiation, activation energy, chemical reactions, and convective boundary conditions are considered. The similarity transformations are used to convert the nonlinear PDEs into ODEs. The impact of embedded factors on velocity, temperature, and concentration profiles is perceived graphically and mathematically by using the HAM technique. The convergence of computed solutions is ensured by h-curves. The significant outcomes from the analysis expressed that the flow distribution increases with slip and suction/injection factors. The concentration of the ternary hybrid nanofluid increases with an increase in thermophoretic diffusion (0.1–0.5), thermal biot number, and solutal biot number (0.1–0.5), however, a declining behavior is perceived with rising quantity of Schmidt number (0.6–0.8) and Brownian motion (0.1–0.5) parameters. Nusselt number shows a dominant behaviour with a higher magnetic factor. Similarly, the skin friction increases with an increase in thermal biot number and thermophoresis factor. It is revealed that the skin friction along x− direction increases from (0.78138, 0.833702, 0.897022, and 0.972526) for ternary hybrid nanofluid. Nusselt number increases from 2 to 5% (0.208936, 0.214288, 0.219799, 0.22555) when the volume fraction varies from 0.01 to 0.04 respectively.

Thin film flow of chemically reactive nonlinear thermally radiative magnetized variable viscosity fluid over a stretchable surface with non-uniform heat source/sink and Fick’s mass flux theory

The study of thin film flow over a stretching sheet holds significant importance from an industrial perspective due to its relevance in various manufacturing and engineering processes. In the present investigation, we delved into the combined influence of non-uniform heat source/sink on the governing heat and mass transfer equations in a thin liquid film on a permeable stretching surface. We have considered the nonlinear thermal radiation and implemented convective-type boundary conditions. Our analysis examined the effects of crucial physical parameters, including non-uniform heat source/sink, thermal radiation, chemical reaction, magnetic parameter , Prandtl number, Schmidt number, and unsteadiness parameter in the range [−3.5, 2.0], [−2, 5], [0, 1], [0.3, 4.0], [1, 7], [0.8, 1.7], [0.7, 2.0], respectively. It is found that a non-uniform heat source/sink mitigated the temperature gradient, while an elevation in the Schmidt number intensified the mass transfer rate. The validation process enhanced the robustness and reliability of our numerical simulations.

Effects of Confinement on Opposed-Flow Flame Spread over Cellulose and Polymeric Solids in Microgravity

Opposed-flow flame spread over solid materials has been investigated in the past few decades owing to its importance in fundamental understanding of fires. These studies provided insights on the behavior of opposed-flow flames in different environmental conditions (e.g., flow speed, oxygen concentration). However, the effect of confinement on opposed-flow flames remains under-explored. It is known that confinement plays a critical role in concurrent-flow flame spread in normal and microgravity conditions. Hence, for a complete understanding it becomes important to understand the effects of confinement for opposed-flow flames. In this study, microgravity experiments are conducted aboard the International Space Station (ISS) to investigate opposed-flow flame spread in different confined conditions. Two materials, cotton-fiberglass blended textile fabric (SIBAL) and 1 mm thick polymethyl methacrylate (PMMA) slab are burned between a pair of parallel flow baffles in a small flow duct. By varying the sample-baffle distance, various levels of confinement are achieved (H = 1–2 cm). Three types of baffles, transparent, black, and reflective, are used to create different radiative boundary conditions. The purely forced flow speed is also varied (between 2.6 and 10.5 cm/s) to investigate its interplay with the confinement level. For both sample materials, it is observed that the flame spread rate decreases when the confinement level increases (i.e., when H decreases). In addition, flame spread rate is shown to have a positive correlation with flow speed, up to an optimal value. The results also indicate that the optimal flow speed for flame spread can decrease in highly confined conditions. Surface radiation on the confinement boundary is shown to play a key role. For SIBAL fabric, stronger flames are observed when using black baffles compared to transparent. For PMMA, reflective baffles yield stronger flames compared to black baffles. When comparing the results to the concurrent-flow case, it is also noticed that opposed-flow flames spread slower and blow off at larger flow speeds but are not as sensitive to the flow speed. This work provides unique long-duration microgravity experimental data that can inform the design of future opposed-flow experiments in microgravity and the development of theory and numerical models.

Magnetohydrodynamic stagnation point flow of Williamson hybrid nanofluid via stretching sheet in a porous medium with heat source and chemical reaction

The stagnation point flow of non-Newtonian fluids has several engineering and industrial applications. In this article, we considered the investigation of the magnetohydrodynamic stagnation point flow of Williamson hybrid nanofluid with chemical reaction and energy generation effects over a porous extending sheet. Similarly, the characteristics of radiation and convective boundary conditions are also taken. Presumptions of boundary layer movement of Williamson hybrid nanofluid facilitate the simplification of the essential mathematical equations for the conservation of mass, energy, momentum and concentration. By introducing the similarity variables, the controlling partial differential equations have been transformed into dimensionless ordinary differential equations. Then, the most effective homotopy analysis method is used to approximate the solutions of reduced ordinary differential equations. Graphical calculations are carried out for hybrid nanofluid [Formula: see text] and nanofluid [Formula: see text]. To investigate the impacts of leading parameters, graphs for the quantities are generated. At the boundary, the local skin friction factor, the Sherwood number and the Nusselt number are also determined. According to the outcomes, it is discovered that when the porosity parameter increases the velocity profile of the hybrid nanofluid [Formula: see text] climbs above that of the nanofluid [Formula: see text]. An increase in thermal radiation parameter and Biot number causes a greater thickness of the thermal boundary layer, which in turn raises the temperature of the hybrid nanofluid. Furthermore, the increased chemical reaction decreases the concentration in both [Formula: see text] hybrid nano liquid and [Formula: see text] mono nanofluid cases.

MHD radiative Gr-Ag-TiO2/H2O ternary hybrid nanofluid flow upon a permeable movable wedge with irreversibility analysis

ABSTRACT The mass-based ternary hybrid nanofluid model is applied for the magnetohydrodynamic (MHD) flow over a moving wedge with wall permeability, thermal radiation, and convective boundary condition. The masses of the nanoparticles and the base fluid are considered instead of the volumetric concentration of the first, the second, and the third nanoparticles. In the base fluid of water, three types of nanoparticles such as titania, silver, and graphene have been embedded. A similarity method is used to reduce variables and also to turn prominent equations of ternary hybrid nanofluid flow into a simplified form. The shooting technique with the Runge-Kutta-Felhberg method has been used to numerically solve the converted boundary layer equations. The largest Nusselt number is related to the ternary hybrid nanofluid, in which a heat transfer enhancement of 6.55% has been obtained in comparison with regular fluid. The Nusselt number for five shapes of the third nanoparticles is obtained (when both the first and second nanoparticles are spherical), and when the third nanoparticle has the shape of the disk, the most heat transfer has occurred. The highest entropy generation is related to the stagnation point case (m = 1) and the lowest belongs t the downhill case (m = –0.0825).

A numerical framework of magneto Williamson hybrid nanofluid over porous sheet; a classical keller box analysis

The current study intends to talk about the unsteady Williamson hybrid nanofluid flow with heat transport across a stretching surface comprising the magnetic hydrodynamic, thermal radiative, suction/injection, and convective boundary condition effects respectively. The study focused on the hybrid Williamson nanofluid, comprising of an EG ethylene glycol (C2H6O2) and two types of nano-solid particles, c zinc oxide and molybdenum disulphide ZnO-MOS2. To accomplish this goal, the modelled expressions are transmitted into dimensionless ODE by making use of several highly established transformations. The aim of the numerical result of the current exploration is studied through Keller Box Analysis (KBA). Tabular data and statistical bar plots are used to compare this strategy. The impact of physical variables such as Magnetic field parameter γ, Williamson fluid variable We, Porous media β, Thermal radiation Rd, Biot number Bi and Prandtl number Pr are analyzed through plots and tables. An augmentation in the strength of the magnetic field and Williamson fluid parameter results in a reduction in velocity. However, a temperature rise is observed for higher values of the Williamson fluid parameter and magnetic parameters. The surface friction drag is diminished by the Forchheimer and Weissenberg values. The rate of mass transfer is strongly positively correlated with both the Schmidt number and chemical reaction. The present study has a remarkable agreement with the results that were previously published, which confirms the application and validation of the Keller-Box scheme.

3D Heat Conduction Solver for Complex Geometries

Abstract: The essential pre-requisites for any solver to tackle real life 3D problems are to handle complex geometries and quick turnaround time. In this direction an Unstructured Finite Volume (FVM) based multi-threaded heat conduction solver has been developed to address both the issues respectively. The solver is object oriented and written in Java language. Unstructured Finite Volume method has been utilized for the space discretization and a four stage Runge-Kutta scheme is used for time integration. This solution methodology is highly parallelizable and extensively used in CFD codes. The present solver can handle non-linear steady state and transient 3D thermal problems with Dirichlet, Neumann and surface radiation boundary conditions. The solver has been validated against bench mark problems. In the present work a 3D complex geometry is discretised into 2.5 lakh hexahedrons has been taken as a test case to demonstrate the efficiency of the solver with multi-threading in dual processor machines. The results obtained are presented.

Mixed convection hybrid nanofluid flow over a stationary permeable vertical cone with thermal radiation and convective boundary condition

AbstractMany real‐world devices, such as heat exchangers, geothermal reservoirs, and cooling systems, utilize the concept of boundary layer flow across a cone geometry. The current study presents and analyses the mathematical formulation for the mixed convection flow of a hybrid nanofluid over a permeable stationary cone. The heat transfer analysis considers the effects of thermal radiation and convective boundary condition. Numerical and statistical analyses of this flow problem yield new, physically significant results. The numerical analysis is carried out using the bvp4c solver in Matlab. Similarity transformations are performed to obtain a system of nonlinear ordinary differential equations from the governing partial differential equations and boundary conditions. In both assisting and opposing flows, spherical‐ and platelet‐shaped nanoparticles are observed to produce the lowest and highest local skin friction coefficient, respectively. The spherical‐ and blade‐shaped nanoparticles also offer the highest and lowest local Nusselt number, respectively, with a difference of 6.4% (assisting) and 6.03% (opposing). Meanwhile, the increase in the mixed convection parameter raised the velocity profile but diminished the temperature profile of the hybrid nanofluid. Then, the relationship of the Biot number , suction , and thermal radiation ) parameters with the local Nusselt number is investigated through the response surface methodology (RSM). The local Nusselt number for the current flow problem is estimated to be maximized at 0.814323 (assisting) and 0.814629 (opposing) when these parameters are at the highest range of , , and . Several researchers had presented experimental studies conducted at different temperatures (15, 25, 35°C), mass flow rates (ranging from 0.00076 to 0.041 kg/s), and nanoparticle concentrations (0.387, 0.992, 3.12, 4.71 mass%).

Spectral approach with iterative clarification of a radiation boundary conditions for modeling of quasimodes of a gyrotrons open cavities

Purpose. The article presents a new method for numerical simulation of quasi-eigenmode oscillations in open resonators of gyrotrons — powerful vacuum generators of electromagnetic waves in the millimeter and submillimeter ranges. The gyrotron cavity has the shape of a weakly inhomogeneous hollow circular metal waveguide. Methods. The proposed approach uses the inhomogeneous string equation with radiation boundary conditions to formulate a nonlinear spectral boundary value problem describing oscillations in a resonator, neglecting the couplings of waves with different radial indices. By linearizing with respect to frequency the radiation boundary conditions, the boundary value problem is reduced to a linear boundary value problem. To discretize this boundary value problem, the finite difference method is used and a linear generalized matrix eigenvalue problem is formulated. This problem is solved by the Arnoldi method with eigenvalues calculation in a shift-invert mode. An iterative algorithm is proposed that makes it possible to sequentially calculate a given number of frequencies and quality factors of quasi-eigenmodes of oscillations. Results. The computer program was developed written in the Wolfram Language and Fortran using the algorithms proposed in the work. The results of test calculations for real gyrotron resonators are presented, which demonstrate the high accuracy of the obtained values of frequencies, quality factors and field distributions of quasi-eigenmode oscillations in the studied resonators. Conclusion. The methods, algorithms and created program proposed in the article can significantly facilitate the process of developing gyrotrons intended for various practical applications and operating in new frequency ranges. The method of iterative refinement of boundary conditions can be generalized to the case of equations of the linear theory of a gyrotron and used to develop new methods for analyzing the starting conditions for the soft self-excitation in gyrotrons — generators.

Finite Element–Boundary Element Acoustic Backscattering with Model Reduction of Surface Pressure Based on Coherent Clusters

Computing backscattering of harmonic acoustic waves from underwater elastic targets of arbitrary shape is a problem of considerable practical significance. The finite element method is commonly applied to the discretization of the target; on the other hand, the boundary element method naturally incorporates the radiation boundary condition at infinity. The coupled model tends to be expensive, primarily due to the need to manipulate large, dense, and complex matrices and to repeatedly solve systems of complex linear algebraic equations of significant size for each frequency of interest. In this article, we develop a model reduction transformation based on the notion of coherence applied to the surface pressures, which considerably reduces the size of the systems to be solved. We found that the proposed model reduction approach delivers acceptably accurate results at a fraction of the cost of the full model. A typical speedup of an order of magnitude was realized in our numerical experiments. Our approach enables backscattering computations with considerably larger models than have been feasible to date.

Study on the Characteristics of Trackside Acoustic Flow Field of High-Speed Train under the Influence of Crosswind.

During the on-track acoustic detection process, a potential flow model and an acoustic finite element mathematical model based on synthetic wind are utilized, taking into account the combined effects of vehicle speed, wind direction angle, and crosswind speed. Simulation and modeling are achieved using Automatic Matching of Acoustic Radiation Boundary Conditions (AML) technology, enabling obtaining a distribution map and sound pressure frequency response curve of the trackside acoustic field under crosswind conditions by setting up field point grids. It is found that sound pressure values at the same location gradually increase as the vehicle speed increases in the frequency range of 10 Hz to 70 Hz, at different vehicle speeds. The sound pressure values and distribution area of the trackside acoustic field are the largest when the crosswind speed is 10 m/s (wind force at level five), allowing for easier location of the sound source when a fault occurs. The study also reveals that under different wind direction angles, the same location's sound pressure value on the trackside gradually decreases as the wind direction angle increases, to lower than that of the non-crosswind condition, severely hindering the reception and diagnosis of acoustic signals.

A novel technique for implementing the finite element method in a shallow water equation

We presented a novel approach to investigate the two-dimensional shallow water equation in its primitive form. Its employs the P1NC−P1 element pair to simulate various cases: standing waves, dam-break planar, and wave absorbing with embedded radiation boundary conditions. Unlike the conventional method, we approximate the free surface variable using a conformal basis P1 whereas the velocity potential is approximated using a non-conformal basis, P1NC. Thus, for each case, the weak form needs to be reformulated as well as the discrete form. The resulting scheme is a first-order ordinary differential system and solved by Crank Nicholson. The mass matrix in the momentum equation contains the multiplication between the two bases, which computed by the mass lumping. So, our method is explicit, flexible and easy to implement. Validation using standing waves demonstrated first-order accuracy, free from numerical damping and convergent to the analytical solution. Dam-break simulation result shown an agreement with ANUGA software. Our scheme's flexibility is demonstrated when it can mimic wave absorbing simulation employing embedded radiation boundary conditions. The reflection at the boundary seems small enough, thus can be neglected. All these findings have shown the robustness and capability of our scheme to predict accurate results for various shallow water flow problems.•A novel technique for solving 2D SWE in primitive form•It is explicit, flexible, easy to implement, accurate, and robust•Our approach is suitable for coastal/oceanographic simulations

Computational analysis of radiative nanofluid flow past an inclined cylinder with slip effects using the Yamada–Ota model

The notion of the paper is to analyse the flow attributes of a carbon nanotube-based hybrid nanofluid over an inclined cylinder. This study accounts for the impacts of mixed convection, thermal radiation, suction/blowing, and slip boundary conditions. The solution of the governing equations is obtained using the "bvp4c solver", and presented through graphs and tables. The obtained results are validated by comparing them with published work. The study reports that increasing the temperature slip parameter led to a reduction in both velocity and temperature distributions. The presence of an electric parameter contributed to an increase in nanofluid flow, while the temperature of the nanofluid exhibited a decrease. Moreover, increasing the Hartmann number from 0.2 to 1.1 results in a 1.39% increase in the heat transfer rate within the hybrid nanofluid model. However, the pure fluid model demonstrates a more substantial enhancement, with a significant 3.8% rise in the heat transfer rate.

Computational investigation of magnetized hybrid nanofluids heat transport and flow through elongational surface with thermal radiation and wall slip

The improved thermal performance of recently discovered hybridized nanofluids has become essential in large scale thermal processes. In fact, this is highly efficient technique to introduce the thermal efficiency of tranditional heat transferring fluids. The behavior of the nanofluid can be significantly impacted by the unsteady heating and magnetic field effects that may be present in many applications. Therefore, the current study investigat the unsteady magnetized flow of hybrid nanofluid with heat transport characteristics subject to thermal radiation and slip at the surface wall. The shrinking/stretching surface is chosen as a flow source, which is frequently occure in polymer technology, which deals with the deformability of elastic sheets, and in metallurgy, where continued strips are cooled. The novel form of shrinking surface flow is fundamentally a reverse flow and exhibits physical characteristics that differ significantly from the channel flow scenario. The distinctive features of this scruinity is the use of empirical relations to approximate the optimum thermophysical attributes of a Cu−Al2O3/ water hybrid nanofluid in order to model the 2-dimensional flow past a flat shrinking/stretching sheet under the action of radiation, Lorentz forces and realastic boundary condition responses. The governing system of modelled equation are assembled using the Tiwari-Das model in conjunction with a hybrid mass-based nanofluid model. The bvp4c algorithm is employed within the computer MATLAB programme. The hybrid nanofluid flow shows conclusive improvement in the frictional coefficient and heat transport performance. However, the effectiveness the unsteadiness parameter deteriorates the heat transmission. In the contiguity of a suction parameter, multiple outcomes appear to arise for both stretched and shrinking instances. The coefficient of energy transport improves as the magnetic factor is augmented, however the skin coefficient of friction exhibits dual behavior for the second solutions. A time-dependence investigation is undertaken to figure out the reliability of the twin solutions, and it is discovered that merely one of them remains stable and aesthetically credible.

A solution for the neutron diffusion equation in the spherical and hemispherical reactors using the residual power series

A novel analytical solution to the neutron diffusion equation is proposed in this study using the residual power series approach for both spherical and hemispherical fissile material reactors. Various boundary conditions are investigated, including zero flux on the boundary, zero flux on the extrapolated boundary distance, and the radiation boundary condition (RBC). The study also shows how two hemispheres with opposing flat faces interact. We give numerical results for the same energy neutrons diffused in pure P239u. By qualitative comparison with the homotopy perturbation method and Bessel function-based solutions, the residual power series method (RPSM) presents accurate series solutions that converge to the exact solutions, as shown in this study. Moreover, numerical results were shown to be improved by the computer implementation of the analytic solutions.

The Role of Quadratic-Linearly Radiating Heat Source with Carreau Nanofluid and Exponential Space-Dependent Past a Cone and a Wedge: A Medical Engineering Application and Renewable Energy

A mathematical analysis for a steady, incompressible, laminar Carreau nanofluid flow over a porous cone and wedge is considered. The novelty of this research work is to scrutinize an exponential space-dependent Cattaneo–Christov heat flux and quadratic Rosseland approximation effects. Two-phase nanofluid model, i.e., Brownian motion, and thermophoretic effects are included. This study also employs non-linear thermal radiation and convective surface boundary conditions to investigate heat transport phenomena. The Carreau nanofluid boundary layer equations are derived using the standard boundary layer approximations. By applying the similarity transformations, the managing set of partial differential equations (PDEs) becomes a system of connected non-linear ordinary differential equations (ODEs). The resultant non-linear ODEs are solved numerically utilizing the numerical method, particularly the bvp4c function in MATLAB. The significances of the fluid motion are visualized by sketching several Carreau nanofluid flow’s relevant parameters using graphic outputs. The effects of a wide range of thermophysical variables on liquid properties including velocity, temperature, concentration, skin-friction, Nusselt number, and Sherwood number are investigated and discussed. This study’s findings are compared to previously announced results within a limited range, where strong validation was seen. The results demonstrate that the opposite mechanism is observed with repercussion of Weissenberg number (We) on velocity profile and concentration, the enhancement of We increases the momentum boundary layer while it reduces the concentration boundary layer. The outcomes could be applied to the cooling of equipment, electronics, and various industrial units.

Enhanced heat transfer analysis of hybrid nanofluid over a Riga plate: Incorporating Lorentz forces and entropy generation

The Riga plate, comprising a configuration of electrodes and permanent magnets, can induce a wall-parallel Lorentz force through external electric and magnetic fields, enabling effective control of fluid flow. This paper focuses on studying the flow characteristics of Al2O3-Cu/water hybrid nanofluid past a Riga plate in the presence of strong suction. The mathematical model incorporates a two-phase approach to describe the behavior of the nanofluid, while considering the Grinberg-term to account for the wall parallel Lorentz force generated by the Riga plate. Several influential factors such as entropy generation, viscous dissipation, heat flux, thermal radiation, slippage, and convective boundary conditions of temperature are considered in our investigation. Entropy generation within thermodynamic systems contributes to energy losses resulting from various factors, including frictional forces, viscosity, and chemical reactions. Minimizing entropy generation is crucial to enhancing system performance. To address the research problem, we utilize dimensionless parameters and assume strong suction to simplify the governing partial differential equations. The dimensionless model is subsequently solved numerically using the Adams-Bashforth technique. Additionally, a comprehensive graphical analysis is conducted to examine the impact of various dimensionless parameters on the flow fields. This study highlights the importance of controlling fluid flow using the Riga plate in the presence of suction and investigates the behavior of a specific nanofluid under these conditions. The results provide valuable insights into the influence of key parameters on the flow characteristics. We conclude that effective utilization of the Riga plate can lead to significant enhancements in fluid flow control. Moreover, the study contributes to reducing energy losses through minimizing entropy generation. The novelty of this work lies in its comprehensive approach, considering multiple influential factors and employing a two-phase model for the nanofluid. Additionally, the inclusion of the Grinberg-term to account for the wall parallel Lorentz force adds to the uniqueness of the study. This research expands upon previous efforts in the literature by providing a more comprehensive analysis of the fluid flow control using the Riga plate, incorporating a broader range of factors, and presenting a numerical solution approach.

A finite element approach for nonlinear, transient heat conduction problems with convection, radiation or contact boundary conditions

Heat conduction problems with convection and/or radiation boundary conditions arise in nuclear and other engineering fields. This paper presents a finite element approach to solve transient, three-dimensional (3-D), nonlinear heat conduction problems using quadratic tetrahedral elements with area/volume coordinates and quadrature integrations. Boundary conditions modeled include surface convection, to-ambient radiation, and surface-to-surface radiation (using the radiosity matrix method, RMM). Instead of the commonly used hemi-cube method, L′Huilier’s theorem is used here to calculate view factors. Contact constraints are also imposed. Interface condition is set up for the interfaces of different material. The one- and two-step backward differentiation are used for time integration. Nonlinearities introduced by temperature-dependent material thermal properties and the Stefan–Boltzmann law for radiation are handled using the Picard and/or Newton–Raphson methods. The convergence rate of the numerical scheme is verified using an analytical solution obtained using the method of manufactured solutions (MMS). Several practical cases are simulated, including that of two spheres in contact with each other, and results are compared to those obtained using commercial codes.

Momentum and thermal transport analysis in MHD nanofluid through the thermally heated square conduit: Finite element method

ObjectiveThe purpose of this investigation is to report the thermal performance of water-based nanofluids with two different types of hybrid nanofluids for the cooling process of the radiator inside the thermally heated square cavity under the addition of thermal radiation and magnetic field by using the finite element method. Research gapThe heat transfer analysis of MHD nanofluid with the suspension of titanium alloy Ti6A14V and aluminum alloy AA7075 in cavity flow problems under the effects of thermal radiation and thermal boundary conditions by using the Galerkin finite element method is not reported before. NoveltyIn this numerical investigation, the novel mathematical model of two types of titanium alloy Ti6A14V (class of titanium) and aluminum alloy AA7075 is proposed first time in the cavity flows under the influence of a uniform magnetic field and non-uniform thermally heated bottom wall. The momentum and energy equations are updated with terms of magnetic field and thermal radiation, respectively. The cavity is filled with AA7075- Ti6A14V/water nanofluids. Two parallel vertical walls of the cavity are set at constant temperatures (Tc) and the top one is adiabatic while the temperature at the lower wall is taken as the variable. Method of solutionThe physical model is composed in terms of nonlinear differential equations and transformed into a dimensionless form by using suitable non-dimensional quantities. The Galerkin finite element method along with iterative Newton’s Raphson method is selected to simulate the problem and obtain the numerical solution with a high degree of accuracy. The results are illustrated for fixed Prandtl number Pr=10.0 throughout the calculation, Rayleigh number 1000≤Ra≤100000, nanoparticle volume friction 0.0≤ϕ≤0.05 Hartman number 0≤Ha≤10 and thermal radiation parameter 1.0≤Ra≤10.0. Both grid independence tests and comparison tests are directed to get the accuracy of the established model. Important findingsThe computational results revealed that the aluminum alloy (AA7075) alloys nanoparticles are more productive as compared to titanium (Ti6Al4V) alloy nanoparticles in terms of enhancing the thermal features of water-based nanofluid. The aluminum alloy nanofluid and titanium alloy nanofluid provide 3.9 % & 5.7 % and 2.9 % & 4.2 % more heat transfer at the bottom and side walls as compared to regular fluid. ApplicationsThe current nanofluid models are more efficient than the conventional model to control the heat transfer rate and flow phenomena. The computational results revealed that if the radiator is assembled by using the modern concept of hybrid nanofluid then that will increase the heat transfer of the engine and enhance the lifespan of the machinery.