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A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate integro‐differential governing equations for a grey and non‐scattering medium with grey and diffuse walls are developed and solved for several model problems. We consider axisymmetric, cylindrical geometries with top and bottom boundaries of arbitrary convex shape. The method is accurate for media of any optical thickness and is capable of handling a wide array of axisymmetric geometries and boundary conditions. Several techniques are presented to reduce computational overhead, such as employing a Swartz‐Wendroff approximation and cut‐off criteria for evaluating radiation integrals. The method is successfully tested against several cases from the literature and is applied to some additional example problems to demonstrate its versatility. Solution of a free‐boundary, combined‐mode heat transfer problem representing the solidification of a semitransparent material, the Bridgman growth of an yttrium aluminium garnet (YAG) crystal, demonstrates the utility of this method for analysis of a complex materials processing system. The method is suitable for application to other research areas, such as the study of glass processing and the design of combustion furnace systems.

This paper aims to study numerically the simulation of convective–radiative heat transfer under an effect of variable thermally generating source in a rotating square chamber. The performed analysis deals with a development of passive cooling system for the electronic devices.

The domain of interest of size H rotating at a fixed angular velocity has heat-conducting solid walls with a constant cooling temperature for the outer boundaries of the vertical walls and with thermal insulation for the outer borders of the horizontal walls. The chamber has a heater on the bottom wall with a time-dependent volumetric heat generation. The internal surfaces of the walls and the energy element are both grey diffusive emitters and reflectors. The fluid is transparent to radiation. Computational model has been written using non-dimensional parameters and worked out by the finite difference technique. The effect of the angular velocity, volumetric heat generation frequency and surface emissivity has been studied and described in detail.

The results show that growth of the surface emissivity leads to a diminution of the mean heater temperature, while a weak rotation can improve the energy transport for low volumetric thermal generation frequency.

An efficient computational approach has been used to work out this problem. The originality of this work is to analyze complex (conductive–convective–radiative) energy transport in a rotating system with a local element of time-dependent volumetric heat generation. To the best of the authors’ knowledge, an interaction of major heat transfer mechanisms in a rotating system with a heat-generating element is scrutinized for the first time. The results would benefit scientists and engineers to become familiar with the analysis of complex heat transfer in rotating enclosures with internal heat-generating units, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

Hybrid nanofluids are of significant engrossment for their considerable heat transport rate. The steady flow of an incompressible viscous electrically conducted hybrid nanofluid is considered over a rotating disk under a magnetic field. Titanium oxide (TiO₂) and ferrous (CoFe₂O₄) nanoparticles are used with their physical properties and water is considered as host liquid. The purpose of this paper is to analyze how hydrothermal integrity varies for hybrid nanosuspension over a spinning disk in the presence of magnetic orientation.

Governing equations with boundary conditions are transformed by similarity transformations and then solved numerically with RK-4 method. A comparison of linear and nonlinear thermal radiation for the above-mentioned parameters is taken and the efficiency of nonlinear radiation is established, the same over nanofluid and hybrid nanofluid is also discussed. Heat lines are observed and discussed for various parameters like magnetic field, concentration, suction and injection parameter, radiation effect and Prandtl number.

Suction and increasing nanoparticle concentration foster the radial and cross-radial velocities, whereas magnetization and injection confirm the reverse trend. The rate of increment of radial friction is quite higher for the usual nanosuspension. The calculated data demonstrate that the rate for hybrid nanofluid is 8.97 percent, whereas for nanofluid it is 15.06 percent. Double-particle suspension amplifies the thermal efficiency than that of a single particle. Magnetic and radiation parameters aid the heat transfer, but nanoparticle concentration and suction explore the opposite syndrome. The magnetic parameter increases the heat transport at 36.58 and 42.71 percent for nonlinear radiation and hybrid nanosuspension, respectively.

Nonlinear radiation gives a higher heat transport rate and for the radiation parameter it is almost double. This result is very significant for comparison between linear and nonlinear radiation. Heat lines may be observed by taking different nanoparticle materials to get some diverse result. Hydrothermal study of such hybrid liquid is noteworthy because outcomes of this study will aid nanoscience and nanotechnology in an efficient way.

Thermo-magnetic convective flow analysis under the impact of thermal radiation for heat and entropy generation phenomena is an active research field for understanding the efficiency of thermodynamic systems in various engineering sectors. This study aims to examine the characteristics of convective heat transport and entropy generation within an inverted T-shaped porous enclosure saturated with a hybrid nanofluid under the influence of thermal radiation and magnetic field.

The mathematical model incorporates the Darcy-Forchheimer-Brinkmann model and considers thermal radiation in the energy balance equation. The complete mathematical model has been numerically simulated through the penalty finite element approach at varying values of flow parameters, such as Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), radiation parameter (Rd) and porosity value (e). Furthermore, the graphical results for energy variation have been monitored through the energy-flux vector, whereas the entropy generation along with its individual components, namely, entropy generation due to heat transfer, fluid friction and magnetic field, are also presented. Furthermore, the results of the Bejan number for each component are also discussed in detail. Additionally, the concept of ecological coefficient of performance (ECOP) has also been included to analyse the thermal efficiency of the model.

The graphical analysis of results indicates that higher values of Ra, Da, e and Rd enhance the convective heat transport and entropy generation phenomena more rapidly. However, increasing Ha values have a detrimental effect due to the increasing impact of magnetic forces. Furthermore, the ECOP result suggests that the rising value of Da, e and Rd at smaller Ra show a maximum thermal efficiency of the mathematical model, which further declines as the Ra increases. Conversely, the thermal efficiency of the model improves with increasing Ha value, showing an opposite trend in ECOP.

Such complex porous enclosures have practical applications in engineering and science, including areas like solar power collectors, heat exchangers and electronic equipment. Furthermore, the present study of entropy generation would play a vital role in optimizing system performance, improving energy efficiency and promoting sustainable engineering practices during the natural convection process.

To the best of the authors’ knowledge, this study is the first ever attempted detailed investigation of heat transfer and entropy generation phenomena flow parameter ranges in an inverted T-shaped porous enclosure under a uniform magnetic field and thermal radiation.

The purpose of this paper is to present a finite element approximation of the low Mach number equations coupled with radiative equations to account for radiative heat transfer. For high-temperature flows this coupling can have strong effects on the temperature and velocity fields.

The basic numerical formulation has been proposed in previous works. It is based on the variational multiscale (VMS) concept in which the unknowns of the problem are divided into resolved and subgrid parts which are modeled to consider their effect into the former. The aim of the present paper is to extend this modeling to the case in which the low Mach number equations are coupled with radiation, also introducing the concept of subgrid scales for the radiation equations.

As in the non-radiative case, an important improvement in the accuracy of the numerical scheme is observed when the nonlinear effects of the subgrid scales are taken into account. Besides it is possible to show global conservation of thermal energy.

The original contribution of the work is the proposal of keeping the VMS splitting into the nonlinear coupling between the low Mach number and the radiative transport equations, its numerical evaluation and the description of its properties.

One‐dimensional radiative heat transfer is considered in a plane‐parallel geometry for an absorbing, emitting, and linearly anisotropic scattering medium subjected to azimuthally symmetric incident radiation at the boundaries. The integral form of the transport equation is used throughout the analysis. This formulation leads to a system of weakly‐singular Fredholm integral equations of the second kind. The resulting unknown functions are then formally expanded in Chebyshev series. These series representations are truncated at a specified number of terms, leaving residual functions as a result of the approximation. The collocation and the Ritz‐Galerkin methods are formulated, and are expressed in terms of general orthogonality conditions applied to the residual functions. The major contribution of the present work lies in developing quantitative error estimates. Error bounds are obtained for the approximating functions by developing equations relating the residuals to the errors and applying functional norms to the resulting set of equations. The collocation and Ritz‐Galerkin methods are each applied in turn to determine the expansion coefficients of the approximating functions. The effectiveness of each method is interpreted by analyzing the errors which result from the approximations.

The analysis of fluid flow and thermal transport performance inside the cavity has found numerous applications in various engineering fields, such as nuclear reactors and solar collectors. Nowadays, researchers are concentrating on improving heat transfer by using ternary nanofluids. With this motivation, the present study analyzes the natural convective flow and heat transfer efficiency of ternary nanofluids in different types of porous square cavities.

The cavity inclination angle is fixed ω = 0 in case (I) and ω=π4 in case (II). The traditional fluid is water, and Fe3O4+MWCNT+Cu/H2O is treated as a working fluid. Ternary nanofluid's thermophysical properties are considered, according to the Tiwari–Das model. The marker-and-cell numerical scheme is adopted to solve the transformed dimensionless mathematical model with associated initial–boundary conditions.

The average heat transfer rate is computed for four combinations of ternary nanofluids: Fe3O4(25%)+MWCNT(25%)+Cu(50%),Fe3O4(50%)+MWCNT(25%)+Cu(25%),Fe3O4(33.3%)+MWCNT(33.3%)+Cu(33.3%) and Fe3O4(25%)+MWCNT(50%)+Cu(25%) under the influence of various physical factors such as volume fraction of nanoparticles, inclined magnetic field, cavity inclination angle, porous medium, internal heat generation/absorption and thermal radiation. The transport phenomena within the square cavity are graphically displayed via streamlines, isotherms, local and average Nusselt number profiles with adequate physical interpretations.

The purpose of this study is to determine whether the ternary nanofluids may be used to achieve the high thermal transmission in nuclear power systems, generators and electronic device applications.

The current analysis is useful to improve the thermal features of nuclear reactors, solar collectors, energy storage and hybrid fuel cells.

To the best of the authors’ knowledge, no research has been carried out related to the magneto-hydrodynamic natural convective Fe3O4+MWCNT+Cu/H2O ternary nanofluid flow and heat transmission filled in porous square cavities with an inclined cavity angle. The computational outcomes revealed that the average heat transfer depends not only on the nanoparticle’s volume concentration but also on the existence of heat source and sink.

This study proposes targeted modernization of the Department of Defense (DoD's) Joint Forces Ammunition Logistics information system by implementing the optimized innovative information technology open architecture design and integrating Radio Frequency Identification Device data technologies and real-time optimization and control mechanisms as the critical technology components of the solution. The innovative information technology, which pursues the focused logistics, will be deployed in 36 months at the estimated cost of $568 million in constant dollars. We estimate that the Systems, Applications, Products (SAP)-based enterprise integration solution that the Army currently pursues will cost another $1.5 billion through the year 2014; however, it is unlikely to deliver the intended technical capabilities.

The paper presents a numerical technique for the simulation of the effects of grey‐diffusive surface radiation on fluid flow using a finite volume procedure for two‐dimensional (plane and axi‐symmetric) geometries. The governing equations are solved sequentially, and the non‐linearities and coupling of variables are accounted for through outer iterations (coefficients updates). In order to reduce the number of outer iterations, a multigrid algorithm was implemented. The radiating surface model assumes a non‐participating medium, semi‐transparent walls and constant elementary surface temperature and radiation fluxes. The calculation of view factors is based on the analytical evaluation for the plane geometry and numerical integration for axi‐symmetric geometry. Ashadowing algorithm was implemented for the calculation of view factors in general geometries. The method for the calculation of view factors was first tested by comparison with available analytical solutions for a complex geometric configuration. The flow prediction code combined with radiation heat transfer was verified by comparisons with analytical one‐dimensional solutions. Further test calculations were done for the flow and heat transfer in a cavity with a radiating submerged body. As an example of the capabilities of the method, transport processes in metalorganic chemical vapour deposition (MOCVD) reactors were simulated.

The current study aims to address the interaction between participating media radiation with thermo-gravitational convection of an electrically conducting fluid enclosed within a tilted enclosure under an externally imposed time-independent uniform magnetic field.

The differentially heated boundaries of the tilted enclosure are considered to be diffuse, gray and the enclosed fluid is assumed to be absorbing, emitting and isotropically scattering. The Navier-Stokes equations, meant for magneto convection are solved using modified MAC method. Gradient dependent consistent hybrid upwind scheme of second order is used for discretization of the convective terms. Discrete ordinate method, with S8 approximation, is used to model radiative transport equation in the presence of radiatively active medium.

Effect of uniform magnetic field with different magnitudes and orientations of cavity has been numerically simulated. The effect of participating media radiation has been investigated for different optical thicknesses, emissivities, scattering albedos and Planks number. The results are provided in both graphical and tabular forms. The flow lines, isotherms bring clarity in the understanding of flow behaviour and heat transfer characteristics.

Despite the idealized nature, the present study is quite essential to understand the cumbersome physics of realistic problem.