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The purpose of this paper is to present a method of solving a thermal conduction equation in three‐zone axially‐symmetrical systems.

In the method developed, the field functions are determined in the analytical way by the superposition of states and separation of variables method. The coefficients of the field functions and eigenvalues of the boundary‐initial problem are computed by the numerical method. The coefficients are the solution to the corresponding sets of equations. These sets are the result of scalar products of non‐orthogonal functions at the respective zones of the cable. The eigenvalues are determined by an algorithm, which uses the field properties and elements of the golden cut method.

The method made it possible to develop a mathematical model of the dynamics of the thermal field in a polymer DC cable. This model has good physical interpretation. The paper also presents the field distributions determined in an analytical form. Some arguments of the expressions derived are however computed numerically. The results obtained by the paper's method and by the finite elements methods were compared. The relative differences are less than 6 per cent.

The method concerns axially‐symmetrical three‐zone systems under nominal conditions.

By means of the method important parameters of DC lines can be determined (e.g. spatial‐temporal heat‐up curves, admissible sustained currents, time constants).

An analytical‐numerical method of analysis of the thermal field in a three‐zone axially‐symmetrical system was developed. Its original element is the algorithm of determination of eigenvalues of the boundary‐initial problem and coefficients of non‐orthogonal field functions.

The purpose of this paper is to analyse the dynamics of a thermal field generated in a tubular bus with rated current by using two models of electrical resistivity of copper.

The boundary-initial problem of the modified heat equation was formulated for the tubular bus. Analytical solutions were obtained by means of Green’s functions as the kernels of the integral operator inverse to the corresponding differential operator. The results were presented graphically and verified using the finite element method. The calculations were made by considering the example of the Storm Power Components tubular bus (USA).

Analytical field models were used to determine time- and space-variable heating curves, time constants and steady-state current ratings.

This paper is related to the structure of a hollow cylinder. Other bus sections can be taken into account by using the coordinate systems of different curvilinear orthogonal symmetry.

Using the analytical method, the influence of the variable (temperature dependent) electrical resistivity on some important parameters and characteristics of the tubular bus was investigated. The system was considered as an element with distributed parameters.

The paper aims to propose a parallel algorithm in order to increase speed and efficiency of an analysis of transient thermal field in layered DC cables.

Initial-boundary problem of thermal field was discretized by means of implicit finite difference method in cylindrical coordinates. A two-stage time decomposition method was applied to introduce parallel computations. An assumed duration of the transient state was decomposed. The system of algebraic equations was being solved with the use of a conjugate gradient method (with diagonal preconditioning) in all time intervals simultaneously.

A method for solving (with the use of parallel computing system) the transient heat conduction equation in a DC cable consisting of arbitrary number of material layers was given. The dependence of the convective heat transfer coefficient on the location on the perimeter of the cable and on its surface temperature (which introduced non-linearity in the boundary condition) was taken into account. The influence of the determined field on the efficiency of the heat source was also taken into consideration in the model.

The main limitation is induced by cylindrical and coaxial structure of the consecutive layers of the system. Thermal field is generated by direct current flow only. The length of the fragment of the cable under consideration should be much greater than its diameter.

The time-spatial distribution of thermal field in the cross-section of the cable can be used for analysis of its reliability and for determination of important characteristics and parameters of the system.

A parallel algorithm of solving initial-boundary parabolic problem was proposed as a result of synthesis of three methods (finite difference, time decomposition and conjugate gradient). An algorithm of minimization of disturbances of the solution introduced at the division points was given. Equations approximating real distribution of heat transfer coefficient from the surface of the cable were proposed.

The purpose of this paper is to prepare procedures for determination of characteristics and parameters of DC cables on the basis of transient and steady thermal field distribution in their cross-sections.

Steady-state current rating was computed iteratively, with the use of steady thermal field distribution in the cable. The iterative process was regulated with respect to this field by changes of the mean surface temperature of the sheath of the cable. It was also controlled with respect to the unknown current rating by deviations of the temperature of the core from the maximum sustained temperature of the insulation (material zone) adjacent to the core. Heating curves were determined (in arbitrarily selected points of the cross-section of the cable) by a parallel algorithm described thoroughly in the first part of the paper. The algorithm was used for computing of transient thermal field distribution throughout the whole cross-section. Thermal time constant distributions were determined by the trapezium rule, where the upper integration limit of respective thermal field distributions was being changed.

Using the methods prepared the following characteristics/parameters of the cable were determined: steady-state current rating, spatial-time heating curves, mean thermal time constant distribution. The results were verified and turned to be in conformance with those of the IEC 287 Standard and a commercial software – Nisa v. 16. Speedup and efficiency of the parallel computations were calculated. It was concluded that the parallel computations took less time than the sequential ones.

The specialized algorithms and software are dedicated to cylindrical DC cables.

The knowledge of the determined characteristics and parameters contributes to optimal exploitation of a DC cable during its use.

The algorithms of determination of the steady-state current rating and thermal time constant are original. The software described in the appendix has also been made by the authors.

The purpose of this article is investigating the impact of the spatially variable heat transfer coefficient on the thermal field in the double insulated wire.

The effect of the air boundary layer was modelled by means of changing the total heat transfer coefficient on the external perimeter of the wire. This leads to an elliptical boundary problem with Hankel’s condition dependent on the angular coordinate. The eigenfunctions of the problem were determined analytically. On the other hand, the unknown coefficients of eigenfunctions and the constants were calculated numerically by solving a respective system of algebraic equations. The steady state current rating was determined with an iterative method.

By means of the presented method, the thermal field distribution deprived of axial symmetry in the double insulated wire was determined. The obtained results have good physical interpretation and were verified with the finite element method (by means of NISA v. 16 software). The determined values of the steady-state current rating were compared with those calculated by means of the equivalent heat transfer coefficient method and the International Electrotechnical Commission (IEC) standard.

The method is applied to analyse scalar fields in layered cylindrical structures. This could be expanded to the case of a wire of any number of insulation layers. What is more, one could also consider heat sources without axial symmetry and located within the external area.

The analytical method of determining a thermal field deprived of axial symmetry in heterogeneous cylindrical system (the wire composed of three different materials) was developed.

The purpose of this study is to carry out a comprehensive analysis of magneto-hydrodynamics (MHD), nanofluidic flow dynamics and heat transfer as well as thermodynamic irreversibility, within a novel butterfly-shaped cavity. Gaining a thorough understanding of these phenomena will help to facilitate the design and optimization of thermal systems with complex geometries under magnetic fields in diverse applications.

To achieve the objective, the finite element method is used to solve the governing equations of the problem. The effects of various controlling parameters such as butterfly-shaped triangle vertex angle (T), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ ) on the hydrothermal performance are analyzed meticulously. By investigating the effects of these parameters, the authors contribute to the existing knowledge by shedding light on their influence on heat and fluid transport within butterfly-shaped cavities.

The major findings of this study reveal that the geometrical shape significantly alters fluid motion, heat transfer and irreversibility production. Maximum heat transfer, as well as entropy generation, occurs when the Rayleigh number reaches its maximum, the Hartmann number is minimized and the angle of the magnetic field is set to 30° or 150°, while the butterfly wings angle or vertex angle is kept at a maximum of 120°. The intensity of the magnetic field significantly controls the heat flow dynamics, with higher magnetic field strength causing a reduction in the flow strength as well as heat transfer. This configuration optimizes the heat transfer characteristics in the system.

Further research can be expanded on this study by examining thermal performance under different curvature effects, orientations, boundary conditions and additional factors. This can be accomplished through numerical simulations or experimental investigations under various multiphysical scenarios.

The geometric configurations explored in this research have practical applications in various engineering fields, including heat exchangers, crystallization processes, microelectronic devices, energy storage systems, mixing processes, food processing, air-conditioning, filtration and more.

This study brings value by exploring a novel geometric configuration comprising the nanofluidic flow, and MHD effect, providing insights and potential innovations in the field of thermal fluid dynamics. The findings contribute a lot toward maximizing thermal performance in diverse fields of applications. The comparison of different hydrothermal behavior and thermodynamic entropy production under the varying geometric configuration adds novelty to this study.

Generally, in computational thermofluid dynamics, the thermophysical properties of fluids (e.g. viscosity and thermal conductivity) are considered as constant. However, in many applications, the variability of these properties plays a significant role in modifying transport characteristics while the temperature difference in the boundary layer is notable. These include drag reduction in heavy oil transport systems, petroleum purification and coating manufacturing. The purpose of this study is to develop, a comprehensive mathematical model, motivated by the last of these applications, to explore the impact of variable viscosity and variable thermal conductivity characteristics in magnetohydrodynamic non-Newtonian nanofluid enrobing boundary layer flow over a horizontal circular cylinder in the presence of cross-diffusion (Soret and Dufour effects) and appreciable thermal radiative heat transfer under a static radial magnetic field.

The Williamson pseudoplastic model is deployed for rheology of the nanofluid. Buongiorno’s two-component model is used for nanoscale effects. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. Extensive validation with earlier studies in the absence of nanoscale and variable property effects is included.

The influence of notable parameters such as Weissenberg number, variable viscosity, variable thermal conductivity, Soret and Dufour numbers on heat, mass and momentum characteristics are scrutinized and visualized via graphs and tables.

Buongiorno (two-phase) nanofluid model is used to express the momentum, energy and concentration equations with the following assumptions. The laminar, steady, incompressible, free convective flow of Williamson nanofluid is considered. The body force is implemented in the momentum equation. The induced magnetic field strength is smaller than the external magnetic field and hence it is neglected. The Soret and Dufour effects are taken into consideration.

The variable viscosity and thermal conductivity are considered to investigate the fluid characteristic of Williamson nanofluid because of viscosity and thermal conductivity have a prime role in many industries such as petroleum refinement, food and beverages, petrochemical, coating manufacturing, power and environment.

This fluid model displays exact rheological characteristics of bio-fluids and industrial fluids, for instance, blood, polymer melts/solutions, nail polish, paint, ketchup and whipped cream.

The outcomes disclose that the Williamson nanofluid velocity declines by enhancing the Lorentz hydromagnetic force in the radial direction. Thermal and nanoparticle concentration boundary layer thickness is enhanced with greater streamwise coordinate values. An increase in Dufour number or a decrease in Soret number slightly enhances the nanofluid temperature and thickens the thermal boundary layer. Flow deceleration is induced with greater viscosity parameter. Nanofluid temperature is elevated with greater Weissenberg number and thermophoresis nanoscale parameter.

To amend the efficiency of engineering processes and electronic devices, it is very urgent to assess the irreversibility in the term entropy generation (EG). The efficiency of energy transportation in a system can be improved by minimization of the rate of EG. In this context, the aim of the present study is to estimate irreversible losses of an unsteady magnetohydrodynamic (MHD) flow of a viscous incompressible electrically conducting non-Newtonian molybdenum disulfide-polyethylene glycol Casson nanofluid past a moving vertical plate with slip condition under the influence of Hall current, thermal radiation, internal heat generation/absorption and first-order chemical reaction. Molybdenum disulfide (MoS₂) nanoparticles are dispersed in the base fluid polyethylene glycol (PEG) to make Casson nanofluid. Casson fluid model is considered to characterize the rheology of the non-Newtonian fluid, whereas Rosseland approximation is adopted to simulate the thermal radiative heat flux in the energy equation.

The closed-form solutions are obtained for the model equations by using the Laplace transform method (LTM). Graphs and tables are prepared to examine the impact of pertinent flow parameters on the pertinent flow characteristics. The energy efficiency of the system via the Bejan number is studied extensively.

Analysis reveals that Hall current has diminishing behavior on entropy production of the thermal system. Strengthening of the magnetic field declines the velocity components and prop-ups the rate of EG. Adding nanoparticles into the base fluid reduces the EG, whereas there are an optimum volume fraction of nanoparticles for which the EG is minimized. Further, the rate of decay of EG is prominent in molybdenum disulfide-polyethylene glycol in comparison to PEG.

The results of this study would benefit the industrial sector in achieving the maximum heat transfer at the cost of minimum irreversibilities with an optimal choice of embedded thermophysical parameters. In view of this agenda, this study would be adjuvant in powder technology, polymer dynamics, metallurgical process, manufacturing dynamics of nano-polymers, petroleum industries, chemical industries, magnetic field control of material processing, synthesis of smart polymers, etc.

The novelty of this study is to encompass the analytical solution by using the LTM. Such an exact solution of non-Newtonian fluid flow is rare in the literature. Limited research articles are available in the field of EG analysis during the flow of non-Newtonian nanoliquid subject to a strong magnetic field.

The purpose of this paper is to review the available reduced order modeling approaches in the literature for predicting the flow and specially temperature fields inside data centers in terms of the involved design parameters.

This paper begins with a motivation for flow/thermal modeling needs for designing an energy‐efficient thermal management system in data centers. Recent studies on air velocity and temperature field simulations in data centers through computational fluid dynamics/heat transfer (CFD/HT) are reviewed. Meta‐modeling and reduced order modeling are tools to generate accurate and rapid surrogate models for a complex system. These tools, with a focus on low‐dimensional models of turbulent flows are reviewed. Reduced order modeling techniques based on turbulent coherent structures identification, in particular the proper orthogonal decomposition (POD) are explained and reviewed in more details. Then, the available approaches for rapid thermal modeling of data centers are reviewed. Finally, recent studies on generating POD‐based reduced order thermal models of data centers are reviewed and representative results are presented and compared for a case study.

It is concluded that low‐dimensional models are needed in order to predict the multi‐parameter dependent thermal behavior of data centers accurately and rapidly for design and control purposes. POD‐based techniques have shown great approximation for multi‐parameter thermal modeling of data centers. It is believed that wavelet‐based techniques due to the their ability to separate between coherent and incoherent structures – something that POD cannot do – can be considered as new promising tools for reduced order thermal modeling of complex electronic systems such as data centers

The paper reviews different numerical methods and provides the reader with some insight for reduced order thermal modeling of complex convective systems such as data centers.

Despite discussions about the universal work station, there is increasing workplace dynamics in US organisations. These dynamics include space configuration changes, space enclosure changes, changes in occupant density and increasing equipment density. At the same time, building infrastructures have not evolved to meet these demands, with little flexibility in the heating, ventilation and air‐conditioning (HVAC), lighting, or electrical/telecommunication systems of new or existing office buildings. This paper examines the effects of organisational workplace dynamics and building infrastructure flexibility on the environmental and technical quality of offices. Resulting from extensive field studies in US buildings, the authors contend that there are numerous statistically significant issues for the design and management of buildings for the dynamic organisation. The study identified numerous factors that affect thermal, air, lighting and technical quality in offices. In relation to infrastructure, for example, occupants who work in office areas provided with greater cooling capacity and more supply air volume, and combined with smaller HVAC zones, appeared to have higher levels of thermal satisfaction. Those who work in areas with higher outlet densities gave higher technical quality ratings; and those provided with relocatable outlets (raised floor and furniture based) gave significantly higher technical satisfaction ratings than those provided with least‐first‐cost ‘tombstones’. In relation to organisational dynamics, increasing occupant densities in existing buildings are related to more thermal and air quality complaints, more complaints about outlet accessibility, as well as more complaints about inadequate light levels on work surfaces. This paper will outline the major findings of a study linking organisational dynamics with building infrastructure, moving towards the definition of innovations in facility design that will more effectively support dynamic organisations.