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This study aims to understand the difference between irreversibility in heat and work transfer processes. It also aims to explain that Helmholtz or Gibbs energy does not represent “free” energy but is a measure of loss of Carnot (reversible) work opportunity.

The entropy of mass is described as the net temperature-standardised heat transfer to mass under ideal conditions measured from a datum value. An expression for the “irreversibility” is derived in terms of work loss (W_loss) in a work transfer process, unaccounted heat dissipation (Q_loss) in a heat transfer process and loss of net Carnot work (CW_net) opportunity resulting from spontaneous heat transfer across a finite temperature difference during the process. The thermal irreversibility is attributed to not exploiting the capability for extracting work by interposing a combination of Carnot engine(s) and/or Carnot heat pump(s) that exchanges heat with the surrounding and operates across the finite temperature difference.

It is shown, with an example, how the contribution of thermal irreversibility, in estimating reversible input work, amounts to a loss of an opportunity to generate the net work output. The opportunity is created by exchanging heat with surroundings whilst transferring the same amount of heat across finite temperature difference. An entropy change is determined with a numerical simulation, including calculation of local entropy generation values, and results are compared with estimates based on an analytical expression.

A new interpretation of entropy combined with an enhanced mental image of a combination of Carnot engine(s) and/or Carnot heat pump(s) is used to quantify thermal irreversibility.

Heat transfer across the metal‐mould interface has been modelled by a generalized equation referred to as the Lewis‐Ransing Correlation. It has been shown that the spatial as well as temporal variation of the interfacial heat transfer coefficient can be optimally designed to achieve a desired solidification pattern. The technique has been validated on two practical examples achieving a complex solidification pattern.

Over the past 20 years, casting process simulation has been an active area of research. The simulation techniques are either based on solving governing partial differential equations using numerical schemes such as the finite element or finite difference methods, or a variety of heuristically based geometry driven methods. Numerical methods are more accurate, but geometry driven methods are computationally less expensive. This paper explores two alternative techniques to overcome some of the limitations of traditional numerical simulation schemes for the casting process simulation. The first technique uses a geometric transformation method known as the medial axis transformation, to predict hot spots whereas the second technique, based on meshless methods, is used for simulating the mould filling process.

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.

A porous cavity flow field generates entropy owing to energy and momentum exchange within the fluid and at solid barriers. The heat transport and viscosity effects on fluid and solid walls irreversibly generate entropy. This numerical study aims to investigate convective heat transfer together with entropy generation in a partially heated wavy porous cavity filled with a hybrid nanofluid.

The governing equations are nondimensionalized and the domain is transformed into a unit square. A second-order finite difference method is used to have numerical solutions to nondimensional unknowns such as stream function and temperature. This numerical computation is conducted to explore a wide range of regulating parameters, e.g. hybrid nano-particle volume fraction (σ = 0.1%, 0.33%, 0.75%, 1%, 2%), Rayleigh–Darcy number (Ra = 10, 10², 10³), dimensionless length of the heat source (ϵ = 0.25, 0.50,1.0) and amplitude of the wave (a = 0.05, 0.10, 0.15) for a number of undulations (N = 1, 3) per unit length.

A thorough analysis is conducted to analyze the effect of multiple factors such as thermal convective forces, heat source, surface corrugation factors, nanofluid volume fraction and other parameters on entropy generation. The flow and temperature fields are studied through streamlines and isotherms. The average Bejan number suggested that entropy generation is entirely dominated by irreversibility due to heat transport at Ra = 10, and the irreversibility due to the viscosity effect is severe at Ra = 10³, but the increment in s augments irreversibility due to the viscosity effect over the heat transport at Ra = 10².

To the best of the authors’ knowledge, this numerical study, for the first time, analyzes the influence of surface corrugation on the entropy generation related to the cooling of a partial heat source by the convection of a hybrid nanofluid.

There is increasing interest in the connection between Industry 4.0 (I4.0) and operational excellence approaches; however, studies on the integration between Six Sigma (SS) and I4.0 have been absent from the literature. Integration with I4.0 technologies can maximize the positive effects of SS. The purpose of this study is to understand what types of relationships exist between SS and I4.0 and with I4.0's technologies, as well as the benefits derived from this integration and future directions for this field of study.

A Systematic Literature Review (SLR) was carried out to analyze studies about connections between I4.0 technologies and SS. SLR analyzed 59 articles from 2013 to 2021 extracted from the Web of Science and Scopus databases, including documents from journals and conferences.

The SLR identified relationships between SS and several I4.0 technologies, the most cited and with the greatest possibilities of relationships being Big Data/Big Data Analytics (BDA) and Internet of Things (IoT). Three main types of relationships were identified: (1) support of I4.0 technologies to SS; (2) assistance from the SS to the introduction of I4.0 technologies, and, to a lesser extent; (3) incompatibilities between SS and I4.0 technologies. The benefits are mainly related to availability of large data sets and real-time information, enabling better decision-making in less time.

In addition, the study can help managers to understand the integration relationships, which may encourage companies to adopt SS/Lean Six Sigma (LSS) in conjunction with I4.0 technologies. The results also drew attention to the incompatibilities between SS and I4.0 to anticipate potential barriers to implementation.

The study focuses on three previously unexplored subjects: the connection between SS and I4.0, the existing relationships with different technologies and the benefits resulting from the relationships. In addition, the study compiled and structured different types of relationships for SS and I4.0 and I4.0's technologies, identifying patterns and presenting evidence on how these relationships occur. Finally, exposes current trends and possible research directions.

The purpose of this paper is to study haemodynamic flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, magnetohydrodynamic (MHD) flow and aneurysm conditions. The findings of this study offer significant insights into the intricate interplay encompassing electro-osmosis, MHD flow, microorganisms, Joule heating and the ternary hybrid nanofluid.

The governing equations are first non-dimensionalised, and subsequently, a coordinate transformation is used to regularise the irregular boundaries. The discretisation of the governing equations is accomplished by using the Crank–Nicolson scheme. Furthermore, the tri-diagonal matrix algorithm is applied to solve the resulting matrix arising from the discretisation.

The investigation reveals that the velocity profile experiences enhancement with an increase in the Debye–Hückel parameter, whereas the magnetic field parameter exhibits the opposite effect, reducing the velocity profile. A comparative study demonstrates the velocity distribution in Au-CuO hybrid nanofluid and Au-CuO-GO ternary hybrid nanofluid. The results indicate a notable enhancement in velocity for the ternary hybrid nanofluid compared to the hybrid nanofluids. Moreover, an increase in the Brinkmann number results in an augmentation in entropy generation.

This study investigates the flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, MHD flow and aneurysm conditions. The governing equations are non-dimensionalised, and a coordinate transformation is applied to regularise the irregular boundaries. The Crank–Nicolson scheme is used to model blood flow in the presence of a ternary hybrid nanofluid (Au-CuO-GO/blood) within the arterial domain. The findings shed light on the complex interactions involving stenosis, MHD flow, aneurysms, Joule heating and the ternary hybrid nanofluid. The results indicate a decrease in the wall shear stress (WSS) profile with increasing stenosis size. The MHD effects are observed to influence the velocity distribution, as the velocity profile exhibits a declining nature with an increase in the Hartmann number. In addition, entropy generation increases with an enhancement in the Brinkmann number. This research contributes to understanding fluid dynamics and heat transfer mechanisms in bifurcated arteries, providing valuable insights for diagnosing and treating cardiovascular diseases.

This final chapter draws together the key findings presented in the preceding pages and considers emergent conclusions and implications for mental health and wellbeing in schools. The author draws upon the evidence presented by the book’s eclectic range of contributors and the health promoting schools’ (HPSs) framework to provide a road map of what an effective whole school approach (WSA) might look like moving forward. Crucially, lessons from recent crises in education, including COVID-19-driven changes in pathways to support, are highlighted as pivotal factors in a future vision which sees schools as an effective and sustainable frontline force to help tackle the global burden of child and adolescent mental health through a proactive, preventive stance. With this future focus in mind, next steps are considered in terms of developing effective and sustainable mental health and wellbeing support for all within healthy school settings.