Constructal theory of global circulation and climate

The constructal law states that every flow system evolves in time so that it develops the flow architecture that maximizes flow access under the constraints posed to the flow. Earlier applications of the constructal law recommended it as a self-standing law that is distinct from the second law of thermodynamics. In this paper, we develop a model of heat transport on the earth surface that accounts for the solar and terrestrial radiation as the heat source and heat sink and with natural convection loops as the transport mechanism. In the first part of the paper, the constructal law is invoked to optimize the latitude of the boundary between the Hadley and the Ferrel cells, and the boundary between the Ferrel and the Polar cells. The average temperature of the earth surface, the convective conductance in the horizontal direction as well as other parameters defining the latitudinal circulation also match the observed values. In the second part of the paper, the constructal law is invoked in the analysis of atmospheric circulation at the diurnal scale. Here the heat transport is optimized against the Ekman number. Even though this second optimization is based on very different variables than in the first part of the paper, it produces practically the same results for the earth surface temperature and the other variables. The earth averaged temperature difference between day and night was found to be approximately 7 K, which matches the observed value. The accumulation of coincidences between theoretical predictions and natural flow configuration adds weight to the claim that the constructal law is a law of nature

Heat transfer and second law analyses of forced convection in a channel partially filled by porous media and featuring internal heat sources

This paper provides a comprehensive study on the heat transfer and entropy generation rates in a channel partially filled with a porous medium and under constant wall heat flux. The porous inserts are attached to the walls of the channel and the system features internal heat sources due to exothermic or endothermic physical or physicochemical processes. Darcy-Brinkman model is used for modelling the transport of momentum and an analytical study on the basis of LTNE (local thermal non-equilibrium) condition is conducted. Further analysis through considering the simplifying, LTE (local thermal equilibrium) model is also presented. Analytical solutions are, first, developed for the velocity and temperature fields. These are subsequently incorporated into the fundamental equations of entropy generation and both local and total entropy generation rates are investigated for a number of cases. It is argued that, comparing with LTE, the LTNE approach yields more accurate results on the temperature distribution within the system and therefore reveals more realistic Nusselt number and entropy generation rates. In keeping with the previous investigations, bifurcation phenomena are observed in the temperature field and rates of entropy generation. It is, further, demonstrated that partial filling of the channel leads to a substantial reduction of the total entropy generation. The results also show that the exothermicity or endothermicity characteristics of the system have significant impacts on the temperature fields, Nusselt number and entropy generation rates

Numerical analysis of conservative unstructured discretisations for low Mach flows

This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. https://authorservices.wiley.com/author-resources/Journal-Authors/licensing-and-open-access/open-access/self-archiving.htmlUnstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions. However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors. An assessment of a low-Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell centred velocity reconstructions the standard first-order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm. Regarding collocated discretisations, the odd-even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable-density flows. Besides, different face interpolations schemes for unstructured meshes are analysed. A kinetic energy preserving scheme is applied to the momentum equations, namely the Symmetry-Preserving (SP) scheme. Furthermore, a new approach to define the far-neighbouring nodes of the QUICK scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not. The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self-igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable-density flows. Furthermore, the QUICK schemes shows close to second order behaviour on unstructured meshes and the SP is reliably used in all computations.Peer ReviewedPostprint (author's final draft

“Constructal Theory: From Engineering to Physics, and How Flow Systems Develop Shape and Structure”

Constructal theory and its applications to various fields ranging from engineering to natural living and inanimate systems, and to social organization and economics, are reviewed in this paper. The constructal law states that if a system has freedom to morph it develops in time the flow architecture that provides easier access to the currents that flow through it. It is shown how constructal theory provides a unifying picture for the development of flow architectures in systems with internal flows (e.g., mass, heat, electricity, goods, and people). Early and recent works on constructal theory by various authors covering the fields of heat and mass transfer in engineered systems, inanimate flow structures (river basins, global circulations) living structures, social organization, and economics are reviewed. The relation between the constructal law and the thermodynamic optimization method of entropy generation minimization is outlined. The constructal law is a self-standing principle, which is distinct from the Second Law of Thermodynamics. The place of the constructal law among other fundamental principles, such as the Second Law, the principle of least action and the principles of symmetry and invariance is also presented. The review ends with the epistemological and philosophical implications of the constructal law

Generation of entropy and forced convection of heat in a conduit partially filled with porous media- Local thermal non-equilibrium and exothermicity effects applied thermal engineering

The performance of a two-dimensional, axisymmetric channel with porous inserts attached to the walls is analyzed from the perspective of the first and second laws of thermodynamics. In this analysis, the flow is assumed to be fully developed with a constant heat flux imposed on the external surfaces of the walls, while heat could be internally generated by the fluid and solid phases. Using a Darcy-Brinkman model of momentum transport along with a two-equation thermal energy model, a convective model was developed to describe the thermal boundary conditions on the porous-fluid interface. The so-called Model A was employed on the walls of the channel and semi-analytical solutions were developed for the hydrodynamic, temperature, entropy generation fields and the Nusselt number, and an extensive parametric study was subsequently, conducted. The results indicated that the inclusion of exothermicity leads to significant modifications in the thermal and entropic behaviour of the system. In particular, through comparison with the recent literature, it was demonstrated that exothermicity can significantly impact the influence of the porous-fluid interface model upon the generation of both the local and total entropy within the system