Tanmay Basak

Present work investigates multiple steady states for mixed convection of fluids within a trapezoidal enclosure involving sliding top lid and Rayleigh–Benard thermal setup. A novel sequence of initiation and continuation schemes involving multiple perturbations has been designed to determine the spectrum of steady states as a function of the Grashof number (Gr) for various Prandtl and Reynolds numbers (Pr=0.7 and 10, Re=1 and 100). The computations are based on steady-state governing equations, and Galerkin finite element method with penalty formulation has been used to solve the equations at various steps of the computation. Current results show that a rich spectrum of steady states do exist for each of the cases. Multiple steady states are found to exist in the natural convection dominant flow regime for Re=1 (slow moving lid) and also for Re=100 in the case of Pr=0.7. On the other hand, multiple steady states are found to exist in the mixed convection zone for Re=100 in the case of Pr=10. The rigorous initiation scheme reveals the co-existence of five steady states at a given Gr for Pr=0.7 and co-existence of up to thirteen (Re=1) or eleven (Re=100) steady states for Pr=10. The regions of the existence of various steady states have been identified via the bifurcation diagrams. Different types of flow structures associated with the steady states and their effect on the thermal characteristics have been illustrated.

Pyrolysis, a process for extracting valuable chemicals from waste materials, leverages computational fluid dynamics (CFD) to optimize reactor parameters, thereby enhancing product quality and process efficiency. This review aims to understand the application of CFD in pyrolysis. Initially, the need for pyrolysis and its role in biomass valorization are discussed, and this is followed by an elaboration of the fundamentals of CFD studies in terms of their application to the pyrolysis process. The various CFD simulations and models used to understand product formation are also explained. Pyrolysis is conducted using both conventional and microwave-assisted pyrolysis platforms. Hence, the reaction kinetics, governing model equations, and laws are discussed in the conventional pyrolysis section. In the microwave-assisted pyrolysis section, the importance of wavelength, penetration depth, and microwave conversion efficiencies on the CFD are discussed. This review provides valuable insights to academic researchers on the application of CFD in pyrolysis systems. The modeling of pyrolysis by computational fluid dynamics (CFD) is a complex process due to the implementation of multiple reaction kinetics and physics, high computational cost, and reactor design. These challenges in the modeling of the pyrolysis process are discussed in this paper. Significant solutions that have been used to overcome the challenges are also provided with potential areas of research and development in the future of CFD in pyrolysis.

A few earlier studies presented infeasible heatline trajectories for natural convection within annular domains involving an inner circular cylinder and outer square/circular enclosure. The purpose of this paper is to revisit and illustrate the correct heatline trajectories for various test cases. Galerkin finite element based methodology and space adaptive grid have been used to simulate natural convective flows within the annular domains. The prediction of heatlines involves derivatives at the nodes, which are evaluated based on finite element basis functions and contributions from neighboring elements. The heatlines in the earlier work indicate infeasible heat flow paths such as heat flow from one portion to the other of isothermal hot walls and heat flow across the adiabatic walls. Current results illustrate physically consistent heat flow paths involving perpendicularly emerging heatlines from hot to cold walls for conductive transport, long heat flow paths around the closed-loop heatline cells for convective transport and parallel layout of heatlines to the adiabatic walls. Results also demonstrate complex heatlines involving multiple flow vortices and complex flow structures. Current work translates heatfunctions from energy flux vectors, which are determined by using basis sets. This work demonstrates the expected heatline trajectories for various scenarios involving conductive and convective heat transport within enclosures with an inner hot object as a first attempt, and the results are precursors for the understanding of energy flow estimates.

The tool “Heatlines” is useful to understand heat flow and thermal management in enclosures experiencing convection. The heatline concept was first introduced by Bejan in the early 80’s. This article starts with the fundamental principles of heatlines or heat flow trajectories followed by a generalized governing equation for heatfunction (Π) applicable for fluid, nanofluid, or fluid-saturated porous medium experiencing steady natural or mixed convection within enclosures. An unified approach on derivation of heatfunction boundary conditions is presented based on Dirichlet conditions at junction of walls while Neumann conditions at walls for Π. The solution of Π also requires the selection of location of Π = 0 and this article outlines a generalized overview on the invariance of heatline trajectories irrespective of the location of Π = 0 for enclosures with or without adiabatic walls. Open loop or end to end heatlines demonstrate the heat flow path for conductive heat transport whereas open loop heatlines cross various regimes of dominant conduction or convection zones connecting the hot walls to the cold walls for convective heat transport. Closed loop heatline vortices (qualitatively similar to the flow vortices) depict the convective heat flow via the trajectories of the fluid flow vortices. A few feasible heatlines for conduction and convection dominant heat transport in enclosures (steady state) have been presented to illustrate the physics of “heatlines.” This article also addresses a few earlier works depicting discrepancies in heatline trajectories [discrepancies: heat flow to and from the same walls (isothermally hot/cold or adiabatic) or heat flow from the hot/cold to the adiabatic wall(s)] and proposes qualitative pictures for feasible heatlines for a few earlier case studies. Understanding the feasible implementation of heatlines is required as the inaccurate representation of heatlines may mislead future researchers in interpreting the energy flow.

Current work involves entropy generation studies within nine porous containers involving identical area for Prm = 155 (engine oil), Dam=10−5−10−2 at Ram=106. The entropy generation maps for lesser values of Dam depict that Sθ is dominant at the boundaries whereas Sψ is dominant at the central zone. On the other hand, for larger values of Dam, Sψ is found to be dominant throughout the porous containers. Zones corresponding to Sθ,max are found at the bottom corners of all porous containers due to the hot cold junction whereas zones corresponding to Sψ,max vary with the shapes of porous containers. An energy efficient process corresponds to larger Nub¯, larger θ̂ and lesser Stotal. Containers with curved walls are found to be thermally efficient for thermal processing of engine oil saturated porous medium.

Purpose: The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed. Design/methodology/approach: This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities. Findings: Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers. Originality/value: This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.