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The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the bottom wall (isothermal/sinusoidal heating). Containers are categorized into three classes based on geometric configurations [Class 1 (square, tilted square and parallelogram), Class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and Class 3 (convex, concave and triangle with curved hypotenuse)].

The governing equations are solved by using the Galerkin finite element method for various processing fluids (Pr = 0.025 and 155) and Rayleigh numbers (10³ ≤ Ra ≤ 10⁵) involving nine different containers. Finite element-based heat flow visualization via heatlines has been adopted to study heat distribution at various sections. Average Nusselt number at the bottom wall ( Nub¯) and spatially average temperature (θ^) have also been calculated based on finite element basis functions.

Based on enhanced heating criteria (higher Nub¯ and higher θ^), the containers are preferred as follows, Class 1: square and parallelogram, Class 2: trapezoidal type 1 and trapezoidal type 2 and Class 3: convex (higher θ^) and concave (higher Nub¯).

The comparison of heat flow distributions and isotherms in nine containers gives a clear perspective for choosing appropriate containers at various process parameters (Pr and Ra). The results for current work may be useful to obtain enhancement of the thermal processing rate in various process industries.

Heatlines provide a complete understanding of heat flow path and heat distribution within nine containers. Various cold zones and thermal mixing zones have been highlighted and these zones are found to be altered with various shapes of containers. The importance of containers with curved walls for enhanced thermal processing rate is clearly established.

The purpose of this paper is to study the kinetics of static recovery in cold-rolled aluminum alloy under different heating rates.

Deformation modeling was first performed to assess the distributions of plastic strain and stress within the deformed alloy. In the next stage, thermal analysis and the rate equation of static recovery were employed to determine the progress of static recovery under non-isothermal conditions. Accordingly, a thermal finite element analysis and the Runge-Kutta method were utilized to handle the transient heat conduction and the progress of static recovery. Finally, low temperature annealing heat treatments were conducted to verify the model predictions. Accordingly, the tensile tests were conducted to measure the yield stresses of cold-rolled plates subjected to the subsequent annealing treatment at different temperatures and durations.

The results indicate that the employed algorithm can be used as an appropriate predictive tool for designing a low temperature heat treatment schedule to achieve the desired yield stress.

The kinetics of non-isothermal recovery and resulting yield stress are well predicted under practical annealing conditions.

This paper aims to focus on linear and non-linear convection in a lid-driven square cavity with isothermal and non-isothermal bottom surface.

It is assumed that the top moving wall is adiabatic and the bottom wall is heated in two modes, and the rest of the walls are maintained at uniform cold temperature. The coupled governing non-linear partial differential equations are solved numerically with MAC algorithm for conducting a parametric study with uniform and non-uniform temperature bottom wall.

The numerical results are depicted in the form of streamlines, temperature contours and variation of local Nusselt number. The local Nusselt number at the bottom wall of the cavity increases in presence of non-linear temperature parameter as compared with linear temperature parameter and heat transfer reduces with increasing of Ha for uniform and non-uniform heating of bottom wall.

The numerical investigation is conducted for unsteady, two-dimensional natural convective flow in a square cavity. An extension of the present study with the effect of inclination of cavity, wavy walls and triangular cavity will be the interest of future work.

This work studies the effect of magnetic field in the presence of linear convection and non-linear convection. This study might be useful to cooling of electronic components, alloy casting, crystal growth and fusion reactors, etc.

This study aims to develop mathematical models for the determination of the effects of heating or cooling on neck growth in Selective Laser Sintering (SLS) and Fused Filament Fabrication (FFF). Two particle shapes are studied: spherical and cylindrical.

The time required for the coalescence (sintering) process is determined by balancing the work of surface tension forces and viscous dissipation. Heating and cooling effects are studied by incorporating temperature dependence of viscosity in an exponential form. Heating by a laser, convective and/or radiative heat transfer is assumed. It is also assumed that there are no temperature gradients within the coalescing molten polymers (lumped parameter heat transfer analysis).

The models predict faster sintering with heating and slower with cooling, as expected because of the effect of temperature on viscosity. For the isothermal case of pairs of cylinders, the present model predicts significantly longer time for completion of sintering than a previously developed and frequently cited model by Hopper.

An isothermal sintering model for two spheres was reworked for two long cylinders, and for the first time it has been compared to other models available in the literature. The mathematical models are capable of predicting neck growth under non-isothermal conditions for both spheres and cylinders. They are useful in assessment of bonding in selective laser sintering and fused deposition fabrication.

The purpose of this paper is to study the non-isothermal degradation kinetics of recycled polybutylene terephthalate, polytrimethylene terephthalate and polyethylene terephthalate using thermogravimetric analysis (TGA) in a nitrogen atmosphere.

To achieve this goal, the author utilized standard kinetic models, such as Coats-Redfern and Kissinger equations, for analysis of the TGA data.

When applied to the TGA data, the Kissinger model resulted in a coefficient of determination (R2) value greater than 0.99.

This study describes the maiden application of the Kissinger model to obtain the pre-exponential factor (A) and activation energy (E) for different polyester systems used in the textile industry.

This paper aims to investigate the role of shapes of containers (nine different containers) on entropy generation minimization involving identical cross-sectional area (1 sq. unit) in the presence of identical heating (isothermal). The nine containers are categorized into three classes based on their geometric similarities (Class 1: square, tilted square and parallelogram; Class 2: trapezoidal type 1, trapezoidal type 2 and triangular; Class 3: convex, concave and curved triangular).

Galerkin finite element method is used to solve the governing equations for a representative fluid (engine oil: Pr = 155) at Ra = 10³–10⁵. In addition, finite element method is used to solve the streamfunction equation and evaluate the entropy generation terms (S_ψ and S_θ). Average Nusselt number ( Nub¯) and average dimensionless spatial temperature ( θ^) are also evaluated via the finite element basis sets.

Based on larger Nub¯, larger θ^ and optimal S_total values, containers from each class are preferred as follows: Class 1: parallelogrammic and square, Class 2: trapezoidal type 1 and Class 3: convex (larger θ^, optimum S_total) and concave (larger Nub¯). Containers with curved walls lead to enhance the thermal performance or efficiency of convection processes.

Comparison of entropy generation, intensity of thermal mixing ( θ^) and average heat transfer rate give a clear picture for choosing the appropriate containers for processing of fluids at various ranges of Ra. The results based on this study may be useful to select a container (belonging to a specific class or containers with curved or plane walls), which can give optimal thermal performance from the given heat input, thereby leading to energy savings.

This study depicts that entropy generation associated with the convection process can be reduced via altering the shapes of containers to improve the thermal performance or efficiency for processing of identical mass with identical heat input. The comparative study of nine containers elucidates that the values of local maxima of S_ψ (S_ψ,max), S_θ (S_θ,max) and magnitude of S_total vary with change in shapes of the containers (Classes 1–3) at fixed Pr and Ra. Such a comparative study based on entropy generation minimization on optimal heating during convection of fluid is yet to appear in the literature. The outcome of this study depicts that containers with curved walls are instrumental to optimize entropy generation with reasonable thermal processing rates.

This paper aims to develop a numerical model of bead spreading architecture of a viscous polymer in fused filament fabrication (FFF) process with different nozzle geometry. This paper also focuses on the manufacturing feasibility of the nozzles and 3D printing of the molten beads using the developed nozzles.

The flow of a highly viscous polymer from a nozzle, the melt expansion in free space and the deposition of the melt on a moving platform are captured using the FLUENT volume of fluid (VOF) method based computational fluid dynamics code. The free surface motion of the material is captured in VOF, which is governed by the hydrodynamics of the two-phase flow. The phases involved in the numerical model are liquid polymer and air. A laminar, non-Newtonian and non-isothermal flow is assumed. Under such assumptions, the spreading characteristic of the polymer is simulated with different nozzle-exit geometries. The governing equations are solved on a regular stationary grid following a transient algorithm, where the boundary between the polymer and the air is tracked by piecewise linear interface construction (PLIC) to reconstruct the free surface. The prototype nozzles were also manufactured, and the deposition of the molten beads on a flatbed was performed using a commercial 3D printer. The deposited bead cross-sections were examined through optical microscopic examination, and the cross-sectional profiles were compared with those obtained in the numerical simulations.

The numerical model successfully predicted the spreading characteristics and the cross-sectional shape of the extruded bead. The cross-sectional shape of the bead varied from elliptical (with circular nozzle) to trapezoidal (with square and star nozzles) where the top and bottom surfaces are significantly flattened (which is desirable to reduce the void spaces in the cross-section). The numerical model yielded a good approximation of the bead cross-section, capturing most of the geometric features of the bead with a reasonable qualitative agreement compared to the experiment. The quantitative comparison of the cross-sectional profiles against experimental observation also indicated a favorable agreement. The significant improvement observed in the bead cross-section with the square and star nozzles is the flattening of the surfaces.

The developed numerical algorithm attempts to address the fundamental challenge of voids and bonding in the FFF process. It presents a new approach to increase the inter-bead bonding and reduce the inter-bead voids in 3D printing of polymers by modifying the bead cross-sectional shape through the modification of nozzle exit-geometry. The change in bead cross-sectional shape from elliptical (circular) to trapezoidal (square and star) cross-section is supposed to increase the contact surface area and inter-bead bonding while in contact with adjacent beads.

The purpose of this paper is to evaluate the fire resistance of an innovative carbon-reinforced PEKK composite for aeronautical applications. To this end, thermal degradation analysis under inert and oxidative atmosphere is carried out. Moreover, a linear model fitting approach is compared to a generally used isoconversional method to validate its reliability for kinetic triplet estimation.

Thermogravimetric analysis carried out under inert and oxidative atmospheres, between 25 and 1000°C for three different heating rates (5, 15, 25°C/min), followed by a qualitative SEM observation of the samples before and after thermal treatment. After the reaction identification by TG/DTG curves, an isoconversional analysis is carried out to estimate the activation energy as a function of the reaction conversion rate. For the identified reactions, the kinetic triplet is estimated by different methods and the results are compared to evaluate their reliability.

In inert case, one global reaction, observed between 500-700°C, seems able to describe the degradation of carbon-PEKK resin. Under oxidative atmosphere, three main reactions are identified, besides the resin degradation, the other two are attributed to char and fiber oxidation. Good agreement achieved between isoconversional and linear model fitting methods in activation energy calculation. The achieved results demonstrate the high thermal resistance of PEKK associated with the ether and ketone bonds between the three aromatic groups of its monomer.

This paper provides a possible degradation model useful for numerical implementation in CFD calculations for aircraft components design, when exposed to high temperatures and fire conditions.

The purpose of this work is to study the effect of surface-radiation on the phenomenon of natural convection flow of a Newtonian fluid in a non-Darcian porous media cavity. The study is mainly focused on the interaction between the inertial resistance of the fluid layers and the surface radiation.

For numerical simulation of transient vorticity transport and energy equations, the paper uses the alternate direct implicit method. Forward Time Central Space descretization is used for the transient and diffusion terms in the alternate direct implicit method, whereas for the convective terms, the method is modified using second upwind differencing technique. ADI method is adopted here, since this technique is unconditionally stable as a complete sweep and is second-order accurate in time for low velocity changes. The stream function equation is solved using the successive over relaxation technique with residual tolerance of order 10-5.

It was found that despite the reduction of flow, the heat transfer increases as the Forschheimer resistance is increased. Further, with the increase in the Planck number, the heat transfer from the bottom radiating wall increases. Darcy drag parameter did not have a significant impact on flow properties except a slight reduction in the flow. Nevertheless, the increase in temperature ratio has a significant impact on flow properties.

The analysis is valid for unsteady, two-dimensional natural convection flow in a fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls. As a first case, the study is conducted for square cavity. An extension to three-dimensional flow case and the study of Darcy-Forschheimer medium with effect of viscous dissipation is left as a part of future work.

The approach is applicable to the modeling of geothermal systems where the inertial resistance to flow also comes into act with the non-uniform temperature distribution. The method is very useful to analyze solar receiver systems, fire research, electronic cooling, brake housing of an aircraft and many environmental geothermal processes.

The study may be of some interest to engineers interested in heat transfer in ventilated rooms or enclosures, the industrial waste, water and atmospheric pollution.

The purpose of this paper is to analyze the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall.

Brinkmann-extended Darcy model is used to simulate the momentum transfer in the porous medium. The Boussinesq approximation is invoked to account for the variation in density arising out of the temperature differential for the porous quadrantal enclosure subjected to uniform heating on the bottom wall. The governing transport equations are solved using the finite element method. A parametric study is carried out for the Rayleigh number (Ra) in the range of 10³ to 10⁶ and Darcy number (Da) in the range of 10⁻⁵-10⁻².

A complex interaction between the buoyant and viscous forces that govern the transport of heat and entropy generation and the permeability of the porous medium plays a significant role on the same. The effect of Da is almost insignificant in dictating the heat transfer for low values of Ra (10³, 10⁴), while there is a significant alteration in Nusselt number for Ra ≥10⁵ and moreover, the change is more intense for larger values of Da. For lower values of Ra (≤10⁴), the main contributor of irreversibility is the thermal irreversibility irrespective of all values of Da. However, the fluid friction irreversibility is the dominant player at higher values of Ra (=10⁶) and Da (=10⁻²).

From an industrial point of view, the present study will have applications in micro-electronic devices, building systems with complex geometries, solar collectors, electric machinery and lubrication systems.

This research examines numerically the buoyancy driven heat transfer irreversibility in a quadrantal porous enclosure that is subjected to uniform temperature heating from the bottom wall, that was not investigated in the literature before.