Solid Temperature Distributions Research Articles

A multiphase heat transfer model for spreading wall film coupled with solid wall temperature field

A simplified model for wall film impingement, spreading and evaporation is proposed in this work. The performance of the model was compared with experimental data. For the experimental data, a 2.8 mm diameter diesel drop at 423 K was impinged on a stainless steel wall. The solid surface and embedded temperature was recorded with time. The variation of film spread fraction, which is the ratio of the film spread diameter to the original drop diameter was also recorded with time. The present model deals with solid, liquid and gas phase physics of the wall film. An analytical expression developed previously for the heat flux from the ambient gas into the liquid gas interface, is used to represent the temperature distribution within the film. The correlation for heat transfer coefficient at the solid–liquid interface was developed and the solid temperature distribution is solved using the semi-infinite solid assumption in the 1-D coordinate system. A simplified film spread model was developed as a function of the maximum film spread fraction, which can be derived from energy conservation principles. A vapor sharing algorithm was also developed for film spreading into the neighboring computational cells. The model results were able to capture the initial rise in solid surface temperature during the initial spread of the film. However, the overall steady state temperature was slightly overpredicted. The solid embedded temperature matched well with experimental results. Variation of temperature within the film and the ambient gas temperature of the cell containing the film with time, obtained from the model was also shown.

An open-source porous media modelling approach to investigate thermohydraulic features of compact printed circuit heat exchangers

An experimental air-foil printed circuit heat exchanger (PCHE) with CO2 as a working fluid is numerically modelled and developed within the OpenFOAM environment as a freely available package for more general PCHE designs. The conjugate heat transfer solver (chtMultiRegionFoam) is adapted to include both the hot and cold fluid streams of the PCHE, along with the solid recuperator body, within three uniquely specified overlapping mesh regions. The fluid stream momentum equation is adapted to incorporate porosity, with the additional streamwise air-foil drag (friction factor) accounted for by the Darcy–Forcheimer porous media model. A simple linear ad-hoc model for the transverse friction factor is evaluated to determine the dispersion of the momentum across the flow. Heat transfer between the fluid streams and the solid body is driven by a volumetric thermal resistance with a cell volume-weighted interpolation method (volume-to-volume coupling), with experimentally determined Nusselt number correlations applied. Temperature-dependent parameters based on isobaric NIST data for CO2 are tabulated as a user library and integrated within the coding package. The model predictions of the solid body temperature distributions are assessed and validated against experimental data with eight equidistant fibre optical measurements across the PCHE core and compared against finite-element-based MATLAB numerical results. Thermal stresses are evaluated and qualitatively evaluated against experimental data, demonstrating the capability of the model to highlight potential design features for improvement.

An experimental and numerical study on the blade tip conjugate heat transfer performance

In the gas turbine, the blade tip is under extreme heat load and thereby it is necessary to adopt cooling method for the tip region. In this work, a blade tip conjugate heat transfer model was conducted in a linear cascade. The tip overall cooling effectiveness (φ) and adiabatic cooling effectiveness (η) were measured by the pressure sensitive paint (PSP) and the Infrared thermography (IR), respectively. Impacts of coolant blowing ratios (M = 1.0 ∼ 2.5), tip gap size (τ = 1.98%, 3.97%C, chord length), and film holes locations on the tip φ distributions were investigated. Then, the numerical simulations were performed to obtain the tip solid temperature distributions, and to reveal the conjugate heat transfer characteristics. Within the scope of this work, both the tip φ distributions and the tip solid temperature distributions indicate that the convection in film holes is a major factor of the tip conjugate heat transfer process. The tip area-averaged φ for the CL_H case are increased evidently by 13.1%∼38.9% with the increased coolant M, whereas the increase of η is not obvious. The tip gap size has less effect on the tip φ distributions than the coolant M, especially at a low M. The higher φ and the lower tip solid temperature region are detected near the film holes for any film hole location. The area-averaged φ values of the cases with film holes along the chamber line are 10.6% and 3.0% higher than those of the cases with film holes along the pressure-side or suction-side rim, respectively. This work revealed the major factor in the tip conjugate heat transfer process and may serve as a guide for tip cooling design.

Endothermic relaxation behavior of gangue in longwall gob: Bidirectional heat transfer model and its simulation validation

The collapse of overlying strata in a goaf during coal mining forms many gangue blocks that vary in size and shape. Because the heat released by the coal–oxygen reaction diffuses around the wind flow, endothermic relaxation occurs when the heated gas contacts the gangue. However, only a few studies have addressed this issue. In this study, we first propose a method to investigate the thermal relaxation behavior by expanding the mathematical space of the problem and then establish a bidirectional heat transfer model of a single-gangue-ball in spherical coordinates combined with the energy conservation law, which is solved numerically using the finite difference method. Finally, the reason for the fluctuation of the solid temperature distribution in the gob is determined by extracting the calculation results and comparing them with the gangue temperature curve under transient heat conduction, and the effects of some key factors on the thermal relaxation efficiency of the gangue are quantitatively investigated. The results show that (i) along the high-temperature path of the goaf, the gangue temperature exhibits the same trend as the ambient temperature, and its external and internal temperature difference decreases gradually with an increase in burial depth; (ii) compared with the change in temperature rise under transient heat conduction, the relaxation phenomenon can result in a calculation error of up to 1.3 °C; (iii) the heat transfer efficiency is related to the gangue characteristics and its surface heat transfer resistance, and the accuracy of spontaneous combustion prediction can be guaranteed by increasing the initial temperature, reducing the heat transfer radius, or decreasing the air flow rate. In this study, the thermal relaxation behavior of the gangue in a gas–solid dual medium in a longwall gob is investigated, and a foundation is laid for the establishment of a four-dimensional temperature field model for the gangue in the future.

Simulation of energy storage unit in existence of sinusoidal obstacles considering nanomaterial

To attain a unit for air conditioning in a building with less entropy generation and high thermal performance, a present system has been introduced in which cylinders of paraffin have been utilized. The problem of pure-paraffin is low conductivity and it can be improved with adding nanoparticles. For attaining the features of nanomaterial, single phase – based formulation have been implemented. The types of paraffin and nano-powders are RT25 and TiO2. In outputs, the components of irreversibility and distribution of solid fraction and temperature have been described. The efficacy of temperature and speed of air flow, distance of cylinders and fraction of additive have been examined. Both irreversibility and thermal productivity of the unit have been scrutinized. The higher temperature of air leads to the conversion of paraffin to liquid. Augmenting the fraction of additives may boost the melting rate around 6.79 %. With augment of “b”, the charging time alters from 17,888 s to 11,479 s. With elevation of inlet speed and temperature, melting rate enhances.

Comparison of Radiation-Conduction Transfer Involving Complex Solid Shapes Determined by Topological Optimization and a Heuristic Technique

Abstract A solid growth method (SGM) and a dual solid method (DSM), both recently developed, are each used to predict solid shapes that provide minimal total (conduction + radiation) resistance to heat transfer in a system involving conduction in a solid whose shape is to be determined, conduction in an adjoining gas, and radiation transfer between opaque, diffuse, and gray surfaces. The performance of each method is illustrated by examining solid configurations and temperature distributions that evolve as the mass of solid is gradually increased (SGM) or reconfigured (DSM). With use of either the SGM or the DSM, the solid evolves in a manner that enhances radiation heat transfer, and it is shown that neglecting radiation in the determination of solid configurations that optimize heat transfer performance is, in general, not justified. Despite the formalism of the DSM, which is based on topological optimization, the thermal performance of the DSM only marginally surpasses that of the SGM in terms of calculated total thermal resistance values, and only for cases involving a high solid thermal conductivity. For low solid thermal conductivity cases, the SGM outperforms the DSM with the difference in performance attributed to the inability of DSM to capture the fine solid structure of the SGM predictions.

ROLL-BOND HEAT EXCHANGER (RHE) DESIGN AND APPLICATION TO A CHOCOLATE COOLING TUNNEL - A NUMERICAL STUDY

The snack sector has a significant market today. It is expected that the snacks will look as promised on the packaging and that the product will have no deformations or defects. The entire area of liquid chocolate- covered snack products entering the chocolate cooling tunnel must be cooled homogeneously. If all surfaces of the chocolate are not sufficiently cooled, a problem of sticking to the conveyor belt can occur. This study investigates the performance of roll-bond heat exchangers under different operating conditions to solve the snack sector’s technical problems. For this purpose, a CAD model of a roll-bond heat exchanger is created. A steady-state heat transfer problem is established in the SolidWorks Flow Simulation environment, and the problem is solve numerically. The maximum, minimum, and average values of the fluid temperature, pressure difference, fluid velocity, and solid temperature distributions are calculated for different inlet velocities and temperatures. In addition, the standard deviations of the solid temperature values are calculated and evaluated. The results show that the roll-bond heat exchanger applies to the chocolate cooling tunnel and is much more efficient for heat transfer than the conventional design.

Magnetohydrodynamic chemically reactive viscoelastic fluid flow through an inclined porous layer

AbstractAnalysis of a time‐independent magnetohydrodynamic viscoelastic fluid flow in a deformable inclined porous layer with first‐order chemical reaction has been investigated. Walters' fluid model has been used to study viscoelastic fluid. The walls are suctioned/injected at a constant rate. The expression representing the solution for solid displacement, fluid velocity, temperature, and concentration distribution is obtained. The effect of applicable parameters on solid displacement, fluid velocity, temperature, and concentration are discussed graphically, while skin friction, heat transfer, and mass transfer are revealed in a tabular structure. It is noticed that solid displacement, fluid velocity, and temperature profiles decrease when the viscoelastic parameter increase. Solid displacement enhances and the velocity of the fluid reduces owing to the influence of increasing drag parameter, whereas the reverse effect is seen for the volume fraction parameter. Nusselt number at the walls shows the opposite behavior for the viscoelastic parameter and Eckert number. Sherwood number at the walls shows opposite behavior for Reynolds number, Schmidt number, and radiation parameter. Also, the entropy generation number rises as a result of the influence of viscoelasticity and Eckert number.

Local Thermal Nonequilibrium (LTNE) Modeling of a Partially Porous Channel With Spatial Variation in Biot Number

Abstract The local thermal nonequilibrium (LTNE) model has been used widely for analyzing heat transfer during internal flow through porous media, including when a channel is only partially filled with a porous medium. In such problems, the Biot number describes the rate of convective heat transfer between solid and fluid phases. While uniform Biot number models are commonly available, recent advances in functionally graded materials necessitate the analysis of spatially varying Biot number in such geometries. This paper presents LTNE-based heat transfer analysis for fully developed flow in a channel partially filled with porous medium and with spatially varying Biot number to describe solid-fluid interactions in the porous medium. Fully uncoupled ordinary differential equations for solid and fluid temperature distributions are derived under three different boundary condition models. Solid and fluid temperature fields are presented for a variety of Biot number distributions, including quadratically and periodically varying functions. An explanation of the nature of temperature distribution predictions for such problems is provided. For special cases, the results presented here are shown to reduce to past work on constant Biot number. This work improves the theoretical understanding of porous media heat transfer and facilitates the use of such theoretical models for functionally graded materials.

Analytical closed-form solution for fluid flow through microchannel heat sinks including axial conduction

An analytical study on the convective heat transfer through a rectangular microchannel heat sink including solid axial conduction, has been performed. The system has been split into two coupled boundary value problems, each addressing the heat transfer to the fluid through different routes (namely, the sidewall or fin and the base wall or substrate). The results are derived in the form of a net wall and fluid temperature rise. The validation of the proposed analytical model has been done using existing experimental data and a three-dimensional conjugate computational model. The results show excellent agreement in terms of solid and fluid temperature distributions. The parametric studies show an increasingly non-linear behaviour in the solid and fluid temperature profiles in the microchannel, if axial conduction is dominant. The simulated results are consistent with the CFD and experimental outcome. It has also been noted that a uniform heat flux applied at the bottom of the microchannel (substrate) cannot ensure the transfer of heat uniformly to the fluid. If axial conduction is high, a significant fraction of the applied heat influx is transmitted to the fluid near the channel entry region with a corresponding reduction in the flux distribution at the channel exit.

High-fidelity investigation of thermochemical conversion of biomass material in a full-loop circulating fluidized bed gasifier

Olive oil production urges the energy companies to exploit the potential of the residues as biomass fuels for clean energy production. Circulating fluidized bed (CFB) gasifier gains global interest within these several years due to its promising solution for converting biomass material to renewable energy. However, the multi-physics processes and multiscale structures inside the gasifier impede the experimental measurements. As an alternative, a reactive multiphase particle-in-cell approach is developed in this work to simulate the gasification process of olive oil waste in a pilot-scale full-loop CFB gasifier. After the model validation, the heat transfer properties of solid phase and the effect of size-induced segregation on solid thermochemical properties are explored. The results show that the low-temperature biomass particles injected highly influence the spatial distribution of solid temperature and solid heat transfer coefficient (HTC). A larger particle size gives rise to a higher HTC. Moreover, the temperature and HTC of biomass are larger than that of sand. A wide and narrow residence time distribution of sand in the riser and cyclone can be observed. The scale of biomass dispersion is respectively larger and the same as that of sand in horizontal and vertical directions. Particles in the dense region have a smaller HTC, Reynolds number, and temperature. Superficial gas velocity improves the uniformity of solid distribution. Elevating the gas velocity and initial bed temperature enhances solid dispersion intensity.

Complex Fourier series expansion for the liquid-solid phase transition in PCM layers: transient and steady state periodic regimes

Semi-analytical solutions to the classical two phase Stefan problem are proposed. Time dependent solutions to the one-dimensional liquid-solid phase transition in a PCM wallboard subjected to isothermal and periodic Dirichlet boundary conditions are obtained. Transient and steady state solutions are found in finite size systems, and the semi-analytical solutions are validated through the asymptotic time limit behaviour of the phase transition. In this work, complex Fourier methods are proposed to find the solutions in the transient and steady state periodic regimes. Semi-analytical solutions based on the heat balance integral method (HBIM) are used to verify the consistency of the proposed method. The Fourier method can be pictured as a generalization of the phasors based method recently introduced by other authors. The proposed method incorporates a complete set of complex functions, which allows finding the transient and steady state response of the system. Finally, solutions for the time dependent interface position, liquid and solid temperature distributions and the thermal energy penetrating through the PCM wallboard, are shown. The solutions from the proposed method are found to be consistent when compared to the semi-analytical solutions estimated through the HBIM.

Effect of asymmetrical wall heat flux and wall temperature ratio on mixed convection in a vertical micro-porous-channel with internal heat generation

Mixed convective heat transfer in a vertical parallel plate micro-porous channel with internal heat generation and viscous dissipation, varying wall heat flux ratio and wall temperature ratio at the boundaries is investigated using the Darcy-Brinkman model under local thermal non-equilibrium assumption. Numerical solution for both fluid and solid temperature distributions are obtained by applying the finite element method. The effect of pertinent parameters such as Brinkman number, Rayleigh number, Darcy number, inter-phase heat transfer coefficient, porosity scaled thermal conductivity ratio and solid internal heat generation are discussed. The results indicate that the Nusselt number increases with the increase in the solid internal heat generation as well as Rayleigh number in both wall heat flux ratio and wall temperature ratio boundary conditions. It is observed that with the quantitative increase in viscous dissipation parameter Br, Nusselt number Nu increases in the presence of internal heat generation and it decreases in the absence of internal heat generation, for a specific range of values of wall heat flux ratio and wall temperature ratio. Beyond this range Nu increases with the increase in Br regardless of internal heat generation. For the cases, constant wall temperature and wall heat flux ratios, good correlation is observed in the results obtained with that of available in the literature.

Performance of ventilation system involving thermal storage unit considering porous media

Abstract Current attempt aims to explore the impact of porous plates on discharging treatment of paraffin. The kind of paraffin is RT28 and to augment its thermal behavior, CuO nanomaterial has been mixed. The wavy shape of duct provides higher interface of cold flow with liquid paraffin and makes the process faster. Low concentration of CuO provides the opportunity for utilizing homogeneous model for NEPCM. Also, selecting structure grids result in more accurate outputs with lower computational cost. Temperature distributions and solid fraction profiles were main outputs. Influence of phase changing was characterized by enthalpy-porosity model and finite volume method has been incorporated for modeling current unsteady phenomena. Influence of porosity (ɛ) on solid fraction and temperature distribution has been reported in outputs. At t = 5h, temperature of air and PCM augment about 0.45% and 1.27% with reduce of ɛ. Temperature of PCM and air decrease about 0.8% and 0.67% with rise of time from 5 to 30h when ɛ=1. At t = 30h, reduce of ɛ leads to augmentation of temperature about 0.26% and 0.51% for PCM and air flow sides, respectively. With incorporating porous foam, the discharging time declines about 19.5%.

Virtual Assessment and Experimental Validation of Power Loss Contributions in Swash Plate Type Axial Piston Pumps

The understanding of the power loss contributions of each loss source is essential for an effective development of swash plate type axial piston pump. However, it is difficult to obtain the assessment of the power loss distribution due to the lack of methodologies that allow an independent evaluation of each source. This paper addresses this challenge using the most recent simulation methods. It describes the determination of each source, along with the corresponding loss of performance, and the principle of their prediction during the design phase. It also reports the validation of the simulation model by comparing the simulated dynamic displacement chamber pressure and the solid body temperature distribution with measurements obtained from a special pump prototype. This proposed virtual assessment of power loss contributions is demonstrated on a commercial hydraulic unit and the detailed results are reported in this paper.

A numerical study on the flame characteristics and pollutant emissions in a premixed burner: Comparison between porous and solid bluff bodies

The effects of porous and solid bluff bodies in the combustion chamber on flame stability limits, gas and solid temperature distributions, pressure drop, methane conversion rate, and CO and NO emissions are examined numerically. The porous and solid bluff bodies are made of SiC with the inner diameter of 50 mm, the outer diameter of 90 mm, and the length of 22 mm. In this study, Renormalization Group k–ε is used for modeling of turbulence. Eddy dissipation concept is selected for modeling of the interaction between turbulence and chemistry. A reduced mechanism based on GRI 3.0 consisting of 16 species and 41 reactions is employed to model methane combustion. The results indicate that the upper flame stability limit can be diminished by adding porous bluff body in the combustion chamber instead of the solid bluff body. Besides, the pressure drop, CO and NO emissions in the combustion chamber with solid bluff body are higher than those of porous bluff body, while the methane conversion rate increases by replacing porous bluff body instead of solid bluff body in the combustion chamber.

A quasi-three-dimensional thermal model for multi-stream plate fin heat exchangers

In this study, a novel pseudo-three-dimensional model is developed to find out both fluid and solid temperature distributions in multi-stream plate fin heat exchangers. In this simulation algorithm, heat exchangers can be in either parallel flow or cross flow configuration. The model considerations include: heat leakage of cap plates and side plates, conduction throughout the solid matrix of the heat exchanger, variable physical properties, and inlet mass flow rate maldistribution. Using the computational code, the effects of different factors such as: the number of layers, mass flow variation, inlet mass flow rate maldistribution, and stacking pattern on the thermal performance of the heat exchanger have been investigated. The results of this investigation show that when the number of layers for each stream is small, a linear nonuniformity in the mass flow rate of a hot stream has a more destructive effect on the thermal performance than that in a cold stream. Moreover, the heat transfer rate of the heat exchanger is more sensitive to mass flow deviation of cold streams than that of hot streams. In the present research, when the number of unit cells are higher than 15, periodic boundary conditions can be applied to reduce the computational cost.

Solidification performance of a latent heat storage unit with innovative longitudinal triangular fins

In this paper, an innovative longitudinal triangular fin was proposed to improve the solidification performance of shell and tube latent heat thermal energy storage (LHTES) device. At first, the solidification behaviors (solid fraction, temperature distribution and solidification time) of two different layouts of innovative fins (Fin-B, Fin-C) were compared with the traditional rectangular fin (Fin-A). Then, the dynamic temperature response of the fins with superior performance were analyzed. In addition, the influences of the fin geometrical parameters, initial temperature and fin materials on the solidification performance were studied and discussed. The results showed that the innovative longitudinal triangular fins can significantly improve the solidification performance of PCM in LHTES, and the Fin-C had better heat transfer efficiency and superior solidification performance among the three types of fins. The solidification time of Fin-C-Ⅰ decreased 38.30% significantly compared with the traditional rectangular Fin-A. Generally, the solidification time decreased by decreasing the initial temperature, or increasing the thermal conductivity and the fin heights. However, the effect of the bottom width of triangular fin on the solidification performance can be neglected. To achieve a faster cooling rate, the recommended temperature difference between the inner wall and PCM was over 20 K.

Studies on die filling of A356 Al alloy and development of a steering knuckle component using rheo pressure die casting system

In this study, a computational fluid dynamics (CFD) model is developed to investigate die filling of semi solid slurry as part of rheo pressure die casting (RPDC) system. The die filling cavity corresponds to that of an automobile steering knuckle, and the slurry is made of A356 aluminium alloy. The rheological model used in the CFD simulation is determined experimentally. The results obtained from present numerical model includes flow field of the slurry within the die cavity, viscosity evolution, solid fraction distribution, temperature and pressure distribution during solidification within cavity during die filling stage. The main objective of the study is to determine the gating arrangement, pouring temperature, and injection conditions for desirable microstructure and mechanical properties of the developed component. To study the effect of injection conditions on die filling capability of the said alloy slurry, five injection profiles are studied, with a variation in final injection velocity between 2–3.2 m/s. In order to corroborate the findings of the present study, microstructural morphology and structure-property correlation have been studied, primarily in the form of optical microscopy and macro hardness measurements, by obtaining samples from different locations of the solidified component.

Peridynamic simulation of thermal failure behaviors in rocks subjected to heating from boreholes

In this paper, a weakly coupled thermo-mechanical model within the framework of ordinary state-based peridynamics is proposed to investigate thermal cracking behaviors of rocks subjected to heating from boreholes. The weakly coupled thermo-mechanical ordinary state-based peridynamic model is decomposed into two parts, i.e., thermal conduction and mechanical deformation. In the first part, temperature distributions in solids are analyzed based on the heat conduction equations. While, in the second part, thermally-induced deformation and fracture can be simulated by the mechanical computations. Moreover, a multi-rate explicit time integration scheme is proposed to model thermal cracking phenomena in rocks to overcome different time-scale problems in multi-physical systems. A benchmark example with analytical solutions is firstly modeled to validate the correctness and accuracy of the proposed numerical method, and numerical convergence studies of the weakly coupled thermo-mechanical ordinary state-based peridynamics are also conducted. The present numerical results are in good agreement with the analytical solutions and the previous experimental data. Then, three numerical examples are performed to investigate thermally-induced cracking behaviors, i.e. cracking patterns and temperature and stress evolutions. The proposed numerical method not only provides a new tool for coupled thermal-mechanical fracture problems in geothermal engineering, but also reveals the mechanism of thermal cracking phenomena in rocks.