Parabolic Temperature Profile Research Articles

Effect of Temperature Gradients and DC Electric Field on Electrothermal Convection in a Rotating Layer of Walter's-B Fluid Saturated Porous Media

Thermal convection in fluid-saturated porous media has diverse applications across geothermal energy utilisation, thermal insulation engineering, grain storage and understanding geodynamic processes. The thermal convection's physics is crucial for optimising the thermofluid system, improving energy efficiency, and enhancing our understanding of natural phenomena. The study examines how the initiation of electrothermal convection in a rotating viscoelastic fluid layer (Walter's B) is influenced by basic temperature gradients and a uniform vertical DC electric field, considering three different types of velocity boundary conditions: free-free, rigid-rigid, and lower rigid and upper free. By applying an electric field to a fluid, studying electrothermal convection helps engineers design effective cooling systems for electronics. The eigenvalue problem is solved by using the Galerkin technique. The Galerkin method is a widely used numerical technique for solving eigenvalue problems. The DC electric field effect exhibits a more stabilising effect for free-free boundaries than rigid and rigid-rigid boundaries. Moreover, the linear temperature profile exhibits a more stabilising effect than the parabolic temperature profile. The control of electrothermal convection on the system with the impact of other physical parameters is also discussed.

Direct numerical simulation of one-sided forced thermal convection in plane channels

We carry out direct numerical simulations (DNS) of turbulent flow and heat transfer in pressure-driven plane channels, by considering cases with heating on both walls, as well as asymmetric heating limited to one of the channel walls. Friction Reynolds numbers up to ${Re}_{\tau } \approx 2000$ are considered, and Prandtl numbers from ${Pr}=0.025$ to ${Pr} = 4$ , the temperature field being regarded as a passive scalar. Whereas cases with symmetric heating show close similarity between the temperature and the streamwise velocity fields, with turbulent structures confined to either half of the channel, in the presence of one-sided heating the temperature field exhibits larger regions with coherent fluctuations extending beyond the channel centreline. Validity of the logarithmic law for the mean temperature is confirmed, as well as universality of the associated von Kármán constant, which we estimate to be $k_{\theta } = 0.459$ . Deviations from the logarithmic behaviour are much clearer in cases with one-sided heating, which feature a wide outer region with parabolic mean temperature profile. The DNS data are exploited to construct a predictive formula for the heat transfer coefficient as a function of both Reynolds and Prandtl number. We find that the reduction of the thermal efficiency in the one-sided case is approximately $20\,\%$ at unit Prandtl number; however, it can become much more significant at low Prandtl number.

Two Component Non-Darcian Benard Marangoni Convection with Uniform and Non-Uniform Temperature Gradients in a Composite Layer with Variable Heat Sources/Sinks

In a composite layer that comprises of a porous layer which is sparsely packed and saturated with two component incompressible fluid and above this porous layer lays a layer of the same fluid, with variable heat sources or sinks in both the layers double diffusive non-Darcian Benard Marangoni (DDNBM) convection is investigated. The upper surface of the composite layer has Marangoni effects which depend on temperature and concentration, whereas the lower surface is rigid. The inverted parabolic, parabolic and linear temperature profile is applied to this composite layer, which is surrounded by adiabatic boundaries. The appropriate thermal Marangoni numbers (TMANs) which are the eigen values (EVs) are calculated for all the three temperature gradients. The impact of different parameters on the EVs with respect to depth ratio is examined, thoroughly. The parameters that effect DDNBM convection are found.

Effects of Uniform and Non-Uniform Temperature Gradients on Marangoni Convection in a Composite Layer with Variable Heat Sources

An investigation is carried out to determine the effect of uniform and non-uniform temperature profiles on single component Darcy-Benard Marangoni (DBM) convection in a composite layer system consisting of an incompressible fluid saturated porous layer on top of which is a layer of the same fluid with variable heat sources in both layers. The upper surface of the fluid layer is free with surface tension effects depending on temperature and the lower surface of the porous layer is rigid. The eigen value, thermal Marangoni number (TMN) is solved exactly for linear, parabolic and inverted parabolic temperature profiles for the adiabatic thermal boundary conditions at the horizontal boundaries of the composite layer. The influence of various dimensionless parameters on the eigen value against depth ratio is discussed in detail.

Effect of non-uniform heating on thermal performance of an enclosure filled with nanofluid

The influence of non-uniform temperature during convective transport in a closed enclosure is examined numerically. This system works using a water-based nanofluid where Cu is used as colloidal suspension of nanoparticles. The numerical simulation is performed in a Computational Fluid Dynamics software constructed using finite volume discretization technique. The investigation is executed in a bottom wall heated (BWH) enclosure by controlling Rayleigh number (Ra) for different heating profiles. The BWH is carried using uniform, parabolic, and linear temperature profiles. For all the cases investigated, the mean temperature of the bottom wall is fixed. The transfer of energy by the convection process is calculated using the Nusselt number. Flow visualizations through streamlines and isotherms reveal that the thermal convection is minimum for uniform temperature and maximum for linear temperature profiles. The irreversibility evolved during different heating profiles is measured with entropy generation (EG). The results reveal that the EG is minimum for uniform heating and maximum for parabolic heating. Further, EG increases with an increase in Ra. The present study can provide useful insights for designing thermal devices.

Model validation of mechanical face seals in two-phase flow conditions

A steady-state one-dimensional axisymmetric numerical model of a mechanical seal in two-phase flow is presented. In this work a non-linear thermal model is implemented using a coupled (monolithic) approach, linking the fluid film and sealing rings. It is solved for the temperature fields of the fluid and solids, heat fluxes between fluids and solids, enthalpy of the fluid, and the vapor mass fraction, using Newtons method. The novelty of this approach lies in 1) the thermal coupling between fluid and solids, and 2) the implementation of saturation curves to couple temperature, enthalpy, and vapor mass fraction. The temperature across the seal gap is described by an analytical parabolic temperature profile by assuming a plane Couette flow in the radial direction. From this assumption, an equation for the wall heat fluxes is derived, which couples the temperature fields of the fluid and solids. The IAPWS-IF97 standard for the thermodynamic properties of water is used to obtain non-linear equations that couples the fluid temperature, enthalpy and the vapor mass fraction. The model and its implementation is described in detail. Several cases of seal behavior and two-phase flow are studied and show good agreement with other results from literature, validating the coupled approach for modelling phase-change in mechanical seals.

Phase-field modeling with the TAF-ID of incipient melting and oxygen transport in nuclear fuel during power transients

• Development of a phase-field model for a two-phase multicomponent system • Coupling of the phase-field model with the TAF-ID • Derivation of a partitioned fixed-point numerical solving • Simulation of incipient fuel melting and oxygen transport in nuclear fuel In this paper, a phase-field model is developed for a two phase compositional (multicomponent) system and combined with the thermodynamic description provided by a CALPHAD database. The model is applied to a uranium-oxygen binary system within a solid/liquid mixture to simulate incipient melting and oxygen transport (oxygen-uranium inter-diffusion and Soret effect) in the fuel with thermodynamic properties coming from the Thermodynamics for Advanced Fuels-International Database (TAF-ID). The interface with the TAF-ID required the coupling of the phase-field model with the OpenCalphad thermochemical solver. This coupling led to the development of a partitioned scheme that is solved at each time step with a fixed-point algorithm. To analyze the response of and to parameterize the phase-field model, two 1D demonstration problems from the open literature have been considered and solved using a finite-difference scheme. The first problem deals with oxygen transport in UO 2.005 fuel under an imposed parabolic temperature profile below liquidus . The second one describes the incipient melting and oxygen transport in oxidized fuel under an increasing temperature profile. Oxygen thermal diffusion is considered both in the solid and liquid phases. All the results presented in this paper are in good agreement with those already published but are here performed considering a direct coupling with the TAF-ID database. They demonstrate the thermodynamic consistency of the phase-field model as well as its capability to simulate incipient melting and oxygen transport in the fuel with advanced thermodynamics databases.

Investigating the influence of residual stresses on fatigue crack growth for additively manufactured titanium alloy Ti6Al4V by using peridynamics

This study presents a numerical approach to predict the influence of the residual stresses on Fatigue Crack Growth Rates (FCGR). The main focus is on the additively manufactured titanium alloy Ti6Al4V with resultant high residual stresses in the samples due to the layer by layer manufacturing. A parabolic temperature profile has been applied to represent the effect of the pre-tension or pre-compression of the sample to account for the existence of the initial residual stresses. The proposed approach has been validated using experimental data available in the literature showing the capability of the tool to predict the FCGR.

Investigating Arcjet Mixing and Enthalpy Loss Using Atomic Oxygen Laser Absorption Spectroscopy

Scanned-direct absorption spectroscopy was implemented to improve sensing capabilities in the mixing volume (MV) of the 60 MW Interaction Heating Facility (IHF) at NASA Ames Research Center. The IHF MV conditions range from 5000 to 8000 K and 1 to 9 atm. The path-average line-of-sight measurements of the temperature and enthalpy were inferred using an electronic atomic oxygen transition near 777 nm. A scanned-DAS sensor was optimized to capture high-add-air and high-pressure conditions that previously had not been measurable, including an increased tuning range () that allowed for full absorbance profile resolution at maximum pressure test conditions. Enhanced sensor capabilities confirmed uniform flow and flat temperature profiles immediately upstream of the arcjet’s converging–diverging nozzle inlet. Less uniform and parabolic temperature profiles were observed immediately downstream of add-air injection. Time-resolved enthalpy measurements ranged from 16 to 27 MJ/kg and are in agreement with the IHF’s current measurement methods. Centerline measurements along the MV confirmed a reduction in achievable enthalpy after installation of the MV. The centerline measurements quantified the mixing process for various add-air conditions, indicating an opportunity for enthalpy recapture. Axial locations of sufficient mixing were identified and provide a potential for reduction of the MV length and improved facility performance.

A Eulerian Multi-Fluid Model for High-Speed Evaporating Sprays

Advancements in internal combustion technology, such as efficiency improvements and the usage of new complex fuels, are often coupled with developments of suitable numerical tools for predicting the complex dynamic behavior of sprays. Therefore, this work presents a Eulerian multi-fluid model specialized for the dynamic behavior of dense evaporating liquid fuel sprays. The introduced model was implemented within the open-source OpenFOAM library, which is constantly gaining popularity in both industrial and academic settings. Therefore, it represents an ideal framework for such development. The presented model employs the classes method and advanced interfacial momentum transfer models. The droplet breakup is considered using the enhanced WAVE breakup model, where the mass taken from the parent droplets is distributed among child classes using a triangular distribution. Furthermore, the complex thermal behavior within the moving droplets is considered using a parabolic temperature profile and an effective thermal conductivity approach. This work includes an uncertainty estimation analysis (for both spatial and temporal resolutions) for the developed solver. Furthermore, the solver was validated against two ECN Spray A conditions (evaporating and non-evaporating). Overall, the presented results show the capability of the implemented model to successfully predict the complex dynamic behavior of dense liquid sprays for the selected operating conditions.

Novel semibatch supersaturation control approach for the cooling crystallization of heat‐sensitive materials

AbstractThis article introduces the application of a novel supersaturation control (SSC) approach for the crystallization of heat‐sensitive materials. Traditional SSC implements parabolic temperature profile with slow initial cooling that maximizes growth over nucleation, however, which may also promote heat degradation. The proposed semibatch SSC fixes the crystallization temperature to a sufficiently low value to minimize thermal degradation, and manipulates the flow rate of a higher temperature feed stream to control the supersaturation. The high temperature feed is produced in a continuous dissolver before feeding, thus the solution spends considerably shorter time at high temperature than in the traditional batch cooling crystallization. This work demonstrates the effectiveness of the semibatch operation for the cooling crystallization of heat‐sensitive substances by thorough simulation study as well as experimental investigations. The experimental validation confirmed the simulation results, and both analyses revealed the superiority of semibatch SSC for the crystallization of heat‐sensitive materials.

Controlling nucleation during unseeded THM growth of CdZnTe crystal

There are always undesired grains formed at the beginning of unseeded THM growth which deteriorate the crystal quality greatly. In this paper, several ingots with the diameter of 27 mm were grown by unseeded THM to investigate the nucleation process. The growth temperature in the experiments was 750 °C and the growth rate was 5 mm/day. The influence of crucible bottom geometry and temperature gradient on nucleation are studied. Numerical simulations of thermal and concentration fields were also performed for the THM process to study the growth process. The simulation results show that square cavity flow's structure and parabolic wall temperature profile are the main reason for secondary nucleation in the radial direction. Dummy crystal with cold finger was introduced in order to stabilize the thermal field and modify the lateral temperature gradient. Subsequent experimental results indicate that a large longitudinal temperature gradient with small lateral temperature gradient is more favor to suppress secondary nucleation and maintain stable growth.

Effects of Non-uniform Temperature Gradients on Triple Diffusive Surface Tension Driven Magneto Convection in a Composite Layer

The problem of triple diffusive surface tension driven magneto convection in a composite layer is investigated for linear, parabolic and inverted parabolic temperature profiles. The corresponding thermal Marangoni numbers are obtained analytically depending on various physical parameters of interest. The parameters which are effective to enhance convection and to control convection are determined. From the investigation it is found that the linear profile is suitable for fluid layer dominant composite layer whereas parabolic and inverted parabolic profiles are conducive for the porous layer dominant composite layer.

Theoretically and experimentally founded simulation of the appendix gap in regenerative machines

Regenerative machines, such as the Stirling engine, may contribute substantially to the solution of the present environmental problems, if they are designed for high efficiency. This requires a thorough understanding and an accurate modelling of the various losses, including the so-called appendix gap loss. For this purpose, some analytical models as well as a few one-dimensional numerical approaches have been developed so far. In this contribution, a comparison of the results obtained by these is performed for the reference case of a well-documented experimental machine. It reveals significant discrepancies regarding the optimum gap width as well as the magnitude of the loss. Particularly for large gap widths, increasing deviations between the analytical and the numerical models are observed. The latter even predict an unrealistic maximum. This discrepancy can be resolved by additionally considering the p,V-work done by the moving seal. Further deviations at small gap widths can be attributed to the interdependence of the loss and the actual wall temperature gradients, which is included in the numerical models. Instead, a preset value is assumed in the analytical models. This also applies to a newly developed, enhanced model, which predicts the optimum width reliably, but overestimates the magnitude of the loss throughout. This underlines a need for one-dimensional differential simulations in addition to analytical modeling. However, these require separate modeling approaches for both the radial and axial energy transport. Unfortunately, the choice of these significantly affects the results. Since none of the approaches proposed so far is theoretically or experimentally founded, there is no basis for a correct choice. To solve this problem, the aforementioned analytical model is considered, since it is theoretically based and further supported by recent experimental results presented in this contribution. It is therefore used to analytically derive correlations for the phase-shifted heat exchange with the walls and the interrelation of enthalpy and mass flow. Thus, a theoretically and experimentally founded reference model is available now. Comparing the results obtained by this reference model and the other numerical approaches, it is found that an empirical model based on the assumption of parabolic radial temperature profiles and ideal plug flow yields almost the same results as the former. Since this model is easier to use, it can therefore be recommended for general practical use. The reference model may, however, be used for countercheck purposes and for further optimization work.

Parabolic Profile in Heat-Conduction Problems. 3. Semi-Bounded Space with a Definite External Heat Flow

Some approaches to the optimization of the exponent n of the parabolic temperature profile for a semi-bounded space with the second-kind boundary condition, implying the prescription of an external heat flow, are considered. An optimization scheme involving the minimization of a new error norm estimating the absolute value of a temperature deviation, more efficient than the scheme of T. Myers with minimization of the Langford norm, as well as new hybrid integral methods are proposed. With the use of these methods, parabolic solutions have been obtained on the basis of the temperature momentum integral in different modifications and the heat-flow momentum integral, and these solutions define the surface temperature with a very high accuracy. As an illustrative example, the problem on the heat conduction of a semi-bounded space with a definite pulsating heat flow at its surface, whose time change is defined by a quadratic parabola, was considered. The approximation errors of the parabolic solutions obtained using the hybrid integral methods proposed comprise hundredths and thousandths of a percent, and they are smaller by one to two orders of magnitude than the errors of the analogous solutions obtained by the known heat balance integral method and refined integral method, involving the optimization of the exponent of a parabolic temperature profile on the basis of minimization of the Langford norm, and by the combined integral method.

Parabolic Profile in Heat-Conduction Problems. 2. Semi-Bounded Space with a Time-Varying Surface Temperature

Some approaches to the optimization of the exponent n in the parabolic temperature profile for a semi-bounded space at a boundary condition with a time-varying surface temperature are considered. It is shown that solutions obtained using the scheme of T. Myers with minimization of the Langford norm are not even close to the optimum ones and that the minimization scheme based on the new error norm estimating the modulus of a temperature deviation is much more efficient. New hybrid integral schemes convenient to use are proposed. Parabolic solutions have been obtained on the basis of a number of integral relations: the temperature-momentum integrals of single and double modifications and the temperature-function integral. On the basis of these solutions in combination with known integral relations, different variations of the hybrid integral method have been developed. It was established that the highest approximation accuracy is provided by the hybrid scheme combining the temperature-momentum integrals of single and double modifications. It is shown that the hybrid integral schemes proposed are much more accurate compared to the known integral methods, including those realized using the scheme with minimization of the Langford norm. In particular, for a semi-bounded space with a surface of constant temperature, the hybrid integral method variant combining the temperature-momentum integral of single modification and the refined integral method makes it possible to obtain a simple cubic parabola representing a substantially better approximation solution compared to the temperature profile obtained on the basis of the refined integral method with optimization of the exponent n by the scheme of T. Myers.

Effects of Non-Uniform Temperature Gradients on Triple Diffusive Marangoni Convection in a Composite Layer

The problem of triple diffusive Marangoni convection is investigated in a composite layer comprising an incompressible three component fluid saturated, sparsely packed porous layer over which lies a layer of the same fluid. The lower rigid surface of the porous layer and the upper free surface are considered to be insulating to temperature, insulating to both salute concentration perturbations. At the upper free surface, the surface tension effects depending on temperature and salinities are considered. At the interface, the normal and tangential components of velocity, heat and heat flux, mass and mass flux are assumed to be continuous. The resulting eigenvalue problem is solved exactly for linear, parabolic and inverted parabolic temperature profiles and analytical expressions of the thermal Marangoni number are obtained. The effects of variation of different physical parameters on the thermal Marangoni numbers for the profiles are compared.

Acoustic resonances in gas-filled spherical bulb with parabolic temperature profile.

Acoustics is used to probe the temperature profile within a sulfur plasma lamp. A spherically symmetric temperature profile is assumed that drops with the square of the radius, consistent with a constant volumetric heating model. Acoustic resonance frequencies are calculated exactly in the case of an ideal gas. Experimental measurement of a few resonant frequencies allows determination of the temperature profile curvature. This technique can be viewed as an extension of ultrasonic resonant spectroscopy to systems that are highly non-uniform due to off-equilibrium energy flow.

Assessment of thermal heat loss from solar cavity receiver with Lattice Boltzmann method

Efficiency of concentrating solar power system (CSP) can be significantly reduced by heat losses from the receiver. So, the assessment of heat losses is the key to improve its thermal performance. This paper attempts to present a numerical simulation to assess the heat losses from a cavity receiver by using Lattice Boltzmann Method (LBM) coupled with net radiation method. Combined natural convection and surface radiation heat losses in open rectangular solar cavity receiver is presented. The wall facing the opening is subjected to parabolic temperature profile. The other walls are insulated. Cavity walls are assumed to be diffuse, gray and opaque while the open boundary is assumed to be a fictitious black surface at ambient temperature. Double distribution functions (D2Q9-D2Q4) with different relaxation times are used to predict dynamic and thermal fields. Influence of surface radiation, operating temperature, inclination angle and aspect ratio on heat losses from the hot wall inside the cavity is analyzed and discussed.It was found that convective heat loss is largely increasing by increasing the inclination angle. Concerning surface emissivity effect, an amplification by coefficient of 4 between ε = 0.2 and ε = 1.0 is accomplished for thermal radiation heat loss whereas convective heat loss is marginally reduced. It was also found that total heat loss from the cavity absorber is influenced by operating temperature and aspect ratio. In fact, increasing of operating temperature enhances heat loss while the increasing of aspect ratio reduces it.

Transient Heat Transfer in a Packed-Bed Elliptic Cylindrical Reactor: A Finite-Volume Approach

This work aims to develop a transient three-dimensional mathematical model using the elliptic cylindrical coordinate system, to predict heat transfer in a elliptic cylindrical packed fixed bed reactor. The model considers variable thermo physical properties and a parabolic temperature profile at the fluid inlet. The governing equation is solved using the finite volume method. Results of temperature profile along the reactor are presented and discussed at different moments.It was verified that the maximum heat transfer rate inside the reactor occurs near the extreme region close to minor semi-axis of the ellipse; the higher temperatures at the reactor surface are also in this region, along the entire height of the bed; the steady-state regime is reached at t = 4.5 s of process, presenting after this time interval,small axial temperature gradients and high radial gradients along of the reactor bed; the parabolic temperature profile give to the bed a predominance of radial temperature gradients, and the radial porosity profile favours a higher heat transfer rate at reactor surface.