Conduction-convection Model Research Articles

Optimization of heat transfer in PCM based triple tube heat exchanger using multitudinous fins and eccentric tube

This study aims to analyze the effect of incorporating a hybrid concept of heat transfer enhancement using extended surfaces and eccentricity of the inner tube in an RT-82 phase change material-based horizontal triple tube heat exchanger. Three types of fins were used, namely longitudinal, arc and triangular shape fins, as per suitability for better heat transfer. Moreover, the concept of eccentricity was also implemented to make PCM melt faster. The novelty of the present study lies in optimizing the heat transfer enhancement by proper placement of the fins and eccentric inner tube arrangement. A conduction-convection model was used to examine the thermal performance of a triple tube heat exchanger. The natural convection of PCM was employed using the Boussinesq approximation. The governing equations were solved using finite volume-based Ansys Fluent 2021 R2 software. The performance study of phase change material was based on transient variation of liquid fraction and average temperature. The optimum model showed a 63.87 % reduction in melting time and a 175.16 % improvement in heat transfer rate compared to a simple triple tube heat exchanger to achieve the unit liquid fraction. It is also observed from the calculation of the Rayleigh number that the conduction became more dominant than the convection phenomenon in the fin based model. The main finding of the present study is the use of triangular fins on the base along with the curved fins at the lower middle section because this arrangement shows high heat penetration capability. The results indicate that fins selection and placement significantly enhance the heat transfer rate.

Field and numerical studies on the thermal performance of air convection embankments to protect side slopes in permafrost environments

Shoulder air convection embankments (ACEs) are sufficient to counter the effect of ground staying relatively warm due to the insulation of snow accumulation on side slopes of northern transportation infrastructure. However, little information is available for the design procedure. This paper aims to propose new design guidelines and an engineering design chart to quantify the heat extraction capacity of shoulder ACEs. The tested shoulder ACE, constructed on the Alaska Highway at Beaver Creek, Yukon, in 2008, provided valuable data for the assessment of field performance and model development. Thermistor strings were installed under the centerline and under the side slope. Measurements indicated that the cooling of ground soils was significant mainly under the side slope during the monitoring years from 2009 to 2013. The data collected were also used to calibrate a coupled conduction-convection model to reproduce the thermal conditions and the changing temperature trend in the subgrade. An engineering design chart was developed based on the calibrated model, and was successfully validated using the thermal data from the Puvirnituq airstrip in Northern Quebec, Canada.

Numerical analysis of the unconditionally stable discontinuous Galerkin schemes for the nonstationary conduction–convection problem

This work aims at employing the discontinuous Galerkin (DG) methods for solving the nonstationary conduction–convection model, which is motivated by advantages of DG methods. The discontinuous element pair Pk-Pk−1-Pk in the space discretization and backward Euler scheme in time are applied, as well as an explicit upwind scheme based on Picard iteration is introduced for the coupled term. Existence and uniqueness of the approximation solutions are proved, along with preserving the unconditional stability of the numerical schemes. The priori error estimates for velocity, pressure and temperature are also derived. Numerical tests are provided to verify the theoretical analysis and to indicate the efficiency of the DG methods in simulating practical problems.

Experimental and numerical study on a lab-scale latent heat storage prototype for cooling applications

Latent thermal energy storage systems using phase change materials (PCMs) represent an effective way of storing thermal energy because of high-energy storage density and the isothermal nature of the storage process. In the current study, the charging and discharging characteristics of a lab-scale latent heat storage (LHTES) prototype for cooling applications are experimentally and numerically studied. Two numerical models are developed to analyse the performance characteristics of the LHTES prototype: a conductive model and a conductive-convective model. Effective heat capacity (EHC) method is implemented to consider the latent heat of the phase change material. The governing equations involved in the models are solved using the finite element based software product, COMSOL Multiphysics, and the initial and the boundary conditions are determined on the basis of the data obtained from the experimental tests. Numerically predicted temperature variations of the models during charging and discharging processes are compared with the experimental data extracted from the lab-scale LHTES prototype, and a good agreement between them is found when the conductive-convective model is used, while high deviation is observed in case of use of the conductive model. Other results are presented in terms of the performance parameters such as charging/discharging time, energy storage charge/discharge rate, and melt fraction.

Comparative study of phase change phenomenon in high temperature cascade latent heat energy storage system using conduction and conduction-convection models

In the current study, a combined conduction-convection model is developed to analyze the effect of natural convection inside the Phase Change Material (PCM) during melting and solidification processes of a cascade Latent Heat Thermal Energy Storage System (LHTESS) and it is compared with pure conduction model. Effective heat capacity method is employed to simulate the phase change phenomena in both combined model and pure conduction models. Boussinesq approximation is used to predict the effect of natural convection inside the PCM in the combined model. The governing equations involved in the model are solved using finite element based simulation software, COMSOL Multiphysics 4.3a. Parametric study is conducted on charging and discharging processes of cascade LHTESS using both the models. The comparative study between combined model and pure conduction model demonstrated that the pure conduction model under predicts the rate of heat transfer between HTF and PCM at lower inlet velocity of HTF, where natural convection plays a significant role in the phase change phenomena. The deviation between the models decreases with increase in the inlet velocity of HTF for both charging and discharging processes. The simulation results indicated that the heat transfer phenomena inside the PCM become more conduction dominant at higher inlet velocity of HTF. The results also revealed that the inlet temperature of HTF plays a major role in decreasing the charging/ discharging time.

Thermal hydraulic parametric investigation of decay heat removal from degraded core of a sodium cooled fast Breeder reactor

Ensuring post accident decay heat removal with high degree of reliability following a Core Disruptive Accident (CDA) is very important in the design of sodium cooled fast reactors (SFR). In the recent past, a lot of research has been done towards the design of an in-vessel core catcher below the grid plate to prevent the core debris reaching the main vessel in a pool type SFR. However, during an energetic CDA, the entire core debris is unlikely to reach the core catcher. A significant part of the debris is likely to settle in core periphery between radial shielding subassemblies and the inner vessel. Failure of inner vessel due to the decay heat can lead to core debris reaching the main vessel and threatening its integrity. On the other hand, retention of a part of debris in core periphery can reduce the load on main core catcher. Towards achieving an optimum design of SFR and safety evaluation, it is essential to quantify the amount of heat generating core debris that can be retained safely within the primary vessel. This has been performed by a mathematical simulation comprising solution of 2-D transient form of the governing equations of turbulent sodium flow and heat transfer with Boussinesq approximations. The conjugate conduction-convection model adopted for this purpose is validated against in-house experimental data. Transient evolutions of natural convection in the pools and structural temperatures in critical components have been predicted. It is found that 50% of the core debris can be safely accommodated in the gap between radial shielding subassemblies and inner vessel without exceeding structural temperature limit. It is also established that a single plate core catcher can safely accommodate decay heat arising due to ∼70% of the core debris by establishing natural circulation in the lower sodium pool. The influence of heat removal rate by natural circulation on availability of the number of decay heat exchangers (DHX) dipped in the upper pool is also analyzed. It is seen that the temperatures in the inner vessel, source plate and the maximum debris temperature do not increase significantly even when the DHXs are deployed 5h after the accident, demonstrating the benefit of large thermal inertia of the pool.

Estimation of ground heat flux from soil temperature over a bare soil

Ground soil heat flux, G 0, is a difficult-to-measure but important component of the surface energy budget. Over the past years, many methods were proposed to estimate G 0; however, the application of these methods was seldom validated and assessed under different weather conditions. In this study, three popular models (force-restore, conduction-convection, and harmonic) and one widely used method (plate calorimetric), which had well performance in publications, were investigated using field data to estimate daily G 0 on clear, cloudy, and rainy days, while the gradient calorimetric method was regarded as the reference for assessing the accuracy. The results showed that harmonic model was well reproducing the G 0 curve for clear days, but it yielded large errors on cloudy and rainy days. The force-restore model worked well only under rainfall condition, but it was poor to estimate G 0 under rain-free conditions. On the contrary, the conduction-convection model was acceptable to determine G 0 under rain-free conditions, but it generated large errors on rainfall days. More importantly, the plate calorimetric method was the best to estimate G 0 under different weather conditions compared with the three models, but the performance of this method is affected by the placement depth of the heat flux plate. As a result, the heat flux plate was recommended to be buried as close as possible to the surface under clear condition. But under cloudy and rainy conditions, the plate placed at depth of around 0.075 m yielded G 0 well. Overall, the findings of this paper provide guidelines to acquire more accurate estimation of G 0 under different weather conditions, which could improve the surface energy balance in field.

New Fourier-series-based analytical solution to the conduction–convection equation to calculate soil temperature, determine soil thermal properties, or estimate water flux

Temperature is an important physical variable of soil. Heat transfer in soils predominantly occurs due to conduction and convection. In this paper, we present a new analytical solution, based upon the Fourier series boundary conditions for soil surface temperature, in which the separation of variables for the heat conduction–convection equation was established. Data that had been collected from the Qinghai-Xizang (Tibet) Plateau (QXP) were used to calculate the thermal diffusivity and the liquid water flux density using different methods. The results of the soil thermal diffusivity using 5cm as the upper boundary for the soil depth were used to calculate the soil temperature using both the single sine wave conduction and conduction–convection model and the Fourier series conduction–convection model. These results were then compared with the values for the temperature of the field soil measured at a depth of 10cm. The average standard error of the estimate (SEE), the normalized standard error (NSEE) and Bias were 0.16°C, 2.70% and 0.11°C for the Fourier series conduction–convection method. The results indicate that the Fourier series model provides a better estimate of observed field temperatures than the sine wave model. This method provides a useful tool for determining soil thermal parameters, simulating soil temperature and the parameterization of land surface processes for modeling permafrost changes under global warming conditions.

General circulation models of the dynamics of Pluto’s volatile transport on the eve of the New Horizons encounter

Pluto’s atmospheric dynamics occupy an interesting regime in which the radiative time constant is quite long, the combined effects of high obliquity and a highly eccentric orbit can produce strong seasonal variations in atmospheric pressure, and the strong coupling between the atmosphere and volatile transport on the surface results in atmospheric flows that are quite sensitive to surface and subsurface properties that at present are poorly constrained by direct observations. In anticipation of the New Horizons encounter with the Pluto system in July 2015, we present a Pluto-specific three-dimensional general circulation model (GCM), PlutoWRF, incorporating the most accurate current radiative transfer models of Pluto’s atmosphere, a physically robust treatment of nitrogen volatile transport, and the flexibility to accommodate richly detailed information about the surface and subsurface conditions as new data become available. We solve for a physically self-consistent, equilibrated combination of surface, subsurface, and atmospheric conditions to specify the boundary conditions and initial state values for each GCM run. This is accomplished using two reduced versions of PlutoWRF: a two-dimensional surface volatile exchange model to specify the properties of surface nitrogen ice and the initial atmospheric surface pressure, and a one-dimensional radiative–conductive–convective model that uses the two-dimensional model predictions to determine the corresponding global-mean atmospheric thermal profile. We illustrate the capabilities of PlutoWRF in predicting Pluto’s general circulation, thermal state, and volatile transport of nitrogen by calculating the dynamical response of Pluto’s atmosphere, based on four different idealized models of Pluto’s surface ice distribution from Young (Young, L.A. [2013]. Astrophys. J. 766, L22) and Hansen et al. (Hansen, C.J., Paige, D.A., Young, L.A. [2015]. Icarus 246, 183). Our GCM runs typically span 30years, from 1985 to 2015, covering the period from the discovery of Pluto’s atmosphere to present. For most periods simulated, zonal winds are strongly forced by a gradient wind balance, relaxing in later (recent) years to an angular momentum conservation balance of the seasonal polar cap sublimation flow. Near-surface winds generally follow a sublimation flow from the sunlit polar cap to the polar night cap, with a Coriolis turning of the wind as the air travels from pole to pole. We demonstrate the strong contribution of nitrogen sublimation and deposition to Pluto’s atmospheric circulation. As New Horizons data become available, PlutoWRF can be used to construct models of Pluto’s atmospheric dynamics and surface wind regimes more constrained by physical observations.

Numerical investigation of thermal regimes in twin-tube-channel heat pipelines using conductive-convective model of heat transfer

The results of numerical investigation are reported on thermal regimes in the systems of heat transport based on the solution of the conjugative problem of conductive-convective heat transfer in the system •twin-tube-channel underground heat pipeline„ environmental medium. It is shown that the use of the proposed approach allows one to perform the comprehensive analysis of the heating regimes in such systems.

A conduction–convection model for self-heating in piezoresistive microcantilever biosensors

Thermal drifting caused by the self-heating in piezoresistive microcantilever biosensors is a major source of inaccuracy. To this use, the present study derives a simple and accurate conduction–convection model to predict the temperature distribution in p-doped piezoresistive microcantilevers because of self-heating. The model is applied to a 4-layer gold-coated piezoresistive silicon dioxide microcantilever biosensor with u-shaped silicon piezoresistor. The analytical results are compared to the numerical results. The effect of convective heat transfer coefficient on temperature profile is also studied. The comparison results show the analytical and numerical results are accurate within 4%. The sensitivity results showed that the resistance change produced by thermal drifting is about five-to-eight times that by the surface stress. Finally, the cantilever temperature profile is found to be strongly affected by the piezoresistor size and the convective heat transfer coefficient.

An investigation of Pluto’s troposphere using stellar occultation light curves and an atmospheric radiative–conductive–convective model

We use a radiative–conductive–convective model to assess the height of Pluto’s troposphere, as well as surface pressure and surface radius, from stellar occultation data from the years 1988, 2002, and 2006. The height of the troposphere, if it exists, is less than 1 km for all years analyzed. Pluto has at most a planetary boundary layer and not a troposphere. As in previous analyses of Pluto occultation light curves, we find that the surface pressure is increasing with time, assuming that latitude and longitude variations in Pluto’s atmosphere are negligible. The surface pressure is found to be slightly higher ( 12.5 - 2.4 + 1.9 μbar in 1988, 18.0 - 1.7 + 11 μbar in 2002, and 18.5 ± 4.7 μbar in 2006) than in our previous analyses with the troposphere excluded. The surface radius is determined to be 1173 - 10 + 20 km . Comparison of the minimum reduced chi-squared values between the best-fit radiative–conductive–convective (i.e., troposphere-included) model and best-fit radiative–conductive (i.e., troposphere-excluded) shows that the troposphere-included model is only a slightly better fit to the data for all 3 years. Uncertainties in the small-scale physical processes of Pluto’s lower atmosphere and consequently the functional form of the model troposphere lend more confidence to the troposphere-excluded results.

Experimental Investigation of Thermal Dispersion in Saturated Soils with One‐Dimensional Water Flow

Microscopic differences in soil pore water velocity cause hydrodynamic dispersion of solute transport. By analogy, thermal dispersion should be considered in soils where water and heat flow occur simultaneously. Few published data are available regarding thermal dispersion in soils. In this study, we investigated thermal dispersion influences on heat transport in saturated soils with one‐dimensional water flow. A new soil container was developed to eliminate wall flow influences on saturated water flow. An inverse model was applied to obtain the thermal dispersion coefficient (λd) by fitting the conduction–convection–dispersion (CCD) model to soil temperature change as a function of time from heat‐pulse measurements. Thermal dispersion became significant when the water flux was higher than a threshold value. In the studied water flux range, the maximum contribution of hydrodynamic dispersion to effective heat conduction [λd/(λd + λ0), where λ0 is the bulk thermal conductivity] was 6, 9, and 12% in a sand, a silt loam, and a sandy clay loam, respectively. A power function relationship was established between λd and the soil water flux density (Jw): λd = kJw0.9, where k is a coefficient related to soil texture. Experimental evaluation indicated that, compared with the conduction–convection model, the CCD model performed better in describing the temperature change vs. time data from heat‐pulse measurements.

Investigation into occurring dynamic strain aging in hot rolling of AA5083 using finite elements and stream function method

Two-dimensional finite element analysis together with stream function and neural network models are employed to determine thermo-mechanical behavior during hot strip rolling of AA5083. An appropriate velocity field and stream function is first determined using the rule of volume constancy and upper bound theorem and then temperature field within the metal is predicted by means of a two-dimensional conduction–convection model. In order to consider the effect of flow stress and its dependence on temperature, strain and strain rate, a neural network model is also employed in the analysis. Based on the performed tensile tests, two different neural network models are constructed one for smooth yielding and the other one for the serrated flow. Then, the ANN models are coupled with the thermo-mechanical analysis. In the next step, by combination of the predicted temperature, strain and strain rates fields and the experimental data achieved from the tensile tests, the occurence of dynamic strain ageing during hot rolling is predicted. The model predictions are then compared with the experimental data and good agreement is observed between the two sets of results that shows the validity of the proposed model.

Evaluation of the Heat Pulse Ratio Method for Measuring Soil Water Flux

Soil water flux is an important hydrologic parameter, yet few techniques for measuring it in situ are available. Here we evaluate the heat pulse ratio method for measuring water flux. We conducted heat pulse measurements of flux in packed columns of sand, sandy loam, and silt loam soil. Water fluxes were calculated from the data following both a traditional temperature increase difference method and a new temperature increase ratio method. Both methods yielded similar estimates of flux, agreeing to within 0.84 cm h−1 on average. The low flow detection limits for both methods were also similar and ranged from 0.1 to 0.4 cm h−1 However, the ratio method was superior in that it permitted simpler calculations, reduced the number of required parameters by four, and exhibited two to three times greater precision. We found strong linear relationships (r2 ≥ 0.98, standard error < 0.4 cm h−1) between estimated and imposed water fluxes up to 40 cm h−1 However, the slopes of these relationships were less than one, ranging from 0.739 for the sand to 0.224 for the sandy loam. These slopes indicate that the sensitivity was less than predicted by the standard conduction–convection model. We have not discovered the cause of these errors, but we did find that the errors could not be explained by increasing the magnitude of the conduction term in the model as has been previously suggested. Instead, the errors could be explained by reducing the magnitude of the convection term. This finding can help direct future research efforts to improve the accuracy of the ratio method.

A minimization procedure for estimating the power deposition and heat transport from the temperature response to auxiliary power modulation

A method commonly used for determining where externally launched power is absorbed inside a tokamak plasma is to examine the temperature response to modulation of the launched power. Strictly speaking, this response merely provides a first good guess of the actual power deposition rather than the deposition profile itself: not only local heat sources but also heat losses and heat wave propagation affect the temperature response at a given position. Making use of this, at first sight non-desirable, effect modulation becomes a useful tool for conducting transport studies. In this paper a minimization method based on a simple conduction–convection model is proposed for deducing the power deposition and transport characteristics from the experimentally measured (electron) energy density response to a modulation of the auxiliary heating power. An L-mode JET example illustrates the potential of the technique.

The Role of an Internal Heat Source for the Eruptive Plumes on Triton

For the first time the role of the internal heat source, due to radioactive decay in Triton's core, is investigated with respect to geyser-like plumes. Triton is one of only three known objects in the Solar System (the other two are Earth and the jovian satellite Io) where eruptive activity has been definitely observed. A new mechanism of energy supply to the Tritonian eruptive plumes is proposed. This mechanism is based on heat transport in the solid-nitrogen polar caps due to thermal convection, in addition to conduction. The conductive–convective model shows that a 1 K increase in the N 2ice subsurface temperature over the surface value is reached much closer to the surface in the region of an upwelling subsurface plume compared with a pure conductive case. This temperature rise is sufficient to double the nitrogen vapor pressure. Therefore, it is enough to drive the atmospheric plumes to the observed height of ≈8 km, provided 1 K warmer nitrogen ice encounters a vent and hence is exposed to the ≈15-μbar Tritonian atmosphere. Solid-state convection onsets if a nitrogen layer is sufficiently thick and the average solid N 2grain size is small enough. Critical values of these parameters are presented for Triton. A possible origin of the subsurface vents on Triton is also suggested.

Layered thermohaline natural convection

The results of two quasi-steady experiments in layered, double-diffusive convection are presented and interpreted in terms of a steady-state model. In the experiments heat and salt are transported upward through two horizontal convecting layers of water which are separated by a thermocline. a region of large temperature and concentration gradients. As the thermocline stability number β cΔC β 1ΔT increases, the thermocline becomes thicker and the fluxes of heat and salt decrease. These two characteristics of the thermohaline system are shown to be consistent with a conduction-convection model which views the thermocline as a conduction region separating two convective boundary layers. That molecular diffusion is the dominating transport process in the central portion of the thermocline is experimentally verified. The thickness of the conducting region is found to vary with the imposed boundary conditions in such a manner as to maintain conditions of near neutral stability across the boundary layers.