This work is focused on the transient heat transfer of non-Newtonian fluid in a coil-cooled stirred tank through experimental and numerical approaches. A modified lumped capacitance method was ...established for a more accurate definition of the time constant at a limited coolant flowrate. The modified method breaks down the time constant into two terms: the first term is based on the system heat transfer capability and the second one on the coolant heat transport capability. Limited by the assumption of an infinite cooling capability, the simple lumped capacitance method attributes all of the time constant solely to the first term. The significant difference between the two models results in fundamentally different derivations used to calculate the overall heat transfer coefficient. Theoretical analysis indicates that the modified method align harmoniously with its original form. The results manifest that: (1) Within the operating range of all tests, the second term contributes 26.5–12.9% to the total time constant as coolant flowrate increases, making it a significant factor that should not be overlooked. (2) The simple method underestimates the overall heat transfer capability by 15.4–29.2% compared to the modified one. It subsequently underestimates the coil external and internal convection coefficients by up to 12.8% and 70.6% in comparison to the modified model, respectively, compared to the modified model. (3) The CFD-predicted overall heat transfer coefficient, coil external convection coefficient, and coil internal convection coefficient deviate by a maximum of 15.2%, 7.2%, and 32.1% respectively compared to the experimental values obtained through the modified lumped capacitance method. By the way, the CFD-predicted coil internal convection coefficient closely aligns with the Nusselt correlation for straight tubes adjusted using Cr = 1.2. (4) A thorough analysis of CFD results reveals complex dynamics in stirred tanks, such as viscosity distribution patterns and areas of limited mass and heat exchange between middle and bottom impellers. This deep understanding enables root cause analysis crucial for optimizing configurations or designing uniquely structured tanks. (5) The revised lumped capacitance method expands on its original version by transitioning from assuming infinite cooling to accounting for limited transient cooling capacity. This shift is more realistic and crucial for thermal management and process control.
•Coil heat transfer coefficients of CMC solution in a stirred tank investigated.•Modified lumped capacitance method was proposed.•Modified time constant depends on both heat transfer capability and heat transport capability.•Coefficients are notably underestimated by simple method.•CFD predictions agree well with experiments and provide meaningful insights.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
The electrochemical performance of lithium-ion batteries is highly temperature dependent. An accurate determination of battery thermal parameters is crucial for research including cell thermal ...analysis, safety design, and multiphysics simulations. This work explores the possibility to use a lumped capacitance model based experimental approach to measure the battery convective heat transfer coefficient and specific heat capacity. In this approach, the transient temperature of the battery and its can (by removing the jellyroll) is measured with an infrared radiation camera. When the Biot number of the battery Bi ≪1, the lumped capacitance model can be used to determine cell specific heat capacity through the measured battery surface temperature, where the convective heat transfer coefficients of both the can and the battery are the same and the specific heat capacity of the can is known. As an example, the specific heat capacity of LG G5 smartphone batteries is measured to demonstrate the proposed approach. The specimens are tested under both natural and forced convection conditions. The measured cell specific heat capacity is very consistent between these two convection conditions.
•Method to measure thermal properties of cells with a small Biot number is presented.•Infrared camera is used to measure cell surface temperature.•An isovalue-based method to calculate cell averaged temperature is proposed.•Measured cell specific heat capacity under two convection conditions is consistent.•Temperature from simulations with measured properties matches experimental results.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Pyrolysis of crushed olive stone particles in a lab scale Bubbling Fluidized Bed (BFB) reactor was investigated. The time evolution of the pyrolysis conversion degree of the olive stone particles, ...while moving freely in the BFB, was determined from the evolution of the mass of olive stones remaining in the bed, measured by a precision scale holding the whole reactor installation. The experimental measurements of the pyrolysis conversion degree were employed to validate a simple model combining heat transfer and chemical kinetics, which is valid for thermally small particles. The model combines the Lumped Capacitance Method (LCM) and the simplified Distributed Activation Energy Model (DAEM) to account for heat transfer and pyrolysis chemical kinetics, respectively. The estimations of the combined LCM-DAEM model for the pyrolysis conversion degree were found to be in good agreement with the experimental measurements for the pyrolysis of olive kernels in a BFB operated at various bed temperatures, fluidizing gas velocities, and biomass particle size ranges. From the combined LCM-DAEM model, the characteristic heating time and the pyrolysis time of the olive stone particles were derived, obtaining a direct relation between these two parameters for constant values of the bed temperature.
•Pyrolysis of olive stones is analyzed in a macro-TGA bubbling fluidized bed (BFB).•A combined heat transfer and kinetic model is proposed to describe pyrolysis.•The combined model is validated with the experimental measurements in the BFB.•Heating and pyrolysis times are obtained for various operating conditions.•Inverse relation of heating to pyrolysis time ratio with bed temperature was found.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•An initial model is developed for a solid cylindrical heat storage unit.•The analytical solution of the model is determined by using Laplace transform method.•A new optimization method for the solid ...storage module design is proposed.•The influence of design parameters on the storage cost is investigated.•The optimization designs for various kinds of system requirement are studied.
Solid sensible heat storage is an attractive option for high-temperature storage applications in terms of investment and maintenance costs. Typical solid thermal energy storage systems use a heat transfer fluid to exchange heat as the fluid flows through a tubular heat exchanger embedded in the solid storage material. The modified lumped capacitance method is used with an effective heat transfer coefficient in a simplified analysis of the heat transfer in solid thermal energy storage systems for a solid cylindrical heat storage unit. The analytical solution was found using the Laplace transform method. The solution was then used to develop an optimization method for designing solid storage modules which uses the system requirements (released energy and fluid outlet temperature) as the constraint conditions and the storage module cost as the objective function for the optimization. Optimized results are then given for many kinds of system configurations.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
► We introduced corrected heat transfer coefficients for solid bodies in fluid. ► Lumped capacitance method can then be applied for bodies with large Biot numbers. ► Corrected heat transfer ...coefficients were obtained for four types of solid bodies. ► Solutions by the corrected lumped capacitance method were compared to analytical results. ► The agreement between the two methods is very good.
In a typical thermal energy storage system, a heat transfer fluid is usually used to deposit/extract heat when it flows through a packed bed of solid thermal storage material. A one-dimensional model of the heat transfer and energy storage/extraction for a packed-bed thermal storage system has been developed previously by the authors. The model treats the transient heat conduction in the thermal storage material by using the lumped capacitance method, which is not valid when the Biot number is large. The current work presents an effective heat transfer coefficient between the solid and fluid for large Biot numbers. With the corrected heat transfer coefficient, the lumped capacitance method can be applied to model the thermal storage in a wide range of Biot numbers. Four typical structures for the solid thermal storage material are considered. Formulas for the effective heat transfer coefficient (and effective Biot number) are presented. To verify the prediction by the lumped capacitance method using the effective heat transfer coefficient, we compare the results to the corresponding analytical solutions. The results are in very good agreement. The effective heat transfer coefficient extended the validity of the lumped capacitance method to large Biot numbers, which is of significance to the analysis of thermal energy storage systems.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
•A simple model is proposed to describe the pyrolysis of thermally small particles.•Lumped Capacitance Method (LCM) was applied to describe transient heat transfer.•Distributed Activation Energy ...Model (DAEM) was used to account for kinetics.•LCM-DAEM model was validated with experimental pyrolysis measurements.•Comparison of model and experiments lead to deviations below 5 °C in all cases.
The pyrolysis process of thermally small biomass particles was modeled combining the Lumped Capacitance Method (LCM) to describe the transient heat transfer and the Distributed Activation Energy Model (DAEM) to account for the chemical kinetics. The inverse exponential temperature increase predicted by the LCM was considered in the mathematical derivation of the DAEM, resulting in an Arrhenius equation valid to describe the evolution of the pyrolysis process under inverse exponential temperature profiles. The Arrhenius equation on which the simple LCM-DAEM model proposed is based was derived for a wide range of pyrolysis reactor temperatures, considering the chemical kinetics data of four lignocellulosic biomass species: pine wood, olive kernel, thistle flower, and corncob. The LCM-DAEM model proposed was validated by comparison to the experimental results of the pyrolysis conversion evolution of biomass samples subjected to various inverse exponential temperature increases in a TGA. To extend the validation, additional biomass samples of Chlorella Vulgaris and sewage sludge were selected due to the different composition of microalgae and sludge compared to lignocellulosic biomass. The deviations obtained between the experimental measurements in TGA and the LCM-DAEM predictions for the evolution of the pyrolysis conversion, regarding the root mean square error of temperature, are below 5 °C in all cases. Therefore, the simple LCM-DAEM model proposed can describe accurately the pyrolysis process of a thermally small biomass particle, accounting for both the transient heat transfer and the chemical kinetics by solving a simple Arrhenius equation.
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GEOZS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPUK, ZRSKP
Thermal behaviors significantly affect the contact stiffness and position accuracy of the rolling linear guide, which worsen the performance of the precision machinery. In this paper, based on the ...modified lumped capacitance method (MLCM) and finite element method (FEM), a thermal model of rolling linear guides has been formulated in terms of the geometric parameters, friction, gyroscopic moment, and loading conditions. Experimental results show that the thermal model can well predict the real-time temperature variation under different working conditions. Further analysis shows that, the applied vertical load, carriage velocity, and toque load significantly influence the temperature variation of linear guides, while the influence of the torque load on temperature variation decreases with increasing vertical load levels. Besides, the reasons of the steady-state temperature variation considering the load distribution model are also discussed.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
•Design of thermal energy storage is important for CSP plants.•Simplification of the analysis of the packed bed storage system is attempted.•We extend the validity range of lumped capacitance method ...to larger Biot numbers.•An effective heat transfer coefficient is derived from the exact analytical solution.•The developed method is generalizable to three dimensions.
Analysis of the transient temperature evolution during charging or discharging of the packed bed thermal storage systems is immensely simplified with the formulation of an effective heat transfer coefficient between the solid storage materials and the heat transfer fluid. It can cut significant computational cost which is otherwise required for a complete numerical simulation. The lumped capacitance method, the simplest of the available options, is restricted only to the low Biot number scenarios and hence is seldom applicable to any real system. The formulation of the effective heat transfer coefficient allows the extension of the lumped capacitance method for moderate Biot numbers. The present work develops such a formulation to simplify the analysis of packed bed storage systems through analytical route. Earlier attempts in this direction were made through weighted average time method which is inherently restricted to the simple one-dimensional heat conduction problems. On the other hand, we find out the effective heat transfer coefficient starting from a general three dimensional analytical solution of the transient heat conduction and proceed with the well-known one term approximation which acts as the basis of the Heisler charts. The method is not dimensionally restricted and hence we can include realistic three dimensional shapes such as cuboid, short cylinder etc. in the formulation. We validate our method by comparing the resulting temperature profiles for the one-dimensional geometries which have been attempted earlier by the weighted average time method. We also provide the accuracy estimation (as a function of increasing Biot number) against the full numerical simulation for the geometries where the weighted average time is not applicable. Therefore, the current study provides the tool for an inexpensive theoretical estimation for the transient heat transfer behaviour in the thermal storage tanks which has long term design implications particularly for the large scale concentrated solar thermal power plants.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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