Multiple Heat Sources Research Articles

Male personal heat exposures and fecundability: A preconception cohort study.

Several studies indicate adverse effects of selected heat exposures on semen quality, but few studies have directly evaluated fertility as an endpoint. We evaluated prospectively the association between male heat exposures and fecundability, the per-cycle probability of conception. We analyzed data from 3041 couples residing in the United States or Canada who enrolled in a prospective preconception cohort study (2013-2021). At enrollment, males reported on several heat-related exposures, such as use of saunas, hot baths, seat heaters, and tight-fitting underwear. Pregnancy status was updated on female follow-up questionnaires every 8weeks until conception or a censoring event (initiation of fertility treatment, cessation of pregnancy attempts, withdrawal, loss to follow-up, or 12 cycles), whichever came first. We used proportional probabilities regression models to estimate fecundability ratios (FR) and 95% confidence intervals (CIs) for the association between heat exposures and fecundability, mutually adjusting for heat exposures and other potential confounders. We observed small inverse associations for hot bath/tub use (≥3vs. 0 times/month: FR=0.87, 95% CI: 0.70-1.07) and fever in the 3 months before baseline (FR=0.94, 95% CI: 0.79-1.12; one cycle of follow-up: FR=0.84, 95% CI: 0.64-1.11). Little association was found for sauna use, hours of laptop use on one's lap, seat heater use, time spent sitting, and use of tight-fitting underwear. Based on a cumulative heat metric, FRs for 1, 2, 3, and ≥4versus 0 heat exposures were 0.99 (95% CI: 0.87-1.12), 1.03 (95% CI: 0.89-1.19), 0.94 (95% CI: 0.74-1.19), and 0.77 (95% CI: 0.50-1.17), respectively. Associations were stronger among men aged ≥30 years (≥4vs. 0 heat exposures: FR=0.60, 95% CI: 0.34-1.04). Male use of hot tubs/baths and fever showed weak inverse associations with fecundability. Cumulative exposure to multiple heat sources was associated with a moderate reduction in fecundability, particularly among males aged ≥30 years.

Effective thermal management of heat sources in sustainable energy devices using a compact flat thermosyphon

Thermal management is critical in improving the efficiency, lifespan, and reliability of sustainable energy devices such as LEDs, batteries, and solar cells. The compact flat thermosyphon (CFT) is more reliable for the effective thermal management of multiple heat sources in energy-intensive devices. A comprehensive study on the thermal performance of a two-phase CFT is conducted in the present study. The volume of the CFT is 72 × 24 × 15 mm3 and is made up of copper. The thermal performance of the CFT is analyzed by varying the filling ratio (20%, 50%, 80%), working fluid (acetone, ethanol, water), number of heat sources, and condenser surface wettability. The best-performing filling ratio is found to be 50%. Water is the best performing working fluid over a wide range of heat fluxes (10 – 70 W/cm2) due to high heat capacity, latent heat, and low vapor pressure. The CFT can safely cool up to four heat sources of size 12 × 24 mm2 at a heat flux of 30 W/cm2 each. The lifespan of the devices can be increased by 2.49 – 6.62 times when the CFT is used to cool multiple heat sources instead of a cold plate. The superhydrophobic condenser surface further improved the thermal performance of the CFT by 28 – 47% because of the quicker return of condensate and dropwise condensation.

Investigation on the two-phase flow and heat transfer behaviors in a new central uniform dispersion-type heat exchanger

In order to improve the temperature uniformity of multiple chips, a new central uniform distributed heat exchanger (CUD) is designed. Firstly, adopting ethanol solution as coolant, the cooling ability of the heat exchanger is numerically investigated by using VOF gas-liquid two-phase flow model, and the two-phase flow experimental system is established to verify the correctness of the numerical results. The results show that the Tavg (average temperature of heat sources) error range between the experimental and numerical values is 1 K ~ 3 K, and the relative error of SDT (standard deviation of temperature) is 6% ~ 10%. This verifies the accuracy of the numerical simulation method. Secondly, the two-phase flow boiling heat transfer behavior are compared with that of single-phase flow with water as coolant. The results show that with the increase of inlet flow, the thermal resistance and average temperature of two-phase flow change are less than that of single-phase flow. This indicating that two-phase flow has better advantages in improving the temperature uniformity of multiple heat sources. Thirdly, the heat transfer characteristics of radiators with different Wi are studied. Compared with Case1, the boiling heat transfer coefficient of Case3 and Case4 can be increased by 12.3% and 18.3%, respectively. However, Case3 is a better choice by weighing the pressure drop. Finally, the prediction functions of the boiling heat transfer coefficient and pressure drop is established, and the multi-objective genetic algorithm is used to obtain the best parameters of this heat exchanger. The average heat transfer coefficient of the optimized heat exchanger can be increased by 7.56%, and the pressure drop can be reduced by 3.54% compared to the exchanger before optimization. Furthermore, the heat dissipation ability of the optimized heat exchanger design is studied numerically. The simulated results are in good agreement with the optimization results.

A quasi-dynamic model and thermal analysis for vapor chambers with multiple heat sources based on thermal resistance network model

The heat and mass transfer mechanism in a vapor chamber is a complex process. The thermal resistance network model is an effective tool to describe the heat transfer behavior of a vapor chamber (VC). An improved quasi-dynamic multi heat source model has been developed in this study to analyze the temperature distribution of a vapor chamber with multiple heat sources under dynamic operating conditions. The accuracy of the proposed model has been validated by experiments. The influence of the VC thickness and thickness ratio has also been analyzed. Different heat source inputs have been used to study the startup characteristics of the vapor chamber. The results from simulations reveal that the optimum thickness ratio for a VC depends on the thermal resistance as well as heat transfer limit. Under the same cooling conditions, a longer startup time for a VC was observed with the increase in heating power. In addition to this, the thermal resistance of a vapor chamber was found to increase slightly at a higher temperature. The model in this study has certain guiding significance for the analysis of heat transfer and the design of a VC under various working conditions. • Thermal resistance network model for vapor chambers with multiple heat sources is established. • Quasi-dynamic approach for transient analysis with high accuracy. • The influences of thickness and optimum thickness ratio are analyzed. • Startup characteristics and thermal resistance are analyzed.

Techno-Economic Optimization of a Low-Temperature Organic Rankine System Driven by Multiple Heat Sources

This study presents the optimization of organic Rankine cycle (ORC) which utilizes low temperature waste heat from the aluminum production process and two low temperature renewable energy sources, solar thermal energy and geothermal energy. As geothermal energy is present at lower temperature level compared to the other two heat sources, two separate ORC cycles are considered. Optimization of the proposed system is performed based on a non-linear programming (NLP) formulation by maximizing the thermodynamic and economic performance of the system. The main variables considered in the model include temperature, pressure, flowrate, mass enthalpy, and energy flows of all the streams in the system. To optimize the variables in the system, correlations were developed, which were formulated as NLP models and optimized by minimizing the sum of least squares. The results show that most of the generated power output can be provided by the waste heat, while the lowest by the solar energy due to the relatively low average solar irradiance at considered location. When monthly time periods are considered, the highest electricity production is generated by the working fluid R1245fa in June, and amounts to 830.4 kW from waste heat, 246.5 kW from geothermal energy and 149.4 kW from solar energy. The proposed system is economically feasible for all three studied working fluids and the discount rates of 2% and higher. The final conclusions indicate that the proposed ORC system utilizing waste heat, geothermal and solar thermal energy, can generate power in a more sustainable way.

A Multi-Source Co-Simulation Method for the Thermal Stability of GaAs Sub-6G Power Amplifier with Adjustable Bias Current

In this paper, the thermal stability of GaAs heterojunction bipolar transistor (HBT) power amplifier (PA) in a sub-6G band has been improved by a multi-source co-simulation method. To reduce the parameter errors caused by the variations of thermal resistances, a co-simulation method for the multiple heat sources of fully-integrated PA is proposed. Specifically, an adjustable bias circuit is applied on the PA for temperature compensation using a zero-to-absolute-temperature (ZTAT) current. To verify the proposed method, a sub-6G PA is realized in the GaAs HBT process. The experimental results show that the variations in power added efficiency and output power is stabilized due to the 3.5% error ZTAT current. The errors between simulation and measurement are reduced from 6% to 1%. According to the thermal factor defined in co-simulation, the working temperature decreases 10 °C, while the area only increases 27%. The above results prove that that thermal stability and the simulation reliability can be co-designed with the minimal area cost.

Experimental investigation on the start-up performance of a novel flat loop heat pipe with dual evaporators

Thermal management for multiple heat sources has been becoming increasingly important, especially under high heat flux conditions. As a passive heat transfer device, loop heat pipes (LHP) with multiple evaporators does not consume extra energy, demonstrating a great potential in thermal management. This paper proposed a flat plate LHP with dual evaporators for the first time. Two flat plate evaporators were adopted, and both of them had their own porous wick, compensation chamber (CC) and vapor line. The condensed liquid converged, then moved along the main liquid line. The CC of two evaporators was joined by a tube, which can ensure the sharing of the returning liquid. To verify the performance of novel flat plate LHP, the start-up test was investigated under different heat load arrangements, involving only a single evaporate was applied heat load, two evaporators were applied with the equal or unequal heat load. Meanwhile, the operation stability was determined by testing the performance with the successionally variable heat load. This system has been shown to operate successfully at heating source temperature below 100 °C with heat load ranging from 10 W–10 W to 130 W–130 W (corresponding to the maximum heat flux of 13.52 W/cm2).

Experimental study on temperature uniformity and heat transfer performance of nitrogen loop heat pipe with large area and multi-heat source

• A large area loop heat pipe with multiple heat sources is designed. • The temperature uniformity and heat transfer performance are tested. • The heat pipe starts up and operates smoothly in anti-gravity. With the development of space technology, the requirements of thermal control on spacecraft are increasing. In space missions, due to the improvement of the detection accuracy, the diameter of deep space telescope is becoming larger and larger. These detection instruments need efficient and reliable thermal management. Thus, the application of the large-scale cryogenic cooling technology, which can provide heat dissipation for the continuous and long life of the detector, has become a difficult problem. In the present study, a large-area cryogenic loop heat pipe is designed for the optical telescope. It is a good combination of multi heat source and large-area cryogenic loop heat pipe. The main evaporator is cylindrical due to fit the lens barrel. The heat exchange area can reach 1 m 2 , and the average temperature performance is less than 5 K. The condenser adopts the form of parallel pipeline to further reduce the system resistance and ensure the smooth operation of loop heat pipe. Its operation stability and temperature uniformity of the main evaporator under different total loads are experimentally studied and analyzed. It is proved that the loop heat pipe is feasible for large area multi-heat source cryogenic loop heat pipe in engineering. It can also start up and run normally under anti-gravity conditions. The experimental results show that the large area multi-source heat collection cryogenic loop heat pipe can be started and run normally in the temperature range of 80–120 K.

Technical and commercial viability assessment of liquid-cooled heat sinks for a circuit board with discrete heat loads

In this contribution, existing gaps in the design process of liquid-cooled heat sinks, i.e., the lack of overall performance assessment metrics and commercial viability analyses, are addressed. This work focused on the design of a cost-effective cooling system for a commercial circuit board with multiple and asymmetric heat sources designed and manufactured by an electronics company. The analysis was performed using 3-D computational fluid dynamics simulations across sixteen different cases, focusing on the effect on performance and manufacturing cost of two primary design features of liquid-cooled heat sinks: the inlet and outlet manifolds and heat transfer enhancing features, where pin fins and minichannels were considered. Specifically, the effect of diameter and spacing of the pin fins and the effect of the distribution and length of the mini channels over an unevenly heated surface were parametrically investigated. The tradeoff between thermal and hydraulic performance of the heat sinks was reconciled using an overall performance parameter, which allowed for a single numerical evaluation of the heat sinks’ global performance spanning several operating flow conditions. Likewise, the tradeoff between cost and performance was investigated by comparing the manufacturing cost of the different heat sink designs, including two heat spreader materials. Lastly, a comprehensive assessment of the potential cooling solutions for the circuit board was done by combining the overall performance and manufacturing cost per prototype through a novel parameter proposed herein. The broader liquid-cooled heat sink design approach reported in this work is a missing aspect in similar contributions, as the focus is solely on technical performance parameters, while commercial implementation issues (manufacturability and production cost) are neglected.

Toolbox for modeling frequency-domain photothermal experiments on multilayers

A general expression (master equation, ME) is derived for the thermal impedance in photothermal experiments in a multilayer system, based on one-dimensional (1D) periodic heat diffusion. The ME in a compact form benefits from newly defined generalized, higher-order thermal reflection and transmission coefficients. The modeled system comprises seven layers among which a semitransparent sample and a transducer that integrates the temperature field within it (e.g., a pyroelectric sensor). The ME can be adapted to various experimental cell structures used in photopyroelectric, photoacoustic, photothermal radiometry, or thermoreflectance methods using volume- or surface-temperature detection, in view of spectroscopic applications or thermophysical properties determination. The derivation of special cases is facilitated by applying simple contraction rules to dimensionless quantities. Modeling multiple heat sources in the system is done by superposition of individual solutions. The possible extension of the 1D model to 2D geometry is demonstrated, in general, and practical criteria are discussed.

Hot spot temperature optimization of customized region in multi-region integrated system based on variational method

Multi-region integrated heat transfer process involving heat conduction and convection is commonly adopted in practical production. Optimization equations from variational method are effective for design of velocity fields in heat convection process. However, equations for optimization of hot spot temperature are not yet been proposed, which is the core issue in cooling problems, especially for microelectronic devices. Moreover, convection of flow region in multi-region system is concerned in previous researches, yet heat conduction of the solid region is usually ignored, which thus fails to obtain the optimal results. In this study, optimization equations which aim at minimizing the hot spot temperature in a multi-region integrated heat transfer system is developed. An objective function to characterize the highest temperature (Tmax) is proposed, based on which the optimization equations of target regions and constraint regions are derived using variational method for minimization of Tmax in target region. A numerical case with multiple heat sources is used to verify the effectiveness of the proposed optimization equations. The results show that the optimal velocity field from the optimization equations remarkably reduces the hot spot temperature of the target regions. When setting all the heat sources as the target regions, Tmax obtained from the optimization equations is 22.6 K lower than that before optimization, and the temperature difference of the heat sources (ΔT) is reduced by 98%. Compared to the optimization equations in the previous study, the developed equations reduce Tmax and ΔT by 1.6 K and 85%, respectively. When choosing one of the heat sources as the target region, Tmax of this heat source after optimization is reduced by 3.6–5.1 K compared with that with all heat sources as target region. The optimization equations aiming at minimizing the proposed objective function exhibit excellent performance in reducing hot spot temperature in multi-region integrated heat transfer process, and the optimal velocity fields from optimization equations can effectively guide the design of enhanced heat transfer system.

High-flux flowing interfacial water evaporation under multiple heating sources enabled by a biohybrid hydrogel

Interfacial water evaporation holds great promise in clean water production. However, developing the evaporator with a high evaporation rate and excellent antifouling property remains a challenge. In this paper, we designed a polypyrrole-coated bacterial cellulose hydrogel (PPy-BCH) with a low evaporation enthalpy of 1.97 MJ kg−1. PPy-BCH was used as the absorber of the flowing evaporator driven by solar irradiation and electro-heating. The highest evaporation rate of 1.78 and 5.88 kg m−2 h−1 was obtained in pure water under 1 sun and 70 ℃ heating conditions, respectively. Benefitting from the superior salt-rejecting ability of this structure and the excellent antifouling properties of the hydrogel, the evaporator enabled a stable performance in seawater and industrial wastewater. The electro-heating platform could be replaced by low-temperature waste heat for large-scale application, considering that the amount of low-temperature waste heat below 200 ℃ is vast worldwide. In addition, the life cycle assessment showed that the flowing evaporator driven by waste heat enabled a lower carbon emission than desalination technologies such as reverse osmosis. Finally, we also demonstrated that the waste heat could enhance the evaporation performance of the evaporator under weak solar irradiation, therefore achieving all-weather clean water production. In conclusion, this study provided a novel way to design a high-flux interfacial water evaporator for fast water treatment and clean water production.

System development and simulation investigation on a novel compression/ejection transcritical CO2 heat pump system for simultaneous cooling and heating

The problems that the expansion work cannot be recovered and the heat source of the evaporator is insufficient have been found in the previous experimental research, and thus this paper proposes a novel compression/ejection transcritical CO2 heat pump system for simultaneous cooling and heating. An ejector and a water source evaporator are added to the novel system, which realizes the improvement of the compressor inlet grade and the utilization of multiple heat sources. The feasibility of the novel system is verified at first, by numerically analyzing the system operating characteristics variation tendency. The simulation results show that COPtotal of the novel system can reach 11.7 in the compressor frequency of 30 Hz and the discharge pressure of 8000 kPa. In addition, the novel system is compared with the basic transcritical CO2 heat pump system and the transcritical CO2 ejector heat pump system in the exergy, energy and economic aspects. The dual-evaporator design helps the novel system achieve the highest total COP. The simulation results show that the novel system owns 12% higher exergy efficiency over the ejector system, and yields the shortest payback period of 1.10 years among the three considered systems.

Design and performance evaluation of a new thermal energy storage system integrated within a coal-fired power plant

Thermal power plants are required to enhance operational flexibility to ensure the power grid stability with the increasing share of intermittent renewable power. Integrating thermal energy storage is a potential solution. This work proposes a novel system of molten salt thermal storage based on multiple heat sources (i.e., high-temperature flue gas and superheated steam) integrated within a coal-fired power plant. To evaluate the performance of the thermal energy storage system, simulation models were established, and exergy analysis was conducted. Results show that the integration of molten salt thermal storage achieves the synergistic improvement of operational flexibility and thermal efficiency of the thermal power system. When the boiler keeps steady combustion, the minimum power load decreases from 30% to 14.51% of the rated load during the charging process because of the integration of the thermal energy storage system. To decrease the power load of the coal-fired power plant, the surplus heat is stored in the thermal storage system to be used later. The equivalent round-trip efficiency of the thermal energy storage system is up to 85.17%, which is achieved by the appropriate match between the heat sources and the thermal storage media.

Spatial variations of PM2.5 emissions and social welfare induced by clean heating transition: A gridded cost-benefit analysis

Clean heating (CH) is regard as a key strategy to address the serious air pollution problem in northern China. A “one-fit-all” CH strategy will harm social welfare and engender resistance, due to the differences in heating habits and residents' income between urban and rural areas. To solve this problem, a 5 km × 5 km gridded cost-benefit analysis model for CH is build. Taking the case city as an example, an improved CH solution integrating multiple heat sources is proposed. By utilizing ISH resources, which are low-cost and low-emission-intensity, the improved solution reduces heating-induced PM2.5 emissions to one-fifth, and achieves higher net social benefits than existing CH strategies. Moreover, the spatial distributions of PM2.5 emission reductions and indoor and outdoor health benefits induced by CH strategy, including coal-to-gas/electricity and the improved strategy we propose, are simulated; revealing that the spillover effects of pollutants make CH will somewhat inevitably bring about a transfer of social welfare from rural areas to urban areas, but this can be compensated by opposite direction subsidies.

Experimental study on the effect of filling ratio on an R141b two-phase thermosyphon loop with a horizontal parallel tube evaporator

A two-phase thermosyphon loop is an ideal heat transfer device to achieve compact and efficient cooling with low energy consumption. In this paper, a two-phase thermosyphon loop with a horizontal parallel tube evaporator for multiple heat source cooling is proposed. The effect of the filling ratio on the transient response of temperature and pressure, heat transfer characteristics, instability issues, as well as flow regimes under different heat loads are investigated experimentally and visually. The filling ratios are divided into three groups according to their unique heat transfer and instability characteristics. The research results show that a too low or too high filling ratio is not conducive to the safe and stable operation of the system. At medium and high filling ratios, temperature and pressure overshoot are prone to occur, threatening the safe operation of the system; geyser boiling is another unstable phenomenon that can be inhibited as the heat load increases. Gravity will lead to uneven distribution of working fluid in the evaporator and further affect the temperature uniformity and heat transfer capability. From the perspective of temperature control performance and heat transfer capability, 30% is the optimal filling ratio in this study, with a minimum thermal resistance of 0.12 ℃ ⋅W-1 and a maximum heat transfer coefficient of 1345.36 W⋅m−2⋅℃−1. This paper provides a basis for designing and applying a two-phase thermosyphon loop for multiple heat source cooling in confined spaces.

Thermal performance of a tandem-dual-channel flat-plate pulsating heat pipe applicable to hypergravity

Thermo-hydrodynamic characteristics of a novel flat-plate pulsating heat pipe (FP-PHP) with a symmetrically tandem dual-serpentine-channel were studied experimentally under the simulated hypergravity by a rotating platform capable of providing an adjustable centrifugal acceleration up to a = 4 g0 (g0 = 9.8 m/s2) on ground. The influences of gravity level, heat load, and orientation (i.e., circumferential orientation (C-O) and radial orientation (R-O)) on thermo-hydrodynamic performance of the FP-PHP were investigated. It is indicated that, similar to the traditional single-serpentine PHPs under the normal gravity, the quasi-steady flow motion in the FP-PHP under the hypergravity could be also classified into five flow patterns, i.e., stop-over, intermittent pulsation, pulsation, pulsation with circulation and circulation. Increasing hypergravity level is not conducive to the start-up process of the FP-PHP, which needs larger start-up heat load and higher start-up temperature. Even so, under a ≤ 4 g0, the FP-PHP can successfully start up within decent temperature level of 58 °C. Growing hypergravity level induces increasing negative influences on the thermo-hydrodynamic performance of the FP-PHP, which is more obvious under the R-O than that under the C-O. Anyway, in general, FP-PHP possesses a good thermal performance uniformity, which has an average coefficients of variation less than 3% in thermal resistance of its two symmetric halves. In addition, FP-PHP has an average equivalent thermal conductivity 4.38 times that of the pure 6063 aluminum alloy plate and a total weight 83.6% of it. The average equivalent thermal conductivity ratio of the FP-PHP under the hypergravity of a ≤ 4 g0 to that under the normal gravity is not smaller than 0.70, indicating a good adaptability of the FP-PHP to hypergravity. Accordingly, the FP-PHP could be regarded as a promising option for modern avionics passive thermal control systems for multiple heat sources.

Tomographic reconstruction from planar thermal imaging using convolutional neural network

In this study, we investigate perspectives for thermal tomography based on planar infrared thermal images. Volumetric reconstruction of temperature distribution inside an object is hardly applicable in a way similar to ionizing-radiation-based modalities due to its non-penetrating character. Here, we aim at employing the autoencoder deep neural network to collect knowledge on the single-source heat transfer model. For that purpose, we prepare a series of synthetic 3D models of a cylindrical phantom with assumed thermal properties with various heat source locations, captured at different times. A set of planar thermal images taken around the model is subjected to initial backprojection reconstruction, then passed to the deep model. This paper reports the training and testing results in terms of five metrics assessing spatial similarity between volumetric models, signal-to-noise ratio, or heat source location accuracy. We also evaluate the assumptions of the synthetic model with an experiment involving thermal imaging of a real object (pork) and a single heat source. For validation, we investigate objects with multiple heat sources of a random location and temperature. Our results show the capability of a deep model to reconstruct the temperature distribution inside the object.

Implementation of the Marangoni effect in an open-source software environment and the influence of surface tension modeling in the mushy region in laser powder bed fusion (LPBF)

Tangential surface tension forces on a gas–liquid interface due to surface tension gradients have been implemented in the computational fluid dynamics (CFD) solver icoReactingMultiphaseInterFoam provided by the open-source software environment of OpenFOAM OpenCFD Ltd (ESI Group) OpenFOAM (online) https://www.openfoam.com/ (accessed 21 May 2021), so that the Marangoni effect can be taken into account, which is a main driver of heat transfer in additive manufacturing processes that comprise a melt pool. The solver surpasses the capabilities of similar open-source projects by considering a wide range of physical effects, e.g. multiple phases, melting, solidification, evaporation, and laser beam heat sources with an arbitrary intensity distribution and thus makes it an appealing framework, especially for the simulation of the laser powder bed fusion (LPBF) process. Herein, all relevant details and derivation considering the Marangoni effect are provided and validated by means of a benchmark problem by comparing the obtained results with the available analytical solution, with the results obtained from a commercial CFD tool and with the results of other authors. The modified solver is additionally validated by comparing the results from LPBF simulations with experimental data. Furthermore, the influence of the surface tension modeling on the mushy region is investigated. The optimized implementation shows improvements of the simulation results in both the dimensions and shape of the melt pool and the resulting surface with regard to the experimental data.

Blackbox optimization for approximating high-fidelity heat transfer calculations in metal additive manufacturing

Heat transfer simulations play an important role in predicting solidification conditions that determine microstructure properties of additive manufactured products. High-fidelity heat transfer models, e.g., Truchas [1], provide a numerical framework capable of resolving many desired physics (e.g., thermal radiation, elemental vaporization, gas-solid-liquid interactions, etc.), but they are often too computationally expensive to simulate the solidification conditions at the AM process-scale. Recently, Stump et al. [2] proposed a low-fidelity analytical heat conduction model capable of simulating solidification conditions on the process-scale. This model makes the problem analytically tractable by neglecting many important physics that may have an impact on the accuracy of the predicted solidification conditions. An effective way of improving the accuracy of the analytical with little computational effort is to determine an optimal set of parameters that minimize the discrepancy between the low-fidelity analytical model and a high-fidelity numerical model. In this work, a model approximation problem is formulated which can be solved by leveraging blackbox optimization methods. Multiple heat sources are used in the analytical model to improve the calibration performance in a flexible framework. Two blackbox optimization methods, i.e., Bayesian optimization and directional Gaussian smoothing methods, are employed to address the challenge that the gradient of the loss function is inaccessible during optimization. The results show that the single-beam analytical model has limitations in fitting the high-fidelity model, but the proposed multi-beam analytical model provides satisfactory approximations to the high-fidelity temperature and melt pool fields.