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Accurate heat load prediction algorithm provides important support for the stable and efficient operation of smart district heating system (SDHS) and helps to realize energy saving and consumption reduction. However, previous researches on heat load prediction are mostly carried out on various regression analyses and modeling prediction, without considering the inherent time delay and spatial dependence between heat exchange stations during regulation. Therefore, a novel heat load prediction model based on the hybrid spatial-temporal attention long short-term memory (STALSTM) is proposed. The STALSTM model introduces the spatial dependence characteristics of heating pipe network into the heat load prediction model, and the influencing factors of heat consumption are considered comprehensively from the time and space dimensions. Then, the LSTM algorithm is used to memory the information of historical data sequence, and the attention mechanism is used to realize the adaptive estimation of the characteristic weight of each influencing factor, which improves the prediction accuracy. And in order to verify the effectiveness of the proposed model, a detailed experimental comparison is made between the STALSTM model and the state-of-the-art algorithms. The results show that the STALSTM model has the best prediction accuracy, and the correctness of introducing the spatial-temporal characteristics and the attention mechanism is also proved.

The energy demand of the district heating system (DHS) occupies an important part in urban energy consumption, which has a great impact on the energy security and environmental protection of a city. With the gradual improvement of people&rsquo, s economic conditions, different groups of people now have different demands for thermal energy for their comfort. Hence, heat metering has emerged as an imperative for billing purposes and sustainable management of energy consumption. Therefore, forecasting the heat load of buildings with heat metering on the demand side is an important management strategy for DHSs to meet end-users&rsquo, needs and maintain energy-saving regulations and safe operation. However, the non-linear and non-stationary characteristics of buildings&rsquo, heat load make it difficult to predict consumption patterns accurately, thereby limiting the capacity of the DHS to deliver on its statutory functions satisfactorily. A novel ensemble prediction model is proposed to resolve this problem, which integrates the advantages of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and support vector regression (SVR), called CEEMDAN-SVR in this paper. The proposed CEEMDAN-SVR algorithm is designed to automatically decompose the intrinsic mode according to the characteristics of heat load data to ensure an accurate representation of heat load patterns on multiple time scales. It will also be useful for developing an accurate prediction model for the buildings&rsquo, heat load. In formulating the CEEMDAN-SVR model, the heat load data of three different buildings in Xingtai City were acquired during the heating season of 2019&ndash, 2020 and employed to conduct detailed comparative analysis with modern algorithms, such as extreme tree regression (ETR), forest tree regression (FTR), gradient boosting regression (GBR), support vector regression (SVR, with linear, poly, radial basis function (RBF) kernel), multi-layer perception (MLP) and EMD-SVR. Experimental results reveal that the performance of the proposed CEEMDAN-SVR model is better than the existing modern algorithms and it is, therefore, more suitable for modeling heat load forecasting.

With the increasing energy demand and environmental protection requirements of heating systems, natural gas (NG), as an efficient and clean alternative energy source for coal, plays an increasingly important role in district heating systems (DHSs). The accurate prediction of the DHS consumption of NG in the whole city is helpful in formulating an efficient energy scheduling plan. However, because the DHS is a complex non-linear system with time-space delay effect and multi-factors, the traditional algorithms have deficiencies in the prediction accuracy of the natural gas consumption for city-level DHS. To achieve accurate prediction, a gas consumption prediction algorithm based on the attention gated recurrent unit (AGRU) model is proposed, which can obtain high-level features of historical data that affect gas consumption prediction. In addition, the attention mechanism can help to select more critical feature inputs and improve the prediction accuracy of gas consumption. Detailed comparative experiments were performed between the proposed AGRU and state-of-art NG consumption prediction algorithms, such as the recurrent neural network (RNN), long short-term memory (LSTM), GRU, attention RNN (ARNN), attention LSTM (ALSTM), support vector regression (SVR), random forest regression (RFR), gradient boosting regression (GBR) and decision tree regression (DTR). An analysis of the experimental results shows that the proposed AGRU algorithm has a prediction accuracy of 95.3%, which is significantly better than other algorithms. In addition, the hyperparameters of the AGRU algorithm are also tested in detail to optimize the selection.

For district heating systems, prediction of the heat load is a very important topic for energy storage and optimized operation. For large and complex heating systems, most prediction models in previous publications only considered the influence of outdoor temperature, whereas the indoor temperature and thermal inertia of buildings were not included. For an energy-efficient residential building in Shijiazhuang (China), the heat load prediction is investigated using various prediction models, including a wavelet neural network (WNN), extreme learning machine (ELM), support vector machine (SVM) and back propagation neural network optimized by a genetic algorithm (GA-BP). In these models, the indoor temperature and historical loads are considered as influencing factors. It is found that the prediction accuracies of the ELM and GA-BP are slightly higher than that of WNN, so the ELM and GA-BP models provide feasible methods for the heat load prediction. The SVM shows smaller relative errors in the model prediction compared with three neural network algorithms.

Refined control is significant to ensure on-demand heating and efficient operation in district heating system (DHS). This paper proposes a dynamic control strategy for substations based on online prediction and indoor temperature measurement. Firstly, cross-correlation function method coupled with variable time window, which is a dynamic time lag analysis method, is introduced to analyze the delay time between indoor and comprehensive outdoor temperature. This time lag is used to decide control period. Then, an online multiple linear regression (MLR) model is introduced to predict the supply temperature. The prediction value is adjusted according to the deviation of the consumers’ set point indoor temperature and the actual indoor temperature before sent to the substation controller. The proposed strategy was applied in a practical DHS engineering, and the results showed that the indoor temperature non-uniformity coefficient was reduced from 0.05 to 0.04, the overall heating season heat consumption index was reduced, and the energy saving rate was about 6%.

Phase change material (PCM) used in building can enhance the thermal inertia of building and improve the indoor thermal comfort. A novel shape-stabilized phase change material wallboard (PCMW), in which paraffin was as the PCM and expanded perlite (EP) was the supporting material, has been prepared through a horizontal vacuum absorption rotate roller (HVARR) in this study. Its melting point and freezing point were measured to be 27.60 °C and 23.56 °C, respectively, and the melting and freezing latent heats reached to be 67.13 J/g and 67.06 J/g, respectively. PCMW was experimentally and numerically studied to analyze the thermal performance. The experimental result in 5 days, which was a demonstration in a container subject to weather conditions typical for the north China, showed that PCMW used in the building can maximally reduce the indoor temperature of 2.53 K. For the numerical study, based on the equivalent heat capacity method, a one-dimensional heat transfer model of PCMW was developed and combined with TRNSYS. This model was validated by the experimental data, and the numerical data agreed well with the experiment data. Under the summer condition, the numerical study of PCMW used in a typical office building during two months showed PCMW can averagely reduce the temperature of 9.22 K in the building operation time (7:00–18:00). Besides, according to the numerical model, an optimal configuration of PCMW in the cold zone of China has been obtained. The studied method provides a comprehensive guide to the PCMW design and application.

Phase change material (PCM) used in buildings can enhance indoor thermal comfort and decrease building energy consumption. A kind of shape-stabilised PCM particle (PCMP) was prepared by liquid paraffin to be absorbed into the micropores of expanded perlite (EP) with a self-made vacuum heating rolling box. A novel composite phase change material wallboard (CPCMW) was fabricated by PCMP, styrene acrylic emulsion and glass fibers under a plate-shape mould. The properties including thermal property, internal microstructure and mechanical property have been characterized by differential scanning calorimeter(DSC), scanning electron microscope (SEM) and electronic universal testing machine. The cold storage performance of CPCMW was experimentally studied in two rooms with the same size, under the summer condition. CPCMW was incorporated with the inside surface of wall and ceiling in a room, which was called PCM room (PCMR); while the other one without PCM was addressed as reference room. Besides, three operation strategies, i.e. natural convection operation with time(NCTI), natural convection operation with temperature (NCTE), and cold storage in closed building were conducted in experiments. In DSC test, the melting point and latent heat of CPCMW were 25.22 °C and 85.63 J/g, respectively. From SEM and electronic universal testing machine analyses, it was found that CPCMW had a compact and firm microstructure, and good strength and toughness. Based on the comparison data of PCMR and reference room in the experiment of cold storage, CPCMW showed a satisfied thermal performance, especially with the operation strategy of NCTE. It can be concluded that the novel CPCMW has a significant opportunity for building application.

Accurate prediction of heating load can help improve operational efficiency of district heating systems (DHSs). The selection of feature variables is of great significance to prediction performance. Most existing methods only use the meteorological data and historical thermal demand data. In this study, correlation analysis method is employed to analyze predominant variables affecting prediction accuracy. The correlation of supply/return temperature, outdoor temperature, and historical load data were examined. The obtained results were used to select minimal input variables subset so as to avoid multiple input variables. The extreme learning machine (ELM) was used to predict the energy consumption of the next 6, 12, and 24 h. The approach was adopted to predict heating load of a DHS in Changchun, China. Historical heating load data were proved to be the most essential prediction inputs. The results show that the root-mean-square error predicted by the ELM model can reach 4.1%.

Recycling heat from local industrial processes is one of the suitable and strategic opportunities for district heating all over the world. However, in northern China, the majority of low-grade energy has been wasted, the main difficulties are of an institutional and commercial character. The rapid development of renewables and constant promotion of time-of-use tariff policy has provided new chances for power-to-heat implementation and thermal energy storage. In this study, a general configuration optimization framework of additional waste heat recovery and storage (WHRS) devices is proposed, which is based on the cost-benefit analysis. Due to the implicit nature of such an optimization problem, conventional economic dispatch, two-stage branch evaluation, linear programming solver, and two kinds of advanced optimization algorithms (i.e., Genetic Algorithm and Pattern Search) have been integrated systematically. Moreover, case studies and sensitivity analyses are conducted to verify the feasibility of the proposed optimization model and to reveal the effects of uncertain economic parameters, respectively. The results show that the average time-consuming of Pattern Search is only 4.9% of the GA optimizations. When introducing additional WHRS devices with optimal configurations, the total operating costs decreased by 6.9% and the cost proportion of gas boiler declines remarkably from 8.6% to 2.0%.

Double-skin facade (DSF), as one of modern architecture envelopes, is beautiful and transparent. However, as transparent building envelope, double-skin facade has shortcomings in thermal performance, such as direct sunlight in summer. In order to overcome these drawbacks, a year-round optimum operation strategy of respiration-type double-layer glass curtain wall, which is one kind of double-skin facade with natural air circulation and blind system, has been researched by an experimental way in an office building. The optimum operation strategies that included changing air circulation and adjusting blind sun shading angle and installation position has been studied through comparative experiments in two identical rooms of the office building. For a year-round using in the cold zone of China, the related experiments were conducted in three stages: summer, winter and transition season. It was found that the optimum operation strategies in three seasons were different, but all of them have obtained well results. First of all, with the sun shading of blinds and the air external circulation, temperatures of air flow duct and room were decreased in summer. And then, with blinds removing, the indoor room can be warmed up by “greenhouse effect” created by respiration-type double-layer glass curtain wall for winter using. At last, in transition season, respiration-type double-layer glass curtain wall has increased the indoor thermal comfort and supplied fresh air.

An accurate heating load prediction algorithm can play an important role in smart district heating systems (SDHS), which is helpful for realizing on-demand heating and fine control. However, most of the traditional heating load prediction algorithms neglect the indoor temperature feedback from the household and cannot form closed-loop control. This paper designs an intelligent sensor based on the Narrow band Internet of Thing (NB-IoT) to collect the indoor temperature of a typical household and proposes an algorithm based on attention long short term memory (ALSTM) to predict the heating load for an integrated "heat exchange station - heat user". The attention mechanism is designed to obtain more accurate nonlinear prediction models between the heating load and influencing factors, such as indoor temperature, outdoor temperature, and historical heat consumption. A performance comparison with other state-of-the-art algorithms shows that the proposed ALSTM algorithm has the best performance, achieving an accuracy of 97.9%. Besides, a Kalman filter is introduced to identify and remove outliers while reducing the random error of the measurement.

The energy efficiency monitoring is an essential precondition for ground source heat pump system’s controlling and energy saving operation. Based on the data monitoring applied in the school building, this work is focused on the parameters acquisition and operation analysis of the GSHP system in Tangshan. Results show the average COPs (coefficient of performance) are 2.85 and 2.70 in summer and winter, respectively, and heat(cold) unbalance underground existed after whole year operation. The analysis of data also indicates that the direct borehole air-conditioning saved some power consumption obviously in the early stage of summer and energy saving of the GSHP system depended remarkably on its operation and management level. Besides the observation points of ground temperature are laid for a large-scale GSHP system, and the hydraulic balance of the pipes group needs to be concerned specially in safeguarding better reliability.

Compared with conventional central circulating pumps (CCCPs) in the district heating system (DHS), the DHS with distributed variable speed pumps (DVSPs) shows a great potential for energy saving. In this paper, a hybrid control scheme both using electric control valves (ECVs) and DVSPs is applied to the district heating system in Shenyang, China. This new hybrid control system results in reduction of the boiler outlet pressure from 1.27 MPa to 0.81 MPa, which ensures safe operation of the heating network. In addition, the hydraulic imbalance of the primary pipelines is effectively reduced by using the DVSPs. It is found that the relative error between the designed and the measured total flow rates is 7.71%. Results show that the annual average value of electricity consumption by using the DVSPs is 28.52% smaller than that in the CCCP system. Therefore, there is a great potential for building energy saving if the DVSPs are installed into the DHS. In order to evaluate the heating quantity and guide the optimal operation for the DHS, indoor temperature acquisition devices will be installed in the near future.

The air-side heat transfer and fluid flow characteristics of wavy fin-and-tube heat exchanger punched with combined rectangular winglet pairs (CRWPs) were numerically analyzed. The influences of several main parameters of the CRWP on heat transfer and friction were examined and compared to rectangular winglet pairs (RWP). The numerical results showed that the wavy fin-and-tube heat exchanger has a better heat transfer performance when the winglets punched on the suction side of the wavy fin. For the wavy fin punched with CRWPs, the Nusselt number and friction factor increase with increases of secondary attack angle, accessory winglet length or accessory winglet width. In comparison with RWP, the vortices generated by CRWP are more, larger and stronger. Hence, CRWP can more effectively improve heat transfer and increase friction.

This article presents a quantitative analysis of the effects of sand–bentonite backfill materials on the thermal performance of borehole heat exchangers (BHEs). Laboratory thermal probe tests were conducted to measure the thermal conductivity of sand–bentonite mixtures under different mixed ratios. Based on microscopic observations, the mechanism of bentonite affecting heat conduction between the sand grains was analyzed. Then field tests were carried out to compare the thermal performance of two double U-shaped BHEs with different backfill materials. Test results showed that the thermal conductivity of sand–bentonite mixtures first increased with increasing percentage of bentonite by dry mass, then reached a peak at the range from 10% to 12%, beyond which the thermal conductivity decreased quickly. For the BHE with an optimal sand–bentonite backfill material, the heat injection and heat extraction rate were enhanced on average by 31.1% and 22.2%, respectively, compared with the case with a common sand–cl...

A novel combined longitudinal vortex generator (LVG), comprising a rectangular wing mounted with an accessory rectangular wing, is developed and the turbulent flow and heat transfer characteristics are numerically analyzed. The influences of six main parameters of the combined rectangular winglet pair (CRWP) on heat transfer enhancement and fluid flow resistance characteristics in a rectangular channel are examined. The parameters include the location of accessory wing on the main wing and geometric sizes of the accessory wing. The Reynolds number range is from 2000 to 16,000. The numerical results show that in the range of the present study, the increase of the six parameters can result in the increase of heat transfer and pressure drop. Specially, the pressure drop decreases at large value of the distance of accessory wing from the channel bottom. In comparison with RWP, the CRWP generates vortices with larger area and lower core. Furthermore, the accessory wings generate vortices that swirl downward the channel bottom and disturb the boundary layer growth more effectively. Hence the heat transfer is enhanced. The numerical result for the Nusselt number of the channel agrees well with the experimental result, indicating the reliability of the present numerical predictions.

Groundwater flow plays an important role in affecting the thermal performance of borehole heat exchangers (BHEs). In the present work, a few field tests are conducted in Shouguang, China, to compare the thermal performance of three BHEs in different aquifers. The results show that there is a good linear correlation between the heat transfer rate of BHEs at steady state and the average fluid temperature. A larger slope usually means a higher heat transfer rate of a BHE, under the same borehole conditions. The thermal performance of BHEs is extremely enhanced, especially in those regions with multiple aquifers, and even the thermal response test results can be enlarged to a great extent by groundwater flow. The enhanced effect of groundwater flow depends mainly on the amount, thickness and depth of aquifers. It is found that when the depth of aquifers covers the middle or lower part of BHEs, at least exceeding the depth of the constant temperature ground layer, the enhancement on the thermal performance of BHEs becomes more intense due to the increase of the heat transfer temperature difference and the decrease of the total thermal resistance from the inner fluid to the surrounding ground. Groundwater flow in aquifers is helpful to reduce the required length of BHEs and the construction cost of ground source heat pump systems. Copyright , Oxford University Press.

High-temperature thermal storage (HTTS) in soils is a promising energy-saving technology for space heating of buildings. Based on a laboratory experimental setup using a vertical borehole heat exchanger (BHE), dynamic changes of the soil temperature and moisture content during the thermal storage process are studied. Effects of the heat injection temperature and initial moisture content on the thermal performance of the BHE are analyzed. The results show that at the first thermal storage stage, the soil temperature and moisture content near the heat source may appear a temporary peak. Its occurrence depends on the initial soil moisture content, the heat injection temperature and the distance from the heat source. As the heat injection temperature increases, the heat transfer rate of the BHE increases greatly. As the initial soil moisture content increases, the temperature profile near the BHE tends to be deviated from the results predicted by heat conduction, thereby influencing the thermal performance of the BHE. The present results can provide useful guidelines for the design of an HTTS system. Copyright , Oxford University Press.

A modified rectangular longitudinal vortex generator (LVG) obtained by cutting off the four corners of a rectangular wing is presented. Fluid flow and heat transfer characteristics of this LVG mounted in rectangular channel are experimentally investigated and compared with those of original rectangular LVG. Results show that the modified rectangular wing pairs (MRWPs) have better flow and heat transfer characteristics than those of rectangular wing pair (RWP). Near the positions of z = ±40 mm from the centerline of the heater plate, the local heat transfer is enhanced due to the strong longitudinal vortices generated by the presence of the LVGs. The down-sweep of the longitudinal vortices is beneficial to the heat transfer enhancement. The distance from the core of the main vortices of MRWP1 to the heater wall is slightly lower than those of RWP, and hence MRWP1 has a comparably better heat transfer characteristic.

Thermal response test (TRT) is crucial for the determination of the ground thermal conductivity and the evaluation of the thermal performance of borehole heat exchangers (BHEs) of ground source heat pump (GSHP) system. This paper presented a novel constant heating-temperature method (CHTM) for TRT. Further, a type of improved TRT equipment was developed and the mathematical model to deal with test data was presented. Based on the measurement of the natural ground temperature distribution, an in situ TRT case was carried out. The experimental results showed that, compared with the conventional TRT with constant heating-flux method (CHFM), CHTM has an obvious advantage of reducing the time period reaching a steady heat-transfer state between the BHE and its surrounding soils. This improved TRT equipment can effectively operate under both heat-injection and heat-extraction modes, and its test data can accurately reflect the thermal properties of the soils as well as the thermal performance of the BHE under different operation conditions. Finally, the advantages and disadvantages between CHTM and CHFM were compared, which can provide a useful reference for the design of GSHP system.

The performance of ground source heat pumps (GSHPs) depends strongly on the heat transfer between the soil and borehole heat exchangers (BHEs). In the present work, a thermal performance experiment of a BHE under groundwater flow was conducted in Baoding, China. Based on the measurement of the natural ground temperature profile, a simplified theoretical model was presented to estimate the characteristics of groundwater flow. The results showed that the presence of groundwater had an obvious influence on the temperature profile in the aquifer. Due to the strong groundwater advection, the thermal performance of the BHE was enhanced. The enhanced effect depends to a great extent on the distribution and thickness percentage of the ground layer with the greatest groundwater flow. In the present case, the heat injection and heat extraction of the BHE were enhanced on average by 9.8% and 12.9%, respectively, compared with the case without groundwater flow, when the total thickness of coarse sand and gravel layer as a percentage of the borehole depth was 10.6%. This enhanced effect is favorable for reducing the possible imbalance between heat injection and extraction from and to the ground, which is helpful for the long-term operation of GSHP systems.

This paper presents a case study of underground thermal storage in a solar-ground coupled heat pump system (SGCHPS) for residential buildings. Based on the experimental results, the operation performance is simulated by the unit modelling. The results show that the performance of underground thermal storage of SGCHPS depends strongly on the intensity of the solar radiation and the matching between the water tank volume and the area of solar collectors. Compared with the solar radiation, the variations of the water tank temperature and the ground temperature raise lag behind and keep several peaks during the day time. In the present study, the experimental efficiency of underground thermal storage based on the absorbed solar energy by the collectors reaches 76%. For the similar design of SGCHPS, it is suggested that the optimal ratio between the tank volume and the area of solar collectors should range from 20 to 40 L/m2.

This paper is performed to analyze the performance of underground thermal storage in a solar-ground coupled heat pump system (SGCHPS) for residential building. Based on the experimental results, the system performance during a longer period is simulated by the unit modeling, and its parametric effects are discussed. The results show that the performance of underground thermal storage of SGCHPS depends strongly on the intensity of solar radiation and the matching between the water tank volume and the area of solar collectors. Compared with the solar radiation, the variations of the water tank temperature and the ground temperature rise lag behind and keep several peaks during the day time. For the case of Tianjin, the efficiency of underground thermal storage based on the total solar radiation and absorbed solar energy by the collectors can reach over 40% and 70%, respectively. It is suggested that the reasonable ratio between the tank volume and the area of solar collectors should be in the range of 20–40 L/m2.

This study is focused on the preparation and performance of a building energy storage panel (BESP). The BESP was fabricated through a mold pressing method based on phase change material particle (PCMP), which was prepared in two steps: vacuum absorption and surface film coating. Firstly, phase change material (PCM) was incorporated into expanded perlite (EP) through a vacuum absorption method to obtain composite PCM; secondly, the composite PCM was immersed into the mixture of colloidal silica and organic acrylate, and then it was taken out and dried naturally. A series of experiments, including differential scanning calorimeter (DSC), scanning electron microscope (SEM), best matching test, and durability test, have been conducted to characterize and analyze the thermophysical property and reliability of PCMP. Additionally, the thermal performance of BESP was studied through a dynamic thermal property test. The results have showed that: (1) the surface film coating procedure can effectively solve the leakage problem of composite phase change material prepared by vacuum impregnation; (2) the optimum adsorption ratio for paraffin and EP was 52.5:47.5 in mass fraction, and the PCMP has good thermal properties, stability, and durability; and (3) in the process of dynamic thermal performance test, BESP have low temperature variation, significant temperature lagging, and large heat storage ability, which indicated the potential of BESP in the application of building energy efficiency.

Phase change material (PCM) used in buildings can reduce the building energy consumption and indoor temperature fluctuation. A composite PCM has been fabricated by the binary eutectic mixture of tetradecanol (TD) and lauric acid (LA) absorbed into the expanded perlite (EP) using vacuum impregnation method, and its thermal conductivity was promoted by aluminium powder (AP) additive. Besides, the styrene-acrylic emulsion has been mixed with the composite PCM particles to form the protective film, so as to solve the problem of leakage. Thus, a novel PCM panel (PCMP) has been prepared using compression moulding forming method. The thermal property, microstructure characteristic, mechanical property, thermal conductivity, thermal reliability and leakage of the composite PCM have been investigated and analysed. Meanwhile, the thermal performance of the prepared PCMP was tested through PCMPs installed on the inside wall of a cell under outdoor climatic conditions. The composite PCM has a melting temperature of 24.9 °C, a freezing temperature of 25.2 °C, a melting latent heat of 78.2 J/g and a freezing latent heat of 81.3 J/g. The thermal conductivity test exposed that the thermal conductivity has been enhanced with the addition of AP and the latent heat has been decreased, but it still remains in a high level. The leakage test result has proven that liquid PCM leaking has been avoided by the surface film method. The thermal performance experiment has shown the significant function of PCMP about adjusting the indoor temperature and reducing the heats transferring between the wall inside and outside. In view of the thermal performance, mechanical property and thermal reliability results, it can be concluded that the prepared PCMP has a promising building application potential.

The heat dissipation performance of a panel type radiator attached with rectangular winglets on the air-side was numerically investigated. The natural convection heat transfer of the oil and air were concerned. The numerical results showed that the application of the rectangular winglets can obviously increase the heat dissipation of the panel type radiator. In the computational range of the present work, the total heat transfer coefficient is increased by 23.6–32.0% and the optimal condition is l = 2 mm, N = 10 and α = 15°. The rectangular winglet generates vortices that swirl down toward the radiator wall and disturb the boundary layer growth. Hence the heat transfer is enhanced.