Oil Mass Flow Rate Research Articles

Oil circulation ratio prediction in a vapor compression system using a discharge side oil separator and mass flow correction

Oil circulation ratio (OCR) is defined as the ratio of the mass flow rate of oil to the total mass flow rate of refrigerant-oil mixture in a vapor compression system. The standard method for measuring OCR uses liquid line sampling as described in ASHRAE Standard 41.4. Sampling is tedious, alters the steady state operation of the system, depends on different parameters, and only applies to miscible refrigerant-oil pairs. A potential method for measuring real-time OCR is by using an oil separator to separate the refrigerant flow from the oil flow and using the individual flow rates to calculate OCR. Neither a liquid line, nor refrigerant-oil miscibility are necessary for this separation-based method. No oil separator is perfect as some oil always escapes with the separated refrigerant, and some refrigerant, dissolved in oil, always escapes with the separated oil. This can significantly reduce the accuracy of the procedure. The present study investigates OCR measurements using an oil separator-based approach for a full vapor compression cycle working with R134a and PAG ISO 46 oil. A full cycle allows sampling to also be performed in parallel for validation. Mass flow corrections were performed to account for refrigerant dissolved in separated oil, and for oil entrained by separated refrigerant. OCR values from the oil separator-based approach, upon mass flow correction, were within 6% of the sampling results. The usefulness of the oil separation efficiencies at the oil and vapor outlet ports for the oil separator-based approach is discussed.

Using fins to enhance heat transfer of cylindrical lithium-ion batteries immersed in electrical insulating oil

This work focused on designing the heat dissipation fins for cylindrical lithium-ion batteries to quickly transfer the heat generated inside the battery to the surrounding immersed insulating oil. The measured instantaneous heat generation rate of a single battery at the discharge rates of 1.0C and 1.5C was adopted as the internal heat source to simulate the surface temperature field of two series and two parallel (2S2P) battery modules immersed in insulating oil in three-dimensional space, respectively. The numerical simulation method has been validated by experimental results, indicating that the scheme of using this internal heat source is feasible. Then, this method was continued to be used to simulate the temperature rise characteristics during higher rate 2.5C discharge processes when the heat transfer was enhanced by circular or serrated fins. The cooling effects of three heat exchange enhancement methods (no fins, circular fins, and serrated fins) were compared under the operating conditions of 25 °C ambient temperature, and 1 g·s−1 rated insulation oil circulation mass flow rate. The maximum temperatures of the batteries in the module were 40.3 °C, 38.4 °C, and 37.5 °C, respectively. The maximum temperature differences between the batteries in the module were 1.63 °C, 1.59 °C, and 1.51 °C, respectively. Therefore, the serrated fins had the best thermal management effect. The orthogonal method was used to analyze the influence of the external structure and quantity of fins, as well as the insulation oil circulation mass flow rate, on heat transfer efficiency, and it was determined that the most significant factor is the mass flow rate of insulation oil. The final optimal parameters suitable for the 2S2P battery module were obtained, which were 16 serrated fins for each battery, with a fin height of 6 mm, a fin width of 3 mm, and a mass flow rate of 7 g·s−1.

Numerical evaluation of thermohydraulic parameters for diverse configurations of shell-and-tube heat exchanger

This research aims to optimize the internal design of shell-and-tube heat exchangers by investigating the thermal performance of various configurations. A comparative study of segmental baffles with plain and finned tube setups and helical baffles with different angular orientations is conducted using numerical simulations with the Galerkin finite element analysis. Key thermohydraulic parameters, such as shell-side pressure difference, heat transport coefficient, and heat transport coefficient per unit pressure drop, are assessed with shell-side mass flow rates. The outcomes direct higher shell-side oil mass flow rates correlate with increased pressure drop and enhanced heat transfer coefficients. Helical baffles exhibit superior performance to segmental baffles, offering a more significant heat transport coefficient per unit pressure drop. Within segmental baffles, finned tubes lead to higher pressure drops and heat transport coefficients than plain tubes while maintaining similar heat transport coefficients per unit pressure drop. Furthermore, lower helix angles (Φ = 10.81°) in helical baffles are associated with higher pressure drops and heat transport coefficients, whereas Φ = 25.52° achieves the highest heat transport coefficient per unit pressure drop.

Minimum Quantity Lubrication (MQL) Supply through Internal Cooling Channels in Drilling Processes

Minimum quantity lubrication (MQL) technologies possess great potential for improving the sustainability of manufacturing processes, which can reduce the absolute quantity of metalworking fluid (MWF) and also enable near-dry chips that are easier to recycle. During drilling in particular, the MWF is transported to the contact zone through internal cooling channels of the drilling tool. The MWF supply and its associated flow behaviour in the transfer from the outlet of the cooling channels to the contact zone have not been sufficiently investigated yet. Great potential is seen in the proper delivery of the MQL into the contact zone. This work aims to visualize and quantify the cooling lubricant supply into the cutting zone using the MQL technique. The visualization of the MQL application is made possible by high-speed shadowgraphic imaging. Detailed image processing is used to evaluate the resulting images. The developed evaluation routine allows for the assessment of the impact of the main process parameters such as the varying pressure of the aerosol generator and the cooling channel diameter. It is found that the oil leaves the cooling channels at the tip of the drill bit in the form of ligaments. An increase in pressure and cooling channel diameter leads to an increase in the frequency of oil ligament separation. Three main flow regimes are identified with different separation frequencies. Low inlet pressures result in intermittently dispersed droplets. The most upper pressure levels lead to an almost continuous dispersion of the oil. At the same time, the air and oil mass flow rates also increase.

An Experimental Study of Heating Heavy Fuel Oil by Hot Air using Helical Fins in a Double-Pipe Heat Exchanger

In present work, the effect of helical fins with height 20 mm and pitch 100 mm on the performance of the double pipe heat exchange investigated experimentally. The heat exchanger had been chosen as a heat recovery device in bricks factory to recover heat from exhaust gases to preheat the heavy fuel oil. Air had been chosen as a hot gas instead of furnace exhaust gases because of the similar thermal properties and it flows in the inner pipe with different velocity (20, 27, and 34) m/s and inlet temperature (200, 225) °C while, heavy fuel oil enters shell side with counter flow at mass flow rates (0.06, 0.08, and 0.1) kg/s and constant inlet temperature of 40 °C. Both of pipes and helical fins are made from stainless steel. The experimental results show that increasing Reynolds number from 139139 to 333934 led to increase heat transfer rate, oil outlet temperature, overall heat transfer coefficient and effectiveness of heat exchanger with (8%, 4%, 5% and 5%) respectively while, increasing oil mass flow rate from (0.06 to 0.1) kg/s cause decreasing oil outlet temperature and effectiveness of with (10% ,14%) respectively. The results shown the double pipe heat exchanger with helical fins produce heat transfer rate and oil outlet temperature higher than smooth double pipe heat with average 15% and 8.6%, as well as increasing Nusselt number, Overall heat transfer coefficient and effectiveness of heat exchanger with average 26%,15% and 13% respectively. The results clear that, for 225°C exhaust air and velocity 27 m/s, the application of double pipe with helical fins by preheat heavy fuel oil could reduce the viscosity and reduce electric power required and save 1.69 MW annually for one factory.

Coordinated control strategy for concentrated solar power systems considering active defocusing

With an increasing proportion of renewable energy in the energy structure, concentrated solar power plants are required to respond rapidly to automatic generation control (AGC) commands, to ensure the grid stability when connected to the grid. Active defocusing affects the collecting capacity of the collector, which not only serves as a safety protection measure for system operation, but also improves the system load shedding rate and provides the possibility of system participation in the auxiliary service of grid frequency regulation. In this paper, a coordinated control strategy for parabolic through concentrated solar power (PTCSP) system considering active defocusing of collector is proposed. The coordinated controller utilizes four manipulated variables, including mass flow rate of heat transfer oil in the collector, active defocusing angle, mass flow rate of molten salt in the heat storage system, and main steam valve opening, to regulate three output variables, namely, collector outlet temperature, turbine power, and main steam pressure. By integrating the steady-state defocusing angle in the optimization function, the controller can utilize the extra control freedom degree to improve the control effect, and ensure that the final steady-state defocusing angle to be small, which reduces the unnecessary heat collection loss. The proposed control strategy improves the power response rate and also avoids excessive heat transfer oil temperature and main steam pressure. In the simulations featuring two 20% variations in load target value, the root mean square error of the outlet temperature of the collectors is reduced by 0.094, and the heat storage is reduced by 0.99 MWh.

Numerical and Experimental Investigations to Assess the Impact of an Oil Jet Nozzle with Double Orifices on the Oil Capture Performance of a Radial Oil Scoop

To study the influence of orifice spacing on the oil–air two-phase flow and the oil capture efficiency of an oil scoop in an under-race lubrication system, an experimental platform for under-race lubrication was built, and a calculation model for the oil–air two-phase flow field was established. The rationality of the experiment and the validity of the numerical model were verified by comparing the experimental and numerical results. The results showed that under the same oil supply pressure, the captured oil mass flow rate of the double-orifice structure was much higher than that of the single-orifice structure, though it was still less than twice that of the single-orifice structure. When applying a tandem layout structure of double orifices to an under-race lubrication system, the orifice spacing of the tandem layout structure should be determined based on a full evaluation of the influence of the orifice spacing and working condition parameters on the oil capture performance. Otherwise, it may lead to a decrease in oil capture efficiency, with the maximum reduction even reaching 12%.

Enhancement of heat transfer in a vertical shell and tube heat exchanger using air injection and new baffles: Experimental and numerical approach

Vertical shell and tube heat exchangers play a critical role in many industrial processes, and their importance lies in their high heat transfer efficiency, versatility, compact size, easy maintenance, and longevity. To improve the hydrothermal performance, this research investigates the influences of air bubbles injection inside the shell with disc and ring baffles with circular holes, which is the first time to be addressed. The experiments used a fixed oil mass flow rate with 0.23 kg/s inside the tube sides and various cold water flow rates on the shell side within the 0.15–0.23 kg/s range. Three baffles’ configurations, such as single segmental (SSB), disc and ring (DRB), and disc and ring with circular holes (DRCHB), were investigated with different volume flow rates of air bubbles injection in the shell experimentally. A numerical model is performed and validated for the three baffles shapes. The performance parameters such as number of transfer units, effectiveness, heat transfer coefficient, pressure drop, and performance evaluation criterion are studied. The experimental findings showed that efficacy improved with the increase of the cold-water mass flow rates, whereas the DRCHB baffle shape with air injection)10 × 10−5 m3/s(achieved the highest effectiveness with an enhancement rate of 202% to 231%. The DRCHB configuration with maximum air injection has the highest values of the number of transfer units, heat transfer coefficient, and performance evaluation criterion compared to the other baffles configurations moreover, the pressure drop is the smallest in this case DRCHB without air injection. The numerical results showed that both novel configurations (DRB and DRCHB) have more uniform velocity and temperature distributions compared to the segmental baffles, which may effectively increase the hydrothermal performance.

Quantitative comparison of the performance of vapor compression cycles with compressor vapor or liquid injection

Increasing the Coefficient of Performance (COP) of vapor compression cycles has been a major focus for decades. Significant improvements can be brought by modifying multistage compressor to flooded single-stage compressor to approach isothermal compression. This work presents the comparative analysis of the cycle performance of a flash tank economized system (FTES), multiple refrigerant injection system (MRIS) and an oil flooded system (OFS). Thermodynamic models of each of these systems using ideal mixing models of refrigerants with the flooding agents are presented. Additionally, mixing effectiveness is introduced as a metric to evaluate the non-ideal mixing of the OFS. Results show that in MRIS, an increase in the number of injection ports significantly increases the COP of the cycle between 18% and 51% for air conditioning and refrigeration applications. The OFS shows that increasing the oil mass flow rate increases the COP significantly above the baseline cycle, benefiting higher temperature lift applications. At evaporating temperature of -40 ℃, relative COP for MRIS with 2 injection points is 7.5% higher than FTES and 5.0% higher than OFS. Further, quantification of the influence of the non-ideal mixing model for OFS showed that a mixing effectiveness of 80% results in 21% degradation of system COP suggesting the ideal mixing assumption has significant influence on the potential for an OFS.

Power generation of annular thermoelectric generator with silicone polymer thermal conductive oil applied in automotive waste heat recovery

The annular thermoelectric generator (ATEG) matches the shape of the exhaust pipe. To improve the power generation efficiency of the ATEG in automobiles, a scheme is proposed to use a silicone polymer-based thermal conductive oil to transfer heat from the exhaust. Based on this concept, a new type of concentric tube heat exchanger is designed. A finite element model of the new system is established by considering temperature gradients, temperature dependence, and fluid resistance characteristics. Numerical simulations are performed to investigate the effects of exhaust parameters, thermal oil parameters, and heat exchanger structure on thermoelectric performance. The findings demonstrate a 15.2% increase in maximum output power of the new generator compared to a conventional ATEG, accompanied by a 19% decrease in the optimal thermoelectric module area. Furthermore, the net power first increases and then decreases with increasing thermal oil mass flow rate. The thermal oil mass flow rate can be adjusted in real-time based on fluctuations in exhaust parameters to achieve peak net output power. Finally, optimal fitting relationships between the heat exchanger dimensionless diameter and the total diameter, as well as between exhaust parameters and the optimal thermal oil mass flow rate, are obtained through parameter analysis and derivation.

Impact of the Lubricant on a Modified Revolving Vane Expander (M-RVE) in an Organic Rankine Cycle System

The expansion device is the critical component of micro-to-small scale organic Rankine cycle (ORC) systems, substantially affecting system efficiency and cost. Low isentropic efficiency and lubrication requirements are the main issues associated with using volumetric expanders in ORC systems. Despite lubrication contributing to reducing internal leakages in an expander, it may compromise the performance of the ORC system by adversely affecting the evaporator’s thermal capacity. This study tests a recently developed and modified revolving vane expander (M-RVE) in a micro-scale ORC test rig by implementing an adjustable oil mass flow rate. The impact of the lubricant oil on the performance of the M-RVE prototype is investigated within a wide range of oil circulation rates (OCR). The results demonstrate a negligible improvement in the filling factor for OCRs higher than 1%. Moreover, the shaft power is not considerably sensitive to OCR, while the calculated isentropic efficiency of the expander improves with OCR. Furthermore, the impact of the lubricant oil on the performance of the evaporator is studied, assuming the exact OCR as the expander and measured temperature and pressure similar to the pure refrigerant for the lubricant-refrigerant mixture in the evaporator. The study shows that the evaporator capacity is penalized with OCR, especially for values higher than 1%. Hence, an OCR of about 1% is a good compromise, and it can be used as a guideline for designing revolving vane expanders for micro-scale ORC systems without a dedicated lubricant oil circuit.

Experimental Research on the Effect of Oil Charge Ratio on the Cooling Performance of CO2 Air Conditioning System for Electric Vehicles

From the perspective of the engineering application, the influence of the oil charge ratio on the cooling performance of the electric vehicle CO2 air conditioning system is experimentally studied in this paper. An online test device for oil circulation rate is set up on the built CO2 air conditioning system test bench. The experiment is conducted under different ambient temperatures and compressor speeds in the fresh air mode. As the oil charge ratio increases, the oil circulation rate increases as well as the oil mass flow rate, while the refrigerant mass flow rate decreases slightly. Under the refrigerant charge amount of 550 g and ambient temperature of 35 °C and 40 °C, this system reaches its best cooling performance when the oil charge ratio is in the range of 20% and 25%. And the maximum COPs are 2.46 and 2.36, respectively. The increase in the oil charge ratio is beneficial to the improvement of the isentropic efficiency and the volumetric efficiency of the compressor. The change in oil circulation rate has less effect on the pressure drop in the gas cooler than that in the evaporator.

Experimental and numerical investigation of multistage sorption energy storage system

In this paper, thermal energy storage is utilized to store heat from solar energy and also use waste heat to counterbalance the demand and supply of energy. A laboratory multistage closed sorption thermal energy storage (STES) unit is designed and tested to study the performance of a cascade sorption system. The experimental unit consists of three sorbent reactors, an ammonia cycle, and an oil cycle. Composite sorbents namely, MnCl₂, CaCl₂, and Nh₄Cl are used with ammonia as sorbate. Expanded natural graphite (ENG) is mixed with sorbents to increase the thermal conductivity and improve the mass transfer performance of sorbents. Further, a computational fluid dynamic model using COMSOL Multiphysics is built to study the performance of triple, double, and single closed STES systems. For the triple experimental STES system, a charging temperature up to 155 °C is used. At Nh3 pressure of 7.5 bar, the discharging temperatures are found to be 132.9 °C, 99.1 °C, and 60.3 °C for MnCl₂-ENG , CaCl₂-ENG , and Nh₄Cl-ENG composite sorbents, respectively, while a total energy storage density (ESD) of 3474.28 kJ/kgsalt has been achieved. For a double experimental STES system, a charging temperature up to 105 °C is used. Discharging temperatures are found to be 95.3 °C and 60.1 °C for CaCl₂-ENG , and Nh₄Cl-ENG composite sorbents, respectively, and a total ESD of 2471.94 kJ/kgsalt is achieved at Nh3 pressure of 7 bar. A parametric study is carried out to study the effect of different parameters on the performance of STES system at different arrangements. Increasing the inlet oil temperature during discharge results in a reduction of total ESD. For the specified design condition, the optimum oil mass flow rate is found to be 0.04 kg/s to achieve the highest ESD.

Improving the technology for the measuring and calculating gas-oil ratio

The article presents the results of the development and field tests of mobile installations for measuring the mass flow rate of crude oil and the volume flow rate of associated petroleum gas, as well as the calculation of the gas factor of oil on their basis. One of the installations for measuring the volume flow of associated gas separated at the reception of the borehole pump and taken from the annulus of the well. The other allows you to select the watered products in the sampling column of the measuring tank and increase the accuracy of measurements of both water and gas. A statistical dependence of the gas separation coefficient at the reception of the electric centrifugal pump is obtained, which allows the installation to be designed in accordance with the amount of gas taken from the annulus of the well. Keywords: gas factor of oil; oil rate; dissolved and free gas; mobile unit; well annulus; gas separation coefficient; pump reception.

The Effect of Operating Conditions on the Purification of Waste Cooking Oil over a Natural Zeolite Catalyst

The waste of cooking oil is a danger to human health. The Heating of waste cooking oil at high temperatures will cause an increase in free fatty acid (FFA) and peroxide number in the oil. Therefore, waste cooking oil needs to be processed before being reused. This paper studies the effect of operation conditions on the purification of waste cooking oil over a natural zeolite catalyst. The stage of the purification process is despicing, neutralization, and bleaching process. The despicing process injected the steam to remove impurities. The effect of the mass flow rate of oil at 1.051; 0.456 and 0.139 Kg/s on FFA value was studied. After that, the neutralization and bleaching process. The Bleaching process was performed using zeolite adsorbent. The results show that the purification method of waste cooking oil decreases of the color of oil, free fatty acid, and peroxide value. In this study, the best performance of the despicing process at the mass flow rate of the oil is 0.139 Kg/s, a temperature of 60°C with 500 rpm stirring for the neutralization process and bleaching process of natural zeolite. The value of free fatty acid content (FFA) is 2.22 mg. KOH/mg fat, peroxide is 6.98 mekO 2 /kg, color degradation is 66.93% and water content is 0.32% (w/w).

CFD investigation of air-oil two-phase flow in oil jet nozzle

In aero-engines applications, nozzle geometric parameters have major effects on the lubricating oil to accurately reach target gears or bearings. To investigate the deviation phenomenon of oil jet flow in the lubrication system, the computational fluid dynamics (CFD) technique integrating with the volume of fluid (VOF) method and SST k- ω turbulence model is adopted to deeply understand the flow characteristics of the nozzle. By leveraging this method, the relationship between nozzle geometry, inlet pressure, jet velocity, and jet deviation are firstly analyzed. The results reveal that a higher average velocity and smaller jet deviation can be determined via adjusting the nozzle geometry. Furthermore, a specific test rig, composed of an oil supply system, target system and data collection system, is set up for oil injection test; experimental outlet velocity and mass flow rate of oil passing through the hole on the target plate are monitored and recorded. The experimental findings compare well with numerical results obtained by the CFD method.

A novel unibody axial flow pump for the lubrication of inverter type hermetic reciprocating compressors

Lubrication at low speeds is a general problem in the hermetic reciprocating compressors for household refrigerators. The aim of this article is to present a new method using a novel 3D printed unibody axial flow pump for the lubrication oil supply system of an inverter type hermetic reciprocating compressor during a low speed (< 2000 rpm) operation. The system is based on a 3D printed unibody bladeless impeller axial flow pump attached to the bottom end of the vertical rotating crankshaft partially immersed in the oil sump inside hermetic reciprocating compressor sealed casing. A Computational Fluid Dynamics (CFD) simulation besides the experiment is used to simulate the flow inside the pump to calculate the mass flow rate of the lubrication oil and to optimize the helix angle of the pump. Volume of Fluid (VoF) and Multi Reference Frame (MRF) methods are used for modeling the two-phase flow (air and lubrication oil) and rotary domain respectively. The mass flow rate and climbing time of the lubrication oil in the unibody axial pump are analyzed. The results show that the designed pump is capable to supply the lubrication oil at a low speed i.e., 1400 rpm. Moreover, results indicate that the mass flow rate of the lubrication oil increases as the viscosity decreases. The average climbing time is observed to be 1 s at 1400 rpm and 0.4 s at 2000 rpm.

Determination of optimal oil pumping plans

This paper presents the results of determining the optimal plans for pumping oil through the main oil pipelines of Kazakhstan. The calculation methodology is based on determining the minimum unit cost of pumping depending on oil flow rate. Oil pumping energy-saving modes are determined under optimal operating conditions of pumping units and heating furnaces at stations. Determination of the optimal pumping plan is implemented as a separate module of the SmartTranPro software. Pumped oil volumes on the oil pipeline sections were determined on the basis of the automated system of control and metering of electrical energy data of KazTransOil JSC. Optimal pumping plans for monthly oil volumes in the Kalamkas – Karazhanbas and Dzhumagaliev – Atasu pipeline sections for cold and warm periods were calculated on the basis of the found dependence of the pumping unit cost. For each range of oil mass flow rate, specific costs for oil pumping and a list of operating pumps at oil pumping stations located along the pipeline section are indicated.

Fatty acid solvent extraction from palm oil using liquid–liquid film contactor: Mathematical model including mass transfer effects

Free fatty acid (FFA) presence in vegetable oils (VO) promotes unwanted organoleptic characteristics. Its traditional removal is carried out by steam distillation (deodorization). However, the high temperature of this process promotes the formation of toxic components such as glycidol esters (GE) and 3-monochloropropane-1,2-diol (3-MCPD). FFA extraction by solvents is an alternative refining process at low temperatures which preserves natural phytonutrients that are thermically destroyed or distilled in deodorization. In this work, a model to predict continuous co-current FFA extraction with a liquid–liquid film contactor (LLFC) using ethanol as a solvent at low temperature (<80 °C) was developed and experimentally validated. This model includes the prediction of the FFA mass transfer from the oil-rich phase to the interface. Experimental validation also assessed the effects of flow rate (0.5–1.5 kg/h), ethanol to oil mass flow rate (1–2), FFA initial concentration (2–4 wt.%), and LLFC stages employed on FFA removal. At the best operational conditions experimentally evaluated, it was possible to reduce the FFA content from 4 wt.% to 0.08 wt.%. The mathematical model shows an approximate description of the LLFC behavior and mass transfer effects that can be used for the scale-up of the technology.

Experimental study and comparative performance analysis on thermal-hydraulic characteristic of a novel longitudinal flow oil cooler

The longitudinal flow heat exchanger possesses lots of merits but it exhibits poor heat transfer coefficient at low Re condition, which makes it difficult to be applied in the high viscosity fluid area. In this paper, a heat transfer augment solution for lubricating oil flowing on shell side of a novel longitudinal flow twisted trifoliate tube oil cooler was proposed. Experiments were conducted to comparatively investigate the thermal–hydraulic performance of a twisted trifoliate tube oil cooler and a conventional segmental baffle oil cooler. The tube side study demonstrates that the Nu and f of the twisted trifoliate tube are 17.5–75.8% and 16.9–62.9% larger than that of the smooth circular tube. The shell side study shows that at the same oil mass flow rate, the shell side heat transfer coefficient of the twisted trifoliate tube oil cooler is 66.3–148.9% higher than that of the conventional segmental baffle oil cooler with pressure drop increased by 31.6–65.2%. Furthermore, the shell side performance evaluation criterion h/ΔP of the twisted trifoliate tube oil cooler is 1.46 times larger than that of the conventional segmental baffle oil cooler on average. The possible mechanisms responsible for the heat transfer enhancement are analyzed. In addition, the predictive correlations of tube side and shell side of the twisted trifoliate tube bundles for Nu and f are deduced based on the experimental data. Results from current research could provide useful correlations and beneficial guidance for design and application of the longitudinal flow heat exchanger in low Re ranging of 40–250.