Local Heat Transfer Coefficient Research Articles

Numerical investigation of heat and mass transfer of SWCNT/MWCNT‐water suspension over a porous stretching sheet using Sisko fluid model

AbstractThis study presents a comprehensive numerical computation of heat‐mass transfer characteristics of single‐walled carbon nanotube (SWCNT)/multi‐walled carbon nanotube (MWCNT)‐water suspension flow over a porous stretching sheet with an inclined magnetic field. The governing equations for fluid flow characteristics are formulated using the Sisko fluid model to capture the Newtonian and non‐Newtonian behavior of the nanotube‐water mixture. The nonlinear coupled partial differential equations are converted into nonlinear dimensionless coupled ordinary differential equations using suitable similarity transformations. These equations are solved using MATLAB by implementing the four‐stage Lobatto IIIa formula. The comprehensive set of computations is performed to explore the influence of pertinent parameters, including Sisko fluid parameters, concentration of nanotubes, stretching sheet velocity, and porous medium characteristics on the flow, heat, and mass transfer profiles. From the graphs and statistical analysis, it is clear that the volume fraction of SWCNT and MWCNTs are strongly correlated. The investigation reveals that increasing the inclination angle affects the fluid velocity. The variation in all flow features is negligible for volume fractions of CNTs between 0% and 10% but a significant effect is observed only beyond 10%. Higher volume fractions of CNTs result in enhanced local heat transfer coefficient. This can be attributed due to the outstanding heat transfer capabilities of CNTs owing to their high thermal conductivity. However, Shear thickening fluids exhibit high heat transfer phenomena when compared to shear‐thinning and Newtonian fluids. This research provides valuable insights into the optimization of CNT‐based nanofluids for efficient heat and mass transfer applications in electronics cooling, heat exchangers, and solar energy systems, offering opportunities to enhance energy efficiency and device performance.

Numerical Study on Heat Transfer Characteristics of Jet Impingement by using MgO Nanofluid

Liquid impingement jet can provide high local heat transfer coefficients between the impinged liquid and the targeted surface. Jet impingement is utilized in the applications which is related to rapid cooling and better control of high temperature in many applications. The studies are carried out numerically by using ANSYS Workbench 18.2. Hexagonal meshing and Shear-Stress Transport (SST) turbulence model is used in the numerical simulation. By using SST turbulence model, the effect of jet Reynolds number, nanofluid volume concentration on the average heat transfer coefficient of the target plate is analysed and discussed. For the effect of varying the Reynolds number, it is observed that the surface average heat transfer coefficient increases at least 76.18% as the Reynolds number increases from 5000 to 10000. Moreover, the heat transfer coefficient increases as the volume concentration increases from 0% to 5%. It is also observed that when the nanofluid with higher thermal conductivity will results in higher heat transfer coefficient where the MgO nanofluid showed the highest heat transfer coefficient. As a conclusion, by increasing Reynolds number, volume concentration and thermal conductivity of nanofluid, the heat transfer coefficient can be enhanced.

Comparative analysis of inlet and outlet cavity designs on the thermal-hydraulic performance of compact heat exchangers for combustion engine exhaust heat recovery

ABSTRACT Improving the Internal Combustion Engines (ICEs) overall thermal efficiency is crucial to reduce fuel consumption and emissions. To achieve this goal, waste heat recovery from exhaust gases remains the most promising strategy, which involves the utilization of compact heat exchangers. This study evaluates the performance of novel Monolithic Integrated Thermal Exchange Matrixes (MITEMs) designs for recovering exhaust heat from a 70 hp diesel engine, focusing on the impact of inlet/outlet cavities. Computational Fluid Dynamics simulations were employed to analyze the heat transfer rate, pressure drop, and overall thermal-hydraulic performance of different MITEM designs. The Rectangular Channels with Large Cavities (RCLC) design exhibited superior performance, enhancing the heat transfer rate by 14.7% compared to the baseline design while limiting pressure drop increase to 9.2%. The RCLC design increased local Nusselt numbers and heat transfer coefficients by up to 60%, achieving peak velocities of 98 m/s within cross-sectional planes. These findings provide valuable insights for optimizing exhaust heat recovery systems in diesel engines.

Boiling heat transfer of water on smooth and square pin fins surfaces in minichannel

In this investigation, flow boiling heat transfer and hydrodynamic instability using deionized water in a minichannel with smooth and square pin fin surfaces was experimentally examined. The study is aimed to assess local and overall heat transfer coefficients, heat transfer coefficients, pressure drop and Nusselt number across various liquid mass flux ranges (50–93 kg m−2 s−1) and a constant heat flux of 46.91 kW/m2. The minichannel, with a hydraulic diameter of 2.85 mm, features a rectangular shape. Experimental testing was conducted on aluminum surface within a minichannel of dimensions 270 mm in length, 30 mm in width, and 1.5 mm height. The square pin fins are integrated at the base of the boiling surfaces, arranged in staggered form. The results revealed that the boiling heat transfer coefficient on square pin fin surfaces was approximately 88 % higher than that on smooth surfaces. Additionally, a notable increase in local heat transfer coefficient was observed for square pin fin surfaces (i.e., 34.64 kW/m2.K) compared to smooth surfaces (8.09 kW/m2.K) at the same mass flux of 50 kg/m2.s. Besides, the square pin fins surface exhibited a lower and stable pressure drop, particularly near annular flow regimes, compared to the smooth surface. Notably, the highest pressure drop observed was 4.8 kPa for the square pin fins surface, while the smooth surface experienced a higher pressure drop of 6.36 kPa, accompanied by more pronounced pressure fluctuations during annular flow.

Experimental study of subcooled flow boiling in microchannel heat sinks integrated with different embedded pin fin arrays microstructures

The optimized microchannel heat sinks could enhance flow boiling for effectively tackling the electronics cooling. The flow boiling experiment for three microchannel heat sinks integrated with different layouts of entrenched pin fins is conducted at flow rate of 273.6–456 kg/(m2.s) and inlet subcooling of 35∼50 K. The overall/local heat transfer features, pressure drop and boiling mechanism are studied. The hybrid pattern presents earliest initial boiling and lower superheat than the microchannel heat sink with uniform pin fins arrangement at moderate and large flow rates. The trend of overall and local HTC (heat transfer coefficient) is similar, which occurs peak at onset nucleation boiling, and then decreasing with increasing heat flux. At the largest flow rate, the hybrid pattern exhibits 2.7–3.5 times peak HTC promotion than other patterns. As for lowest flow rate, the hybrid pattern does not manifest remarkably superior performance due to downstream vapor cores clogging effect. The hybrid pattern shows largest pressure drop, and the smaller inlet subcooling manifests inferior heat transfer and resistance performance. The comprehensive performance factor (CPF) is proposed, and the pattern with uniform small-sized pin fins shows optimal CPF especially for low flow rate, which is considerable compared with the reference heat sink structures until high heat flux. This study may provide some insight into the design of microchannel for flow boiling heat dissipation.

Numerical simulation on the condensation heat transfer and flow characteristics outside smooth and enhanced tubes

Most of the current studies only conducts two-dimensional simulations of condensation heat transfer and flow outside enhanced tubes, which cannot accurately reflect the flow and heat transfer characteristics of liquid film outside enhanced tubes. In order to provide theoretical support for the design optimization of enhanced tubes, this study adopts the VOF multiphase model and Lee condensation model to simulate the condensation heat transfer(HTC) of refrigerants outside smooth and enhanced tubes. The instantaneous film flow characteristics of the liquid film outside the horizontal smooth and enhanced tubes are analyzed, and the thickness of the liquid film and the relationship with the condensation heat transfer coefficient of the smooth and enhanced tubes under different working conditions are calculated. The refrigerants are compared under the same working conditions, and the results are shown: The simulation results are in good agreement with the experimental data and the Nusselt analytical solution, and the error is all within 15%; the distribution of liquid film is highly sensitive to the magnitude of local condensation heat transfer coefficients, and the condensation HTC outside the enhanced tube is approximately six times of that of smooth tube. Combining the distribution of the liquid film and the thermophysical properties of the refrigerants, it was determined that R410A has the highest HTC, while R1234yf has the lowest HTC.

The influence of longitudinal duct profiling on unsteady gas dynamics and the heat transfer of pulsating gas flows in the outlet system of reciprocating-engine

Heat machines based on reciprocating-engines remain in demand in various fields of engineering and technology. Therefore, further research is needed to improve the efficiency, reliability, and environmental friendliness of engines. The thermomechanical improvement of non-stationary processes in outlet systems is an appropriate way to improve engine performance. The purpose of this research is to obtain and analyse the gas-dynamic and heat transfer characteristics of pulsating gas flows in an outlet system with ducts of various designs, using a laboratory model to simulate the outlet process in an engine. Thermal anemometry is used to receive data on the instant velocity values and local heat transfer coefficient of unsteady flows in ducts. The article examines two designs of outlet ducts, namely cylindrical (basic) and conical (with a taper of 0.0225) ducts. Spectral analysis of velocity, pressure and heat transfer coefficient pulsations, assessment of turbulence intensity, and calculation of flow characteristics of pulsating flows were performed to obtain detailed information on gas dynamics in the outlet system. The use of a conical duct (in comparison with a cylindrical one) leads to a slight increase in the turbulence intensity by up to 12 %, a decrease in the heat transfer coefficient by 15–20 %, and a change in volumetric gas flow within ± 7.5 %. Thus, the use of a conical duct will lead to the stabilisation of the flow in the outlet system, improved cleaning of the cylinder from outlet gases, a reduction in thermal stress, and a slight growth in the specific power of engines.

Micro segment analysis and machine learning prediction for thermal-hydraulic parameters of propane condensation flow in a PCHE straight channel

In the LNG regasification process, the printed circuit heat exchangers(PCHE) is an ideal choice for vaporizer, with propane as the intermediate working medium in the hot side of PCHE. In this work, numerical simulations of propane condensation flow and heat transfer at different operating parameters was carried out in a semi-circular straight channel of PCHE. The micro-segment analysis method was used to present the local heat transfer coefficient and pressure drop in the channel. The results indicate that the propane condensation process can be divided into three stages: the “constant temperature condensation stage” in the droplet condensation state, the “varying temperature condensation stage” in the film condensation state, and the “subcooled stage” in the liquid phase state. Different operating parameters can affect the start and end position of each stage, as well as the parameter values in the same state. An artificial neural network method was used to predict the local heat transfer coefficient and pressure drop, with the predicting error of less than 5 % and 10 % respectively. This study provides a machine learning method to accurately predict the flow and heat transfer parameters for propane condensation flow in PCHE channel and valuable for future design of LNG vaporizer.

Flow boiling in a rectangular micro/mini channel with self-rewetting and non-rewetting fluids

In this experimental investigation the influence of self-rewetting during flow boiling was studied in a horizontal microchannel during one-sided uniform heating. The channel had a width and height of 6 mm and 0.3 mm respectively. Local wall temperature and direct in-time flow visualisation was performed. The working fluids under consideration included water as base reference, pure 1-butanol, pure ethanol, dilute butanol-water self-rewetting mixtures, and a dilute ethanol-water binary mixture. Tests were conducted at mass fluxes of 10, 15 and 25 kg/m2s, over a range of heat fluxes to produce both single phase and two-phase quasi steady state flow data. Within the wall temperature ranges of interest, the butanol-water mixtures (5 % and 7 % by volume butanol) had surface tension characteristics that would draw liquid toward local wall hotspots. Local and average wall temperatures and heat transfer coefficients were obtained and considered against the governing flow pattern visualisations. In contrast to the other fluids, the self-rewetting butanol-water mixtures exhibited significantly more stable flow and more predictable saturation flow boiling heat transfer coefficient trends across all heat fluxes under consideration. At the lowest mass flux, it was found that an increase in the heat flux resulted in an improvement in the self-rewetting fluids heat transfer performance, while at higher mass fluxes this dependence was diminished. Across all mass fluxes and heat fluxes the 5 % butanol-water outperformed its 7 % butanol-water counterpart. The tendency of self-rewetting to reduce local dry-out, even at low mass fluxes are demonstrated.

Inverse Estimation of Swirl Cooling Heat Transfer Coefficient

Swirl cooling is one of the most widely studied techniques in the field of heat transfer enhancement. This paper presents a novel, non-intrusive, and rather inexpensive inverse method to estimate the local heat transfer coefficient along the swirl chamber. First, the direct problem of two-dimensional heat conduction inside the chamber’s wall is solved numerically. The optimal number of sensors, their axial and radial positions, and other parameters concerning the inverse algorithm are determined using simulated experiments. The experimental setup is built based on these parameters. Transient temperature readings from several thermocouples embedded inside the chamber wall are fed to an inverse algorithm based on the conjugate gradient method. This algorithm takes advantage of an adjoint differential equation and the sensitivity differential equation to calculate the gradients and optimal step sizes, respectively. The local transient heat transfer coefficient is estimated for three Reynolds numbers along four straight lines parallel to the axis of the chamber.

Non-invasive mass flow and local heat transfer coefficient measurements in pulsating heat pipes

A single loop Pulsating Heating Pipe (PHP) experimental setup was developed for non-invasive measurement of the local heat transfer coefficient and the mass flow along the PHP evaporator. These measurements are valuable to validate modeling tools used in the design of PHP. A two-step differential heat input method was used for measurement of mass flow and the results were compared with the optical and theoretical results. The conditions tested in the PHP were 50, 60 and 70% filling ratio, R134a as working fluid, internal diameter of 2 mm, saturation temperature of between 30 to 40 °C, inclination angles from 30 to 90° (vertical bottom heat mode) and heat loads on the evaporator from 10 up to 68 W. The results indicate a high performance in heat transfer of the PHP, with minimum internal thermal resistance values close to 0.008 K/W as well as local heat transfer coefficients greater than 10 kW/m2K for observed values of mass velocities between 60 and 140 kg/m2s. The results were compared with correlations from the literature and these were able to predict the results with a 20% average error margin, suggesting many similarities with convective boiling mechanisms.

Simulating film boiling with sharp interface and direct calculation of mass transfer to investigate the hydrodynamic and thermal transport phenomena near the interface

The current study presents a computational fluid dynamics (CFD) model for film boiling using two fluids, including liquid nitrogen. Ansys Fluent was customized using user-defined functions (UDFs) to accurately model thermal and fluid dynamic interactions. The UDFs accommodate mass transfer at the liquid-vapor interface, maintaining a sharp interface by accounting for the saturation temperature. Direct heat and mass transfer calculations are implemented rather than relying on empirical correlations. Mesh analysis was performed with grid sizes of 615, 410, 307, and 123 μm, with the 307 μm grid selected for its agreement with average Nusselt number values and accurate bubble shape and height. Verification using the Stefan problem showed a maximum error of 0.45 % for interface displacement and 0.1 % for temperature distribution. Validation against the Berenson correlation demonstrated good agreement in Nusselt number values. Qualitative validation of the developed method is performed using the shapes of the growing bubble. The results obtained show that the sharp interface is preserved throughout the simulation, with temperature contours showing significant variations during bubble growth and departure. Local heat transfer coefficient analysis identified peak values of 2170 W/m²-K at locations of minimal film thickness. Velocity vector analysis revealed velocities of 2 m/s in the vapor phase, influencing bubble shape during growth and departure. The study highlights the impact of thermal film thickness on heat transfer, with the highest Nusselt number of 5.69 observed at a film thickness of 0.5 mm. The results demonstrate the application of VOF sharp interface tracking and direct calculation of interfacial conditions utilizing customized Ansys Fluent in the modeling of film boiling as a way to understand the fundamental aspects of the fluid and thermal behavior.

Heat transfer characterization of SCO2 in non-uniformly heated rectangular cooling tubes under large mass flow and heat flux conditions

A Thermoelectric Conversion System (TECS) with SCO2 as the circulating mass can effectively mitigate the fuel heat sink and electrical energy shortage problems of hypersonic vehicles. However, there is still a lack of research on the use of SCO2 in the harsh thermal conditions in scramjet. In this paper, the heat transfer mechanism of SCO2 in rectangular cooling tubes are numerically analyzed for the first time based on the actual working environment of scramjet. The effects of uneven heat flux (q) axial and circumferential allocations and circumferential and axial tilting of the tube are innovatively considered. Meanwhile, we analyze the heat transfer mechanism of SCO2 under different operating parameters. The results show that the uneven allocation of axial q can suppress the heat transfer deterioration (HTD), and the overall heat transfer coefficient (HTC) can be increased by 11.68 % when the q allocation is Gaussian. The increase of the tube inclination angle can improve its heat transfer performance, and the local HTC can be increased by up to 5.64 % when θ2 = 180°.Increasing the mass flow rate (G) and inlet temperature (Tin) can increase the overall HTC of the tube. This paper can provide guidance for the design and improvement of TECS.

Investigation on the heat transfer characteristics of rotor-stator cavity with different disk roughness

In this study, we numerically investigated the rotor-stator cavity for different disk surface roughness (rough rotor-RR, rough stator-RS, and rough rotor & stator-RRS) with the aim of determining the effect of surface roughness on the heat transfer characteristics of the disk cavity over a range of parameters. First, we experimentally verified that the numerical simulation has high accuracy. Next, the third-generation vortex identification method-Ω vortex identification method is used to preliminarily analyze the effect of different disk cavity roughness on the heat transfer in the rotor-stator cavity. The results indicate that the roughness of the rotor surface plays a dominant role in influencing the flow in the disk cavity. Third, we qualitatively and quantitatively analyzed the temperature field in the disk cavity. Interestingly, we discovered that the roughness of the stator decreases the temperature in the disk cavity to some extent. Thus, we judged the effect of stator surface roughness on the flow in the disk cavity based on the pressure variation in the rotor-stator cavity and gave an optimal roughness range for the stator. This will help to improve the cooling effect in the disk cavity. Finally, we investigated the effect of roughness on the rotor-stator heat transfer capacity. The effect of roughness on overall heat transfer in disc cavities is quantified based on average local heat transfer coefficient. It was concluded that the local heat transfer coefficient of the disk cavity is sensitive to the wall roughness, even for small wall roughness. We then added a roughness term to our previous work on average Nusselt number predictions for disk cavities. This provides a more accurate prediction of the heat transfer capacity of the disk cavity. On the basis of our results, it can provide some assistance to the relevant designers to quickly and accurately predict the heat transfer capacity of the rotor-stator cavity.

Determination of Local Heat Transfer Coefficients and Friction Factors at Variable Temperature and Velocity Boundary Conditions for Complex Flows

Transient conjugate heat transfer measurements under varying temperature and velocity inlet boundary conditions at incompressible flow conditions were performed for flat plate and ribbed channel geometries. Therefrom, local adiabatic wall temperatures and heat transfer coefficients were determined. The data were analyzed using typical heat transfer correlations, e.g., Nu=CRemPrn, determining the local distributions of C and m. It is shown that they are closely linked. A relationship lnC=A−mB is observed, with A and B as modeling parameters. They could be related to parameters in log-law or power-law representations for turbulent boundary layer flows. The parameter m is shown to have a close link to local pressure gradients and, therewith, near wall streamlines as well as friction factor distributions. A normalization of the C parameter allows one to derive a Reynolds analogy factor and, therefrom, local wall shear stresses.

Thermal measurement of a unitized regenerative fuel cell during mode switching using thin film sensors

The research on temperature and heat flux during mode switching process of unitized regenerative fuel cells is importance. Thus, in this paper, the local temperature and heat flux are measured during mode switching using self-made thin film sensors, and heat transfer coefficient is also obtained. The results of the experiment exhibit that the temperature and heat flux change significantly during mode switching, and periodically change with periodic mode switching, the heat generation is greater than the heat dissipation inside the cell. During mode switching, the temperature and heat flux are higher in upstream, and the temperature and local heat transfer coefficient increase along main gas flow direction. The fuel cell current density has a great influence on heat transfer when cell mode switches. At different current density, the temperature and heat flux show different changing trend when the cell switches from electrolytic cell mode to the fuel cell mode. These experimental results can provide guidance to make fuel cell run more efficiently in practical application.

Local heat transfer measurements of the fin on the blade crown by infrared thermography

Current research on heat transfer of the labyrinth surface mainly focuses on the whole structure made of the same material, but the heat conduction from the tip to the root will affect the measurement of the heat transfer coefficient. To minimize the influence of heat conduction, copper strips are embedded on the surface of the fin made of bakelite. The inverse heat transfer problem is solved using the temperatures collected by an infrared thermal imager to determine the local convective heat transfer coefficient. The error of the lumped parameter method is smaller compared to the differential solution. Constant heat flux experiments are used to validate the experimental results, and numerical analysis is performed to analyze the heat transfer mechanism. The flow field, the Nu number distribution, and fitting correlations of the fins are obtained. By comparing and analyzing the heat transfer coefficients obtained by the three methods, it is found that the lumped parameter method can eliminate the influence of heat conduction on the surface. Taking the lumped parameter method as a reference, the errors of stable heat flow and numerical calculation were 21 % and 4.7 %, respectively. Due to the influence of the vortex direction, the Nu number distribution along the height of the windward surface of the second fin is different from the others. The Nu number distribution along the x-direction on the top surface of the fin is similar to the tip of the windward surface. Along the flow direction, the average Nu number on the top surface of the first fin is 1.2 times that of the second one.

Simulation of the effect of the structure and location of non-closed droplet microchannel on flow/ thermal performance

In order to investigate the effects of geometric parameters and flow modes on the fluid flow morphology, resistance and heat transfer effect in the non-closed droplet pin fin array, in this manuscript, a numerical simulation has been conducted under Re = 100–700 with different pin fin heights (Hp = 0.3 mm, 0.5 mm, 0.7 mm) and pin fin densities (β = 0.046, 0.059, 0.072), with different flow directions under heat flux (10 W/cm2 – 50 W/cm2) studied as well. It is discovered that increasing the height and density of the non-closed droplet pin fin increases the interference with the fluid, resulting in a greater flow resistance phenomenon. However, the enhancement of turbulence not only exacerbates the flow instability in microchannels, but also further promotes the mixing of hot and cold fluids, making the internal temperature distribution more uniform. In which way, the effect of optimizing heat transfer performance achieves. In addition, as q > 20 W/cm2, the overall heat transfer capacity of flow direction B (the tip of the pin fin as upstream fluid direction) is better than that of flow direction A (the cavity of the pin fin upstream as upstream fluid direction). When q = 30 W/cm2, there is a process transferring from single-phase flow to two-phase flow along with the direction of working fluid flow in the microchannel. Under this condition, the local maximum heat transfer coefficient is 15,502.4 W/(m2·K) in flow direction A and 16,094.8 W/(m2·K) in flow direction B. Furthermore, the comprehensive evaluation concludes that the channel flow/thermal performance is the best with Hp = 0.7 mm, β = 0.046.

Measurement of local boiling heat transfer coefficient (HTC) within a brazed plate heat exchanger (BPHE) and heat transfer assessment of low-GWP R134a replacements

This article shows the local boiling HTCs of R134a and three low-GWP replacements, R1234yf, R1234ze(E) and R152a within a (BPHE). The experimentation was performed in a test-section specially set up for the measurement of the local two-phase HTC at a saturation temperature of 10 °C, with a refrigerant mass velocity from 9.5 to 35.2 kg m−2 s−1, incoming vapour quality between 0.2 and 0.3 and almost complete vaporisation. Both nucleate boiling and forced-convection boiling play an important role in these tests, depending, mainly, on the location along the plate. The comparison with theoretical models shows that both Longo et al. (2015) and Amalfi et al. (2016) models reproduce very well the experimental HTCs. The measurement of local temperature profiles within the BPHE allows to couple the evaluation of thermal and hydraulic performances of refrigerants into a single parameter named Total Temperature Penalty (TTP). The TTP analysis highlights similar boiling performance for R134a, R1234yf and R152a refrigerants, while R1234ze(E) displays worse performance.

Numerical investigation on dynamic flow characteristics of methane condensation in microchannels

Microchannel condensers play an essential role in cryogenic two-phase heat management systems due to their efficient heat transfer characteristics. Thus, it is worth conducting an in-depth study on microscale condensation characteristics of cryogenic fluids. This paper delves into the flow condensation process of methane in microchannels. A two-dimensional transient model with high accuracy for cryogenic fluids has been developed by combining a self-defined program for the source term of the phase transition model. The model fully considers the boundary layer thickness and accurately explores the mesh accuracy. The complete condensation flow patterns are captured for various vapor quality, mass flux, and wall subcooling degrees. The injection flow is a unique flow regime for condensation in microchannels. The decrease in wall subcooling degree and increase in mass flux leads to the separation point at the neck of the injected flow moving towards the exit, while the annular flow region is expanding and the flow pattern transition is lagging. The mass flux improves the heat transfer coefficient more significantly at high vapor quality. During injection and bubble flow, the wall shear stress and local heat transfer coefficient are subject to bouncing and oscillations, which may induce fluctuations in the upstream annular flow. The prediction performance of six classical heat transfer correlations is evaluated. The results indicate that the Nie et al. correlation has the highest comprehensive prediction accuracy with MRD and MARD of -5.00 % and 15.83 %, respectively.