The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform

Afshin J. Ghajar - One of the best experts on this subject based on the ideXlab platform.

  • Development of A Unified Flow Regime Map for A Horizontal Pipe with The Support Vector Machines
    2010
    Co-Authors: H. K. Tam, Afshin J. Ghajar, L. M. Tam, C. W. Cheong
    Abstract:

    Flow Regime Map is a very useful tool. Based on the defined dimensionless parameters, the correct Flow Regime can be found from the Map. It is also a common practice that well proven heat transfer correlations are also provided in the Flow Regime Map such that thermal engineers can immediately select the correct correlation for design purposes. Different Flow Regime Maps were necessary to be established for different boundary conditions, different pipe orientations, and various pipe inlet configurations. For horizontal circular pipes fitted with three different inlet configurations (re‐entrant, square‐edged, bell‐mouth) under uniform wall heat flux boundary condition, Ghajar and Tam [1] developed Flow Regime Maps for the determination of the boundary between single‐phase forced and mixed convection using experimental data [2]. Based on the ratio of the local peripheral heat transfer coefficient at the top and the bottom, the heat transfer data was classified as either forced or mixed convection among the ...

  • Development of a Flow Regime Map for a Horizontal Pipe With the Multi-Classification Support Vector Machines
    Heat Transfer: Volume 1, 2008
    Co-Authors: Lap Mou Tam, Afshin J. Ghajar, H. K. Tam, Sik Chung Tam
    Abstract:

    For horizontal circular pipes under uniform wall heat flux boundary condition and three different inlet configurations (re-entrant, square-edged, bell-mouth), Ghajar and Tam (1995) developed Flow Regime Maps for the determination of the boundary between single-phase forced and mixed convection using experimental data of Ghajar and Tam (1994). Based on the ratio of the local peripheral heat transfer coefficient at the top and the bottom, the heat transfer data was classified as either forced or mixed convection among the different Flow Regimes. The forced-mixed convection boundary was then obtained by empirical correlations. From the Flow Maps, heat transfer correlations for different Flow Regimes were recommended. Recently Trafalis et al. (2005) used the Multiclass Support Vector Machines (SVM) method to classify vertical and horizontal two-phase Flow Regimes in 4 pipes with good accuracy. In this study, the SVM method was applied to the single-phase experimental data of Ghajar and Tam (1994) and new Flow Regime Maps were developed. Five Flow Regimes (forced turbulent, forced transition, mixed transition, forced laminar, mixed laminar) were identified in the Flow Maps using Reynolds and Rayleigh numbers as the identifying parameters. The Flow Regimes on the boundaries of the new Maps were represented by the SVM decision functions. The results show that the new Flow Regime Maps for the three types of inlets can classify the forced and mixed convection experimental data in different Flow Regimes with good accuracy.Copyright © 2008 by ASME

  • Transitional Heat Transfer in Plain Horizontal Tubes
    Heat Transfer Engineering, 2006
    Co-Authors: Lap Mou Tam, Afshin J. Ghajar
    Abstract:

    In this study, the heat transfer behavior in the transition region for plain horizontal tubes under a uniform wall heat flux boundary condition is discussed in detail. In particular, the influence of inlet configuration and free convection superimposed on the forced convection (or mixed convection) at the start and end of the transition region and the magnitude of heat transfer are addressed. The available correlations to predict the heat transfer coefficient in the transition region are reviewed, and their performance are evaluated based on 1290 experimental data points obtained under a wide range of experimental conditions. Appropriate correlations for the mixed and forced convection transition regions are recommended. Finally, a Flow Regime Map for determination of the boundary between forced and mixed convection in horizontal tubes with different inlets is presented.

  • heat transfer measurements and correlations for air water Flow of different Flow patterns in a horizontal pipe
    Experimental Thermal and Fluid Science, 2002
    Co-Authors: Dong Woo Kim, Afshin J. Ghajar
    Abstract:

    Abstract Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different Flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the Flow patterns was supplemented with photographic data, and the results were plotted on the Flow Regime Map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different Flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.

  • Heat transfer measurements and correlations for air–water Flow of different Flow patterns in a horizontal pipe
    Experimental Thermal and Fluid Science, 2002
    Co-Authors: Dong Woo Kim, Afshin J. Ghajar
    Abstract:

    Abstract Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different Flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the Flow patterns was supplemented with photographic data, and the results were plotted on the Flow Regime Map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different Flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.

Lap Mou Tam - One of the best experts on this subject based on the ideXlab platform.

  • Development of a Flow Regime Map for a Horizontal Pipe With the Multi-Classification Support Vector Machines
    Heat Transfer: Volume 1, 2008
    Co-Authors: Lap Mou Tam, Afshin J. Ghajar, H. K. Tam, Sik Chung Tam
    Abstract:

    For horizontal circular pipes under uniform wall heat flux boundary condition and three different inlet configurations (re-entrant, square-edged, bell-mouth), Ghajar and Tam (1995) developed Flow Regime Maps for the determination of the boundary between single-phase forced and mixed convection using experimental data of Ghajar and Tam (1994). Based on the ratio of the local peripheral heat transfer coefficient at the top and the bottom, the heat transfer data was classified as either forced or mixed convection among the different Flow Regimes. The forced-mixed convection boundary was then obtained by empirical correlations. From the Flow Maps, heat transfer correlations for different Flow Regimes were recommended. Recently Trafalis et al. (2005) used the Multiclass Support Vector Machines (SVM) method to classify vertical and horizontal two-phase Flow Regimes in 4 pipes with good accuracy. In this study, the SVM method was applied to the single-phase experimental data of Ghajar and Tam (1994) and new Flow Regime Maps were developed. Five Flow Regimes (forced turbulent, forced transition, mixed transition, forced laminar, mixed laminar) were identified in the Flow Maps using Reynolds and Rayleigh numbers as the identifying parameters. The Flow Regimes on the boundaries of the new Maps were represented by the SVM decision functions. The results show that the new Flow Regime Maps for the three types of inlets can classify the forced and mixed convection experimental data in different Flow Regimes with good accuracy.Copyright © 2008 by ASME

  • Transitional Heat Transfer in Plain Horizontal Tubes
    Heat Transfer Engineering, 2006
    Co-Authors: Lap Mou Tam, Afshin J. Ghajar
    Abstract:

    In this study, the heat transfer behavior in the transition region for plain horizontal tubes under a uniform wall heat flux boundary condition is discussed in detail. In particular, the influence of inlet configuration and free convection superimposed on the forced convection (or mixed convection) at the start and end of the transition region and the magnitude of heat transfer are addressed. The available correlations to predict the heat transfer coefficient in the transition region are reviewed, and their performance are evaluated based on 1290 experimental data points obtained under a wide range of experimental conditions. Appropriate correlations for the mixed and forced convection transition regions are recommended. Finally, a Flow Regime Map for determination of the boundary between forced and mixed convection in horizontal tubes with different inlets is presented.

  • Flow Regime Map for a horizontal pipe with uniform wall heat flux and three inlet configurations
    Experimental Thermal and Fluid Science, 1995
    Co-Authors: Afshin J. Ghajar, Lap Mou Tam
    Abstract:

    Abstract A Flow Regime Map for determination of the boundary between forced and mixed convection in a horizontal circular straight tube with reentrant, square-edged, and bell-mouth inlets under uniform wall heat flux boundary condition is developed. The Flow Regime Map is applicable to all Flow Regimes (laminar, transition, turbulent). From the Flow Regime Map, for any forced Flow represented by a given Reynolds number, the value of the parameter GrPr at a particular x D location indicates whether it is necessary to consider bouyancy effects. For the identified pure forced or mixed convection heat transfer Regime, a heat transfer correlation is recommended.

Jiange Xiao - One of the best experts on this subject based on the ideXlab platform.

  • Void fraction and Flow Regime of in-tube condensation in a vapor-compression system.
    2019
    Co-Authors: Jiange Xiao
    Abstract:

    In vapor-compression systems, superheated vapor condenses with temperature gradient. A “3-zone” (superheated, two-phase and subcooled) approach is not fully representative of the process because condensation happens earlier and later than bulk quality 1 and 0 respectively. The new approach, which is “5-zone” (additional condensing superheated and condensing subcooled), addresses those issues by capturing the non-equilibrium effects. Void fraction and Flow Regime measured in 4 and 6 mm smooth horizontal round tubes are used to validate the new approach in the range: mass flux from 50 to 400 kg m-2 s-1; heat flux 5 to 15 kW m-2; condensing temperatures 30 and 50°C. The refrigerants explored are R32, R134a, R1234ze(E), R245fa and R1233zd(E). Comparing to the “3-zone” approach, the new void fraction correlation and Flow Regime Map expend the prediction range by finding the real onset and end of condensation, providing grounds for new heat transfer and pressure drop models.

  • a Flow Regime Map for condensation in macro and micro tubes with non equilibrium effects taken into account
    International Journal of Heat and Mass Transfer, 2019
    Co-Authors: Jiange Xiao, Pega Hrnjak
    Abstract:

    Abstract A Flow Regime Map for condensation from superheated vapor is proposed in this paper. The Flow Regime Map takes the non-equilibrium effects into account by following the development of liquid film from the real onset of condensation to the end. It can be applied to both conventional tubes and microchannels. The transition mechanism between annular and stratified-wavy Flow is determined to be the force balance between the shear force, gravity and surface tension. The transition mechanism from annular to intermittent Flow is found to be the comparison between wave heights and tube diameter. The transition mechanism for stratified-wavy and fully-stratified is kept the same as elaborated by Xiao and Hrnjak (2017). The connections between the dimensionless number We, Fr and Bo and the transition criteria are analyzed. The Flow Regime Map is validated by the experimental data in Xiao and Hrnjak (2017) and some current visualizations, which includes diabatic visualizations of R134a, R1234ze(E), R32, R245fa and R1233zd(E) condensing at 30 and 50 °C in 1, 4 and 6 mm tubes.

  • Flow Regimes during condensation from superheated vapor
    International Journal of Heat and Mass Transfer, 2019
    Co-Authors: Jiange Xiao, Predrag Stojan Hrnjak
    Abstract:

    Abstract Two-phase Flow during condensation in smooth horizontal round tubes of R245fa, R1233zd(E), R1234ze(E), R134a, R32 from superheated vapor is visualized and presented in this paper. Flow Regimes under different mass fluxes, heat fluxes, saturation pressures, specific enthalpies and tube sizes (1, 4, 6 mm) are identified. The paper describes to the Flow Regime transitions according to the visualizations. The driving force behind the annular-stratified Flow transition is identified to be the force balance between shear, gravity and surface tension. The mechanism that dictates the annular-intermittent Flow transition is the comparison between wave-height and the tube size. The slip ratio, which generates the Kelvin-Helmholtz instability, is considered to be the reason of transition from stratified-wavy to the fully-stratified Flow. The more complicated scenarios where characteristics of different Flow Regimes coexist are detailed and methods for simplification are provided. The results are also compared to two different Flow Regime Maps. The Flow Regime Map that does not consider the non-equilibrium effects does not provide information beyond bulk quality 1 and 0. Additionally, it does not capture the annular entrance during condensation either. The Flow Regime Map with non-equilibrium taken into account addresses issues above while having its own defects. For instance, it is highly empirical and some transition lines do not properly reflect experimental observations. A more mechanistic Flow Regime Map is recommended.

  • Pressure drop model for condensation from superheated vapor.
    2018
    Co-Authors: Jiange Xiao, Predrag Stojan Hrnjak
    Abstract:

    A new pressure drop model based on Flow Regime Map is proposed for condensation inside horizontal smooth round tubes accounting for the non-equilibrium in a vapor compression system. Conventionally, a pressure drop model for two-phase Flow only accounts for the prediction between bulk quality 1 and 0. The temperature gradient during condensation, however, creates the non-equilibrium that guarantees two-phase Flow beyond bulk quality 1 and 0. The new model determines the onset and end of condensation by tracing the development of the liquid film when the superheated vapor is condensed on the tube wall. The Flow Regime Map designed specifically for condensation from superheated vapor is used to predict the Flow Regime when the Flow is two-phase. Two Flow Regime transitions are recognized. One is from annular Flow to the stratified Flow under low mass fluxes; the other is from annular Flow to the intermittent Flow under high mass fluxes. The annular Flow is treated as a uniform ring; the stratified Flow is treated as a combination of annular Flow on the upper part of the tube and liquid pool at the bottom part of the tube; the intermittent Flow is treated as a combination of annular Flow and single-phase liquid Flow that occurs intermittently. The weights designated to each Flow Regime is calculated from the void fraction model that also accounts for non-equilibrium and is used in the Flow Regime Map. The prediction of the new model is compared with experimental data of R32, R134a and R1233zd(E) mass fluxes from 100 to 400 kg/m2-s, heat fluxes from 5 to 15 kW/m2 and tube diameters of 4.0 and 6.1 mm at saturation temperatures of 30 oC. The comparison shows that the new model provides good agreements with experimental data. Additionally, by accounting for the non-equilibrium in the condensation process, the new model seamlessly connects the single-phase and two-phase regions with the corresponding mechanisms that occurs in a real vapor compression system.

  • Flow Regime Map for condensation from superheated vapor.
    2018
    Co-Authors: Jiange Xiao, Predrag Stojan Hrnjak
    Abstract:

    An update on the Flow Regime Map for condensation inside horizontal smooth round tubes accounting for the non-equilibrium existed in a vapor compression system is introduced. It is usually by default to assume that a Flow Regime Map should be made between bulk quality 1 and 0. However, the temperature gradient required by condensation means that the thermal equilibrium assumed in a thermodynamic point of view does not exist in a real condenser, especially at the entrance stages of a condenser in a vapor compression system. By focusing on the development of the liquid film when the superheated vapor is condensed on the tube wall whose temperature is below saturation temperature at the corresponding pressure, the real onset and end of condensation could be theoretically calculated. The Flow Regime Map, therefore, should be constructed in between the real onset and end of condensation that are manually set as superficial quality 1 and 0. Two-phase Flows of R32, R134a, R1234ze(E), R245fa and R1233zd(E) under mass fluxes from 100 to 400 kg/m2-s, heat fluxes from 5 to 10 kW/m2, and tube diameters of 4.0 and 6.1 mm at saturation temperatures of 30 and 50 oC are observed in transparent tube-in-tube heat exchangers where refrigerants are cooled by glycol. The visualizations shows three deficiencies in a conventional Flow Map. First, a conventional Flow Map does not provide any information beyond quality 1 and 0 where there is two-phase Flow as mentioned above. Second, at the entrance stages of the condensation, the film-forming mechanism guarantees an annular Flow. This mechanism, however, is usually not employed in a conventional Flow Map. Third, the conventional Flow Regime Map does not provide information for both micro and macro tubes. The Flow Map for those two different sized tubes are usually separately made while putting surface tension into the picture could potentially unify them. The transition criteria with the non-equilibrium is taken into account are redefined and the new Flow Regime Map addresses the issues above. A comparison between visualization and the prediction of the new Flow Map shows good agreement.

Predrag Stojan Hrnjak - One of the best experts on this subject based on the ideXlab platform.

  • Flow Regimes during condensation from superheated vapor
    International Journal of Heat and Mass Transfer, 2019
    Co-Authors: Jiange Xiao, Predrag Stojan Hrnjak
    Abstract:

    Abstract Two-phase Flow during condensation in smooth horizontal round tubes of R245fa, R1233zd(E), R1234ze(E), R134a, R32 from superheated vapor is visualized and presented in this paper. Flow Regimes under different mass fluxes, heat fluxes, saturation pressures, specific enthalpies and tube sizes (1, 4, 6 mm) are identified. The paper describes to the Flow Regime transitions according to the visualizations. The driving force behind the annular-stratified Flow transition is identified to be the force balance between shear, gravity and surface tension. The mechanism that dictates the annular-intermittent Flow transition is the comparison between wave-height and the tube size. The slip ratio, which generates the Kelvin-Helmholtz instability, is considered to be the reason of transition from stratified-wavy to the fully-stratified Flow. The more complicated scenarios where characteristics of different Flow Regimes coexist are detailed and methods for simplification are provided. The results are also compared to two different Flow Regime Maps. The Flow Regime Map that does not consider the non-equilibrium effects does not provide information beyond bulk quality 1 and 0. Additionally, it does not capture the annular entrance during condensation either. The Flow Regime Map with non-equilibrium taken into account addresses issues above while having its own defects. For instance, it is highly empirical and some transition lines do not properly reflect experimental observations. A more mechanistic Flow Regime Map is recommended.

  • Void fraction and Flow Regimes of R134a in horizontal and vertical round tubes in developed adiabatic conditions.
    2018
    Co-Authors: Hongliang Qian, Predrag Stojan Hrnjak
    Abstract:

    This paper presents Flow Regimes and void fraction in horizontal and vertical round tubes ID 7 mm with R134a in the adiabatic conditions and low mass flux (40-150 kg/m2s for horizontal tubes and 65-115 kg/m2s for vertical tubes) captured by a high-speed camera. Horizontal Flow patterns are compared to Wojtan-Ursenbacher-Thome Flow Regime Map and some modifications are proposed. Void fraction results for both horizontal and vertical tubes are compared to some widely used correlations. Influences of tube orientation and mass flux on void fraction are discussed. At the same vapor quality condition, void fraction of horizontal tubes is larger than that of vertical tubes. Higher mass flux also results in larger void fraction compared that of lower mass flux.

  • Pressure drop model for condensation from superheated vapor.
    2018
    Co-Authors: Jiange Xiao, Predrag Stojan Hrnjak
    Abstract:

    A new pressure drop model based on Flow Regime Map is proposed for condensation inside horizontal smooth round tubes accounting for the non-equilibrium in a vapor compression system. Conventionally, a pressure drop model for two-phase Flow only accounts for the prediction between bulk quality 1 and 0. The temperature gradient during condensation, however, creates the non-equilibrium that guarantees two-phase Flow beyond bulk quality 1 and 0. The new model determines the onset and end of condensation by tracing the development of the liquid film when the superheated vapor is condensed on the tube wall. The Flow Regime Map designed specifically for condensation from superheated vapor is used to predict the Flow Regime when the Flow is two-phase. Two Flow Regime transitions are recognized. One is from annular Flow to the stratified Flow under low mass fluxes; the other is from annular Flow to the intermittent Flow under high mass fluxes. The annular Flow is treated as a uniform ring; the stratified Flow is treated as a combination of annular Flow on the upper part of the tube and liquid pool at the bottom part of the tube; the intermittent Flow is treated as a combination of annular Flow and single-phase liquid Flow that occurs intermittently. The weights designated to each Flow Regime is calculated from the void fraction model that also accounts for non-equilibrium and is used in the Flow Regime Map. The prediction of the new model is compared with experimental data of R32, R134a and R1233zd(E) mass fluxes from 100 to 400 kg/m2-s, heat fluxes from 5 to 15 kW/m2 and tube diameters of 4.0 and 6.1 mm at saturation temperatures of 30 oC. The comparison shows that the new model provides good agreements with experimental data. Additionally, by accounting for the non-equilibrium in the condensation process, the new model seamlessly connects the single-phase and two-phase regions with the corresponding mechanisms that occurs in a real vapor compression system.

  • Flow Regime Map for condensation from superheated vapor.
    2018
    Co-Authors: Jiange Xiao, Predrag Stojan Hrnjak
    Abstract:

    An update on the Flow Regime Map for condensation inside horizontal smooth round tubes accounting for the non-equilibrium existed in a vapor compression system is introduced. It is usually by default to assume that a Flow Regime Map should be made between bulk quality 1 and 0. However, the temperature gradient required by condensation means that the thermal equilibrium assumed in a thermodynamic point of view does not exist in a real condenser, especially at the entrance stages of a condenser in a vapor compression system. By focusing on the development of the liquid film when the superheated vapor is condensed on the tube wall whose temperature is below saturation temperature at the corresponding pressure, the real onset and end of condensation could be theoretically calculated. The Flow Regime Map, therefore, should be constructed in between the real onset and end of condensation that are manually set as superficial quality 1 and 0. Two-phase Flows of R32, R134a, R1234ze(E), R245fa and R1233zd(E) under mass fluxes from 100 to 400 kg/m2-s, heat fluxes from 5 to 10 kW/m2, and tube diameters of 4.0 and 6.1 mm at saturation temperatures of 30 and 50 oC are observed in transparent tube-in-tube heat exchangers where refrigerants are cooled by glycol. The visualizations shows three deficiencies in a conventional Flow Map. First, a conventional Flow Map does not provide any information beyond quality 1 and 0 where there is two-phase Flow as mentioned above. Second, at the entrance stages of the condensation, the film-forming mechanism guarantees an annular Flow. This mechanism, however, is usually not employed in a conventional Flow Map. Third, the conventional Flow Regime Map does not provide information for both micro and macro tubes. The Flow Map for those two different sized tubes are usually separately made while putting surface tension into the picture could potentially unify them. The transition criteria with the non-equilibrium is taken into account are redefined and the new Flow Regime Map addresses the issues above. A comparison between visualization and the prediction of the new Flow Map shows good agreement.

Dong Woo Kim - One of the best experts on this subject based on the ideXlab platform.

  • heat transfer measurements and correlations for air water Flow of different Flow patterns in a horizontal pipe
    Experimental Thermal and Fluid Science, 2002
    Co-Authors: Dong Woo Kim, Afshin J. Ghajar
    Abstract:

    Abstract Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different Flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the Flow patterns was supplemented with photographic data, and the results were plotted on the Flow Regime Map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different Flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.

  • Heat transfer measurements and correlations for air–water Flow of different Flow patterns in a horizontal pipe
    Experimental Thermal and Fluid Science, 2002
    Co-Authors: Dong Woo Kim, Afshin J. Ghajar
    Abstract:

    Abstract Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different Flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the Flow patterns was supplemented with photographic data, and the results were plotted on the Flow Regime Map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different Flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.