Graetz Number

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Milad Jalali - One of the best experts on this subject based on the ideXlab platform.

  • Heat transfer and presser drop of copper oxide–thermal oil in upward single-phase flow in inclined microfin tube under constant wall temperature
    Journal of Thermal Analysis and Calorimetry, 2019
    Co-Authors: Farhad Hekmatipour, Milad Jalali
    Abstract:

    The effects of using copper oxide–thermal oil on convective heat transfer and pressure drop in an upward flow in an inclined microfin tube is studied experimentally in this research project. The flow regime and wall temperature are laminar and constant, respectively. The effects of nanofluid, Graetz Number, Prandtl Number and positive inclination angles on convective heat transfer augment moderately with the boom in nanoparticles mass concentration. The result shows that the forced heat transfer and Darcy friction factor increase with the increment of mass nanoparticle concentration, Reynolds Number and inclination angle. The ratio of Darcy friction factor increases up to 64% in microfin tube. The Nusselt Number boosts to reach 62 when mass nanoparticle concentration and inclination angle were 1.5% and 30º, respectively. Two correlations are advised to estimate Nusselt Number and Darcy friction factor in upward single-phase flow in microfin tube under constant wall temperature and laminar flow in microfin pipe. The maximum aberrations of Nusselt Number and Darcy friction factor are 20% and 18%, respectively, which are admissible to predict experimental data. Accompaniment of heat transfer ratio with pumping power ratio is presented in this paper. If the increment of pressure drop is more than heat transfer enhancement, it will not be appropriate to use CuO-thermal oil, inclination angles and microfin tube. The maximum FOM is 59% which is calculated with 1.5% nanoparticle mass concentration and inclination angle of 60º at Prandtl Number of 349.

  • Application of copper oxide–thermal oil (CuO-HTO) nanofluid on convective heat transfer enhancement in inclined circular tube
    Journal of Thermal Analysis and Calorimetry, 2019
    Co-Authors: Farhad Hekmatipour, Milad Jalali
    Abstract:

    The influence of using copper oxide–thermal oil on convective heat transfer and pressure drop in an upward flow in an inclined smooth tube is studied experimentally in this paper. The flow regime and wall temperature are laminar and constant, respectively. The effects of nanofluid, Graetz Number, Prandtl Number, negative inclination angle on convective heat transfer rate rise moderately with the augmentation of nanoparticles mass concentration. Both correlations are recommended to evaluate Nusselt Number and Darcy friction factor in an upward flow under constant wall temperature and laminar flow in smooth pipe. The maximum deviations are 19% and 21%, respectively, which are acceptable for scientific research to be used in industrial applications. Accompaniment of heat transfer ratio with pumping power ratio is presented in this paper. If the increment of pressure drop is more than heat transfer enhancement, it will not be appropriate to use CuO–thermal oil, negative inclination angles and smooth tube. The figure of merit increases up to 1.58% which is calculated with 1.5% nanoparticle mass concentration and inclination angle of 30° at Prandtl Number of 387. The results show that most of the values are more than unity, so the heat transfer enhancement is more than increment of pressure drop.

Farhad Hekmatipour - One of the best experts on this subject based on the ideXlab platform.

  • Heat transfer and presser drop of copper oxide–thermal oil in upward single-phase flow in inclined microfin tube under constant wall temperature
    Journal of Thermal Analysis and Calorimetry, 2019
    Co-Authors: Farhad Hekmatipour, Milad Jalali
    Abstract:

    The effects of using copper oxide–thermal oil on convective heat transfer and pressure drop in an upward flow in an inclined microfin tube is studied experimentally in this research project. The flow regime and wall temperature are laminar and constant, respectively. The effects of nanofluid, Graetz Number, Prandtl Number and positive inclination angles on convective heat transfer augment moderately with the boom in nanoparticles mass concentration. The result shows that the forced heat transfer and Darcy friction factor increase with the increment of mass nanoparticle concentration, Reynolds Number and inclination angle. The ratio of Darcy friction factor increases up to 64% in microfin tube. The Nusselt Number boosts to reach 62 when mass nanoparticle concentration and inclination angle were 1.5% and 30º, respectively. Two correlations are advised to estimate Nusselt Number and Darcy friction factor in upward single-phase flow in microfin tube under constant wall temperature and laminar flow in microfin pipe. The maximum aberrations of Nusselt Number and Darcy friction factor are 20% and 18%, respectively, which are admissible to predict experimental data. Accompaniment of heat transfer ratio with pumping power ratio is presented in this paper. If the increment of pressure drop is more than heat transfer enhancement, it will not be appropriate to use CuO-thermal oil, inclination angles and microfin tube. The maximum FOM is 59% which is calculated with 1.5% nanoparticle mass concentration and inclination angle of 60º at Prandtl Number of 349.

  • Application of copper oxide–thermal oil (CuO-HTO) nanofluid on convective heat transfer enhancement in inclined circular tube
    Journal of Thermal Analysis and Calorimetry, 2019
    Co-Authors: Farhad Hekmatipour, Milad Jalali
    Abstract:

    The influence of using copper oxide–thermal oil on convective heat transfer and pressure drop in an upward flow in an inclined smooth tube is studied experimentally in this paper. The flow regime and wall temperature are laminar and constant, respectively. The effects of nanofluid, Graetz Number, Prandtl Number, negative inclination angle on convective heat transfer rate rise moderately with the augmentation of nanoparticles mass concentration. Both correlations are recommended to evaluate Nusselt Number and Darcy friction factor in an upward flow under constant wall temperature and laminar flow in smooth pipe. The maximum deviations are 19% and 21%, respectively, which are acceptable for scientific research to be used in industrial applications. Accompaniment of heat transfer ratio with pumping power ratio is presented in this paper. If the increment of pressure drop is more than heat transfer enhancement, it will not be appropriate to use CuO–thermal oil, negative inclination angles and smooth tube. The figure of merit increases up to 1.58% which is calculated with 1.5% nanoparticle mass concentration and inclination angle of 30° at Prandtl Number of 387. The results show that most of the values are more than unity, so the heat transfer enhancement is more than increment of pressure drop.

Wilko Rohlfs - One of the best experts on this subject based on the ideXlab platform.

  • entrance length effects on Graetz Number scaling in laminar duct flows with periodic obstructions transport Number correlations for spacer filled membrane channel flows
    International Journal of Heat and Mass Transfer, 2016
    Co-Authors: Wilko Rohlfs, John H Lienhard
    Abstract:

    Abstract Self-similarity and scaling laws are powerful tools in engineering and thus useful for the design of apparatus. This self-similarity is well understood for the heat and mass transfer in laminar empty channel flows, including the fully developed region as well as inlet length effects in the developing region (Graetz problem). In this study, we examine the validity of the scaling behavior arising from the Graetz solution for channel flows disturbed by periodic obstructions. Simulation results show that entrance length effects and scaling laws do not change due to the presence of obstructions if the flow field remains steady in time and the dimensionless inlet length is given by X T / D h ≈ C inl . · Re · Pr , where C inl . ≈ 0.01 for the local and C inl . ≈ 0.03 for the average Nusselt Number. The Nusselt Number in the inlet region for an internal flow scales by Nu = ( Re · Pr ) 1 / 3 , similar to the empty channel flow (Shah and London, 1978). If the analogy between heat and mass transfer holds, same conclusions and relations are valid for the Sherwood Number, Sh ∝ ( Re · Sc ) 1 / 3 , where Sc denotes the Schmidt Number. In the fully developed region, the Nusselt Number depends slightly on the Reynolds and Prandtl Numbers owing to the loss in self-similarity of the velocity field (contrary to the empty channel flow). The limit of the classical self-similarity is the onset of temporal oscillations (instability) in the flow field. Beyond this limit, the length of the thermal entrance region is strongly reduced. Furthermore, a strong dependency of the Nusselt Number in the fully developed region on the Prandtl Number is found.

Chii-dong Ho - One of the best experts on this subject based on the ideXlab platform.

  • Double-pass Flow Heat Transfer In A Circular Conduit By Inserting A Concentric Tube For Improved Performance
    Chemical Engineering Communications, 2020
    Co-Authors: Chii-dong Ho, Wen-yi Yang
    Abstract:

    ABSTRACT A double-flow laminar counterflow heat exchanger device is an open circular tube divided into two subchannels with uniform wall temperature, inserted in parallel into an impermeable, resistless tube. Heat transfer performance was considerably improved, compared with an open circular tube (without an impermeable, resistless tube inserted), using an orthogonal expansion technique with eigenfunction power series expansion. The impermeable tube location can effectively enhance the heat transfer efficiency, leading to improved performance. The dimensionless outlet temperature and average Nusselt Number decrease with increasing Graetz Number (Gz) as the subchannel thickness ratio (κ) moves away from 0.5, especially for κ > 0.5, for flow pattern A. Heat transfer rate improvement occurs for flow pattern B for any Graetz Number with κ 

  • Analytical and experimental studies for power-law fluids in a double-pass parallel-plate heat exchanger under asymmetric isotherm conditions
    International Journal of Heat and Mass Transfer, 2017
    Co-Authors: Chii-dong Ho
    Abstract:

    Abstract The double-pass parallel-plate heat exchanger under asymmetric isotherm conditions referred to conjugated Graetz problem was proposed to enhance the thermal performance and investigated theoretically and experimentally. The analytical solutions were obtained using the separation of variables, superposition principle and an orthogonal expansion technique in terms of power series. The dependence of the average Nusselt Number on the Graetz Number and power-law index was formulated in a simplified expression. The theoretical predictions show that the power-law fluids in such a double-pass operation come up with the considerable heat-transfer efficiency improvement as compared with those in an open conduit (without an impermeable resistless sheet inserted), especially when the double-pass device was operated in larger Graetz Numbers. This work shows that the good agreement was obtained between the experimental results and theoretical predictions. The effects of the ratio of asymmetric wall temperatures, impermeable-sheet position and power-law index on both the device performance enhancement and power consumption increment have also been presented.

  • Theoretical and experimental studies of CO2 absorption by the amine solvent system in parallel-plate membrane contactors
    Separation and Purification Technology, 2016
    Co-Authors: Chii-dong Ho, Luke Chen, Jing-wei Liou
    Abstract:

    Abstract The absorption efficiency of CO 2 in ethanolamine (MEA) solvent system of a parallel-plate membrane contactor with both concurrent- and countercurrent-flow operations was investigated theoretically and experimentally. A two-dimensional modeling equation for predicting the concentration distribution and total absorption rate was developed, and the analytical solution for the resultant partial differential equations is obtained using the separated variables method with an orthogonal expansion technique. The theoretical predictions of the absorption efficiency, total absorption rate, average Sherwood Number and concentration distributions were presented graphically with the mass-transfer Graetz Number, inlet CO 2 concentration, and both gas feed and absorbent flow rates as parameters.

  • Recycle effect on heat transfer enhancement in double-pass heat exchangers under asymmetric isotherm conditions ☆
    International Communications in Heat and Mass Transfer, 2015
    Co-Authors: Chii-dong Ho, Yi-chin Chen
    Abstract:

    Abstract The mathematical formulation of a heat transfer flow problem in the recycling parallel-plate heat exchanger under asymmetric wall temperatures was developed theoretically with ignoring axial conduction, and the analytical solution was obtained using a superposition principle and an orthogonal expansion technique in extended power series. The influences of the design parameters of the impermeable-sheet position (∆), and the operating parameters of the Graetz Number (Gz), wall temperature ratio (σ) and recycle ratio (R) are examined. Significant heat transfer improvement is obtainable by employing double-pass devices instead of using single-pass ones for a larger Graetz Number system. A technical feasibility of the new double-pass device was investigated in terms of the Nusselt Number and device performance improvement under the effect of wall temperature ratios.

  • Heat transfer modeling of conjugated Graetz problems in double-pass parallel-plate heat exchangers under asymmetric wall temperatures
    Journal of The Chinese Institute of Engineers, 2013
    Co-Authors: Chii-dong Ho, Yi-chin Chen, Hsuan Chang, Shung-wen Kang
    Abstract:

    The heat transfer of a Graetz problem is investigated theoretically. The problem involves an improvement to the design of a parallel-plate heat exchanger using an inserted plate which forms a double-pass device with recycle operation. The parallel plates are at different temperatures. The theoretical mathematical model is solved analytically using the separation of variables, superposition principle, and an orthogonal expansion technique in extended power series. Significant heat transfer improvement can be realized by the design compared to a single-pass device. The improvement is greater for a larger Graetz Number system. For a small Graetz Number system, the single-pass design is preferred. The optimal location of the inserted plate is when the two subchannels are at the same height.

John H Lienhard - One of the best experts on this subject based on the ideXlab platform.

  • entrance length effects on Graetz Number scaling in laminar duct flows with periodic obstructions transport Number correlations for spacer filled membrane channel flows
    International Journal of Heat and Mass Transfer, 2016
    Co-Authors: Wilko Rohlfs, John H Lienhard
    Abstract:

    Abstract Self-similarity and scaling laws are powerful tools in engineering and thus useful for the design of apparatus. This self-similarity is well understood for the heat and mass transfer in laminar empty channel flows, including the fully developed region as well as inlet length effects in the developing region (Graetz problem). In this study, we examine the validity of the scaling behavior arising from the Graetz solution for channel flows disturbed by periodic obstructions. Simulation results show that entrance length effects and scaling laws do not change due to the presence of obstructions if the flow field remains steady in time and the dimensionless inlet length is given by X T / D h ≈ C inl . · Re · Pr , where C inl . ≈ 0.01 for the local and C inl . ≈ 0.03 for the average Nusselt Number. The Nusselt Number in the inlet region for an internal flow scales by Nu = ( Re · Pr ) 1 / 3 , similar to the empty channel flow (Shah and London, 1978). If the analogy between heat and mass transfer holds, same conclusions and relations are valid for the Sherwood Number, Sh ∝ ( Re · Sc ) 1 / 3 , where Sc denotes the Schmidt Number. In the fully developed region, the Nusselt Number depends slightly on the Reynolds and Prandtl Numbers owing to the loss in self-similarity of the velocity field (contrary to the empty channel flow). The limit of the classical self-similarity is the onset of temporal oscillations (instability) in the flow field. Beyond this limit, the length of the thermal entrance region is strongly reduced. Furthermore, a strong dependency of the Nusselt Number in the fully developed region on the Prandtl Number is found.