Estimation of a Nusselt Correlation for the Numerical Prediction of Frost Thickness on a Tube Banks of Triangular Arrangement

2014 ◽  
Vol 353 ◽  
pp. 121-125
Author(s):  
Raquel da Cunha Ribeiro da Silva ◽  
C.T. Salinas ◽  
P.A. Delgado ◽  
K.A.R. Ismail
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Nusselt Number ◽  
Heat Exchangers ◽  
Tube Bank ◽  
Empirical Relations ◽  
Complex Heat Transfer ◽  
Tube Banks ◽  
The Heat Transfer Coefficient

This paper presents a frost numerical model for predicting the frosting behavior in terms of the correlation of the heat transfer coefficient, Nusselt number. In this work the correlations of the Nusselt number from various references is examined and compared with experimental data. In this study, a mathematical model that can predict the behavior of the frost growth on a bank of triangularly arranged tubes is developed. Because of the complex heat transfer during frost formation on a tube bank, this subject is receiving much attention. Heat transfer in flow across a bank of tubes has particular importance in the design of heat exchangers. For this study various empirical relations are analyzed to determine the Nusselt number and compared with experimental data.

The Dynamics of Liquid Cooling in Half-Coil Jackets

2008 ◽  
Vol 3 (1) ◽  
Author(s):  
Jayakumar Natesan Subramanian ◽  
Farouq S. Mjalli
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Liquid Temperature ◽  
Liquid Cooling ◽  
Shell Side ◽  
Stirred Vessel ◽  
Model Predictions ◽  
Temperature Dynamics ◽  
The Heat Transfer Coefficient

The heat transfer cooling of a hot liquid in a stirred vessel has been studied experimentally with coolant flowing through a half-coil around the vessel. Correlations have been developed for the heat transfer coefficient of the half coil jacket. A mathematical model for the half coil jacket liquid temperature dynamics and its analytical solution is used to find the shell side temperature profile as a function of time. It is found that the model predictions are in satisfactory agreement with the experimental data and that the developed correlation is superior to previously published correlations for similar systems.

scholarly journals Determination of the Reference Temperature for a Convective Heat Transfer Coefficient in a Heated Tube Bank

2021 ◽  
Vol 11 (22) ◽  
pp. 10564
Author(s):  
Stanislav Kotšmíd ◽  
Zuzana Brodnianská
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Turbulent Flows ◽  
Convective Heat Transfer Coefficient ◽  
Reference Temperature ◽  
Tube Bank ◽  
Heated Tube ◽  
Tube Banks

The paper presents a theoretical analysis of heat transfer in a heated tube bank, based on the Nusselt number computation as one of the basic dimensionless criteria. To compute the Nusselt number based on the heat transfer coefficient, the reference temperature must be determined. Despite the value significance, the quantity has several different formulations, which leads to discrepancies in results. This paper investigates the heat transfer of the inline and staggered tube banks, made up of 20 rows, at a constant tube diameter and longitudinal and transverse pitch. Both laminar and turbulent flows up to Re = 10,000 are considered, and the effect of gravity is included as well. Several locations for the reference temperature are taken into consideration on the basis of the heretofore published research, and the results in terms of the overall Nusselt number are compared with those obtained by the experimental correlations. This paper provides the most suitable variant for a unique reference temperature, in terms of a constant value for all tube angles, and the Reynolds number ranges of 100–1000 and 1000–10,000 which are in good agreement with the most frequently used correlating equations.

The Correlation of Heat Transfer Coefficients for the Laminar Natural Convection in a Circular Finned-Tube Heat Exchanger

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Hie Chan Kang ◽  
Se-Myong Chang
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Nusselt Number ◽  
Natural Convection ◽  
Heat Exchanger ◽  
Heat Exchangers ◽  
Finned Tube ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Laminar Natural Convection

This study proposes an empirical correlation for laminar natural convection applicable to external circular finned-tube heat exchangers with wide range of configuration parameters. The transient temperature response of the heat exchangers was used to obtain the heat transfer coefficient, and the experimental data with their characteristic lengths are discussed. The data lie in the range from 1 to 1000 for Rayleigh numbers based on the fin spacing: the ratio of fin height to tube diameter ranges from 0.1 to 0.9, and the ratio of fin pitch to height ranges from 0.13 to 2.6. Sixteen sets of finned-tube electroplated with nickel–chrome were tested. The convective heat transfer coefficients on the heat exchangers were measured by elimination of the thermal radiation effect from the heat exchanger surfaces. The Nusselt number was correlated with a newly suggested composite curve formula, which converges to the quarter power of the Rayleigh number for a single cylinder case. The proposed characteristic length for the Rayleigh number is the fin pitch while that for the Nusselt number is mean flow length, defined as half the perimeter of the mean radial position inside the flow region bounded by the tube surface and two adjacent fins. The flow is regarded as laminar, which covers heat exchangers from a single horizontal cylinder to infinite parallel disks. Consequently, the result of curve fitting for the experimental data shows the reasonable physical interpretation as well as the good quantitative agreement with the correction factors.

A Mathematical Model For Steady Operation of Stirling-Type Engines

1968 ◽  
Vol 90 (1) ◽  
pp. 45-50 ◽  
Author(s):  
E. B. Qvale ◽  
J. L. Smith
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Heat Exchangers ◽  
Correction Factors ◽  
Transfer Rates ◽  
Flow Friction ◽  
Independent Variables ◽  
Basic Performance ◽  
Good Agreement

A mathematical model of Stirling-type engines has been developed. The complexity of the problem has been reduced by analyzing the various components of the engine (heat exchangers, regenerator, and cylinders) separately for cyclically steady conditions, and by selecting pressure, temperature, and mass as the independent variables. The required piston displacements are a computed result. Losses due to flow friction, piston blow-by, and finite heat transfer rates have been accounted for by applying correction factors to the basic performance which is computed without these effects. The theory has been carried out for engines, but it is equally valid for refrigerators with minor modification. The theory is in good agreement with available experimental data.

A Study About Performance Evaluation Criteria of Tube Banks With Various Shapes and Arrangements Using Numerical Simulation

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Amin Jodaei ◽  
Kamiar Zamzamian
Keyword(s):  
Heat Transfer ◽  
Performance Evaluation ◽  
Heat Exchangers ◽  
Three Dimensional ◽  
Evaluation Criteria ◽  
Cross Flow ◽  
Transfer Coefficients ◽  
Tube Bank ◽  
Shaped Tube ◽  
Tube Banks

Tube bank heat exchangers are designed to efficiently transfer heat between two fluids. Shapes and arrangements of tubes in heat exchangers have significant effects in heat transfer and pressure drop of fluid. In this study, the three-dimensional (3D) numerical investigation is performed to determine heat transfer coefficients, friction factor, and performance evaluation criteria (PEC) of cam-shaped tube banks in aerodynamic and inverse aerodynamic directions in the cross flow air and compared with those of elliptical tube banks in heat exchanger. The arrangements of tubes are aligned and staggered with longitudinal pitch of 44.88 mm and transverse pitch of 28.05 mm. Reynolds number in the range of 11,500–18,500 was used, and the tube surface temperature was fixed and considered 352 K. Results indicate the superior heat transfer of elliptical tube bank over the cam-shaped tube banks in inverse aerodynamic and aerodynamic directions in both arrangements. Moreover, the PEC of the cam-shaped tube banks with inverse aerodynamic and aerodynamic directions and elliptical tube bank in aligned arrangement are approximately 1.4, 1.1, and 1.6, respectively. The obtained results for staggered arrangements are also 1.5, 1.3, and 1.8, respectively.

scholarly journals Transient behavior of a plate-fin-and-tube heat exchanger taking into account different heat transfer coefficients on the individual tube rows

2019 ◽  
Vol 137 ◽  
pp. 01036
Author(s):  
Dawid Taler ◽  
Jan Taler ◽  
Katarzyna Wrona
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Exchangers ◽  
Experimental Studies ◽  
Analytical Formula ◽  
Cfd Modeling ◽  
Individual Tube ◽  
The Heat Transfer Coefficient

Plate-fin and tube heat exchangers (PFTHE) are made of round, elliptical, oval or flat tubes to which continuous fins ( lamellas) are attached. Liquid flows inside the tubes and gas flows outside the tubes perpendicularly to their axes and parallel to the surface of continuous fins. Experimental studies of multi-row plate-fin and tube heat exchangers show that the highest average heat transfer coefficient on the air side occurs in the first row of tubes when the air velocity in front of the exchanger is less than approximately 3.5 m/s when a Reynolds number based on an equivalent hydraulic diameter equal to the distance between tube rows in the direction of air flow is less than 10,000. In the subsequent rows of tubes up to about the fourth row the heat transfer coefficient decreases. In the fifth and further rows, it can, that the heat transfer coefficient is equal in each tube row. It is necessary to find the relationships for the air-side Nusselt number on each tube row to design a PFTHE with the appropriate number of tube rows. The air-side Nusselt number correlations can be determined experimentally or by CFD modeling (Computational and Fluid Dynamics). The paper presents a new mathematical model of the transient operation of PFTHE, considering that the Nusselt numbers on the air side of individual tube rows are different. The heat transfer coefficient on an analyzed tube row was determined from the equality condition of mass- average air temperature differences on a given tube row determined using the analytical formula and CFD modeling. The results of numerical modeling were compared with the results of the experiments.

scholarly journals Application of porous materials in heat exchangers of heat supply system

2020 ◽  
Vol 22 (3) ◽  
pp. 3-13
Author(s):  
N. V. Rydalina ◽  
B. G. Aksenov ◽  
O. A. Stepanov ◽  
E. O. Antonova
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Heat Exchanger ◽  
Heat Exchange ◽  
Porous Materials ◽  
Heat Exchangers ◽  
Porous Metals ◽  
Porous Aluminum ◽  
Heat Exchange Equipment

Heat exchange capacity increase is one of the main concerns in the process of manufacturing modern heat exchange equipment. Constructing heat exchangers with porous metals is an advanced technique of heat exchange increase. A construction of heat exchangers with porous aluminum is described in this paper. The first heat transfer agent (hot water) flows through thin copper tubes installed within the porous aluminum. The second heat transfer agent (freon) flows through the pores of aluminum. Laboratory facility was created to study such a heat exchanger. Series of experiments were carried out. The purpose of the research presented here is to create a mathematical model of heat exchangers with porous metals, to perform analytical calculation of the heat exchangers and to confirm the results with the experimental data. In this case, one can`t use the standard methods of heat exchangers calculation because the pores inner surface area is indeterminate. The developed mathematical model is based on the equation describing the process of cooling the porous plate. A special mathematical technique is used to take into account the effect of tubes with water. The model is approximate but its solution is analytic. It is convenient. One can differentiate it or integrate it, which is very important. Comparison of calculated and experimental data is performed. Divergence of results is within the limits of experimental error. If freon volatilizes inside the heat exchanger, the heat of phase transition has to be taken into account alongside with heat capacity. The structure of the mathematical model makes it possible. The results presented in this paper prove the practicability of using porous materials in heat exchange equipment.

A Model of Heat Transfer in Fluidized Beds

1972 ◽  
Vol 94 (1) ◽  
pp. 105-110 ◽  
Author(s):  
Benjamin T. F. Chung ◽  
L. T. Fan ◽  
C. L. Hwang
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Fluidized Beds ◽  
Transfer Coefficients ◽  
Surface Renewal ◽  
Heat Transfer Coefficients ◽  
Fluidized System ◽  
The Heat Transfer Coefficient

An expression for estimating the heat transfer coefficient in a fluidized bed has been developed based on the surface renewal and penetration concept. The predicted heat transfer coefficients between walls and beds agree well with experimental results. The result of this analysis shows that, in general, the effect of thermal conductivity of particle on heat transfer is insignificant. The maximum possible Nusselt number for the gas fluidized system is determined theoretically as 13.5. This value appears to be reasonable in light of the majority of available experimental data.

Oscillatory Heat Transfer in a Pipe Subjected to a Laminar Reciprocating Flow

1996 ◽  
Vol 118 (3) ◽  
pp. 592-597 ◽  
Author(s):  
T. S. Zhao ◽  
P. Cheng
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Flux ◽  
Nusselt Number ◽  
Numerical Study ◽  
Temperature Cycle ◽  
Uniform Heat Flux ◽  
Fluid Temperature ◽  
Cycle Space ◽  
Reciprocating Flow

An experimental and numerical study has been carried out for laminar forced convection in a long pipe heated by uniform heat flux and subjected to a reciprocating flow of air. Transient fluid temperature variations in the two mixing chambers connected to both ends of the heated section were measured. These measurements were used as the thermal boundary conditions for the numerical simulation of the hydrodynamically and thermally developing reciprocating flow in the heated pipe. The coupled governing equations for time-dependent convective heat transfer in the fluid flow and conduction in the wall of the heated tube were solved numerically. The numerical results for time-resolved centerline fuid temperature, cycle-averaged wall temperature, and the space-cycle averaged Nusselt number are shown to be in good agreement with the experimental data. Based on the experimental data, a correlation equation is obtained for the cycle-space averaged Nusselt number in terms of appropriate dimensionless parameters for a laminar reciprocating flow of air in a long pipe with constant heat flux.

Tube Banks Heat Transfer Enhancement Using Conical Fins

2010 ◽  
Author(s):  
Ignacio Carvajal-Mariscal ◽  
Florencio Sanchez-Silva ◽  
Georgiy Polupan
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Pressure Drop ◽  
Finned Tube ◽  
Hot Water ◽  
Experimental Results ◽  
Tube Bank ◽  
Finned Tubes ◽  
Tube Banks ◽  
Annular Fins

In this work the heat transfer and pressure drop experimental results obtained in a two step finned tube bank with conical fins are presented. The tube bank had an equilateral triangle array composed of nine finned tubes with conical fins inclined 45 degrees in respect with the tube axis. The heat exchange external area of a single tube is approximately 0.07 m2. All necessary thermal parameters, inlet/outlet temperatures, mass flows, for the heat balance in the tube bank were determined for different air velocities, Re = 3400–18400, and one constant thermal charge provided by a hot water flow with a temperature of 80 °C. As a result, the correlations for the heat transfer and pressure drop calculation were obtained. The experimental results were compared against the analytical results for a tube bank with annular fins with the same heat exchange area. It was found that the proposed tube bank using finned tubes with conical fins shows an increment of heat transfer up to 58%.

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