CORRELATION OF OVERALL HEAT TRANSFER COEFFICIENT IN THE THREE ZONES OF WIRE AND TUBE CONDENSER

Numerical and experimental analysis has been studied to estimate the overall heat transfer coefficient in the three zones along wire and tube condenser. The model is based on the empirical formulation of the refrigerant and air sides heat transfer coefficients in finite sections along condenser tube which is solved using EES software. To validate the obtained result from the numerical model, a test rig for a vapour compression refrigeration system with R-134a builds for this purpose. Investigating the temperature distribution and heat transfer coefficient along the length of condenser under different operating conditions have shown that, the de-superheated, two-phase and sub-cooled zones are approximately occupied 15 %, 80% and 5% of the total condenser length respectively. The ratio of Overall heat transfer coefficient to the saturated heat transfer coefficient was significantly affected by the variations of the ambient temperature. Comparison between experimental and numerical results has displayed maximum deviation of 5.5% which is reasonably acceptable. Finally, an acceptable relation has been made to summarize all the important parameter that’s effects directly on the heat transfer contributions of the de-superheating, saturated, and subcooling in one equation to simplex the boring calculations of overall heat transfer coefficient. Proposed correlation presents a mean square error about 3.1 %.


INTRODUCTION
Wire and tube condenser is widely used in commercial and domestic refrigeration systems refers to its simplicity and cost wise.Wire and tube condenser ingredient of a steel tube bent into a single passage serpentine shape.Pairs of steel wires are welded on both sides of serpentine tube are welded bundle to the extended surface (fins).Wire and tube condensers dissipate the heat by natural convection to the air.Always the refrigerant leaves the compressor toward the condenser in a completely vapor phase then de-superheated and change to saturated liquid by remove heat to an ambient (air).Sometimes the refrigerant exit the condenser as sub-cooled liquid, depend on temperature level of the cooling medium and the shape of the condenser.Investigating the heat transfer coefficient at desuperheat, two-phase and sub-cooled zones and therefore the overall of heat transfer coefficient determining associated with the locations of these regions along condenser length represents important aspects in designing and analysis of Wire-and-tube condenser to ensure satisfactory performance of the refrigeration system [1].
Many researchers have modelled the three-zones of this type of condenser and investigated the heat transfer coefficient in these regions numerically and experimentally.Bansal and Chin developed a numerical model to analyse wire and tube condensers that are always utilize in house refrigerators.A numerical model was developed using the finite element method [2].G.A Quadir et al. analysed the wire-on-tube heat exchangers under normal operating conditions, free convection environment using finite element method [3].The effects of ambient temperatures and mass flow rates of the refrigerant on phase change location are determined.A. Ameen et al. experimental investigation and developed a numerical analysis of a wire-and-tube condenser performance [4].All zones model was proposed and an analysis according to its position and the related mass flow rate of refrigerant and ambient temperature.Joaquim M. Goncalvesa et al. presented a semi-empirical modelling approach for simulating the steadystate behaviour of vapour-compression refrigeration systems [5].They used the zones numerical model for the condenser coupled with models for refrigeration cycle to estimate the steady-state COP.
Hofmanas and Paukstaitis studied the external heat transfer of a wire and tube condenser numerically [6].Numerical investigations were carried out in the two circumstances, under the natural and mixed convection state.The main results of the investigations are the visualizations of the distribution of velocity and temperature fields.Matheus et al. presented two simulation models to estimate the thermal-fluid behaviour of condensers used in house refrigerators [7].For both models simplifying assumptions were made, flow and heat transfer was considered onedimensional.
The aim of this research is to provide the worker in the field of condenser design a fast and simple prediction of the overall heat transfer coefficient of wire and tube condenser as a ratio of saturated zone heat transfer without wading in calculating the other two zones (superheat and subcooled) and condenser geometric details

MODELLING AND THEORETICAL ANALYSIS
The performance of the wire-and-tube condenser was modelled using a developed methodology based on finite element approach.In this approach, the wire and tube condenser was divided into three zones, desuperheated, two-phase and sub-cooled based on state of refrigerant conditions.The numerical model to predict heat transfer coefficients for refrigerant side and airside based on heat transfer analysis and suitable empirical correlations at finite equal segments along condenser tube as shown in Figure 1 and Figure 2 and then solved the governing equations using engineering equations solver (EES) software.

General
In general, the refrigerant enters the condenser as superheated vapour and leaves as a subcooled liquid.The heat remove from sections of the condenser could be estimate by evaluating enthalpies of the refrigerant at each section between the inlet and outlet as shown in the p-h diagram in Figure 3.
Where qsh, qtp, and qsc are heat rejected per unit mass for superheated, two-phase and sub-cooled sections respectively.The heat transfer rate (Q) in each section of the condenser is given by: The convective heat transfer coefficients are different on the air and refrigerant side of the condenser, but the (UA) product is the same on both sides because all of the heat which is taken from the refrigerant must be transferred to the air [8,9].
The total heat transfer rate Qtot of the condenser is a combination of the heat transfer from the three zones, which represents the summation of heat transferred from all elements given by [2]: The element of tube length heat transfer can be expressed as: The conductance, UAel can be applied to each elements [10]: Assume the elemental length is equal to the pitch of the wire, ΔL = pw and the outside heat transfer area of the elemental Aa is: The efficiency of fin (wire) calculated by assuming the fin as thin rod and the fin efficiency calculate from equation: Convective and radiative heat transfer coefficient can be calculate if the mean surface temperature of the heat exchanger Tex is found, which is expressed by [2]: Where GP is a geometric parameter which is given by the following relation: Airside Heat Transfer Modelling The air side heat transfer coefficient represents the summation of natural convection and a radiative heat transfer coefficients: The coefficient of radiative heat transfer is calculated by [11] ℎ  =   ( Where εapp is the apparent thermal emittance.Bansal and Chin [2] suggested a good agreement with experimental results by using (εapp = 0.88).
The average convective heat transfer for overall wire-and-tube condenser was found using Tagliafico and Tanda semi-empirical formula as follows [11]: The ranges of parameter in the proposed relationship as follows [11] This value of ( , ) compared with the initial (input) value, when the relative error is more than 0.01 °C, a new value of Tt,o is replace into Equation ( 12) and the calculation are repeated until the required error is reaches.
Enthalpy of the refrigerant at the element exit can be found by:

Single-Phase Heat Transfer Coefficient
The heat transfer coefficients in the single-phase region (subcooled and superheated) are calculated using the correlation of Kays and London as follows [12,13] ℎ , =

Two-phase heat transfer coefficient
Different flow patterns can exist during condensation process inside a tube of the condenser including slug, bubbly, wavy, stratified and annular flows.For the two-phase region of the wire and tube condenser, the predictive model by Thom is used in present work, because it was developed to compute the heat transfer coefficient during condensation inside horizontal tubes with low mass flow rate [14].
The average heat transfer coefficient for condensation in the tube (hr,tp) is calculated by: Where: ℎ  and hl are heat transfer coefficients of the falling film condensate and the liquid condensate at the bottom of the tube.
: Angle of stratified around upper the perimeter of the condenser tube ℎ  : Computed from Nusselt condensation theory as follows [14]: Void fraction  is the vapor fraction of the liquid vapor mixture by volume.
It is directly related to the dryness fraction or quality (x) and the densities of the mixture.
The convection flows heat transfer coefficient is calculate from a relation of forced convection in tubes.
= 0.003   0.74   0.5   (30) The Reynolds number Rel is estimate using the thickness of liquid layer   as the characteristic dimension Using the properties of liquid to calculate Prandtl number Prl The interfacial roughness factor fi is near the unity for thin films and is increased as the ratio of the vapor to liquid velocity is increasing.It can be correlated: Where τ is the surface tension and determine for the damping effect of surface tension on Where τ is the surface tension and determine for the damping effect of surface tension on surface waves created by the movement of vapour over the liquid.
And   ,   ,   are computed using the following equations Stratified angle is evaluated using the following expression [14]:

EXPERIMENTAL WORK
The experimental setup shown in Figures ( 4) and ( 5) have been used to verify and validate the numerical result.The experimental unit is consisting of, wire-and-tube condenser, Shell and coil evaporator, reciprocating compressor, Expansion device (capillary tube) and cycle accessories.Table (1) illustrates the specifications of components.The operating conditions and geometric parameters of the condenser are illustrated in Table (2).The system was at first operated for 15-20 minutes to ensure steady-state operation, and the water flow rate inside the evaporator shell was regulated to obtain the suitable thermal load on the evaporator.Temperatures, pressures, refrigerant and water flow rates have been recorded every 5 min via data acquisition system.

Effect of Main Parameter
Overall heat transfer coefficient and other thermal factors of the wire and tube condenser in the de-superheated, saturated, and sub-cooled zones are investigated in this study.Refrigerant and surface temperatures distribute in the three zones along condenser length are shown in Figure 6.The surface temperature is lower than the refrigerant temperature in the range from 2.7 to 0.4 °C due to the heat transfer resistance of the condenser tube wall.The de-superheat zone occurs in the range of (0-7.3)% of the condenser length where the temperature drop is steep due to the sensible heat rejection to the air.The saturation zone is reached within the range of (7.3-89) % of the condenser length where the temperature is approximately constant due to the phase change in this region, and the latent heat of condensation is rejected to the air.Sub-cooled zone starts at approximately 89 % of the condenser length with 8 °C degree of sub-cool.Figure7 shows the variation of refrigerant-side heat transfer coefficient along condenser length; it can be seen that there are no significant variations in the value of the coefficient in the de-superheat region and then increases steeply when the two-phase zone starts.The high rise in heat transfer coefficient in this region is due to the combined effect of latent heat and buoyancy produced as a result of the density difference between vapour and liquid refrigerant which enhances the heat transfer rate in the two-phase region.The heat transfer coefficient then decreases progressively along two-phase region due to the reduction in vapour quality to reach a minimum value at the sub-cooled zone.

Pressure gage
The variation of outside convection and radiation heat transfer coefficients at three zones along condenser length is clear in Figure 8; it can be concluded from this figure that; a higher value of heat transfer coefficient can be found in the de-superheat zone and the convection heat transfer is dominant.This behaviour can also be observed in Figure 9 which depict the variation of the overall heat transfer coefficient (U) along condenser length.It can be concluded that the value of U is directly proportional to that of refrigerant-side heat transfer coefficient except for some variations in three zones resulting from numerical calculations.Similar behaviour can be observed in Figure 10 which displays the variation of (U) in zones, with different degree of subcooling and consequence their length portion affects.

Comparative between Uo and Usat
Figures 11 Explore the ratio of overall heat transfer coefficient (Uo) to saturated heat transfer coefficient (Usat) with variable conditions could be occurred in the condenser, one of the important conclusions can be stated here that the Uo is very close to the Usat according to the dominants of saturated zone length as shown later The effect of outside air temperature and condenser pressure are depicted in Figure 12 and 13 its evident that the decreasing in outside air temperature enhance the overall heat transfer coefficient (Uo/Usat), and the reverse action occurred when condenser inlet pressure increases this behavior is due to the increase in the dissipated of heat rate acording to increase in temperature difference between the condenser surface and outside air.

Experimental Results and Numerical Validation
Figure 14 shows the comparison between the experimental and numerical results of the tube wall temperature distribution along condenser length.It can be observed that the experimental results are fairly close to the numerical results.The experimental results are relatively lower than numerical results with a slight difference in the range of 3%.The difference between the experimental and numerical results of the average outside heat transfer coefficient was in the range of 5.5 %, 1.9 % and 2.8 % in the de-superheated, saturated and sub-cooled zones respectively as shown in Figure 15.While the difference in the overall heat transfer coefficient was lesser and equal 1.2 % which is extremely acceptable taking into consideration approximations of the numerical model and variations in the experimental measurements.

Correlation
As mentioned before especially in figure 11, 12, and 13 the variation of the over all heat transfer coefficient to the saturated heat transfer coefficient (Uo/Usat) is very limited and not less than 93 % in worst cases.This impressive result lead us to correlate the main parameter effect on condenser performance, and then the value of overall heat transfer coefficient refers to saturated zone heat transfer coefficient with acceptable error utilize the Multiple Regression Technique as shown in the equation below

CONCLUSIONS
It can be concluded that the estimation of heat transfer coefficient of saturated zone in wire and tube condenser is very adequate to predict the overall heat transfer coefficient of the whole condenser with help of simple corrections covered most of the important design parameter.The comparing with experimental work which depicts very low average deviations (about 1.2 %) reinforced the result and gave a good acceptance.
Besides that, it can be mentioned the large amount of heat dissipate (about 80 % of the total heat reject) occurred in the saturated section and the remains are to the other sections.

Figure 1 :
Figure 1: (a).Schematic of a wire and tube condenser, (b) Dimension of the tube and wire

Figure 2 :Figure 3 :
Figure 2: Element of wire and tube condenser

Figure 4 :
Figure 4: Schematic diagram of the refrigeration system

Figure 6 :
Figure 6: Surface and refrigerant temperatures distribution along condenser length.

Figure 7 :
Figure 7: Refrigerant side heat transfer coefficient variation along condenser length.

Figure 8 :Figure 9 :
Figure 8: Outside heat transfer coefficients variation along condenser length

Figure 10 :Figure 11 :
Figure 10: Overall heat transfer coefficient variation along condenser length with different degree of subcooled

Figure 12 :Figure 13 :Figure 14 :Figure 15 :
Figure 12: Overall heat transfer coefficient ratio variation With different outside air temperature 2 = 264.0K, and   and   are geometric parameters defined by

Table 1 :
Experimental test rig specifications gauges, K-type thermocouples with digital readers and other accessories.