Thermo-hydraulic Analysis of Fluid Flowing Through Circular Pipe with Wire Mesh Inserts having Varying Mesh Porosity

The experimental investigation was made to analysis the rate of heat transfer of fluid flowing through a heat exchanger with varying wire-mesh porosity inserts. The Nusselt number (Nu), friction factor (f), and overall heat transfer rate (Q) were evaluated using experiments. Three different wire mesh inserts of square, hexagonal and diamond porosity were examined. The SS 316 stainless wire mesh with a porosity of 9 pores per inch (PPI) were inserted normal to the flow field with a pitch distance of 5 cm for each shape of wire mesh. The experiments were conducted on test rig with air as a working fluid for turbulent flow regime having Reynolds number ranging from 6,000 to 16,000. Experiments were performed on computerized test rig with heated air flowed in one direction through inner pipe and counter flow cold water flowing through the outer concentric pipe. The circular inner pipe of 40 cm long having 4 cm inner diameter (Di), and 3 mm thick was used for experimentation. The experimental results showed that Nusselt number (Nu) increases with decrease in friction factor (f) with increase in Reynolds number (Re). Also, it is observed that the hexagonal porosity shape of wire mesh insert provides higher material contact and gain more energy absorption from hot air resulted in improvement in heat transfer coefficient as compared to diagonal and square porosity shapes of wire mesh inserts, under similar operating conditions. The friction factor and pressure drop for square porosity shape of wire mesh insert is higher as compared to hexagonal and diagonal porosity shapes of wire mesh inserts respectively. This is due to the fact that square porosity wire mesh provides more obstruction in the flow field compared with hexagonal and diagonal porosity shapes of wire mesh inserts. The hexagonal porosity shape of wire mesh insert provides better option for heat exchange applications.


Dh
Hydraulic diameter (m) f Friction factor k Thermal conductivity, (W/mK) Re Reynolds number Pr Prandtl number

Introduction
Many researchers have carried their research in the field of heat exchanger.They made efforts to modify the heat exchanger design to enhance the rate of heat transfer with optimum pressure drop.Various methods have adopted to improve the heat exchanger performance.The modifications have been made to reduce the energy consumption with reduction in material cost.However, for many techniques these modifications resulted in increase in pumping power of fluid flowing through the heat exchanger resulted in increase in cost.
Heat transfer devices have been utilized in variety industrial and residential applications to convert and recover heat.As a result, many experimental and numerical work have been conducted over past years in order to improve the performance of heat exchangers using metallic porous inserts in test section.
Pavel et al. [1] conducted experimental and numerical analysis to evaluate the impact of porous mesh inserts on convective heat transfer in the heat exchanger.They analysed the heat exchanger with air as a working fluid for contact heat flux conditions.The investigation was done with varying radius ratio (Rp).They concluded that for low porosity wire mesh when Rp is equal to 0.8, the rate of heat transfer is maximum with optimum pressure drop.
Chatchawan and Sanitjai [2] investigated effect of different material wire mesh inserts on convective heat transfer for air as a working fluid under constant surface temperature conditions.They used mild steel, aluminium and brass as porous inserts.They resulted that the convective coefficient increases with increase in effective thermal conductivities and porous layer thickness but opposite results for decrease in porosity range and aspect ratio.
Sarada et al. [3] analysed heat transfer with copper wire mesh inserts having 0.28 mm wire diameter with air as a fluid flowing through the horizontal pipe.They conducted investigation for constant surface temperature conditions.They examined twelve wire mesh inserts with porosity in the range of 99.73 to 99.98 for different inner diameter and pitch.
Kurian et al. [4] investigated effect on heat transfer with brass as a material for wire mesh inserts in a vertical channel.They conducted the experiments with a velocity of flowing fluid ranging from 0 to 2 m/s.They insert the wire mesh block between the flat plates maintained at the constant temperature.The results indicate twice increase in Nusselt number with wire mesh insert compared with bare channel under identical fluid flow conditions.
Peamsuwan et al. [5] conducted the number of experiments with wire mesh inserts having varying PPI ranging from 4,8,10 and 12.They conducted experiments with varying wire mesh thickness of thickness ratio 1,2,3 and 4 respectively.They concluded increase in Nusselt number with increase in pores per inch and thickness of wire mesh layers.
To further extend the research work in the field of heat exchanger with wire mesh inserts, in the present research experimental investigation was made to analysis the rate of heat transfer of fluid flowing through a heat exchanger with varying wire-mesh porosity inserts.The aim of present research is to evaluate Nusselt number (Nu), friction factor (f), and overall heat transfer rate (Q) for varying wire-mesh porosity inserts under turbulent flow regime having Reynolds number ranging from 6,000 to 16,000.The main aim of the present research is to find best possible shape porosity of wire mesh inserts out of three different wire mesh inserts of square, hexagonal and diamond porosity which would improve the system performance and optimize the pressure drop.The experiments were conducted with and without the wire mesh inserts.For the experimentation, three different types of wire mesh insert with varying wire-mesh porosity for the constant case of surface temperature was used.Three different wire mesh porosity used are square, hexagonal and diamond.The air is heated by using the heating coil before it is circulated through the tube and the cold water is made to circulate over the tube to gain the heat from heated air.A blower is used for flowing the hot air through inner pipe and centrifugal pump is used for circulated the water through concentric outer pipe.An Anemometer is used to measure the air velocity and Rotameter as a flow measuring device is used to measure the mass flow rate of water.A Micromanometer is used to measure the pressure drop across the test section.For experimentation, circular inner pipe is used with 40 cm long having inner diameter as 4 cm and thickness of 3 cm.In order to measure the surface temperature of test section, the thermocouples have been fixed on surface.
The first stage of experimentation deals with the conduction of experiments with conventional bare straight tube by varying water flow rate conditions flowing across the test pipe.The temperature of air and water at intel and exit of heat exchanger for each testing were recorded.In second stage, experiments were conducted separately for each type of wire insert as square, hexagonal and diamond respectively.For each wire mesh 5 cm pitch is used.The operating conditions for each stage of experiment is kept constant.The reading obtained from each experiment is noted down.

Energy Equations
The different equations which were used to evaluate the different parameters of the heat exchanger is mentioned as follows.The rate of heat transfer from hot air while flowing through the heat exchanger is evaluated using the equation Where,   ̇ is the mass flow rate of air flowing through the test section in Kg/s,  , is the specific heat of air in kJ/KgK,  , is the temperature of air leaving the heat exchanger in 0 K,  , is the temperature of air entering the heat exchanger in 0 K.The heat gained by cold water is evaluated as Where,   ̇ is the mass flow rate of water flowing through the test section in Kg/s,  , is the specific heat of water in kJ/KgK,  , is the temperature of water leaving the heat exchanger in 0 K,  , is the temperature of water entering the heat exchanger in 0 K.The overall heat transfer coefficient is calculated by using equation Where, U is the overall heat transfer coefficient in kW/m 2 K, ∆Tln is the logarithmic temperature difference in o K. To evaluate the heat transfer coefficient of inner (air) and outer (water) side of heat exchanger following equation is used

𝑘
The friction factor is evaluated across the test section during experimentations using following equation.

𝑓 = 2di∆p Lρv^2
Where, L is the length of test section in m, ρ is the density of working fluid in Kg/ m 3 , v is velocity of working fluid in m/s, ∆p is the pressure drop across the test section measured using the micromanometer.Finally, the thermo-hydraulic performance (heat convection and resistance of fluid flow) of the pipe with all the three different wire mesh porosity viz.square, hexagonal and diamond is evaluated using Webb's performance evaluation criteria (PEC) [6].
Where, Nus and fs are the Nusselt number, and the friction factor of plain pipe.The maximum uncertainty values for Nusselt number (Nu), Reynolds number (Re) and friction factor (f) are found to be 4.08%, 3.89% and 3.78% respectively.

Validation of Experimental results
Before conducting experimentation on heat exchanger with wire mesh inserts, the heat exchanger test rig with conventional circular pipe without wire mesh inserts is evaluated and validated by comparing the experimental readings with the results obtained from standard correlations Dittus-Boelter [7] and Petukhov [8].wire mesh inserts are consistent with the results obtained from standard correlations for Nu and f.The average error obtained between the results found to be 4% and 6% for Nu and f respectively.This indicates the reliability of experimental test rig.

Nu
Graphical representation in Fig. 5 indicates the variation of Nu with Re for fluid flowing through pipe with wire mesh insert with three different porosities viz.square, hexagonal and diamond and its comparison with pipe without insert.The operating parameters were kept constant for all conditions.The results indicate that for wire mesh insert with three different porosities, Nu improves with increase in Re because of the turbulence created by wire mesh as flowing fluid flows through it.It is observed that at same Re, hexagonal porosity shape of wire mesh gives higher Nu when compared with the diagonal and square porosity shapes of wire mesh, under similar operating conditions.This is due to the fact that hexagonal porosity shape of wire mesh provides higher material contact and gain more energy absorption from hot air resulted in improvement in overall heat transfer coefficient as compared to diagonal and square porosity shapes of wire mesh, under similar operating conditions.It is observed that pipe with hexagonal wire mesh porosity gives maximum 1.59 to 1.16 times higher Nu than that of pipe with square and diagonal wire mesh porosity inserts respectively and 2.06 times higher than that of pipe without insert.Graphical representation in Fig. 6 depicts change in friction factor f with Re for fluid flowing through pipe with varying mesh porosity and without wire mesh inserts.It is observed that with increase in Re, f decreases for all the cases of experimentation.For same Re, it is observed that wire mesh insert with square porosity gives 1.86 to 2.89 times higher f than that of wire mesh insert with hexagonal and diagonal porosity respectively and 3.12 times higher than that of pipe without inserts.This is because of flow barrier offered by inserts for the flowing fluid.It is observed that wire mesh with square porosity offers more flow resistance compared with wire mesh with hexagonal and diagonal porosity which increases the friction factor and hence the pressure drop.It is observed that wire mesh insert with hexagonal porosity gives higher PEC values when compared with wire mesh insert with diagonal and square porosity over the whole range of Re.It is observed that pipe with wire mesh insert gives better results for rate of heat transfer but with increment in flow resistance for flowing fluid when compared with the pipe without wire mesh insert.

Conclusion
The existing research investigates the possible effect of varying wire mesh porosity inserts of SS 316 stainless steel having pores per inch (PPI) of 9, to enhance the convective heat transfer characteristics between heated air flowing through inner test section and water flowing around test section, under identical conditions of constant surface temperature and pitch distance.The tests were conducted with air having a turbulent fluid flow ranging from Reynolds number of 6,000 to 16,000.From investigation the performance characteristics such Nusselt number, friction factor and performance index were evaluated.A hexagonal porosity shape of wire mesh insert gives higher Nusselt number (Nu) compared with diagonal and square wire mesh porosity inserts respectively under similar operating conditions.It was clarified by the hexagonal porosity shape of wire mesh insert provides higher material contact and gain more energy absorption from hot air resulted in improvement in heat transfer coefficient as compared to diagonal and square porosity shapes of wire mesh inserts in flow field.The friction factor and pressure drop for square wire mesh porosity insert is better as associated to hexagonal and diagonal porosity shapes of wire mesh inserts respectively due to rise of flow impediment.The hexagonal porosity shape of wire mesh insert indicates an effective porous media for enhancing the heat transfer rate having minimum pressure drop in heat exchanger application.

Fig 2 .
Fig 1.Schematic of Experimental Set-up

Fig 6
Fig 6 Friction factor (f) Vs Re