Analysis on heat transfer enhancement by using triangular shaped inserts as secondary fins in cross flow plate fin heat exchanger.

Sachdeva, Gulshan ; Kasana, K.S. ; Vasudevan, R. 等

Introduction

Parallel plate heat exchangers are widely used in automotive, power, process, aerospace, air-conditioning and so many industries. It is also well known that on the gas side, thermal resistance is very high. To overcome the thermal resistance, one of the best techniques is to increase the surface area density. Surface area density can be increased by inserting the secondary fins of various shapes i.e. rectangular, triangular, wavy, offset, perforated, louvered etc into the parallel plates of plate fin heat exchanger. These may also act as spacers in between the plates. The symmetry of the plate fin heat exchanger reduces the geometry into the rectangular channel. Various numerical and experimental investigations are carried out on the rectangular channel. Use of the vortex generators in rectangular channels are widely studied by the researchers. G.Biswas and H. Chattopadhyay [1] studied the characteristics of heat transfer in a channel with built-in wing type vortex generators and find out the 34% increase in combined spanwise average Nusselt number over the plane channel. Various geometries of vortex generators are being studied by Fiebig et. al. [2]. So many researchers have done work on the combinations of vortex generator and plate fin heat exchanger [3-5]. Plate fin heat exchanger having triangular inserts are studied by Vasudevan et al.[6] along with the winglet type vortex generator. These vortex generators are either punched on the slant surfaces of the triangular inserts or built in by the joining process. Pressure loss penalty is also studied with this combination as the pressure drop due to the obstacle and secondary fins. Plate fin isosceles triangular ducts are investigated for the hydrodynamically developed laminar forced flow by Zhang [7]. Conductance of the fin from 0 to infinite and convection of the fluid is also considered which makes it a conjugate problem. Apex angles of the triangular inserts are varied from 30[degrees] to 120[degrees]. The Nusselt number increases with the increase in fin conductance. Our objective is to find the effect of triangular fins of apex angle 90[degrees] in a plate fin heat exchanger. Modified MAC algorithm is used for the computation. The augmentation in heat transfer, mean temperature and the drop in the pressure is studied for the present configuration.

Description of the Geometry

A cross flow plate fin heat exchanger with triangular inserts is shown in figure 1. A single element of the heat exchanger without inserts consists of parallel plates. Between any two parallel plates, the domain for the computation is considered. The channel aspect ratio ([alpha]) and non dimensional length of the channel (L) are taken 2 and 8 respectively. Triangular inserts are having symmetry about their apex so one slant surface is considered for the computation as shown in figure 2. Along the top and bottom surfaces and the inclined surface of the triangular inserts, no slip boundary conditions are used for the fluid flow as shown in figure 3. The axial flow is considered at the entrance of the channel i.e. V=0, W=0 and U=[U.sub.av] =1.0. At the exit, a smooth transition through the outflow boundary is ensured by setting the condition due to Orlanski [8].

[partial derivative][phi] / [partial derivative][tau] + [U.sub.c] [partial derivative][phi]/[partial derivative]X = 0

[phi] is any of the dependent variable u, v, w or [theta]. The quantity [U.sub.c] is the mean channel outflow velocity and taken equal to 1.0.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The Fundamental Equations

The dimensionless equations for continuity, momentum and energy are expressed in the conservative form as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In the above equations, all the lengths are non dimensionlized by the characteristic dimension H, velocities in all the three directions are non dimensionlized by the average incoming velocity [U.sub.av] at the duct inlet and the pressure by [rho][U.sup.2.sub.av]. The Reynolds number is expressed by the average axial velocity at the inlet and the characteristic dimension H.

Method of solution

A modified version of Marker and Cell method by Harlow and Welch [9] and Hirt and Cook [10] is used to solve the governing equations. This method is explained by many researchers [1, 3].Staggered grid arrangement is used. Here the velocities are calculated at the centre of the cell faces while the pressure and temperature is find out at the centre of the cell itself.

Validation is done for the rectangular channel at Reynolds number 500 from the results available by G. Biswas [11] and is found to be in good approximation for the combined spanwise average Nusselt number. This variation may be due to the different exit boundary conditions.

Results and Discussion

The effects of the triangular inserts are analyzed by three parameters i.e. combined spanwise average Nusselt number which tells about the efficacy of the heat transfer, bulk temperature which is a measure of thermal energy and pressure drop which is basically a penalty for the augmentation of heat transfer. Combined spanwise average Nusselt number is the average of local Nusselt number and is computed by the relation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Figure 4 shows that even at the exit, the combined spanwise Nusselt number in a channel with triangular inserts increases by 91.20% as compare to plain channel at Reynolds no 100. Increasing the Reynolds number further increases the Nusselt number. Bulk Temperature or the mean temperature is find out by [[theta].sub.b] (x) = ([SIGMA]U[theta]/[SIGMA]U]). As the cold fluid travels in heat exchanger, it takes heat from the hot fluid and consequently its mean temperature increases. It is very clear from the figure 5 that for the Reynolds number 100, the bulk temperature increases by 36.45% as compare to the plain channel at same Reynolds number. Here by increasing the Reynolds number, the inertia of the fluid increases and it results in more transfer of fluid in the same time, therefore the mean temperature decreases by increasing the Reynolds number. The plane rectangular channel at Reynolds number 200 has 30.25% less bulk temperature at the exit than the same in the plane channel at Reynolds no. 100. Similar are the trends with having triangular inserts. The static pressure difference is simply the pressure difference at any axial location with the exit pressure. This comparison shows the additional pressure requirements along the length of the channel. In all the cases the exit pressure is set to zero just to visualize the results. There is a huge pressure difference by having the triangular secondary inserts as shown in figure 6. At the inlet, with triangular secondary inserts in plane channel, pressure requirement is increased by 208% at Reynolds number 100. At higher Reynolds number friction of the fluid is decreased so drop in the pressure is less in comparison to the lower Reynolds number.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Conclusion and scope for further study:

It can be concluded from the results analysis that by the use of triangular secondary inserts in plane rectangular channels, heat transfer can be enhanced at the cost of more pumping power requirement. Furthermore, the compactness of the heat exchanger can be done for the same exit bulk temperature.

This analysis may be extended for different type of secondary fins and compared. The combinations with some type of vortex generators can also be included in the study. Furthermore, the thickness of the inserts can be considered to make the study more realistic.

Symbols

h Heat transfer coefficient

H Characteristic length dimension (Vertical Distance between the plates)

k Thermal conductivity of the fluid

[Nu.sub.sa] Combined spanwise average Nusselt number

P Non-dimensional pressure

Re Reynolds number

T Temperature

Pr Prandtl number

q Heat flux

U,V,W axial, normal and spanwise component of velocity (non-dimensional)

V Kinematic viscosity of the fluid

[theta] Temperature (non-dimensional)

Subscript

w wall

b bulk condition

References

[1] Biswas, G., and Chattopadhyay, H.,1992, "Heat Transfer in a Channel with Built-in Wing-type Vortex Generators," lnt. Journal of Heat Mass Transfer. , 35(4), pp. 803-814.

[2] Fiebig, M., Kallweit, P., Mitra, N., and Tiggelbeck, S., 1991, "Heat Transfer Enhancement and Drag by longitudinal Vortex Generators in Channel Flow," Exp. Thermal Fluid Sci., 4, pp.103-114.

[3] Deb, P., Biswas, G., Mitra, N.K., 1995, "Heat Transfer and Flow Structure in Laminar and Turbulent Flows in a Rectangular Channel with Longitudinal Vortices," lnt. Journal of Heat Mass Transfer. , 38(13), pp. 2427-2444.

[4] Biswas, G., Torii, K., Fujii, D., Nishino, K.,1996,"Numerical and Experimental Determination of Flow Structure and Heat Transfer Effects of Longitudinal Vortices in a Channel Flow. lnt. Journal of Heat Mass Transfer. , 39, pp. 3441-3451.

[5] Sohankar, A., Davidson, L., 2000, "Effect of Inclined Vortex Generators on Heat Transfer Enhancement in a Three-Dimensional Channel," Numerical Heat Transfer. , 39, pp. 433-448.

[6] Vasudevan, R., Eswaran, V., and Biswas, G., 2000, "Winglet-type Vortex Generators for Plate Fin Heat Exchangers using Triangular Fins," Numerical Heat Transfer., 58, pp. 533-555.

[7] Zhang, Zhi-Li., 2007, "Laminar Flow and Heat Transfer in Plate Fin Triangular Ducts in Thermally Developing Entry Region," Int. Journal of Heat Mass Transfer., 50, pp.1637-1640.

[8] Orlanski, I., 1976, "A simple boundary condition for unbounded flows," J. Comput. Phys., 21, pp. 251-269.

[9] Harlow, F. H., and Welch, J. E., 1965, "Numerical Calculation of Time Dependent Viscous Incompressible Flow of Fluid with Free surface," Phys. Fluids, 8, pp. 2182-2188.

[10] Hirt, C.W., and Cook, J.L., 1972, "Calculating Three Dimensional Flows around Structures and over Rough Terrain.," J. Comput. Phys, 10, pp. 324-340.

[11] Biswas, G., Deb, P., Biswas, S., 1994, "Generation of Longitudinal Streamwise Vortices-A device for Improving Heat Exchanger Design," J. Heat transfer,116, pp. 588-597.

* Gulshan Sachdeva, * K.S. Kasana and (#) R. Vasudevan

* Department of Mechanical Engineering, N.I.T. Kurukshetra, India

(#) RCAMLab, S.M.U. Dallas, U.S.A

E-Mail: gulshan4you@gmail.com, kasanaks_nitkkr@rediffmail.com and rvdevan27@gmail.com