# Numerical and heat transfer analysis of shell and tube heat exchanger with circular and elliptical tubes

- J. Bala Bhaskara Rao
^{1}Email author and - V. Ramachandra Raju
^{2}

**11**:6

**DOI: **10.1186/s40712-016-0059-x

© Rao and Raju. 2016

**Received: **19 December 2015

**Accepted: **4 May 2016

**Published: **23 May 2016

## Abstract

### Background

Heat exchanger is a device in many industrial applications and energy conversion systems. Various heat exchangers are designed for different industrial processes and applications. Shell and tube heat exchanger (STHE) has its own importance in the process industries.

### Methods

Experimental and numerical simulations are carried for a single shell and multiple pass heat exchangers with different tube geometries i.e. circular tubes to elliptical tubes. The experiment was carried out with hot fluid in tube side and cold fluid in shell side with circular tubes at 600 tube orientation and 25 % baffle cut. Heat transfer rates and pressure drops are calculated for various Reynolds numbers from 4000 to 20000. Fluent software is used for numerical investigations. Both circular and elliptical tube geometries with 450,600 and 900 orientations are used for the numerical studies. In addition to 25 % baffle cut, quarter baffle cut and mirror quarter baffle cut arrangements are used for comparison. The experimental values of heat transfer rates and pressure drops over shell side and tube side along the length of STHE are compared with those obtained from fluent software.

### Results and Conclusion

It is found that the elliptical tube geometry with mirror quarter baffle cut at 450 tube orientation is 10 % higher than existing shell and tube heat exchanger and the pressure drop decrement in tube side shows up to 25 %.

### Keywords

Shell and tube heat exchanger Elliptical tubes Heat transfer Pressure drop## Background

Heat exchanger is a universal device in many industrial applications and energy conversion systems. Various heat exchangers are designed for different industrial processes and applications. In heat exchangers, shell and tube heat exchanger presents great sustainability to meet requirements and gives efficient thermal performance. Shell and tube heat exchanger (STHE) is widely used in petro-chemical industry, power generation, energy conservation, and manufacturing industry (Qian 2002). The baffle member plays an important role in STHE, and it supports tube bundle and also equally distribute the fluid in the shell side. When segmental baffles are used in STHE which have many disadvantages (Kern 1950a; Li & Kottke 1998a), the low heat transfer is achieved due to the flow stagnation, i.e., dead zones which are created at the corners between the baffle and the shell wall (Li & Kottke 1998b). It requires higher pumping power, and it creates a high pressure drop under the same heat load. The orientation of tubes will influence the annular surface area surrounded by the fluid. It is also influences the heat transfer rate. The new baffle cut arrangement achieved higher heat transfer rates and lower pressure drops (Master et al. 2006; Mukherjee 1992; Li & Kottke 1998c; Lei et al. 2008), so it is required to develop a new type STHE using different baffle cut arrangements to achieve a higher heat transfer rate. For the last few years, already described methods have been used to calculate heat transfer and pressure drop in the shell side of the STHE with different baffles (Peng et al. 2007). The different calculation procedures have been checked against experimental measurements on a small-scale heat exchanger. Kern method, Tinker method, and Delaware method (Palen & Taborek 1969; Kern 1950b; Tinker 1951) gave the best results in comparison to other methods in literature. The shell side design under the inside flow phenomenon must be understood by experimental and numerical analysis. The shell and tube heat exchanger design was explained by Gay et al. (Bell 1963) who worked on heat transfer, while Halle et al. (Gay et al. 1976) and Pekdemir et al. investigated pressure drop (Halle et al. 1988; Pekdemir et al. 1994; Li & Kottke 1998d). Nowadays, the numerical methods have become an economical alternative for the research of STHE, and through a detailed flow pattern and a temperature field, it could be obtained with much less difficult (Seemawute & Eiamsa-ard 2010; Rhodes & Carlucci 1983; Huang et al. 2001; Stevanovic et al. 2001). The collective effect of all the above parameters on heat transfer is quite interesting to design STHE with the optimistic approach. Baffle cuts are placed to increase the flow rate in the shell side and also reduce the vibrations of the shell and tube heat exchanger. A STHE with 12 copper tubes and a stainless steel shell is used for the proposed system. Numerical analysis is conducted with elliptical tubes which are replaced by circular tubes. The modifications in the tube and shell overall pressure losses in the shell from the entrance to the exit points of the fluid are determined. The pressure drops over the tube and shell sides are altered with tube orientations to give maximum heat transfer efficiency. The baffle cuts are provided at 25 % with respect to the diameter and quarter baffle cut with respect to the cross sectional area. Mirror quarter baffle cut also is considered for effective heat transfer. It is observed that heat transfer rate increases with the increase of the surface area.

## Methods

### Experimental setup

#### Shapes of tubes and baffles

##### Elliptical tubes with different orientations

##### Different shape of the baffles

The flow of the cold fluid is controlled by the shape of the baffle. The degree of turbulence created and energy utilized in the turbulence are governed by the baffles. Different baffle cuts, i.e., 25 % baffle cut, quarter baffle cut, and mirror quarter baffle cut are used for this analysis. The baffles are not only meant for structural support but also increase the external surface area of the tubes which resulted in improvement in the heat transfer.

### Numerical analysis and validation of the work

For the numerical analysis, the actual model is represented as a virtual computer model using CATIA software package and analysis is performed with the help of a finite volume method as a computational fluid dynamics (CFD) tool. The inlet and outlet boundary conditions for the analysis are carried out as follows.

#### Geometric modeling and fluid properties for the analysis

Based on the above experimental model, a virtual model is prepared for CFD analysis and whatever the geometric parameters are for the actual model, the same dimensions are considered for virtual also. Hence, the geometry scale between the actual model and the virtual model is 1:1. As a result, one can minimize the deviation of CFD analysis values and the practical values obtained. The heat exchanger is designed with water working fluid for both hot and cold conditions. The properties of water are directly implemented for the analysis. For the shell, stainless steel is considered, and for the tube, copper material is considered as per the actual model. The diameter and thickness of the tube of the heat exchanger consider the Reynolds number calculated for different mass flow rates of hot water and cold water in the heat exchanger. The Reynolds numbers are greater than 4000 for the different inlet mass flow rates as mentioned in the boundary conditions. Hence, the flow in the pipe as well as the shell is considered as turbulent. The maximum temperature of the hot fluid is 348 K at atmospheric pressure, and it is in the liquid phase and water is an incompressible fluid; hence, Mach number is considered in the incompressible region. The model is prepared as a three-dimensional geometric model for the analysis.

#### Inlet and outlet boundary conditions for the analysis of shell and tube heat exchanger

##### Inlet and outlet conditions for hot fluid

The hot water is entered at a temperature of 348 K, and different mass flow rates such as 0.15785, 0.3827, 0.55763, and 0.71782 kg/s are given at the inlet of the heat exchanger tube side nozzle. From the tube, the flow is considered to atmosphere pressure only. Based on the given inlet and outlet conditions, the inbuilt program of Fluent software calculated the remaining parameters.

##### Inlet and outlet conditions for cold fluid

The cold fluid enters at a temperature of 298 K, and different mass flow rates such as 0.34589, 0.8403, 1.2245, and 1.5762 kg/s are given at the inlet of the heat exchanger shell side nozzle. The flow of the cold water is guided by the baffles provided over the tubes; the water is entered at 298 K and atmospheric pressure and it is exited from the shell outer nozzle into atmospheric pressure. Hence, the pressure boundary is defined at the outlet of the shell.

##### Other boundary conditions and grid generation

No slip condition for the tube shell inner and outer surfaces is given. The tube shell and inlet outlet nozzles with uniform cross sections are defined for the analysis. The direction of the flow was defined normal to the boundary. Hydraulic diameter and turbulent intensity were specified at the inlet nozzle of both hot and cold fluids. The flow is assumed as an incompressible turbulent flow; the gradient of temperature is required at all the points of the heat exchanger. Hence, the separate grid is generated for both tube and shell side fluids, and they are separated by the boundaries.

#### Grid generation

#### Numerical solution chosen for the analysis

- 1.Integration of fluid governing differential equations over each control volume of computational domain.
- 2.
Discretization of an integrated equation into an algebraic equation/form which will be converted into a solution algorithm.

- 3.
The control volume that will be solved in this discretized form equation will be used to write a solution algorithm for every iterative process until it satisfies the convergence criteria and stability.

- 2.

where *φ* = property of fluid

*ρ* = density of fluid

*Γ* = diffusion coefficient

*S* = source term

where \( \begin{array}{l}\kern2em {a}_w=\frac{\varGamma_w\kern0.5em {A}_w}{\delta {x}_{\mathrm{WP}}},{a}_E=\frac{\varGamma_e\kern0.5em {A}_e}{\delta {x}_{\mathrm{PE}}}\&\kern0.5em {a}_P=\left({a}_W+{a}_E-{S}_P\right)\\ {}{a}_P\kern0.5em {\phi}_P={a}_W\kern0.5em {\phi}_W+{a}_E\kern0.5em {\phi}_E+{S}_u-2\end{array} \)

The resulting system of the linear algebraic equations is solved to obtain the distribution of the property Ø at the nodal point. The algebraic equations are solved by using direct methods (Cramer’s rule, matrix inversion, and Gauss elimination) and indirect or iterative methods (Jacobi and Gauss-Seidel). The flow is incompressible turbulent; hence, the K-ε model is considered for the analysis. The K-ε model is the simplest turbulence model for which only initial boundary conditions need to be supplied and used for 3D analysis in which the changes in the flow direction are always so slow that the turbulence can adjust itself to local conditions. As per the grid density, the number of algebraic equations are generated for unite volume and the algebraic equations are solved numerically.

#### Validation of the analysis

Comparison of the numerical analysis with the experimental results

Reynolds number | Inlet temp (K) | Heat transfer (watts) | Percent of error | ||
---|---|---|---|---|---|

Cold fluid | Hot fluid | Value by expt | Value by numbers | ||

4418 | 298 | 348 | 3419.85 | 3691.38 | 7.93 |

10,733 | 298 | 348 | 6799.85 | 7170.84 | 5.45 |

15,640 | 298 | 348 | 9018.42 | 9485.87 | 5.18 |

20,132 | 298 | 348 | 10164.25 | 10965.60 | 7.8 |

### Data appreciation

*Q*= average heat flux between the cold and hot fluid in watts

*m*
_{c} and *m*
_{h} are the cold and hot fluid mass flow rates in kg/s, respectively

*c*
_{pc} and *c*
_{ph} are the specific heats under constant pressure of cold and hot fluids in kJ/kg K, respectively

^{2}

where *N* = number of tubes

Do = outlet tube diameter in meters

*L* = effective length of the tube in meters

∆*T*
_{m} = logarithm mean temperature difference for hot and cold fluid in kelvins

where *t*
_{1} and *t*
_{2} are the shell side inlet and outlet temperatures, respectively, and *T*
_{1} and *T*
_{2} are the tube side inlet and outlet temperatures in kelvins, respectively.

From the above calculations, the overall heat transfer coefficient can be obtained by Eq. (1).

For water \( \frac{\mu_f}{\mu_w} = 1 \)

where *N*
_{U} = Nusselt number for the tube side

di = inner diameter of the tube in meters

*K* = thermal conductivity of hot fluid in W/m K

where *h*
_{
i
} and *h*
_{
o
} are heat transfer coefficients for the tube side and the shell side in W/m^{2} K, respectively.

*k*
_{1} = thermal conductivity of the copper tube in W/m K

The shell side film coefficient (*h*
_{o}) can be obtained from the above equation.

where *f* = friction factor *e*
^{(0.576 − 0.19 ln Re)}

(From *Heat Exchangers: Selection, Rating and Thermal Design*, by Sadik Kakac and Hongtan Liu).

## Results and discussion

The flow parameters are varied by introducing different tube geometries, different tube orientations, and different baffle cuts. Subsequently, more heat transfer rate is created in the flow by introducing more surface area, and a mathematical model is reformed for more numerical analysis. As per this type of analysis, observation is found that more heat transfer efficiency for dropping the pressures along the length of the shell and tube of the STHE.

### Circular tube and elliptical tubes

#### Heat transfer analysis

### Heat transfer with different baffle cuts

In the case of the quarter baffle cut, the direction of the flow of the cold fluid changes in the *X*-*Y* plane and also in the *Z* direction. As a result, the total length of the flow increased and the heat transfer rate also proportionately increased. In the circular tube, the heat transfer rate increases up to 11 % when the 25 % baffle cut is replaced by quarter baffle cut (90 baffle cut) and it is up to 10 % when the elliptical tubes are used from Figs. 15, 16, and 17. This is due to the increase flow length in the *Z* direction. In the case of the mirror quarter baffle cut (M90 baffle cut), the flow of the cold fluid splits in two streams and follows the helical path due to the baffle shape. Separation of the cold fluid and increase in flow length leads to a better heat transfer rate. Figures 15, 16. and 17 indicate that the heat transfer rate increases up to 14 % when quarter baffle cut is replaced by mirror quarter baffle cut in the circular tube, and it is up to 16 % if elliptical tubes are used.

### Heat transfer with different tube orientation

The tube orientation influences the diagonal, vertical, and horizontal space between the tubes. At particular arrangement, the space is uniform and it may help for a better heat transfer rate. The temperature difference between the hot fluid and the cold fluid also influences the heat transfer rate. Hence, for the tubes, different orientations 45°, 60°, and 90° are considered to find heat transfer variation along the tube side as well as the shell side. From all the graphs in Figs. 18, 19, and 20, values impose tube orientation from 60° to 90° heat transfer rate increases and the same against 90° to 45°. The heat transfer rate increases up to 6 % when the tube orientation changes from 60° to 90° in the circular tubes, and it is up to 8 % in the elliptical tubes. If the tube orientation changes from 90° to 45°, the heat transfer rate increases up to 6 % in the circular tubes and 9 % in the elliptical tubes.

### Comparison of heat transfer on the shell side and the tube side of the shell and tube heat exchanger

#### Pressure drop analysis on shell side

Fluid flow pressure, volume, and temperature are the three inter dependent parameters. The heat transfer is high when the temperature difference in hot and cold fluids is more and pressure drop is also high. But in the case of the heat exchanger, sudden high pressure drops are not to be encouraged. To avoid a high pressure drop in the heat exchanger, a uniform transfer of heat energy through the heat exchanger is required. With this view, the pressure drop is calculated with different arrangements for the better performance of the heat exchanger.

### Pressure drop with different baffle cuts

### Pressure drop with different tube orientations

### Comparison of shell side pressure drop on the shell and tube heat exchanger

#### Pressure drop analysis on tube side

### Pressure drop with different tube orientation

### Comparison of tube side pressure drop on shell and tube heat exchanger

## Conclusions

- a.
The overall heat transfer rate in the Reynolds number range between 4000 to 20,000 increases with mirror baffle cut, 45° tube orientation, and the elliptical tube geometry is 10 % higher than the existing shell and tube heat exchanger.

- b.
Pressure drop reduction in the shell side is more influenced by baffle cuts. The pressure drop is minimum in the case of 45° tube orientation and mirror quarter baffle cut with elliptical tubes due to a uniform heat transfer through the heat exchanger.

- c.
If the tube geometry changes from circular to elliptical, the pressure drop over the tube side will be decreased. The pressure drop decrement for the circular tube to the elliptical tube in tube with mirror baffle cut, 45° tube orientation shows up to be 25 %.

## Declarations

### Funding

This research received no specific grant from any funding agency from the public, commercial, or not-for-profit sectors.

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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