THERMO-MECHANICAL ANALYSIS IN PERFORATED ANNULAR FIN USING ANSYS

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1 THERMO-MECHANICAL ANALYSIS IN PERFORATED ANNULAR FIN USING ANSYS Kunal Adhikary 1, Dr. Ashis Mallick 2 1,2 Department of Mechanical Engineering, IIT(ISM), Dhanbad , Jharkhand, India Abstract Thermal stresses in perforated annular fin with constant thermal conductivity, due to convective and radiative heat transfer, are presented in this paper. Perforating a fin is a common option for enhancing the heat transfer. Due to the perforation the thermal stress and thermal strain can be affected. Steady-State Thermal and Static Structural analyses are performed for investigating temperature distribution and thermal stress respectively in both non-perforated and perforated annular fins. The preparation of models and the analyses are carried out using ANSYS The results have shown that thermal stress is significantly affected after the perforation but it can be minimized by perforating near the tip of the fin. Keywords Perforated annular fins, Convective heat transfer, Thermal stresses, ANSYS. I. INTRODUCTION Heat Transfer has a vital role in numerous engineering fields. Fins are widely used for enhancing heat transfer in various thermal applications such as heat exchangers, super heaters, internal combustion engines, economizers etc. Reduction in cost and size of fins are the most important aim of fin industry. The heat transfer from the fin surface is caused in convection and radiation processes. These heat transfers are generally depend on effective surface area of the fin and the temperature difference between fin surface and surroundings. However, increasing the surface area causes increasing material size and cost. In this case, increasing the ratio of surface area to volume, by perforating the model, is the best option to enhance the heat transfer [1]. Permeable fins increased the heat transfer area without suppressing the convection currents, as is the case of solid fins. First, Vafai et. al. proposed that external boundary can be enhanced by replacing the non-porous material with a porous material [2]. Though they found that heat transfer is retarded for that modification. But later, Kiwan and Al-Nimr introduced a novel method and suggested the improvement of heat transfer from the given surface by substituting the conventional fin with a porous fin [3]. However, perforated fin can also be used for increasing the heat transfer from the outer surface. Sara et. al. proposed that heat transfer can be increased from a flat surface by using perforated rectangular blocks [4]. Awasarmol and Pise experimentally investigated on perforated rectangular fin and found that convective heat transfer is gradually increasing with the increase of perforation size [5]. Lee et. al. showed the enhancement of heat transfer with perforated circular hole in finned tube [6]. Nowadays, thermal stresses play an important role in fin industry. Yu and Chen analyzed thermal stress of the convection and radiation in thin annular fin with constant thermal parameter, using hybrid method [7]. Thermal stresses in isotropic circular fins with temperaturedependent thermal conductivity have been studied by Chiu and Chen, applying the decomposition method [8]. Mallick et. al. proposed homotopy perturbation method for thermal stress in annular fin with variable thermal conductivity [9]. As mentioned in the previous literatures, numerous approaches have been studied for the enhancement of convective heat transfer of annular fins. Most of these approaches focused on the DOI: /IJRTER VG7R 391

2 heat transfer enhancement. Some have been studied to find only the thermal stresses in annular fin. But it is found that, the thermal stress should not be ignored while enhancing the heat transfer. In this project various types of perforation pattern are chosen for analysis. The goal of this present work is to study the thermal stresses in both the non-perforated and perforated fins, along with the enhancement of heat transfer after the perforation and find out the preferable type of perforation pattern. II. FINITE ELEMENT MODELING A simple annular fin of 4mm thickness, made of a homogeneous and isotropic material, with the dimensions, is shown in Fig. 1. Holes of 1mm diameter are created in the solid annular fin for perforation. Various types of configurations, shown in Fig. 2, are selected here for perforating. Types of these configurations: Type 1 Seven line of 12 holes zigzag perforation Type 2 Three line of 12 holes zigzag perforation near base Type 3 Three line of 12 holes zigzag perforation near tip The temperature at the base of the 600K and 300K. fin and surroundings are assumed to be constant, respectively 0.12m 0.04m Figure 1. Non-perforated annular fin Figure 2. Configurationn of perforation of Type 1, Type 2 and Type 3 The following values of Table 1 are the mechanical properties of the material, considered for the present study. The reference temperature of these material properties is ambient temperature (300K).

3 Table 1. Material Properties K (W/m.K) E (GPa) Poisson s Ratio α (10-6 /K) III. DETAILS OF ANALYSIS Design the suitable perforation in solid annular fin is the main objective of this work perforation Study the temperature distribution and thermal stress, after analyzing thermal distribution and thermal stresses in these fins. This work contains design of perforated and non-perforated annular fins and Finite Element Method (FEM) is set up using ANSYS. Maximize heat transfer from the surface is the main reason behind using fin. However, users do many changes in the fin for getting more heat transfer. Thermal stress will be affected for these changes, which can be a big issue for the fins. That s why the thermal stress plays a crucial role in fin industry Modeling: An annular fin, with 20mm inner radius, 60mm outer radius and 4mm thickness, is prepared in Design Modeler, an application of ANSYS. Then the holes are created in the solid fin in above four configurations. The diameters of the holes are 1mm Meshing: Sweep meshing is applied to form the hexagonal brick mesh. Usually brick mesh gives the correct result. Total nodes and elements are created in non-perforated fin after meshing. Figure 3. Meshing of Non-perforated fin 3.3. Boundary Conditions: An annular fin is always attached with a cylindrical surface. But in this work the fin is only considered for simulation purpose for simplifying the problem. The temperature at the base of the fin is taken 600K, while the atmospheric temperature is 300K. The tip of the fin is not insulated. The coefficient of convection from fin to the ambient is considering 50W/m 2 K and emissivity of the fin is 0.8 during radiation. There is no other load applied in the fin. The uneven temperature distribution is occurred in the fin due to the convection and radiation. For this reason, the thermal strain will be varying along the radial direction, which will cause thermal stress. All the data of this boundary condition and the material properties are taken from Chiu and Chen s paper [8] Solution: Thermo-mechanical coupled solution is done in ANSYS Workbench. After preparing the mathematical model, it is solved in Steady-State Thermal analysis system to get the All Rights Reserved 393

4 distribution in the fin. Then this result is imported in Static Structural analysis system to find the thermal stresses. The body temperature of fin is the only load to be imported. IV. RESULTS AND DISCUSSION Thermal stresses caused by the unequal temperature distribution in fin are investigated here. The temperature distribution obtained in the non-perforated fin using ANSYS is shown in Fig. 3. To check the accuracy the results obtained from the simulation are compared with the results of Chiu and Chen [8]. Fig. 3-5 show that the temperature and thermal stresses obtained from the simulation in ANSYS are same as in Chiu and Chen for constant thermal conductivity. Figure 3. Comparison of temperature distribution in annular fin for convection-radiation, pure convection and pure radiation heat All Rights Reserved 394

5 Figure 4. Comparison of radial stress in annular fin for convection-radiation, pure convection and pure radiation heat All Rights Reserved 395

6 Figure 5. Comparison of tangential stress in annular fin for convection-radiation, pure convection and pure radiation heat transfer Heat is transferred from the base to the other sections of the fin through conduction mode, and then some amount of the conducted heat is dissipated from the surface area to the ambient air through convection and radiation mode. So, all the amount of heat can t be carried from the base to the tip. That s why temperature at tip is always less than base. However, the convection and radiation process are affected with the surface area. Heat transfer is enhanced with increasing the surface area. After the perforation new surface will be created. Heat is dissipated from these newly created surfaces too. There are lot of works have been done on the enhancement of heat transfer from a perforated fin. This work focuses on the change of thermal stresses after the perforation. Temperature distribution along the fin is shown in Fig. 6 for convection-radiation, pure convection and pure radiation. It is observed that temperature always decreases from base to tip of the fin. It is also seen that temperature in the tip is lesser after the perforation in every cases because of the enhancement of heat transfer from the fin surfaces. The temperature in the tip is minimum in case of type 1 perforation due to the creation of more open surfaces after the perforation. However, the temperature profiles are almost same for type 2 and type 3 perforation because of the same numbers of newly created All Rights Reserved 396

7 Figure 6. temperature distribution in non-perforated and perforated annular fin for convectionradiation, pure convection and pure radiation The radial and tangential stresses along the fins, in all the three cases of heat transfer, are shown in Fig Figure 7. Radial stress for convection-radiation heat transfer Figure 8. Tangential stress for convection-radiation heat All Rights Reserved 397

8 Figure 9. Radial stress for pure convection heat transfer Figure 10. Tangential stress for pure convection heat transfer Figure 11. Radial stress for pure radiation heat transfer Figure 12. Tangential stress for pure radiation heat transfer All these above stress related graphs (Fig. 7-12) show that the natures of the stresses are almost same after the perforation as these are taken in solid portion. But it is seen that the equivalent stress, i.e, Von-Mises stress s behavior is different in the perforated portion. The maximum value of equivalent stress is seen in the surface adjacent to perforation portion. Fig show the equivalent stresses in the All Rights Reserved 398

9 (d) Figure 13. Equivalent stress for convection-radiation heat transfer in Non-perforated, type 1, type 2 and (d) type 3 perforated annular fin Figure 14. Equivalent stress for pure convection heat transfer in Non-perforated, type 1, type 2 and (d) type 3 perforated annular fin All Rights Reserved 399

10 Figure 15. Equivalent stress for pure radiation heat transfer in Non-perforated, type 1, type 2 and (d) type 3 perforated annular fin It is clearly seen that the maximum equivalent stress is increased after the perforation. But for type 1 perforation it is very high w.r.t. the non-perforated annular fin. However for type 3 it will attain quite smaller amount among the all three type of perforation. V. CONCLUSION The present work is mainly focused on the thermal stresses in annular fin after the perforation, as the enhancement of heat transfer after the perforation is already investigated by various researchers. It is found that the temperature at the tip fin is quite smaller amount in perforated fin than the nonperforated. However it will be minimum for type 1 perforated annular fin. But the resultant stress will be maximum for this case. So, type 1 perforated annular fin will not be chosen if the stress is a major factor for the fin. In that case, for the type 3 perforation the resultant stress attain the minimum value in the fin. Therefore, this type of perforation is better choice for the perforation of annular fin. Moreover, some mass of the non-perforated fin will be removed after the perforation. This will decrease the fin weight as well as the material cost. (d) REFERENCES I. A. Bassam and K. Abu-Hijleh, Natural Convection Heat Transfer From a Cylinder With High Conductivity Permeable Fins, J. Heat Transfer, vol. 125, no. 2, p. 282, II. K. Vafai and S.-J. Kim, Analysis of Surface Enhancement by a Porous Substrate, J. Heat Transfer, vol. 112, no. 3, p. 700, All Rights Reserved 400

11 III. S. Kiwan and M. A. Al-Nimr, Using Porous Fins for Heat Transfer Enhancement, J. Heat Transfer, vol. 123, no. 4, pp , IV. O. N. Sara, T. Pekdemir, S. Yapici, and M. Yilmaz, Heat-transfer enhancement in a channel flow with perforated rectangular blocks, Int. J. Heat Fluid Flow, vol. 22, no. 5, pp , V. U. V. Awasarmol and A. T. Pise, An experimental investigation of natural convection heat transfer enhancement from perforated rectangular fins array at different inclinations, Exp. Therm. Fluid Sci., vol. 68, pp , VI. D. H. Lee, J. M. Jung, J. H. Ha, and Y. I. Cho, Improvement of heat transfer with perforated circular holes in finned tubes of air-cooled heat exchanger, Int. Commun. Heat Mass Transf., vol. 39, no. 2, pp , VII. L.-T. Yu and C.-K. Chen, Application of the hybrid method to the transient thermal stresses response in isotropic annular fins, J. Appl. Mech., vol. 66, no. June 1999, pp , VIII. C. H. Chiu and C. K. Chen, Application of the decomposition method to thermal stresses in isotropic circular fins with temperature-dependent thermal conductivity, Acta Mech., vol. 157, no. 1 4, pp , IX. A. Mallick, S. Ghosal, P. K. Sarkar, and R. Ranjan, Homotopy perturbation method for thermal stresses in an annular fin with variable thermal conductivity, J. Therm. Stress., vol. 38, no. 1, pp , All Rights Reserved 401