Document Type : Article

**Authors**

College of Engineering and Technology (CET), Bhubaneswar-751029, Odisha, India

**Abstract**

This paper aimed at developing an empirical correlation for heat transfer from a protruded surface in the presence of a cross-flow jet. Finite volume method has been used to solve the governing differential equations for mass, momentum, energy as well as turbulence by imposing appropriate boundary conditions. Extensive numerical computations have been carried out to vary each of the independent variables to collect data for area-weighted average Nusselt number. Both the duct and the nozzle Reynolds number are varied from 6,000-20,000. The volume fraction and Prandtl number are also varied in the range of and , respectively. The number of protrusion (n) is varied from 1 to 4. A nonlinear regression analysis has been executed using CFD data to develop an empirical correlation for the Nusselt number in terms of pertinent independent parameters. The volume fraction of the nanofluid is found to be the most significant parameter to influence heat transfer rate among all other parameters. It has been observed that the predicted Nusselt number matches well with the computed one. The variations of the Nusselt number as the function of the independent parameters has been demonstrated. The present numerical methodologies have been validated with some open literature.

**Keywords**

**Main Subjects**

References:

1. Choi, S.U.S. "Enhancing thermal conductivity of fluids with nanoparticles", ASME International Mechanical Engineering Congress & Exposition, San Francisco, CA (1995).

2. Lee, S., Choi, S.U.S., Li, S., and Eastman, J.A. "Measuring thermal conductivity of fluid containing oxide nanoparticles", Journal of Heat Transfer, 121, pp. 280-289 (1999).

3. Eastman, J.A., Choi, S.U.S., Li, S., Yu, W., and Thompson, L.J. "Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles", Applied Physics Letters, 78, pp. 718-720 (2001).

4. Karthikeyan, N.R., Philip, J., and Raj, B. "Effect of clustering on the thermal conductivity of nanofluids", Materials Chemistry and Physics, 109, pp. 50-55 (2008).

5. Chandrasekar, M., Suresh, S., and Bose, A.C. "Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid", Experimental Thermal Fluid Science, 34, pp. 210-216 (2010).

6. Yu, W., Xie, H., Chen, L., and Li, Y. "Enhancement of thermal conductivity of kerosene based Fe3O4 nanofluids prepared via phase-transfer method", Colloids Surfaces A, 355, pp. 109-113 (2010).

7. Pak, B.C., and Cho, Y.I. "Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particle", Experimental Heat Transfer, 11, pp. 151-170 (1998).

8. Wen, D., and Ding, Y. "Experimental investigation into convective heat transfer of nanofluid at the entrance region under laminar flow conditions", International Journal of Heat and Mass Transfer, 47, pp. 5181-5188 (2004).

9. Li, Q., Xuan, Y., and Wang J. "Experimental investigation on transport properties of magnetic fluids", Experimental Thermal and Fluid Science, 30, pp. 109- 116 (2005).

10. Xuan, Y. and Li, Q. "Investigation on convective heat transfer and flow features of nanofluids", Journal of Heat Transfer, 125, pp. 151-155 (2003).

11. Vajjha, R.S., Das, D.K., and Ray, D.R. "Development of new correlations for the Nusselt number and the friction factor under turbulent flow of nanofluids in at tubes", International Journal of Heat and Mass Transfer, 80, pp. 353-367 (2015).

12. Suresh, S., Venkitaraj, K.P., Selvakumar, P., et al. "Effect of Al2O3-Cu/water hybrid nanofluid in heat transfer", Experimental Thermal and Fluid Science, 38, pp. 54-60 (2012).

13. Xuan, Y. and Roetzel, W. "Conception for heat transfer correlation of nanofluids", International Journal of Heat and Mass Transfer, 43, pp. 3701-3707 (2000).

14. Raji, P., Akhavan-Behabadi, M.A., and Saeedinia, M. "Pressure drop and thermal characteristics of CuObase oil nanofluid laminar flow in attened tubes under constant heat flux", International Communications in Heat and Mass Transfer, 8, pp. 964-971 (2011).

15. Zhang, H., Shao, S., Xu, H., et al. "Heat transfer and flow features of Al2O3-water nanofluids flowing through a circular microchannel experimental results and correlations", Applied Thermal Engineering, 61, pp. 86-92 (2013).

16. Jafarimoghaddam, A. and Aberoumand, S. "An empirical investigation on Cu/ethylene glycol nanofluid through a concentric annular tube and proposing a correlation for predicting Nusselt number", Alexandria Engineering Journal, 55, pp. 1047-1052 (2016).

17. Sajadi, A.R. and Kazemi, M.H. "Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube", International Communications in Heat and Mass Transfer, 38, pp. 1474-1478 (2011).

18. Duangthongsuk, W. and Wongwises, S. "An experimental study on the heat transfer performance and pressure drop of TiO2-water nanofluids flowing under a turbulent flow regime", International Journal of Heat and Mass Transfer, 53, pp. 334-344 (2010).

19. Abbasin Arani, A.A. and Amani, J. "Experimental investigation of diameter effect on heat transfer performance and pressure drop of TiO2-water nanofluid", Experimental Thermal and Fluid Science, 44, pp. 520-533 (2013).

20. Anoop, K.B., Sundararajan, T., and Das, S.K. "Effect of particle size on the convective heat transfer in nanofluid in the developing region", International Journal of Heat and Mass Transfer, 52, pp. 2189-2195 (2009).

21. Sheikholeslami, M., Gorji-Bandpy, M., and Ganji, D.D. "Natural convection in a nanofluid filled concentric annulus between an outer square cylinder and an inner elliptic cylinder", Scientia Iranica B, 20, pp. 1241-1253 (2013).

22. Nemati, H., Farhadi, M., Sedighi, K., et al. "Magnetic field effects on natural convection flow of nanofluid in a rectangular cavity using lattice Boltzmann model", Scientia Iranica B, 20, pp. 1241-1253 (2013).

23. Khorasanizadeh, H., Amani, J., and Nikfar, M. "Numerical investigation of Cu-water nanofluid natural convection and entropy generation within a cavity with an embedded conductive baffle", Scientia Iranica F, 19, pp. 1996-2003 (2012).

24. Wei, W., Cai, J., Hu, X., Han, Q., et al. "Fractal analysis of the effect of particle aggregation distribution on thermal conductivity of nanofluids", Physics Letters A, 380, pp. 2953-2956 (2016).

25. Siavashi, M., Yousofvand, R., and Rezanejad, S. "Nanofluid and porous fins effect on natural convection and entropy generation of flow inside a cavity", Advanced Powder Technology, 29, pp. 142-156 (2018).

26. Mukherjee, A., Rout, S., and Barik, A.K. "Heat transfer and entropy generation analysis of protruded surface in presence of a cross- flow jet using Al2O3- water nanofluid", Thermal Science and Engineering Progress, 5, pp. 327-338 (2018).

27. Bianco, V., Chiacchio, F., Manca, O., et al. "Numerical investigation of nanofluids forced convection in circular tubes", Applied Thermal Engineering, 29, pp. 3632-3642 (2009).

28. Maiga, S.E.B., Palm, S.J., Nguyen, C.T., et al. "Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension", International Journal of Numerical Methods for Heat & Fluid Flow, 16, pp. 275-292 (2006).

29. Akbarinia, A. and Behzadmehr, A. "Numerical study of laminar mixed convection of nanofluid in horizontal curved tubes", Applied Thermal Engineering, 27, pp. 1327-1337 (2007).

30. Wang, X., Xu, X., and Choi, S.U.S. "Thermal conductivity of nanoparticle-fluid mixture", Journal of Thermophysics and Heat Transfer, 13, pp. 474-480 (1999).

31. Lee, S., Choi, S.U.S., Li, S., et al. "Measuring thermal conductivity of fluids containing oxide nanoparticles", Journal Heat Transfer, 121, pp. 280-289 (1999).

32. Barik, A.K., Dash, S.K., and Guha, A. "Experimental and numerical investigation of air entrainment into an infrared suppression device", Applied Thermal Engineering, 75, pp. 33-44 (2015).

33. Boertza, H., Baars, A., Cieslinskib, J.T. et al. "Numerical study of turbulent flow and heat transfer of nanofluids in pipes", Heat Transfer Engineering, 39, pp. 241-251 (2018). Doi:/10.1080/01457632.2017.1295739.

34. Mentor, F.R. "Two-equation eddy-viscosity turbulence models for engineering applications", AIAA Journal, 32, pp. 1598-1605 (1994).

35. Barik, A.K., Rout, S., and Mukherjee, A. "Numerical investigation of heat transfer enhancement from protruded surface by cross-flow jet using Al2O3-water nanofluid", International Journal of Heat and Mass Transfer, 101, pp. 550-561 (2016).

36. Launder, B.E. and Spalding, D.B. "The numerical computation of turbulent flows", Computer Methods in Applied Mechanics and Engineering, 3, pp. 2869-2879 (1974).

37. Zuckerman, N. and Lior, N. "Impingement heat transfer: correlations and numerical modeling", Journal of Heat Transfer, 127, pp. 544-552 (2005).

38. Barik, A.K., Mukherjee, A., and Patro, P. "Heat transfer enhancement from a small rectangular channel with different surface protrusions by a turbulent cross flow jet", International Journal of Thermal Sciences, 98, pp. 32-41 (2015).

39. Bouhalleb, M. and Abbassi, H. "Numerical investigation of heat transfer by CuO-water nanofluid in rectangular enclosures", Heat Transfer Engineering, 37, pp. 13-23 (2016).

40. Sun, B., Qu, Y., and Yang, D. "Heat transfer of single impinging jet with Cu nanofluids", Applied Thermal Engineering, 102, pp. 701-707 (2016).

2. Lee, S., Choi, S.U.S., Li, S., and Eastman, J.A. "Measuring thermal conductivity of fluid containing oxide nanoparticles", Journal of Heat Transfer, 121, pp. 280-289 (1999).

3. Eastman, J.A., Choi, S.U.S., Li, S., Yu, W., and Thompson, L.J. "Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles", Applied Physics Letters, 78, pp. 718-720 (2001).

4. Karthikeyan, N.R., Philip, J., and Raj, B. "Effect of clustering on the thermal conductivity of nanofluids", Materials Chemistry and Physics, 109, pp. 50-55 (2008).

5. Chandrasekar, M., Suresh, S., and Bose, A.C. "Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid", Experimental Thermal Fluid Science, 34, pp. 210-216 (2010).

6. Yu, W., Xie, H., Chen, L., and Li, Y. "Enhancement of thermal conductivity of kerosene based Fe3O4 nanofluids prepared via phase-transfer method", Colloids Surfaces A, 355, pp. 109-113 (2010).

7. Pak, B.C., and Cho, Y.I. "Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particle", Experimental Heat Transfer, 11, pp. 151-170 (1998).

8. Wen, D., and Ding, Y. "Experimental investigation into convective heat transfer of nanofluid at the entrance region under laminar flow conditions", International Journal of Heat and Mass Transfer, 47, pp. 5181-5188 (2004).

9. Li, Q., Xuan, Y., and Wang J. "Experimental investigation on transport properties of magnetic fluids", Experimental Thermal and Fluid Science, 30, pp. 109- 116 (2005).

10. Xuan, Y. and Li, Q. "Investigation on convective heat transfer and flow features of nanofluids", Journal of Heat Transfer, 125, pp. 151-155 (2003).

11. Vajjha, R.S., Das, D.K., and Ray, D.R. "Development of new correlations for the Nusselt number and the friction factor under turbulent flow of nanofluids in at tubes", International Journal of Heat and Mass Transfer, 80, pp. 353-367 (2015).

12. Suresh, S., Venkitaraj, K.P., Selvakumar, P., et al. "Effect of Al2O3-Cu/water hybrid nanofluid in heat transfer", Experimental Thermal and Fluid Science, 38, pp. 54-60 (2012).

13. Xuan, Y. and Roetzel, W. "Conception for heat transfer correlation of nanofluids", International Journal of Heat and Mass Transfer, 43, pp. 3701-3707 (2000).

14. Raji, P., Akhavan-Behabadi, M.A., and Saeedinia, M. "Pressure drop and thermal characteristics of CuObase oil nanofluid laminar flow in attened tubes under constant heat flux", International Communications in Heat and Mass Transfer, 8, pp. 964-971 (2011).

15. Zhang, H., Shao, S., Xu, H., et al. "Heat transfer and flow features of Al2O3-water nanofluids flowing through a circular microchannel experimental results and correlations", Applied Thermal Engineering, 61, pp. 86-92 (2013).

16. Jafarimoghaddam, A. and Aberoumand, S. "An empirical investigation on Cu/ethylene glycol nanofluid through a concentric annular tube and proposing a correlation for predicting Nusselt number", Alexandria Engineering Journal, 55, pp. 1047-1052 (2016).

17. Sajadi, A.R. and Kazemi, M.H. "Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube", International Communications in Heat and Mass Transfer, 38, pp. 1474-1478 (2011).

18. Duangthongsuk, W. and Wongwises, S. "An experimental study on the heat transfer performance and pressure drop of TiO2-water nanofluids flowing under a turbulent flow regime", International Journal of Heat and Mass Transfer, 53, pp. 334-344 (2010).

19. Abbasin Arani, A.A. and Amani, J. "Experimental investigation of diameter effect on heat transfer performance and pressure drop of TiO2-water nanofluid", Experimental Thermal and Fluid Science, 44, pp. 520-533 (2013).

20. Anoop, K.B., Sundararajan, T., and Das, S.K. "Effect of particle size on the convective heat transfer in nanofluid in the developing region", International Journal of Heat and Mass Transfer, 52, pp. 2189-2195 (2009).

21. Sheikholeslami, M., Gorji-Bandpy, M., and Ganji, D.D. "Natural convection in a nanofluid filled concentric annulus between an outer square cylinder and an inner elliptic cylinder", Scientia Iranica B, 20, pp. 1241-1253 (2013).

22. Nemati, H., Farhadi, M., Sedighi, K., et al. "Magnetic field effects on natural convection flow of nanofluid in a rectangular cavity using lattice Boltzmann model", Scientia Iranica B, 20, pp. 1241-1253 (2013).

23. Khorasanizadeh, H., Amani, J., and Nikfar, M. "Numerical investigation of Cu-water nanofluid natural convection and entropy generation within a cavity with an embedded conductive baffle", Scientia Iranica F, 19, pp. 1996-2003 (2012).

24. Wei, W., Cai, J., Hu, X., Han, Q., et al. "Fractal analysis of the effect of particle aggregation distribution on thermal conductivity of nanofluids", Physics Letters A, 380, pp. 2953-2956 (2016).

25. Siavashi, M., Yousofvand, R., and Rezanejad, S. "Nanofluid and porous fins effect on natural convection and entropy generation of flow inside a cavity", Advanced Powder Technology, 29, pp. 142-156 (2018).

26. Mukherjee, A., Rout, S., and Barik, A.K. "Heat transfer and entropy generation analysis of protruded surface in presence of a cross- flow jet using Al2O3- water nanofluid", Thermal Science and Engineering Progress, 5, pp. 327-338 (2018).

27. Bianco, V., Chiacchio, F., Manca, O., et al. "Numerical investigation of nanofluids forced convection in circular tubes", Applied Thermal Engineering, 29, pp. 3632-3642 (2009).

28. Maiga, S.E.B., Palm, S.J., Nguyen, C.T., et al. "Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension", International Journal of Numerical Methods for Heat & Fluid Flow, 16, pp. 275-292 (2006).

29. Akbarinia, A. and Behzadmehr, A. "Numerical study of laminar mixed convection of nanofluid in horizontal curved tubes", Applied Thermal Engineering, 27, pp. 1327-1337 (2007).

30. Wang, X., Xu, X., and Choi, S.U.S. "Thermal conductivity of nanoparticle-fluid mixture", Journal of Thermophysics and Heat Transfer, 13, pp. 474-480 (1999).

31. Lee, S., Choi, S.U.S., Li, S., et al. "Measuring thermal conductivity of fluids containing oxide nanoparticles", Journal Heat Transfer, 121, pp. 280-289 (1999).

32. Barik, A.K., Dash, S.K., and Guha, A. "Experimental and numerical investigation of air entrainment into an infrared suppression device", Applied Thermal Engineering, 75, pp. 33-44 (2015).

33. Boertza, H., Baars, A., Cieslinskib, J.T. et al. "Numerical study of turbulent flow and heat transfer of nanofluids in pipes", Heat Transfer Engineering, 39, pp. 241-251 (2018). Doi:/10.1080/01457632.2017.1295739.

34. Mentor, F.R. "Two-equation eddy-viscosity turbulence models for engineering applications", AIAA Journal, 32, pp. 1598-1605 (1994).

35. Barik, A.K., Rout, S., and Mukherjee, A. "Numerical investigation of heat transfer enhancement from protruded surface by cross-flow jet using Al2O3-water nanofluid", International Journal of Heat and Mass Transfer, 101, pp. 550-561 (2016).

36. Launder, B.E. and Spalding, D.B. "The numerical computation of turbulent flows", Computer Methods in Applied Mechanics and Engineering, 3, pp. 2869-2879 (1974).

37. Zuckerman, N. and Lior, N. "Impingement heat transfer: correlations and numerical modeling", Journal of Heat Transfer, 127, pp. 544-552 (2005).

38. Barik, A.K., Mukherjee, A., and Patro, P. "Heat transfer enhancement from a small rectangular channel with different surface protrusions by a turbulent cross flow jet", International Journal of Thermal Sciences, 98, pp. 32-41 (2015).

39. Bouhalleb, M. and Abbassi, H. "Numerical investigation of heat transfer by CuO-water nanofluid in rectangular enclosures", Heat Transfer Engineering, 37, pp. 13-23 (2016).

40. Sun, B., Qu, Y., and Yang, D. "Heat transfer of single impinging jet with Cu nanofluids", Applied Thermal Engineering, 102, pp. 701-707 (2016).

Transactions on Mechanical Engineering (B)

May and June 2020Pages 1218-1229