Effect of Sinusoidal Heating on Natural Convection Coupled to Thermal Radiation in a Square Cavity Subjected to Cross Temperature Gradients

Affiliation(s)

Laboratory of Flows and Transfers Modelling (LAMET), Physics Department, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Béni-Mellal, Morocco.

Laboratory of Fluid Mechanics and Energetics (LMFE), Unit Affiliated to CNRST (URAC 27), Physics Department, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakech, Morocco.

Laboratory of Flows and Transfers Modelling (LAMET), Physics Department, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Béni-Mellal, Morocco.

Laboratory of Fluid Mechanics and Energetics (LMFE), Unit Affiliated to CNRST (URAC 27), Physics Department, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakech, Morocco.

ABSTRACT

Coupled natural convection and surface radiation within a square cavity, filled with air and submitted to discrete heating and cooling from all its walls, is studied numerically. The thermally active elements are centrally located on the walls of the cavity. Two heating modes, called ** SB **and

Cite this paper

Ayachi, R. , Raji, A. , Naïmi, M. , Elharfi, H. and Hasnaoui, M. (2013) Effect of Sinusoidal Heating on Natural Convection Coupled to Thermal Radiation in a Square Cavity Subjected to Cross Temperature Gradients.*Journal of Electronics Cooling and Thermal Control*, **3**, 7-21. doi: 10.4236/jectc.2013.31002.

Ayachi, R. , Raji, A. , Naïmi, M. , Elharfi, H. and Hasnaoui, M. (2013) Effect of Sinusoidal Heating on Natural Convection Coupled to Thermal Radiation in a Square Cavity Subjected to Cross Temperature Gradients.

References

[1] C. Balaji and S. P. Venkateshan, “Interaction of Surface Radiation with Free Convection in a Square Cavity,” International Journal of Heat Fluid Flow, Vol. 14, No. 3, 1993, pp. 260-267. doi:10.1016/0142-727X(93)90057-T

[2] M. Akiyama and Q. P. Chong, “Numerical Analysis of Natural Convection with Surface Radiation in a Square Cavity,” Numerical Heat Transfer Part A, Vol. 31, No. 4, 1997, pp. 419-433. doi:10.1080/10407789708913899

[3] G. Colomer, M. Costa, R. Consul and A. Oliva, “Three Dimensional Numerical Simulation of Convection and Radiation in a Differentially Heated Cavity Using the Discrete Ordinates Method,” International Journal of Heat Mass Transfer, Vol. 47, No. 2, 2004, pp. 257-269. doi:10.1016/S0017-9310(03)00387-9

[4] C. Y. Han and S. W. Baek, “The Effects of Radiation on Natural Convection in a Rectangular Enclosure Divided by Two Partitions,” Numerical Heat Transfer Part A, Vol. 37, No. 3, 2000, pp. 249-270. doi:10.1080/104077800274280

[5] E. H. Ridouane, M. Hasnaoui, A. Amahmid and A. Raji, “Interaction between Natural Convection and Radiation in a Square Cavity Heated from Below,” Numerical Heat Transfer Part A, Vol. 45, No. 3, 2004, pp. 289-311. doi:10.1080/10407780490250373

[6] R. El Ayachi, A. Raji, M. Hasnaoui and A. Bahlaoui, “Combined Effect of Radiation and Natural Convection in a Square Cavity Differentially Heated with a Periodic Temperature,” Numerical Heat Transfer Part A, Vol. 53, No. 12, 2008, pp. 1339-1356. doi:10.1080/10407780801960043

[7] M. Corcione, “Effects of the Thermal Boundary Conditions at the Sidewalls upon Natural Convection in Rectangular Enclosures Heated from Below and Cooled from Above,” International Journal of Thermal Sciences, Vol. 42, No. 2, 2003, pp. 199-208. doi:10.1016/S1290-0729(02)00019-4

[8] C. Cianfrini, M. Corcione and P. P. Dell’Omo, “Natural Convection in Tilted Square Cavities with Differentially Heated Opposite Walls,” International Journal of Thermal Sciences, Vol. 44, No. 5, 2005, pp. 441-451. doi:10.1016/j.ijthermalsci.2004.11.007

[9] Q.-H. Deng, “Fluid Flow and Heat Transfer Characteristics of Natural Convection in Square Cavities Due to Discrete Source—Sink Pairs,” International Journal of Heat Mass Transfer, Vol. 51, No. 25-26, 2008, pp. 5949-5957. doi:10.1016/j.ijheatmasstransfer.2008.04.062

[10] R. El Ayachi, A. Raji, M. Hasnaoui, A. Abdelbaki and M. Naimi, “Combined Effects of Radiation and Natural Convection in a Square Cavity Submitted to Cross Gradients of Temperature: Case of Partial Heating and Cooling,” Computational Thermal Sciences, Vol. 3, No. 1, 2011, pp. 73-78. doi:10.1615/ComputThermalScien.v3.i1.60

[11] J. L. Lage and A. Bejan, “The Resonance of Natural Convection in a Horizontal Enclosure Heated Periodically from the Side,” International Journal of Heat Mass Transfer, Vol. 36, No. 8, 1993, pp. 2027-2038. doi:10.1016/S0017-9310(05)80134-6

[12] E. K. Lakhal, M. Hasnaoui, P. Vasseur and E. Bilgen, “Convection Naturelle Dans une Cellule Carrée Chauffée Périodiquement par le Bas: étude Numérique,” Revue Generale de Thermique, Vol. 392, No. 392-393, 1994, pp. 480-485.

[13] E. K. Lakhal, M. Hasnaoui, P. Vasseur and E. Bilgen, “Natural Convection in a Square Enclosure Heated Periodically from Part of the Bottom Wall,” Numerical Heat Transfer Part A, Vol. 27, No. 3, 1995, pp. 319-333. doi:10.1080/10407789508913703

[14] E. K. Lakhal, M. Hasnaoui and P. Vasseur, “Numerical Study of Transient Natural Convection in a Cavity Heated Periodically with Different Types of Excitations,” International Journal of Heat Mass Transfer, Vol. 42, No. 21, 1999, pp. 3927-3941. doi:10.1016/S0017-9310(99)00070-8

[15] B. V. Antohe and J. L. Lage, “Amplitude Effect on Convection Induced by Time-Periodic Horizontal Heating,” International Journal of Heat Mass Transfer, Vol. 39, No. 6, 1996, pp. 1121-1133. doi:10.1016/0017-9310(95)00207-3

[16] H. S. Kwak and J. M. Hyun, “Natural Convection in an Enclosure Having a Vertical Sidewall with Time Varying Temperature,” Journal of Fluid Mechanics, Vol. 329, 1996, pp. 65-88. doi:10.1017/S0022112096008828

[17] H. S. Kwak, K. Kuwahara and J. M. Hyun, “Resonant Enhancement of Natural Convection Heat Transfer in a Square Enclosure,” International Journal of Heat Mass Transfer, Vol. 41, No. 18, 1998, pp. 2837-2846. doi:10.1016/S0017-9310(98)00018-0

[18] B. Abourida, M. Hasnaoui and S. Douamna, “Transient Natural Convection in a Square Enclosure with Horizontal Walls Submitted to Periodic Temperatures,” Numerical Heat Transfer Part A, Vol. 36, No. 7, 1999, pp. 737-750. doi:10.1080/104077899274543

[19] B. Abourida, M. Hasnaoui and S. Douamna, “Convection Naturelle Dans une Cavité Carrée Avec des Parois Verticales Soumises à des Températures Périodiques,” Revue Generale de Thermique, Vol. 37, No. 9, 1998, pp. 788-800.

[20] S. Douamna, M. Hasnaoui and B. Abourida, “Two-Dimensional Transient Natural Convection in a Repetitive Geometry Submitted to Variable Heating from Below: Numerical Identification of Routes Leading to Chaos,” Numerical Heat Transfer Part A, Vol. 37, No. 7, 2000, pp. 779-799. doi:10.1080/104077800274073

[21] F. Y. Zhao, D. Liu and G. F. Tang, “Resonant Response of Fluid Flow Subjected to Discrete Heating Elements,” Energy Conversion Management, Vol. 48, No. 9, 2007, pp. 2461-2472. doi:10.1016/j.enconman.2007.04.008

[22] R. El Ayachi, A. Raji, M. Hasnaoui and A. Bahlaoui, “Combined Effect of Radiation and Natural Convection in a Square Cavity Differentially Heated with a Periodic Temperature,” Numerical Heat Transfer Part A, Vol. 53, No. 12, 2008, pp. 1339-1356. doi:10.1080/10407780801960043

[23] H. C. Hottel and A. F. Saroffim, “Radiative Heat Transfer,” McGraw-Hill, New York, 1967.

[24] S. Kimura and A. Bejan, “The Heatline Visualization of Convective Heat Transfer,” ASME Journal of Heat Transfer, Vol. 105, No. 4, 1983, pp. 916-919. doi:10.1115/1.3245684

[1] C. Balaji and S. P. Venkateshan, “Interaction of Surface Radiation with Free Convection in a Square Cavity,” International Journal of Heat Fluid Flow, Vol. 14, No. 3, 1993, pp. 260-267. doi:10.1016/0142-727X(93)90057-T

[2] M. Akiyama and Q. P. Chong, “Numerical Analysis of Natural Convection with Surface Radiation in a Square Cavity,” Numerical Heat Transfer Part A, Vol. 31, No. 4, 1997, pp. 419-433. doi:10.1080/10407789708913899

[3] G. Colomer, M. Costa, R. Consul and A. Oliva, “Three Dimensional Numerical Simulation of Convection and Radiation in a Differentially Heated Cavity Using the Discrete Ordinates Method,” International Journal of Heat Mass Transfer, Vol. 47, No. 2, 2004, pp. 257-269. doi:10.1016/S0017-9310(03)00387-9

[4] C. Y. Han and S. W. Baek, “The Effects of Radiation on Natural Convection in a Rectangular Enclosure Divided by Two Partitions,” Numerical Heat Transfer Part A, Vol. 37, No. 3, 2000, pp. 249-270. doi:10.1080/104077800274280

[5] E. H. Ridouane, M. Hasnaoui, A. Amahmid and A. Raji, “Interaction between Natural Convection and Radiation in a Square Cavity Heated from Below,” Numerical Heat Transfer Part A, Vol. 45, No. 3, 2004, pp. 289-311. doi:10.1080/10407780490250373

[6] R. El Ayachi, A. Raji, M. Hasnaoui and A. Bahlaoui, “Combined Effect of Radiation and Natural Convection in a Square Cavity Differentially Heated with a Periodic Temperature,” Numerical Heat Transfer Part A, Vol. 53, No. 12, 2008, pp. 1339-1356. doi:10.1080/10407780801960043

[7] M. Corcione, “Effects of the Thermal Boundary Conditions at the Sidewalls upon Natural Convection in Rectangular Enclosures Heated from Below and Cooled from Above,” International Journal of Thermal Sciences, Vol. 42, No. 2, 2003, pp. 199-208. doi:10.1016/S1290-0729(02)00019-4

[8] C. Cianfrini, M. Corcione and P. P. Dell’Omo, “Natural Convection in Tilted Square Cavities with Differentially Heated Opposite Walls,” International Journal of Thermal Sciences, Vol. 44, No. 5, 2005, pp. 441-451. doi:10.1016/j.ijthermalsci.2004.11.007

[9] Q.-H. Deng, “Fluid Flow and Heat Transfer Characteristics of Natural Convection in Square Cavities Due to Discrete Source—Sink Pairs,” International Journal of Heat Mass Transfer, Vol. 51, No. 25-26, 2008, pp. 5949-5957. doi:10.1016/j.ijheatmasstransfer.2008.04.062

[10] R. El Ayachi, A. Raji, M. Hasnaoui, A. Abdelbaki and M. Naimi, “Combined Effects of Radiation and Natural Convection in a Square Cavity Submitted to Cross Gradients of Temperature: Case of Partial Heating and Cooling,” Computational Thermal Sciences, Vol. 3, No. 1, 2011, pp. 73-78. doi:10.1615/ComputThermalScien.v3.i1.60

[11] J. L. Lage and A. Bejan, “The Resonance of Natural Convection in a Horizontal Enclosure Heated Periodically from the Side,” International Journal of Heat Mass Transfer, Vol. 36, No. 8, 1993, pp. 2027-2038. doi:10.1016/S0017-9310(05)80134-6

[12] E. K. Lakhal, M. Hasnaoui, P. Vasseur and E. Bilgen, “Convection Naturelle Dans une Cellule Carrée Chauffée Périodiquement par le Bas: étude Numérique,” Revue Generale de Thermique, Vol. 392, No. 392-393, 1994, pp. 480-485.

[13] E. K. Lakhal, M. Hasnaoui, P. Vasseur and E. Bilgen, “Natural Convection in a Square Enclosure Heated Periodically from Part of the Bottom Wall,” Numerical Heat Transfer Part A, Vol. 27, No. 3, 1995, pp. 319-333. doi:10.1080/10407789508913703

[14] E. K. Lakhal, M. Hasnaoui and P. Vasseur, “Numerical Study of Transient Natural Convection in a Cavity Heated Periodically with Different Types of Excitations,” International Journal of Heat Mass Transfer, Vol. 42, No. 21, 1999, pp. 3927-3941. doi:10.1016/S0017-9310(99)00070-8

[15] B. V. Antohe and J. L. Lage, “Amplitude Effect on Convection Induced by Time-Periodic Horizontal Heating,” International Journal of Heat Mass Transfer, Vol. 39, No. 6, 1996, pp. 1121-1133. doi:10.1016/0017-9310(95)00207-3

[16] H. S. Kwak and J. M. Hyun, “Natural Convection in an Enclosure Having a Vertical Sidewall with Time Varying Temperature,” Journal of Fluid Mechanics, Vol. 329, 1996, pp. 65-88. doi:10.1017/S0022112096008828

[17] H. S. Kwak, K. Kuwahara and J. M. Hyun, “Resonant Enhancement of Natural Convection Heat Transfer in a Square Enclosure,” International Journal of Heat Mass Transfer, Vol. 41, No. 18, 1998, pp. 2837-2846. doi:10.1016/S0017-9310(98)00018-0

[18] B. Abourida, M. Hasnaoui and S. Douamna, “Transient Natural Convection in a Square Enclosure with Horizontal Walls Submitted to Periodic Temperatures,” Numerical Heat Transfer Part A, Vol. 36, No. 7, 1999, pp. 737-750. doi:10.1080/104077899274543

[19] B. Abourida, M. Hasnaoui and S. Douamna, “Convection Naturelle Dans une Cavité Carrée Avec des Parois Verticales Soumises à des Températures Périodiques,” Revue Generale de Thermique, Vol. 37, No. 9, 1998, pp. 788-800.

[20] S. Douamna, M. Hasnaoui and B. Abourida, “Two-Dimensional Transient Natural Convection in a Repetitive Geometry Submitted to Variable Heating from Below: Numerical Identification of Routes Leading to Chaos,” Numerical Heat Transfer Part A, Vol. 37, No. 7, 2000, pp. 779-799. doi:10.1080/104077800274073

[21] F. Y. Zhao, D. Liu and G. F. Tang, “Resonant Response of Fluid Flow Subjected to Discrete Heating Elements,” Energy Conversion Management, Vol. 48, No. 9, 2007, pp. 2461-2472. doi:10.1016/j.enconman.2007.04.008

[22] R. El Ayachi, A. Raji, M. Hasnaoui and A. Bahlaoui, “Combined Effect of Radiation and Natural Convection in a Square Cavity Differentially Heated with a Periodic Temperature,” Numerical Heat Transfer Part A, Vol. 53, No. 12, 2008, pp. 1339-1356. doi:10.1080/10407780801960043

[23] H. C. Hottel and A. F. Saroffim, “Radiative Heat Transfer,” McGraw-Hill, New York, 1967.

[24] S. Kimura and A. Bejan, “The Heatline Visualization of Convective Heat Transfer,” ASME Journal of Heat Transfer, Vol. 105, No. 4, 1983, pp. 916-919. doi:10.1115/1.3245684