Second Law Analysis of Mixed Convection of Magnetohydrodynamic Flow in an Inclined Square Lid-Driven

Elif Büyük Öğüt

doi:10.18186/thermal.655023

Article Open Access1 January 2019

Second Law Analysis of Mixed Convection of Magnetohydrodynamic Flow in an Inclined Square Lid-Driven

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Elif BÜYÜK ÖĞÜT ¹

¹Kocaeli University

Journal of Thermal Engineering 2019, Vol. 5, Issue 6, pp. 240-251; doi.org/10.18186/thermal.655023

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Abstract

Second law of thermodynamics analysis is formulated for the case of laminar mixed convection in an inclined square lid-driven enclosure in the presence of magnetic field. Vertical sides of the enclosure moves upward when inclination angle is zero. Governing equations of flow and temperature in the form of stream function-vorticity formulation were solved numerically using the differential quadrature method. Governing parameters are: Richardson number (from 0.01 to 100), Prandtl number (from 0.1 to 1.0), inclination angle of enclosure (from 0 to 180), Hartmann number (from 0 to 100) and magnetic field direction (0). It is found that the inclination angle of enclosure is effective parameter on entropy generation especially for higher Richardson number (Ri > 1) due to domination of natural convection. However, Hartmann number is effective on both heat transfer and entropy generation for all values of Richardson and Prandtl numbers and it decreases the convective fluid flow and entropy generation.

Keywords: Lid-driven Enclosure; Mixed Convection; Entropy Generation; Magnetic Field

References

Shankar, P. N., Deshpande, M. D. (2000). Fluid mechanics in the driven cavity. Annual review of fluid mechanics, 32(1), 93-136.
Ghia, U. K. N. G., Ghia, K. N., Shin, C. T. (1982). High-Re solutions for incompressible flow using the Navier- Stokes equations and a multigrid method. Journal of computational physics, 48(3), 387-411.
Sharif, M. A. R. (2007). Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom. Applied thermal engineering, 27(5-6), 1036-1042.
Torrance, K., Davis, R., Eike, K., Gill, P., Gutman, D., Hsui, A., Zien, H. (1972). Cavity flows driven by buoyancy and shear. Journal of Fluid Mechanics, 51(2), 221-231.
Iwatsu, R., Hyun, J. M., Kuwahara, K. (1993). Mixed convection in a driven cavity with a stable vertical temperature gradient. International Journal of Heat and Mass Transfer, 36(6), 1601-1608.
Mohamad, A., Viskanta, R. (1993). Flow and thermal structures in a lid-driven cavity heated from below. Fluid Dynamics Research, 12(3), 173.
Ogut, E. B. (2017). Effects of Prandtl number and Magnetic field on Mixed Convection Heat Transfer in an Inclined Lid-driven Enclosure. Karaelmas Science and Engineering Journal, 7(1), 145-153.
Ece, M. C., Büyük, E. (2006). Natural-convection flow under a magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls. Fluid Dynamics Research, 38(8), 564.
Chamkha, A. J. (2002). Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal heat generation or absorption. Numerical Heat Transfer: Part A: Applications, 41(5), 529-546.
Chamkha, A. J. (1998). Mixed convection flow along a vertical permeable plate embedded in a porous medium in the presence of a transverse magnetic field. Numerical Heat Transfer, Part A Applications, 34(1), 93-103.
Mahmud, S., Fraser, R. A. (2004). Magnetohydrodynamic free convection and entropy generation in a square porous cavity. International Journal of Heat and Mass Transfer, 47(14-16), 3245-3256.
Yilbas, B. S., Shuja, S. Z., Gbadebo, S. A., Al‐Hamayel, H. A., Boran, K. (1998). Natural convection and entropy generation in a square cavity. International journal of energy research, 22(14), 1275-1290.
Magherbi, M., Abbassi, H., Brahim, A. B. (2003). Entropy generation at the onset of natural convection. International Journal of Heat and Mass Transfer, 46(18), 3441-3450.
Narusawa, U. (2001). The second-law analysis of mixed convection in rectangular ducts. Heat and Mass Transfer, 37(2-3), 197-203.
Mansour, R. B., Galanis, N., Nguyen, C. T. (2006). Dissipation and entropy generation in fully developed forced and mixed laminar convection. International journal of thermal sciences, 45(10), 998-1007.
Tasnim, S. H., Mahmud, S. (2002). Mixed convection and entropy generation in a vertical annular space. Exergy, An International Journal, 2(4), 373-379.
Mahmud, S., Fraser, R. A. (2002). Analysis of mixed convection—Radiation interaction in a vertical channel: Entropy generation. Exergy, an International journal, 2(4), 330-339.
Bellman, R., Kashef, B. G., Casti, J. (1972). Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of computational physics, 10(1), 40-52.
Shu, C. (2000). Mathematical Fundamentals of Differential Quadrature Method: Linear Vector Space Analysis and Function Approximation. In Differential Quadrature and Its Application in Engineering (pp. 1-24). Springer, London.
De Vahl Davis, G. (1983). Natural convection of air in a square cavity: a bench mark numerical solution. International Journal for numerical methods in fluids, 3(3), 249-264. 250 Journal of Thermal Engineering, Research Article, Vol. 5, No. 6, Special Issue 10, pp. 240-251, December, 2019
Shu, C., Ding, H., & Yeo, K. S. (2003). Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier–Stokes equations. Computer methods in applied mechanics and engineering, 192(7-8), 941-954. 251

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Öğüt, E.B. Second Law Analysis of Mixed Convection of Magnetohydrodynamic Flow in an Inclined Square Lid-Driven. Journal of Thermal Engineering 2019, Vol. 5, pp. 240-251. https://doi.org/10.18186/thermal.655023

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Second Law Analysis of Mixed Convection of Magnetohydrodynamic Flow in an Inclined Square Lid-Driven

¹Kocaeli University

Abstract

References

Shankar, P. N., Deshpande, M. D. (2000). Fluid mechanics in the driven cavity. Annual review of fluid mechanics, 32(1), 93-136.
Ghia, U. K. N. G., Ghia, K. N., Shin, C. T. (1982). High-Re solutions for incompressible flow using the Navier- Stokes equations and a multigrid method. Journal of computational physics, 48(3), 387-411.
Sharif, M. A. R. (2007). Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom. Applied thermal engineering, 27(5-6), 1036-1042.
Torrance, K., Davis, R., Eike, K., Gill, P., Gutman, D., Hsui, A., Zien, H. (1972). Cavity flows driven by buoyancy and shear. Journal of Fluid Mechanics, 51(2), 221-231.
Iwatsu, R., Hyun, J. M., Kuwahara, K. (1993). Mixed convection in a driven cavity with a stable vertical temperature gradient. International Journal of Heat and Mass Transfer, 36(6), 1601-1608.
Mohamad, A., Viskanta, R. (1993). Flow and thermal structures in a lid-driven cavity heated from below. Fluid Dynamics Research, 12(3), 173.
Ogut, E. B. (2017). Effects of Prandtl number and Magnetic field on Mixed Convection Heat Transfer in an Inclined Lid-driven Enclosure. Karaelmas Science and Engineering Journal, 7(1), 145-153.
Ece, M. C., Büyük, E. (2006). Natural-convection flow under a magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls. Fluid Dynamics Research, 38(8), 564.
Chamkha, A. J. (2002). Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal heat generation or absorption. Numerical Heat Transfer: Part A: Applications, 41(5), 529-546.
Chamkha, A. J. (1998). Mixed convection flow along a vertical permeable plate embedded in a porous medium in the presence of a transverse magnetic field. Numerical Heat Transfer, Part A Applications, 34(1), 93-103.
Mahmud, S., Fraser, R. A. (2004). Magnetohydrodynamic free convection and entropy generation in a square porous cavity. International Journal of Heat and Mass Transfer, 47(14-16), 3245-3256.
Yilbas, B. S., Shuja, S. Z., Gbadebo, S. A., Al‐Hamayel, H. A., Boran, K. (1998). Natural convection and entropy generation in a square cavity. International journal of energy research, 22(14), 1275-1290.
Magherbi, M., Abbassi, H., Brahim, A. B. (2003). Entropy generation at the onset of natural convection. International Journal of Heat and Mass Transfer, 46(18), 3441-3450.
Narusawa, U. (2001). The second-law analysis of mixed convection in rectangular ducts. Heat and Mass Transfer, 37(2-3), 197-203.
Mansour, R. B., Galanis, N., Nguyen, C. T. (2006). Dissipation and entropy generation in fully developed forced and mixed laminar convection. International journal of thermal sciences, 45(10), 998-1007.
Tasnim, S. H., Mahmud, S. (2002). Mixed convection and entropy generation in a vertical annular space. Exergy, An International Journal, 2(4), 373-379.
Mahmud, S., Fraser, R. A. (2002). Analysis of mixed convection—Radiation interaction in a vertical channel: Entropy generation. Exergy, an International journal, 2(4), 330-339.
Bellman, R., Kashef, B. G., Casti, J. (1972). Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of computational physics, 10(1), 40-52.
Shu, C. (2000). Mathematical Fundamentals of Differential Quadrature Method: Linear Vector Space Analysis and Function Approximation. In Differential Quadrature and Its Application in Engineering (pp. 1-24). Springer, London.
De Vahl Davis, G. (1983). Natural convection of air in a square cavity: a bench mark numerical solution. International Journal for numerical methods in fluids, 3(3), 249-264. 250 Journal of Thermal Engineering, Research Article, Vol. 5, No. 6, Special Issue 10, pp. 240-251, December, 2019
Shu, C., Ding, H., & Yeo, K. S. (2003). Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier–Stokes equations. Computer methods in applied mechanics and engineering, 192(7-8), 941-954. 251

Share and Cite

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[1] Shankar, P. N., Deshpande, M. D. (2000). Fluid mechanics in the driven cavity. Annual review of fluid mechanics, 32(1), 93-136.

[2] Ghia, U. K. N. G., Ghia, K. N., Shin, C. T. (1982). High-Re solutions for incompressible flow using the Navier- Stokes equations and a multigrid method. Journal of computational physics, 48(3), 387-411.

[3] Sharif, M. A. R. (2007). Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom. Applied thermal engineering, 27(5-6), 1036-1042.

[4] Torrance, K., Davis, R., Eike, K., Gill, P., Gutman, D., Hsui, A., Zien, H. (1972). Cavity flows driven by buoyancy and shear. Journal of Fluid Mechanics, 51(2), 221-231.

[5] Iwatsu, R., Hyun, J. M., Kuwahara, K. (1993). Mixed convection in a driven cavity with a stable vertical temperature gradient. International Journal of Heat and Mass Transfer, 36(6), 1601-1608.

[6] Mohamad, A., Viskanta, R. (1993). Flow and thermal structures in a lid-driven cavity heated from below. Fluid Dynamics Research, 12(3), 173.

[7] Ogut, E. B. (2017). Effects of Prandtl number and Magnetic field on Mixed Convection Heat Transfer in an Inclined Lid-driven Enclosure. Karaelmas Science and Engineering Journal, 7(1), 145-153.

[8] Ece, M. C., Büyük, E. (2006). Natural-convection flow under a magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls. Fluid Dynamics Research, 38(8), 564.

[9] Chamkha, A. J. (2002). Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal heat generation or absorption. Numerical Heat Transfer: Part A: Applications, 41(5), 529-546.

[10] Chamkha, A. J. (1998). Mixed convection flow along a vertical permeable plate embedded in a porous medium in the presence of a transverse magnetic field. Numerical Heat Transfer, Part A Applications, 34(1), 93-103.

[11] Mahmud, S., Fraser, R. A. (2004). Magnetohydrodynamic free convection and entropy generation in a square porous cavity. International Journal of Heat and Mass Transfer, 47(14-16), 3245-3256.

[12] Yilbas, B. S., Shuja, S. Z., Gbadebo, S. A., Al‐Hamayel, H. A., Boran, K. (1998). Natural convection and entropy generation in a square cavity. International journal of energy research, 22(14), 1275-1290.

[13] Magherbi, M., Abbassi, H., Brahim, A. B. (2003). Entropy generation at the onset of natural convection. International Journal of Heat and Mass Transfer, 46(18), 3441-3450.

[14] Narusawa, U. (2001). The second-law analysis of mixed convection in rectangular ducts. Heat and Mass Transfer, 37(2-3), 197-203.

[15] Mansour, R. B., Galanis, N., Nguyen, C. T. (2006). Dissipation and entropy generation in fully developed forced and mixed laminar convection. International journal of thermal sciences, 45(10), 998-1007.

[16] Tasnim, S. H., Mahmud, S. (2002). Mixed convection and entropy generation in a vertical annular space. Exergy, An International Journal, 2(4), 373-379.

[17] Mahmud, S., Fraser, R. A. (2002). Analysis of mixed convection—Radiation interaction in a vertical channel: Entropy generation. Exergy, an International journal, 2(4), 330-339.

[18] Bellman, R., Kashef, B. G., Casti, J. (1972). Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of computational physics, 10(1), 40-52.

[19] Shu, C. (2000). Mathematical Fundamentals of Differential Quadrature Method: Linear Vector Space Analysis and Function Approximation. In Differential Quadrature and Its Application in Engineering (pp. 1-24). Springer, London.

[20] De Vahl Davis, G. (1983). Natural convection of air in a square cavity: a bench mark numerical solution. International Journal for numerical methods in fluids, 3(3), 249-264. 250 Journal of Thermal Engineering, Research Article, Vol. 5, No. 6, Special Issue 10, pp. 240-251, December, 2019

[21] Shu, C., Ding, H., & Yeo, K. S. (2003). Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier–Stokes equations. Computer methods in applied mechanics and engineering, 192(7-8), 941-954. 251

Published	1 January 2019
Version	v1
Access	Open Access

Published	1 January 2019
Version	v1
Access	Open Access

Second Law Analysis of Mixed Convection of Magnetohydrodynamic Flow in an Inclined Square Lid-Driven

Abstract

References

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Second Law Analysis of Mixed Convection of Magnetohydrodynamic Flow in an Inclined Square Lid-Driven

Abstract

References

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