Abstract.
The present study discovers the numerical simulations of MHD non-isothermal flow of a micropolar fluid in a porous trapezoidal container under the impact of a constantly heated bottom wall. The top wall of the container is insulated while inclined boundaries have low temperature as compared to the lower boundary. The eminent numerical scheme (FEM) is employed to simulate the nonlinear field equations of the present study. The results are presented in term of streamlines, temperature contours, local and average Nusselt number for diverse values of involved physical parameters. The numerical algorithm is verified against the previously published numerical results. It is observed that the average Nusselt number diminishes with increasing the strength of the applied magnetic field. In contrast, the average Nusselt number increases slightly with enhancing the micro-gyration parameter. The analysis of the present study can be useful in solar engineering for the construction of trapezoidal solar collectors, porous heat exchangers, construction of thermal insulation structures, and geophysical fluid mechanics. The strength of stream function decreases and heat transfer phenomenon inside the cavity becomes conduction dominated with increasing the micropolar parameter.
Similar content being viewed by others
References
T. Basak, S. Roy, A.R. Balakrishnan, Int. J. Heat Mass Transfer 49, 4525 (2006)
T. Basak, S. Roy, I. Pop, Int. J. Heat Mass Transfer 52, 2471 (2009)
T. Basak, S. Roy, S.K. Singh, I. Pop, Int. J. Heat Mass Transfer 52, 4135 (2009)
T. Basak, S. Roy, A. Singh, I. Pop, Int. J. Heat Mass Transfer 52, 70 (2009)
T. Basak, S. Roy, A. Singh, B.D. Pandey, Int. J. Heat Mass Transfer 52, 4413 (2009)
A.C. Eringen, Int. J. Eng. Sci. 2, 205 (1964)
A.C. Eringen, J. Appl. Math. Mech. 16, 1 (1966)
A.C. Eringen, J. Math. Anal. Appl. 38, 480 (1972)
G. Łukaszewicz, Micropolar Fluids: Theory and Application (Birkhäuser, Basel, 1999)
A.C. Eringen, Microcontinuum Field Theories, Vols. I, II (Springer, New York, 2001)
T. Ariman, M.A. Turk, N.D. Sylvester, Int. J. Eng. Sci. 11, 905 (1973)
T. Ariman, M.A. Turk, N.D. Sylvester, Int. J. Eng. Sci. 12, 273 (1974)
M. Turkyilmazoglu, Int. J. Heat Mass Transfer 106, 127 (2017)
M. Turkyilmazoglu, Int. J. Heat Mass Transfer 72, 388 (2014)
M. Turkyilmazoglu, Int. J. Non-Linear Mech. 83, 59 (2016)
N.S. Gibanov, M.A. Sheremet, I. Pop, Int. J. Heat Mass Transfer 99, 831 (2016)
M.A. Sheremet, I. Pop, A. Ishak, Int. J. Heat Mass Transfer 105, 610 (2017)
M. Sheremet, T. Grosan, I. Pop, Int. J. Numer. Methods Heat Fluid Flow 27, 504 (2017)
I.V. Miroshnichenko, M.A. Sheremet, I. Pop, Int. J. Mech. Sci. 120, 182 (2017)
M. Zadravec, M. Hribersek, L. Skerget, Eng. Anal. Bound. Elem. 33, 485 (2009)
S.E. Ahmed, M.A. Mansour, A.K. Hussein, S. Sivasankaran, Eng. Sci. Technol. Int. J. 19, 364 (2016)
T. Javed, M.A. Siddiqui, J. Mol. Liq. 249, 831 (2018)
M. Nazeer, N. Ali, T. Javed, Can. J. Phys. 96, 576 (2018)
N. Ali, M. Nazeer, T. Javed, M.A. Siddiqui, Heat Transf. Res. 49, 457 (2018)
F.M., White, Fluid Mechanics (WCB/McGraw-Hill, Boston, MA, 1999)
T. Basak, S. Roy, S.K. Singh, I. Pop, Int. J. Heat Mass Transfer 52, 4135 (2009)
T. Basak, R.S. Kaluri, A.R. Balakrishnan, Numer. Heat Transf. A 59, 372 (2011)
M. Nazeer, N. Ali, T. Javed, Can. J. Phys. https://doi.org/10.1139/cjp-2017-0904
M. Nazeer, N. Ali, T. Javed, Int. J. Numer. Methods Heat Fluid Flow, https://doi.org/10.1108/HFF-10-2017-0424 (2018)
N. Ali, F. Nazeer, M. Nazeer, Z. Naturforsch. A 73, 265 (2018)
J.N. Reddy, An Introduction to the Finite Element Method (McGraw Hill, New York, 1993)
N. Ali, Z. Asghar, O. Anwar Bég, M. Sajid, J. Theor. Biol. 397, 22 (2016)
T. Javed, Z. Mehmood, M.A. Siddiqui, J. Braz. Soc. Mech. Sci. Eng. 39, 3897 (2017)
M. Nazeer, N. Ali, T. Javed, F. Abbas, Meccanica 53, 3279 (2018)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nazeer, M., Ali, N., Javed, T. et al. Natural convection through spherical particles of a micropolar fluid enclosed in a trapezoidal porous container. Eur. Phys. J. Plus 133, 423 (2018). https://doi.org/10.1140/epjp/i2018-12217-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2018-12217-5