Darcy–Brinkman bio-thermal convection in a suspension of gyrotactic microorganisms in a porous medium
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On the basis of Darcy–Brinkman model, linear stability analysis is used to study bio-thermal convection in a suspension of gyrotactic microorganisms in a highly porous medium heated from below. A Galerkin method is performed to solve the governing equations generating a correlation between the traditional thermal Rayleigh number and the critical value of the bioconvection Rayleigh number. The effects of three variables including the bioconvection Péclet number, the gyrotaxis number and the modified Darcy number on both the wave number and the critical bioconvection Rayleigh number are analyzed and shown graphically. Results indicate that the critical bioconvection Rayleigh number becomes larger with increasing Darcy number.
KeywordsDarcy–Brinkman model Bioconvection Linear stability Porous medium
This work is supported by the National Natural Science Foundation of China (No.11672164, 51509145, 11672163), Fundamental Research Funds of Shandong University (Grant No.2015JC019) and the Natural Science Foundation of Shandong Province (Grant No. ZR2014AM031, ZR2015EQ005).
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Conflict of interest
The authors declare that there is no conflict of interest.
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