Numerical Investigation of Thermo-Bioconvection of Oxytactic Micro-Organism in a Tilted Square Porous Cavity Heated Sinusoidally

Abstract

This study examines the thermo-bioconvective flow in a square tilted porous cavity heated sinusoidally and contains oxytactic microorganisms. The bio-convection flow in porous material is formulated using the Darcy model with Boussinesq approximation. The governing equations are expressed in terms of dimensionless stream function, concentrations, and temperature. For a wide variety of relevant parameters, including bioconvection Rayleigh number Rb = 100, 10, Rayleigh number Ra = 100, 10, Lewis number Le = 10, 1 Peclet number Pe = 1, 0.1, and slanted angle (ɛ) = 0°, 30°, 60°, 90°, numerical results are produced using the implicit finite difference approach. Average Nusselt number (<mml:math><mml:mover><mml:mrow><mml:mi>N</mml:mi><mml:mi>u</mml:mi></mml:mrow><mml:mo accent="false">¯</mml:mo></mml:mover></mml:math>), Average Sherwood number of oxygen concentration (<mml:math><mml:mover><mml:mrow><mml:mi>S</mml:mi><mml:mi>h</mml:mi></mml:mrow><mml:mo accent="false">¯</mml:mo></mml:mover></mml:math>), and average Sherwood number of microorganisms (<mml:math><mml:mover><mml:mrow><mml:mi>N</mml:mi><mml:mi>n</mml:mi></mml:mrow><mml:mo accent="false">¯</mml:mo></mml:mover></mml:math>) are thoroughly analyzed. It has been found that effect of tiltedness (ɛ) of the cavity on average Sherwood number of microorganism (<mml:math><mml:mover><mml:mrow><mml:mi>N</mml:mi><mml:mi>n</mml:mi></mml:mrow><mml:mo accent="false">¯</mml:mo></mml:mover></mml:math>) is insignificant at left wall and at the right wall average Sherwood number of microorganism (<mml:math><mml:mover><mml:mrow><mml:mi>N</mml:mi><mml:mi>n</mml:mi></mml:mrow><mml:mo accent="false">¯</mml:mo></mml:mover></mml:math>) is highly influenced by ɛ. Also tiltedness of the cavity weakens the flow strength for higher bioconvection Rayleigh number at Pe = 0.1.