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Effect of oblique irradiation on the onset of thermal phototactic bioconvection in non-scattering medium

S. K. Rajput, M. K. Panda

Abstract

The linear stability of a suspension of phototactic algae is investigated numerically with particular emphasis on the effects of the angle of incidence of the illuminating oblique collimated irradiation with thermal effects. The suspension is illuminated by the oblique collimated irradiation from the top and heated/cooled from the bottom. The linear stability analysis shows that the suspension becomes more unstable as the angle of incidence increases.

Effect of oblique irradiation on the onset of thermal phototactic bioconvection in non-scattering medium

Abstract

The linear stability of a suspension of phototactic algae is investigated numerically with particular emphasis on the effects of the angle of incidence of the illuminating oblique collimated irradiation with thermal effects. The suspension is illuminated by the oblique collimated irradiation from the top and heated/cooled from the bottom. The linear stability analysis shows that the suspension becomes more unstable as the angle of incidence increases.
Paper Structure (13 sections, 83 equations, 3 figures)

This paper contains 13 sections, 83 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. MATHEMATICAL FORMULATION
  3. Phototaxis coupled with self-shading in suspensions of algae
  4. Governing equations
  5. Boundary conditions
  6. Scaling of the equations
  7. The basic solution
  8. Linear stability of the problem
  9. SOLUTION PROCEDURE
  10. NUMERICAL RESULTS
  11. Case I: Stress-free upper surface
  12. Case-II: Rigid upper surface
  13. Conclusion

Figures (3)

  • Figure 1: Oblique collimated irradiation on the upper surface of an absorbing and non-scattering algal suspension with thermal effect on the lower surface.
  • Figure 2: The Neutral curves for various values of the angle of incidence $\theta_i$. Here, the upper surface is stress-free and the other governing parameters $V_c=10$, $\tau_H=0.5$ and $R_T=50$ are fixed.
  • Figure 3: The Neutral curves for various values of the angle of incidence $\theta_i$. Here, the upper surface is rigid and the other governing parameters $V_c=10$, $\tau_H=1$ and $R_T=50$ are fixed.