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The present investigation centers around a numerical study of the impact of the presence of phototactic microorganisms on the thermo-bioconvection inside a wavy-walled horizontal porous annulus that is saturated with a Newtonian fluid. Consequently, an equation describing the movement of the microorganism cells is added to the mathematical model of natural convection. The thermal equilibrium, Oberbeck–Boussinesq approximations and Darcy law are taken into consideration. The transformed dimensionless partial differential equations with the temperature-concentration-stream function formulation are discretized applying the alternate direction implicit finite difference scheme. Results confirm that in the absence of microorganisms the Nusselt number decreases with the increase of the amplitude of wall waviness. It was also observed that the wall waviness influence the thermo-bioconvective instabilities and the flow regime structure. [ABSTRACT FROM AUTHOR]

• The Lewis number impacts the onset of thermo-bioconvection. • The hybrid nanofluid enhances the heat transfer in case of thermos-bioconvective flow in a porous horizontal cylindrical annulus. • The waviness parameters impact the flow pattern and the heat transfer rate. • An increase of the bioconvection Rayleigh number enhances the fluid velocity due to extra buoyancy forces. Transport phenomena related to thermo-bioconvection have recently emerged as an intriguing area of study because of their multi-physical applications such as bio-energy systems, food industries, solar collectors, pollutant dispersion in aquifers, biological wastes processing, chemical catalytic converters, geothermal energy usage, petroleum oil reservoirs, enhanced oil recovery, thermal energy storage, chemical processing equipment, fuel cell technology, medical application, microfluidic devices, and others. In this context, it is highly challenging to design and regulate a system with multi-physical transport in a complex geometry. The goal of the current study is to analyze the thermo-bioconvective heat transfer induced by a gradient of temperature and a motile of phototactic microorganisms with the presence of two types of nanoparticles inside a wavy-walled horizontal cylindrical porous annulus. The originality of this investigation is analyzing the influence of microorganisms, waviness parameters and hybrid nanofluid on thermo-convective instabilities. The effects of the wall waviness parameters, bioconvection Rayleigh number (R a b), thermal Rayleigh number (R a T), nanoparticles volume fraction ϕ and Lewis number (L e) on the flow structure, temperature, and isoconcentrations of microorganisms are investigated and explained in detail. The key findings showed that the Lewis number impacts the onset of thermo-convection and bioconvection and convection phenomena begins rapidly for small values of Lewis number. The nanoparticles enhance the heat transfer in case of thermo-bioconvective flow in a horizontal porous cylindrical system. The average Nusselt number N u ¯ decreases as the wall waviness parameters, amplitude λ , and undulation number η increase. It was also shown that thermo-convective instabilities may develop depending on thermal Rayleigh number, bioconvection Rayleigh number, nanoparticles volume fraction and wall waviness parameters. [ABSTRACT FROM AUTHOR]

The effect of temperature modulation on natural convection in a horizontal porous annulus is investigated in this paper. The porous medium is confined between the inner and outer cylinders of the annulus which is subjected to time-dependent temperature. It is assumed that the time-dependent modulation is periodic with frequency σ and amplitude λ. The model consists of the heat equation and the equations of motion under the Darcy law. The derived problem with the stream function-temperature formulation is solved numerically using the alternating direction implicit method. It is shown that a stabilizing effect can be gained for appropriate values of the frequency σ and the amplitude λ. [ABSTRACT FROM AUTHOR]