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The purpose of this paper is to investigate a combined bioconvection and thermal instability problem in a horizontal layer of finite depth with a basic temperature gradient inclined to the vertical. The basic flow, driven by the horizontal component of temperature gradient, is the Hadley circulation, which becomes unstable when the vertical temperature difference and density stratification induced by upswimming of microorganisms that are heavier than water become sufficiently large.

Linear stability analysis of the basic state is performed; the numerical problem is solved using the collocation method.

The steady‐state solution of this problem is obtained. Linear stability analysis of this steady‐state solution for the case of three‐dimensional disturbances is performed; the numerical problem is solved using the collocation method. The stability problem is governed by three Rayleigh numbers: the bioconvection Rayleigh number and two thermal Rayleigh numbers characterizing temperature gradients in the vertical and horizontal directions, respectively.

Further research should address the application of weakly non‐linear analysis to this problem.

The dependence of the critical bioconvection Rayleigh number on the two thermal Rayleigh numbers and other relevant parameters is investigated.

This paper presents what is believed to be the first research dealing with the effect of inclined temperature gradient on the stability of bioconvection in a suspension of gyrotactic microorganisms.

The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface.

Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters.

It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically.

Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.

The aim of this paper is to investigate the onset of bio‐thermal convection in a shallow fluid layer; the convection is thus driven by the combined effect of swimming of oxytactic microorganisms and inclined temperature gradient.

Linear stability analysis of the basic state is performed; the numerical problem is solved using the collocation method.

The most interesting outcome of this analysis is the correlation between three Rayleigh numbers, two traditional, “thermal” Rayleigh numbers, which are associated with the vertical and horizontal temperature gradients in the fluid layer, and the bioconvection Rayleigh number, which is associated with the density variation induced by the upswimming of microorganisms.

Further research should address the application of weakly nonlinear analysis to this problem.

The increase of the horizontal thermal Rayleigh number stabilizes the basic flow. The effect of increasing the horizontal thermal Rayleigh number is to distort the basic temperature profile away from the linear one. The increase of the Schmidt number stabilizes the basic flow. The increase of the Prandtl number first causes the bioconvection Rayleigh number to decrease and then to increase.

To the best of the authors’ knowledge, this is the first research dealing with the effect of inclined temperature gradient on the stability of bioconvection.

The purpose of this paper is to investigate the stability of a suspension containing both gyrotactic and oxytactic microorganisms for the case when the suspension occupies a horizontal layer of finite depth. The lower boundary of the layer is assumed rigid while at the upper boundary both situations of rigid and stress‐free boundary conditions are considered.

Linear instability analysis is utilized, and the obtained eigenvalue problem is solved analytically using a one‐term Galerkin method.

The obtained eigenvalue equation relates three Rayleigh numbers, the traditional thermal Rayleigh number and two bioconvection Rayleigh numbers, for gyrotactic and oxytactic microorganisms.

Only the case of non‐oscillatory instability (which always occurs when heating from the bottom is considered) is analyzed. Further experimental research is needed to elucidate possible interaction between gyrotactic and oxytactic microorganisms. The developed theory is applicable only for dilute suspensions.

This paper extends the traditional theory of bio‐thermal convection to the case when the suspension contains two types of motile microorganisms exhibiting different behaviors.

The purpose of this study is to investigate the influence of the second order slip velocity on the boundary layer stagnation point flow of a nanofluid past a non-aligned stretching/shrinking sheet.

Proper similarity variables are used to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then solved numerically using the bvp4c solver in MATLAB software. As in the papers by Kuznetsov and Nield (2010, 2013) and Fang et al. (2009), the authors considered the stretching/shrinking parameter λ, the first-order (a₁, a₂) and second-order (b₁) slip parameters and the Lewis number Le, Nb the Brownian parameter and Nt the thermophoresis parameter fixed at Le = 10, Nb = Nt = 0.5 when the Prandtl number Pr is fixed at Pr = 1.

Dual solutions are found as the sheet is shrunk in the horizontal direction. Stability analysis shows that the first solution is physically realizable, whereas the second solution is not practicable.

The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Wang (2008) and Lok et al. (2011) to the case of nanofluids.

The purpose of this paper is to present a numerical investigation of the transient two-dimensional natural convective boundary-layer flow of a nanofluid past an isothermal vertical plate by incorporating the effects of Brownian motion and thermophoresis in the mathematical model.

The problem is formulated using the Oberbeck–Boussinesq and the standard boundary-layer approximations. The governing coupled non-linear partial differential equations for conservation of mass, momentum, thermal energy and nanoparticle volume fraction have been solved by using an efficient implicit finite-difference scheme of the Crank–Nicolson type, which is stable and convergent. Numerical computations are performed and the results for velocity, temperature and nanoparticle volume fraction are presented in graphs at different values of system parameters such as Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, Prandtl number, Lewis number and dimensionless time. The results for local and average skin-friction and Nusselt number are also presented graphically and discussed thoroughly.

It is found that the velocity, temperature and nanoparticle volume fraction profiles enhance with respect to time and attain steady-state values as time progresses. The local Nusselt number is found to decrease with increasing thermophoresis parameter, while it increases slightly with increasing Brownian motion parameter. To validate the present numerical results, the steady-state local Nusselt number results for the limiting case of a regular fluid have been compared with the existing well-known results at different Prandtl numbers, and the results are found to be in an excellent agreement.

The present analysis is limited to the transient laminar natural convection flow of a nanofluid past an isothermal semi-infinite vertical plate in the absence of viscous dissipation and thermal radiation. The unsteady natural convection flow of a nanofluid will be investigated for various physical conditions in a future work.

Unsteady flow devices offer potential performance improvements as compared with their steady-state counterparts, and the flow fields in the unsteady flow devices are typically transient in nature. The present study provides very useful information for heat transfer engineers to understand the heat transfer enhancement with the nanofluid flows. The present results have immediate relevance in cooling technologies.

The present research work is relatively original and illustrates the transient nature of the natural convective nanofluid boundary-layer flow in the presence of Brownian motion and thermophoresis.

This paper aims to study the magnetohydrodynamic (MHD)-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganism.

The benefits of adding motile microorganisms to the suspension include enhanced mass transfer, microscale mixing and anticipated improved stability of the nanofluid. The model includes equations expressing conservation of total mass, momentum, thermal energy, nanoparticles, microorganisms and oxygen. Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model.

It has been found that the Hartmann number suppresses the heat and mass transfer, while the cavity and magnetic field inclination angles characterize a non-monotonic behavior of the all considered parameters. A rise of the Hartmann number leads to a reduction of the influence rate of the magnetic field inclination angle.

The present results are original and new for the study of MHD-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganisms.

The paper aims to present the advanced mathematical and numerical models of conjugated heat and mass transfer in a multi-layer protective clothing, human skin and muscle subjected to incident external radiative heat flux.

The garment was made of three layers of porous fabric separated by the air gaps, whereas in the tissue, four skin sublayers and muscle layer were distinguished. The mathematical model accounted for the coupled heat transfer by conduction and thermal radiation with the associated phase transition of the bound water in the fabric fibres and diffusion of the water vapour in the clothing layers and air gaps. The skin and muscle were modelled with two equation model which accounted for heat transfer in the tissue and arterial blood. Complex thermal and mass transfer conditions at the internal or external boundaries between the fabric layers, air gaps and skin were assumed. Special attention was paid to modelling of thermal radiation emitted by external heat source, for example, a fire, penetrating through the protective clothing and being absorbed by the skin and muscle.

Temporal and spatial variations of temperature in the protective garment, skin and muscle, as well as volume fractions of the water vapour and bound water in the clothing, were calculated for various intensity of incident radiative heat flux. The results of numerical simulation were used to estimate the risk of the first-, second- and third-degree burns.

Because of the small thickness of the considered system in comparison to its lateral dimensions, the presented model was limited to 1D heat and moisture transfer. The convective heat transfer through the clothing was neglected.

The model may be applied for design of the new protective clothing and for assessment of thermal performance of the various types of protective garments. Additionally, the proposed approach may be used in the medicine for estimation of degree of thermal destruction of the tissue during treatment of burns.

The novel advanced thermal model of the multi-layer protective garment, skin and muscle layer was developed. For the first time, non-grey optical properties and various optical phenomena at the internal or external boundaries between the fabric layers, air gaps and skin were accounted for during simulation of thermal interactions between the external heat source (e.g. a fire), protective clothing and human skin.

This study aims to explore magnetohydrodynamic (MHD) thermo-bioconvection of oxytactic microorganisms in multi-physical directions addressing thermal gradient, lid motion, porous substance and magnetic field collectively using a typical differentially heated two-sided lid-driven cavity. The consequences of a range of pertinent parameters on the flow structure, temperature, oxygen isoconcentration and microorganisms’ isoconcentration are examined and explained in great detail.

Two-dimensional governing equations in a two-sided lid-driven porous cavity heated differentially and packed with oxytactic microorganisms under the influence of the magnetic field are solved numerically using the finite volume method-based computational fluid dynamics code. The evolved flow physics is analyzed assuming a steady laminar incompressible Newtonian flow within the validity of the Boussinesq approximation. The transport of oxytactic microorganisms is formulated by augmenting the continuum model.

The mechanisms involved with MHD-mixed thermo-bioconvection could have potential benefits for industrial exploitation. The distributions of fluid flow, temperature, oxygen and motile microorganisms are markedly modified with the change of convection regime. Both speed and direction of the translating walls significantly influence the concentration of the motile microorganisms. The concentration of oxygen and motile microorganisms is found to be higher at the upper portion of the cavity. The overall patterns of the fluid flow, temperature and the oxygen and microorganism distributions are markedly affected by the increase of magnetic field strength.

The concept of the present study could be extended to other areas of bioconvection in the presence of gravity, light or chemical attraction.

The findings of the present study could be used to multi-physical applications like biomicrosystems, pollutant dispersion in aquifers, chemical catalytic converters, geothermal energy usage, petroleum oil reservoirs, enhanced oil recovery, fuel cells, thermal energy storage and others.

The MHD-mixed thermo-bioconvection of oxytactic microorganisms is investigated under different parametric conditions. The effect of pertinent parameters on the heat and mass transfers are examined using the Nusselt number and Sherwood number.

The purpose of this study is to address magnetohydrodynamic (MHD) bioconvection caused by the swimming of oxytactic microorganisms in a linearly heated square cavity filled with porous media and Cu–water nanofluid. The effects of different multiphysical aspects are demonstrated using local distributions as well as global quantities for fluid flow, temperature, oxygen concentration and microorganisms population.

The coupled transport equations are converted into the nondimensional partial differential equations, which are solved numerically using a finite volume-based computing code. The flow of Cu–water nanofluid through the pores of porous media is formulated following the Brinkman–Forchheimer–Darcy model. The swimming of oxytactic microorganisms is handled following a continuum model.

The analysis of transport phenomena of bioconvection is performed in a linearly heated porous enclosure containing Cu–water nanofluid and oxytactic microorganisms under the influence of magnetic fields. The application of such a system could have potential impacts in diverse fields of engineering and science. The results show that the flow and temperature distribution along with the isoconcentrations of oxygen and microorganisms is markedly affected by the involved governing parameters.

Similar study of bioconvection could be extended further considering thermal radiation, chemical attraction, gravity and light.

The outcomes of this investigation could be used in diverse fields of multiphysical applications, such as in food industries, chemical processing equipment, fuel cell technology and enhanced oil recovery.

The insight of the linear heating profile reveals a special attribute of simultaneous heating and cooling zones along the heated side. With such an interesting feature, the MHD bioconvection of oxytactic microorganisms in nanofluid-filled porous substance is not reported so far.