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The purpose of this paper is to investigate the bioconvection flow in a porous square cavity saturated with both oxytactic microorganism and nanofluids.

The impacts of the effective parameters such as Rayleigh number, bioconvection number, Peclet number and thermophoretic force, Brownan motion and Lewis number reduces the flow strength in the cavity on the flow strength, oxygen density distribution, motile isoconcentrations and heat transfer performance are investigated using a finite volume approach.

The results obtained showed that the average Nusselt number is increased with Peclet number, Lewis number, Brownian motion and thermophoretic force. Also, the average Sherwood number increased with Brownian motion and Peclet number and decreased with thermophoretic force. It is concluded that the flow strength is pronounced with Rayleigh number, bioconvection number, Peclet number and thermophoretic force. Brownan motion and Lewis number reduce the flow strength in the cavity.

There is no published study in the literature about sensitivity analysis of Brownian motion and thermophoresis force effects on the bioconvection heat transfer in a square cavity filled by both nanofluid and oxytactic microorganisms.

The purpose of this study is to investigate heat transfer and electrokinetic non-Newtonian flow in a rectangular microchannel in the developed and transient states.

The Carreau–Yasuda model was considered to capture the non-Newtonian behavior of the fluid. The dimensionless forms of governing equations, including the continuity equation for the Carreau–Yasuda fluid, are numerically solved by considering the volumetric force term of electric current (DC).

The impact of pertinent parameters such as electrokinetic diameter (R), Brinkman number and Peclet number is examined graphically. It is observed that for increasing R, the bulk velocity decreases. The velocity of the bulk fluid reaches from the minimum to the maximum state across the microchannel over time. At the electrokinetic diameter of 400, the maximum velocity was obtained. Temperature graphs are plotted with changes in the various Brinkman number (0.1 < Br < 0.7) at different times, and local Nusselt are compared against changes in the Peclet number (0.1 < ℘e < 0.5). The results of this study show that by increasing the Brinkman number from 0.25 to 0.7, the temperature along the microchannel doubles. It was observed that increasing the Peclet number from 0.3 to 0.5 leads to 200% increment of the Nusselt number along the microchannel in some areas along the microchannel. The maximum temperature occurs at Brinkman number of 0.7 and the maximum value of the local Nusselt number is related to Peclet number 0.5. Over time in the transient mode, the Nusselt number also decreases along the microchannel. By the increasing of time, the temperature increases at given value of Brinkman, which is insignificant at Brinkman number of 0.1. The simulation results have been verified by Newtonian and non-Newtonian flows with adequate accuracy.

This study contributes to discovering the effects of transient flow of electroosmotic flow for non-Newtonian Carreau–Yasuda fluid and transient heat transfer through rectangular microchannel. To the authors’ knowledge, the said investigation is yet not available in existing literature.

The purpose of this paper is to numerically investigate the convective heat transfer of water-based CuO nanofluids flowing through a square cross-section duct under constant heat flux in the turbulent flow regime.

The numerical simulation is carried out at various Peclet numbers and particle concentrations (0.1, 0.2, 0.5, and 0.8 vol%). The finite volume formulation is used with the semi-implicit method for pressure-linked equations algorithm to solve the discretized equations derived from the partial nonlinear differential equations of the mathematical model.

The heat transfer coefficients and Nusselt numbers of CuO-water nanofluids increase with increases in the Peclet number as well as particle volume concentration. Also, enhancement of the heat transfer coefficient is much greater than that of the effective thermal conductivity at the same nanoparticle concentration.

Simulation of nanofluids turbulent forced convection at very high Reynolds number is worth for further study.

The heat transfer rates through non-circular ducts are smaller than the circular tubes. Nevertheless, the pressure drop of the non-circular duct is less than that of the circular tube. This study clearly presents that the nanoparticles suspended in water enhance the convective heat transfer coefficient, despite low volume fraction between 0.1 and 0.8 percent. Adding nanoparticles to conventional fluids may enhance heat transfer performance through the non-circular ducts, leading to extensive practical applications in industries for the non-circular ducts.

Few papers have numerically studied convective heat transfer properties of nanofluids through non-circular ducts. The present numerical results show a good agreement with the published experimental data.

A numerical study has been made to investigate the effect of internal heating and precursory cooling during quenching of an infinite tube. The finite difference solution gives the quench front temperature as a function of various model parameters such as Peclet number, Biot number and dimensionless heat flux. The parametric dependence of the rewetting rate is obtained by the condition that the surface can only be wetted when its temperature is below the quench front temperature. Also, the critical heat flux is obtained by setting Peclet number equal to zero, which gives the minimum heat flux required to prevent the hot surface being rewetted. The numerical model is validated by comparing the results with known closed form solutions.

The purpose of this paper is to discuss free convection peristaltic flow in an asymmetric channel with nanofluid containing gyrotactic microorganism.

The governing equations for proposed model are simplified using “long wavelength and low Reynolds number approximation.” Numerical solutions have been presented for “velocity, pressure gradient, the solid volume fraction nanoparticles, temperature profile and density of motile microorganisms.” The effects of various flow parameters, i.e Hartmann number, the solid volume fraction of the nanoparticles amplitude ratio, Prandtl number, bioconvection Péclet number, bioconvection constant, bioconvection Rayleigh number are presented.

The author finds that the pressure rise increases with an increase in Hartmann number, Grashof number bioconvection, Rayleigh number and buoyancy ratio in the peristaltic pumping section.

The peristaltic flow nanofluid containing gyrotactic microorganism is explored in the literature for the first time.

In the present work, a numerical method, based on the well established enthalpy technique, is developed to simulate the growth of binary alloy equiaxed dendrites in presence of melt convection. The paper aims to discuss these issues.

The principle of volume-averaging is used to formulate the governing equations (mass, momentum, energy and species conservation) which are solved using a coupled explicit-implicit method. The velocity and pressure fields are obtained using a fully implicit finite volume approach whereas the energy and species conservation equations are solved explicitly to obtain the enthalpy and solute concentration fields. As a model problem, simulation of the growth of a single crystal in a two-dimensional cavity filled with an undercooled melt is performed.

Comparison of the simulation results with available solutions obtained using level set method and the phase field method shows good agreement. The effects of melt flow on dendrite growth rate and solute distribution along the solid-liquid interface are studied. A faster growth rate of the upstream dendrite arm in case of binary alloys is observed, which can be attributed to the enhanced heat transfer due to convection as well as lower solute pile-up at the solid-liquid interface. Subsequently, the influence of thermal and solutal Peclet number and undercooling on the dendrite tip velocity is investigated.

As the present enthalpy based microscopic solidification model with melt convection is based on a framework similar to popularly used enthalpy models at the macroscopic scale, it lays the foundation to develop effective multiscale solidification.

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.

This study aims to investigate numerically a two-dimensional fully developed mean turbulent fluid flow, and heat transfer in a circular duct is numerically investigated using FORTRAN 95 code that applies the finite difference method to solve the thermal problem for the two thermal boundary conditions, constant surface temperature, constant heat and steady, axisymmetric flow. Several important results have been drawn and discussed from thermal analysis. Finally, the numerical results of the model developed in the document have been validated in good accuracy by comparing them with some correlation results available in the specialized literature.

The methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas' algorithm, a program in FORTRAN version 95 was developed to numerically solve the discretized form of the system of equations describing the problem.

The profiles of the solutions are provided from which the authors infer that the numerical and literature correlation agreed very well. Another result that they obtained from this study is the number of Nusselt in the thermal entrance region to which a parametric study based on Reynolds and Peclet numbers, and the longitudinal coordinate, was carried out and discussed well for the impact of the scientific contribution.

The novelty of the work is the application of the finite difference method programed on the FORTRAN code, as a sequential numerical method of an ODEs system, to determine the number of Nusselt in both uniform wall temperature and wall heat flux uniform.

The purpose of this paper is to develop new semi-empirical heat transfer correlations for turbulent flow of liquid metals in the tubes, and then to compare these correlations with the experimental data. The Prandtl and Reynolds numbers can vary in the ranges: 0.0001 ≤ Pr ≤ 0.1 and 3000 ≤ Re ≤ 10⁶.

The energy conservation equation averaged by Reynolds was integrated using the universal velocity profile determined experimentally by Reichardt for the turbulent tube flow and four different models for the turbulent Prandtl number. Turbulent heat transfer in the circular tube was analyzed for a constant heat flux at the inner surface. Some constants in different models for the turbulent Prandtl number were adjusted to obtain good agreement between calculated and experimentally obtained Nusselt numbers. Subsequently, new correlations for the Nusselt number as a function of a Peclet number was proposed for different models of the turbulent Prandtl number.

The inclusion of turbulent Prandtl number greater than one and the experimentally determined velocity profile of the fluid in the tube while solving the energy conservation equation improved the compatibility of calculated Nusselt numbers, with Nusselt numbers determined experimentally. The correlations proposed in the paper have a sound theoretical basis and give Nusselt number values that are in good agreement with the experimental data.

Heat transfer correlations proposed in this paper were derived assuming a constant heat flux at the inner surface of the tube. However, they can also be used for a constant wall temperature, as for the turbulent flow (Re > 3,000), the relative difference between the Nusselt number for uniform wall heat flux and uniform wall temperature is very low.

Unified, systematic approach to derive correlations for the Nusselt number for liquid metals was proposed in the paper. The Nusselt number was obtained from the solution of the energy conservation equation using the universal velocity profile and eddy diffusivity determined experimentally, and various models for the turbulent Prandtl number. Four different relationships for the Nusselt number proposed in the paper were compared with the experimental data.

The purpose of this study is to investigate the interaction between magnetotactic bacteria and Fe₃O₄–water nanofluid (NF) in a wavy enclosure in the presence of 2D natural convection flow.

Uniform magnetic field (MF), Brownian and thermophoresis effects are also contemplated. The dimensionless, time-dependent equations are governed by stream function, vorticity, energy, nanoparticle concentration and number of bacteria. Radial basis function-based finite difference method for the space derivatives and the second-order backward differentiation formula for the time derivatives are performed. Numerical outputs in view of isolines as well as average Nusselt number, average Sherwood number and flux density of microorganisms are presented.

Convective mass transfer rises if any of Lewis number, Peclet number, Rayleigh number, bioconvection Rayleigh number and Brownian motion parameter increases, and the flux density of microorganisms is an increasing function of Rayleigh number, bioconvection Rayleigh number, Peclet number, Brownian and thermophoresis parameters. The rise in buoyancy ratio parameter between 0.1 and 1 and the rise in Hartmann number between 0 and 50 reduce all outputs average Nusselt, average Sherwood numbers and flux density of microorganisms.

This study implies the importance of the presence of magnetotactic bacteria and magnetite nanoparticles inside a host fluid in view of heat transfer and fluid flow. The limitation is to check the efficiency on numerical aspect. Experimental observations would be more effective.

In practical point of view, in a heat transfer and fluid flow system involving magnetite nanoparticles, the inclusion of magnetotactic bacteria and MF effect provide control over fluid flow and heat transfer.

This is a scientific study. However, this idea may be extended to sustainable energy or biofuel studies, too. This means that a better world may create better social environment between people.

The presence of magnetotactic bacteria inside a Fe₃O₄–water NF under the effect of a MF is a good controller on fluid flow and heat transfer. Since the magnetotactic bacteria is fed by nanoparticles Fe₃O₄ which has strong magnetic property, varying nanoparticle concentration and Brownian and thermophoresis effects are first considered.