Natural convection boundary layer flow over a truncated cone in a porous medium saturated by a nanofluid

This work studies the natural convection boundary layer flow over a truncated cone embedded in a porous medium saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A suitable coordinate transformation is performed, and the obtained nonsimilar equations are solved by the cubic spline collocation method. The effect of the Brownian motion parameter and thermophoresis parameter on the temperature, nanoparticle volume fraction and velocity profiles are discussed. The effects of the thermophoresis parameter, Brownian parameter, Lewis number, and buoyancy ratio on the local Nusselt number have been studied. Results show that an increase in the thermophoresis parameter or the Brownian parameter tends to decrease the local Nusselt number. Moreover, the local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased.     

Free convection of non-Newtonian nanofluids about a vertical truncated cone in a porous medium

This work studies the free convection heat transfer over a truncated cone embedded in a porous medium saturated by a non-Newtonian power-law nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar equations are solved by the cubic spline collocation method. The effects of the power-law index, Brownian motion parameter, thermophoresis parameter and buoyancy ratio on the temperature, nanoparticle volume fraction and velocity profiles are discussed. The reduced Nusselt numbers are plotted as functions of the power-law index, thermophoresis parameter, Brownian parameter, Lewis number, and buoyancy ratio. Results show that increasing the thermophoresis parameter or the Brownian parameter tends to decrease the reduced Nusselt number. Moreover, the reduced Nusselt number increases as the power-law index is increased.     

Free convection heat and mass transfer from a horizontal cylinder of elliptic cross section in micropolar fluids

This work examines the natural convection heat and mass transfer near a horizontal cylinder of elliptic cross section with constant wall temperature and concentration in a micropolar fluid. The transformed governing equations are then solved by the cubic spline collocation method. Results for local Nusselt and Sherwood numbers are presented as functions of vortex viscosity parameter and aspect ratio. The heat and mass transfer rates of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, the heat and mass transfer rates from an elliptical cylinder in Newtonian fluids are higher than those in micropolar fluids.     

The effect of temperature-dependent viscosity on the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature-dependent viscosity. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of viscosity-variation parameter, aspect ratio, and Prandtl number. The total heat transfer rate and the total skin friction of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, increasing the viscosity-variation parameter tends to enhance the heat transfer rates from a horizontal elliptical cylinder.     

Natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and internal heat generation

In this paper the natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and temperature dependent internal heat generation is investigated. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. An increase in the aspect ratio of the elliptical cylinder decreases the average surface temperature of the elliptical cylinder with blunt orientation, while it increases the average surface temperature of the elliptical cylinder with slender orientation. Moreover, an increase in the heat generation parameter for natural convection flow over a horizontal elliptic cylinder with constant heat flux leads to an increase in the average surface temperature of the elliptical cylinder.     

Boundary-layer flow of nanofluids over a moving surface in a flowing fluid

The steady boundary-layer flow of a nanofluid past a moving semi-infinite flat plate in a uniform free stream is investigated. The plate is assumed to move in the same or opposite directions to the free stream. The resulting system of nonlinear ordinary differential equations is solved numerically using the Keller-box method. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and the nanoparticle volume fraction profiles for some values of the governing parameters, namely, the plate velocity parameter, Prandtl number, Lewis number, the Brownian motion parameter and the thermophoresis parameter. The results indicate that dual solutions exist when the plate and the free stream move in the opposite directions.     

Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet

The unsteady boundary layer flow of a nanofluid over a permeable stretching/shrinking sheet is theoretically studied. The governing partial differential equations are transformed into ordinary ones using a similarity transformation, before being solved numerically. The results are obtained for the skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and the nanoparticle fraction profiles for some values of the governing parameters, namely, the unsteadiness parameter, the mass suction parameter, the Brownian motion parameter, the thermophoresis parameter, Prandtl number, Lewis number and the stretching/shrinking parameter. It is found that dual solutions exist for both stretching and shrinking cases. The results also indicate that both unsteadiness and mass suction widen the range of the stretching/shrinking parameter for which the solution exists.     

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

Double diffusion from a horizontal cylinder of elliptic cross section with uniform wall heat and mass fluxes in a porous medium

This work studies the double diffusion near a horizontal cylinder of elliptic cross section with uniform wall heat and mass fluxes in a fluid-saturated porous medium. A coordinate transformation is used to obtain the non-similar governing boundary layer equations. The transformed equations are solved numerically by an efficient cubic spline collocation method. Results for the local surface temperature and the local surface concentration are presented as functions of the Lewis number, the buoyancy ratio, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). As the Lewis number is increased, the local surface concentration decreases while the local surface temperature increases. Moreover, an increase in the buoyancy ratio tends to decrease both the local surface temperature and the local surface concentration.     

A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model

This work uses a thermal non-equilibrium model to study the free convection boundary layer flow driven by temperature gradients near a permeable horizontal cylinder of elliptic cross-section with constant wall temperature in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar boundary layer equations. The transformed boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt numbers are presented as functions of the porosity scaled thermal conductivity ratio, the heat transfer coefficient between solid and fluid phases, the transpiration parameter, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). An increase in the porosity scaled thermal conductivity ratio or the heat transfer coefficient between the solid and fluid phases increases the heat transfer rates. Moreover, the use of suction (positive transpiration parameter) tends to increase the heat transfer rates between the porous medium and the surface.     

Stagnation point flow of Maxwell nanofluid containing gyrotactic micro‐organism impinging obliquely on a convective surface

A numerical study is performed to discuss the nonaligned stagnation of a rate type fluid over a convective surface. The rheology of the fluid is presented by the constitutive equation of the Maxwell fluid model. Buongiorno's model is used to elaborate on the effects of Brownian motion and thermophoresis and motile microorganisms are introduced for the stability of the nanoparticles. The governing equations were solved by the implicit finite difference method. Graphical illustrations for velocity, temperature, nanoparticle concentration and motile microorganism profiles for various involved parameters are presented for both convective and nonconvective surfaces. It is depicted that the temperature, nanoparticle, and microorganism concentration profiles decease while both axial and tangential velocities increase with the velocity ratio parameter for both Newtonian and Maxwellian fluids. The magnitude of temperature, nanoparticle, and microorganism concentration profiles is large for the nonconvective surface as compared to the convective surface. The Nusselt number, Sherwood number, and motile organism number decrease as we move from Newtonian fluid to non‐Newtonian fluid. Furthermore, the increase in the Brownian motion parameter and thermophoresis parameter decreases the density of the motile organism over the convective as well as nonconvective surface.     

The onset of natural convection in a horizontal nanofluid layer heated from below

A linear stability analysis is performed for the onset of natural convection in a horizontal nanofluid layer heated from below. The motion of nanoparticles is characterized by both the thermophoresis and Brownian diffusion effects. Different from previous studies in the literature, both the dependences of thermophoresis on nanoparticle volume fraction and Brownian motion on temperature are taken into consideration in the theoretical model. The result reveals that the base flow is mainly dominated by the effect of thermophoresis and the Brownian diffusion coefficient can be treated as a constant reasonably when a finite temperature difference is imposed across the nanofluid layer. Accordingly, a novel base solution of nanoparticle volume fraction is derived. It is found that the profile of nanoparticle concentration depends heavily on the magnitude of thermophoretic diffusion, which may exhibit a nonlinear distribution across the nanofluid layer once the effect of thermophoresis is significant. The suspended nanoparticles produce a strong destabilizing effect and a tiny volume fraction of nanoparticles is sufficient to trigger the onset of convection and make the nanofluid layer become unconditionally unstable. The dispersion spectra of unstable modes are demonstrated and the most unstable mode with the maximum growth rate is explored. The growth rate of the most unstable mode is found to increase significantly with increasing nanoparticle concentration, while the influence of heat capacity ratio of nanoparticle to base fluid on the behavior of thermal convection is negligible.     

Numerical investigation of MHD convective free stream nanofluid flow influenced by radiation and chemical reaction over stretching cylinder

Chemically reacting magnetohydrodynamic radiative flow of convective free stream nanofluid through a stretching cylinder using Buongiorno's model is discussed. The behavior of Brownian motion and thermophoresis is also appropriate. By adopting the similarity transformation, the partial differential equation is diminished into a first-order ordinary differential equation (ODE). Since transformed equations are highly nonlinear these ODEs are solved by using mathematical simulation. The shooting procedure has been adopted to resolve converted equations along the attendant Runge–Kutta–Fehlberg technique. The reason behind the present work is to research the effects of different parameters of fluid, namely, magnetic parameter, free stream velocity, Brownian motion, thermophoresis, chemical reaction, heat radiation, Lewis number on nanoparticle concentration, temperature, and velocity distribution. The impact of significantly participating parameters on velocity, concentration, and temperature distribution is distinguished with appropriate physical significance. The convergence of solutions for temperature, velocity, and concentration profiles is studied carefully. The measured challenges of nanofluids are scale-up capacity, increase in nanofluid viscosity, nanoparticle dispersion, and nanofluid cost. It is observed that nanoparticle temperature rises for more value of Brownian motion parameter while it declines for higher Lewis number. The current study in the cylindrical region is related to novel free stream flow in the presence of chemical reactions along with convective conditions which find applications in electronic systems like microprocessors and in a wide variety of industries and in the field of biotechnology. The current research helps control the transport phenomena, helping production companies to find the quality of the desired product.     

A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a horizontal concentric annulus

A numerical study of transient natural convection heat transfer of aqueous nanofluids in a horizontal annulus between two coaxial cylinders is presented. The effective thermophysical properties of water in the presence of copper oxide nanoparticles with four different volume fractions are predicted using existing models, in which the effects of the Brownian motion of nanoparticles are taken into consideration. The predicted development of convective flow and heat transfer of nanofluids is presented by means of the average Nusselt number over the outer cylinder. The flow development time towards a steady state and the time-averaged Nusselt number are predicted and scaled with Rayleigh number. It is shown that at constant Rayleigh numbers, the time-averaged Nusselt number is gradually lowered as the volume fraction of nanoparticles is increased. In addition, the time-averaged Nusselt number will be overestimated if the Brownian motion effects are not considered.     

Numerical analysis of MHD nanofluid flow over a wedge,including effects of viscous dissipation and heat generation/absorption,using Buongiorno model

The key purpose of this article is to examine magnetohydrodynamics flow, generative/absorptive heat, and mass transfer of nanofluid flow past a wedge in the presence of viscous dissipation through a porous medium. The investigation is completely theoretical, and the present model expresses the influence of Brownian motion and thermophoresis using the nanofluid Buongiorno model. The fundamental model of partial differential equations is reframed into the structure of ordinary differential equations implementing the nondimensional similarity transformation, which are tackled through the fourth–fifth-order Runge–Kutta–Fehlberg algorithm together with the shooting scheme. The analysis of sundry nondimensional controlling parameters, such as magnetic parameter, Eckert number, heat generation/absorption parameter, porosity parameter, Brownian motion parameter, and thermophoresis parameter on velocity, temperature, and concentration profiles are discussed graphically. The effects of the physical factors on the rate of momentum and heat and mass transfer are also determined with appropriate analysis in terms of skin friction, Nusselt number, and Sherwood number. The outcomes illustrate that the local Nusselt number and local Sherwood number are reduced for higher values of the thermophoresis parameter. Besides, it is found that higher estimations of heat generation/absorption and viscous dissipation parameters increase temperature. Moreover, it is found that the temperature profile increases with the involvement of the Brownian motion parameter, while an opposite trend is observed in the concentration profile. A comparison is also provided for limiting cases to authenticate our obtained results.     

Coupled heat and mass transfer by natural convection adjacent to a permeable horizontal cylinder in a saturated porous medium

The heat and mass transfer characteristics of free convection about a permeable horizontal cylinder embedded in porous media under the coupled effects of thermal and mass diffusion are numerically analyzed. The surface of the horizontal cylinder is maintained at a uniform wall temperature and uniform wall concentration. The transformed governing equations are obtained and solved by Keller box method. Numerical results for the dimensionless temperature profiles, the dimensionless concentration profiles, the Nusselt number and the Sherwood number are presented. Increasing the buoyancy ratio N and the transpiration parameter f_w increases the Nusselt number and the Sherwood number. For thermally assisting flow, when Lewis number Le increases, the Nusselt (Sherwood) number decreases (increases). Whereas, for thermally opposing flow, both the Nusselt number and the Sherwood number increase with increasing the Lewis number.     

Natural convective boundary-layer flow of a nanofluid past a vertical plate

The natural convective boundary-layer flow of a nanofluid past a vertical plate is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented. This solution depends on a Lewis number Le, a buoyancy-ratio number Nr, a Brownian motion number Nb, and a thermophoresis number Nt. For various values of Pr and Le, the variation of the reduced Nusselt number with Nr, Nb and Nt is expressed by correlation formulas. It was found that the reduced Nusselt number is a decreasing function of each of Nr, Nb and Nt.     

Flow and heat transfer in a porous medium saturated with a Sisko nanofluid over a nonlinearly stretching sheet with heat generation/absorption

This work is focused on steady flow and heat transfer in a porous medium saturated with a Sisko nanofluid (non‐Newtonian power‐law) over a nonlinearly stretching sheet in the presence of heat generation/absorption. Nonlinear PDEs are transformed into a system of coupled nonlinear ODEs with related boundary conditions using similarity transformation. The reduced equations are then solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method (RKF45) with Maple 14.0 software. The solutions depend on the power‐law index n and the effect of pertinent parameter such as the Brownian motion parameter, thermophoresis parameter, Lewis number, the permeability, and the heat generation/absorption on the dimensionless velocity, temperature, and nanoparticles volume fraction and also on the skin friction, local Nusselt, and Sherwood numbers are produced for values of the influence parameter. A rapprochement of the numerical results of the actual study with formerly published data detected an excellent agreement.     

Stagnation Point Flow of a Nanofluid Past a Permeable Cylinder with Chemical Reaction

The primary objective of the present paper is to investigate the novel aspect of nanofluid flow near the stagnation‐point past a permeable cylinder with chemical reaction. The prescribed surface heat and nanoparticle fluxes are also taken into account. The improved homotopy analysis method is introduced to obtain the recursively analytic solutions with high precision. The convergence of the obtained series solution is discussed explicitly. Besides, the effects of physically significant parameters on skin friction coefficient, local Nusselt number, local Sherwood number, as well as profiles of velocity, temperature, and nanoparticle volume fraction are examined and discussed in detail. It is found that the local Sherwood number increases when a chemical reaction occurs in the nanofluid. It is also indicated that the increase of the reaction rate parameter leads to a higher temperature and a lower nanoparticle volume fraction.     

Rayleigh–Benard convection in water-based alumina nanofluid: A numerical study

Rayleigh–Benard (R-B) convection in water-based alumina (Al₂O₃) nanofluid is analyzed based on a single-component non-homogeneous volume fraction model (SCNHM) using the lattice Boltzmann method (LBM). The present model accounts for the slip mechanisms such as Brownian and thermophoresis between the nanoparticle and the base fluid. The average Nusselt number at the bottom wall for pure water is compared to the previous numerical data for natural convection in a cavity and a good agreement is obtained. The parameters considered in this study include the Rayleigh number of the nanofluid, the volume fraction of alumina nanoparticle and the aspect ratio of the cavity. For the Al₂O₃/water nanofluid, it is found that heat transfer rate decreases with an increase of the volume fraction of the nanoparticle. The results are demonstrated and explained with average Nusselt number, isotherms, streamlines, heat lines, and nanoparticle distribution. The effect of nanoparticles on the onset of instability in R-B convection is also analyzed.