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This paper aims to investigate numerically buoyancy-induced convection from a pair of differentially heated horizontal circular cylinders set side by side in a nanofluid-filled adiabatic square enclosure, inclined with respect to gravity so that the heated cylinder is located below the cooled one, using a two-phase model based on the double-diffusive approach assuming that the Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase.

The system of the governing equations of continuity, momentum and energy for the nanofluid, and continuity for the nanoparticles, is solved by a computational code based on the SIMPLE-C algorithm. Numerical simulations are performed for Al₂O₃ + H₂O nanofluids using the average volume fraction of the suspended solid phase, the tilting angle of the enclosure, the nanoparticle size, the average nanofluid temperature and the inter-cylinder spacing, as independent variables.

The main results obtained may be summarized as follows: at high temperatures, the nanofluid heat transfer performance relative to that of the pure base liquid increases with increasing the average volume fraction of the suspended solid phase, whereas at low temperatures it has a peak at an optimal particle loading; the relative heat transfer performance of the nanofluid has a peak at an optimal tilting angle of the enclosure; the relative heat transfer performance of the nanofluid increases notably as the average temperature is increased, and just moderately as inter-cylinder spacing is increased and the nanoparticle size is decreased.

The two-phase computational code used in the present study incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity and the coefficient of thermophoretic diffusion, all based on a high number of literature experimental data.

The purpose of this paper is to theoretically investigate the effects of nanoparticle migration on the heat transfer enhancement at film boiling of nanofluids. The modified Buongiorno model is used for modeling the nanofluids to observe the effects of nanoparticle migration.

The governing partial differential equations including continuity, momentum, energy and nanoparticle continuity are transformed to ordinary ones and solved numerically. For nanoparticle distribution, an analytical expression has been found. The results have been obtained for different parameters, including the Brownian motion to thermophoretic diffusion N_BT, saturation nanoparticle volume fraction ϕ_sat and normal temperature difference.

A closed-form expression for nanoparticle distribution is obtained, and it is indicated that nanoparticle migration significantly affects the flow fields and thermophysical properties of nanofluids. It was shown that temperature gradient at heated wall grows as the migration of nanoparticles increases, which has positive effects on the heat transfer rate. However, decrement of thermal conductivity at heated wall because of nanoparticle depletion plays a negative role in heat transfer enhancement. In fact, there is a tradeoff between thermal conductivity reduction and an increment in temperature gradient at the wall, which determines the net enhancement/deterioration of the heat transfer rate.

Flow has been assumed to be laminar, and the vapor temperature is constant such that boiling is the only heat transfer mechanism between the liquid-vapor interface. Also, the shear stress at the liquid-vapor interface is assumed to be negligible. The film thickness is small relative to the plate length to justify the boundary layer assumptions. Inertia forces are neglected relative to shear stress forces.

Outcomes of the present study are suitable for several heat exchange purposes such as evaporation and condensation in heat pipes, immersion, microchannel cooling of microelectronics and crystal growth.

The novelty of this paper has three aspects: modeling the film boiling of nanofluids considering the effects of nanoparticle migration; how it influences the cooling performance; and an analytical expression for the nanoparticle distribution at film boiling of nanofluids.

The purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick heat-radiating nanofluid over a linearly stretching sheet in the presence of uniform transverse magnetic field taking Dufour and Soret effects into account.

The governing boundary layer equations are transformed into a set of highly non-linear ordinary differential equations using suitable similarity transforms. Finite element method is used to solve this boundary value problem. Effects of pertinent flow parameters on the velocity, temperature, solutal concentration and nanoparticle concentration are described graphically. Also, effects of pertinent flow parameters on the shear stress, rate of heat transfer, rate of solutal concentration and rate of nanoparticle concentration at the sheet are discussed with the help of numerical values presented in graphical form. All numerical results for mono-diffusive nanofluid are compared with those of double-diffusive nanofluid.

Numerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Viscoelasticity, magnetic field and nanoparticle buoyancy parameter tend to enhance the wall velocity gradient, whereas thermal buoyancy force has a reverse effect on it. Radiation, Brownian and thermophoretic diffusions tend to reduce wall temperature gradient, whereas viscoelasticity has a reverse effect on it. Nanofluid Lewis number tends to enhance wall nanoparticle concentration gradient.

Study of this problem may find applications in engineering and biomedical sciences,e.g. in cooling and process industries and in cancer therapy.

Laminar natural convection of nanofluids in a square cooled cavity enclosing a heated horizontal cylinder is studied numerically. This paper aims to investigate in what measure the nanoparticle size and average volume fraction, the cavity width, the cylinder diameter and position, the average temperature of the nanofluid and the temperature difference imposed between the cylinder and the cavity walls, affects the basic heat and fluid flow features, as well as the thermal performance of the nanofluid relative to that of the base liquid.

The four-equation system of the mass, momentum and energy transfer governing equations has been solved using a computational code incorporating three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity and the coefficient of thermophoretic diffusion, all based on a high number of experimental data available in the literature. The SIMPLE-C algorithm has been used to handle the pressure-velocity coupling. Simulations have been performed using Al₂O₃ + H₂O, for different values of the average volume fraction of the suspended solid phase in the range 0-0.04, the diameter of the nanoparticles in the range 25-75 nm, the temperature difference imposed between the cylinder and the cavity walls in the range 5-20 K, the average nanofluid temperature in the range 300-330 K, the ratio between the cylinder diameter and the cavity width in the range 0.1-0.5 m, the ratio between the distance of the cylinder axis from the bottom wall and the cavity width in the range 0.2-0.8 and the ratio between the distance of the cylinder axis from the left sidewall and the cavity width in the range 0.2-0.5.

The main results obtained may be summarized as follows: the overall solid phase migration from hot to cold results in a cooperating solutal buoyancy force which tends to compensate the friction increase consequent to the viscosity growth due to the dispersion of the nanoparticles into the base fluid; the effect of the increased thermal conductivity consequent to the nanoparticle dispersion into the base fluid plays the major role in determining the heat transfer enhancement of the nanofluid, at least in the upper range of the investigated average temperatures; at high temperatures, the nanofluid heat transfer performance relative to that of the pure base liquid increases with increasing the average volume fraction of the suspended solid phase, whereas at low temperatures, it has a peak at an optimal particle loading; the relative heat transfer performance of the nanofluid increases notably with increasing the average temperature, and just moderately as the imposed temperature difference, the width of the cavity and the distance of the cylinder from the bottom of the cavity, are increased; the relative heat transfer performance of the nanofluid increases as the nanoparticle size, the cylinder diameter and the distance of the cylinder from the sidewall, are decreased; as a consequence of the local competition between the thermal and the solutal buoyancy forces, a periodic flow arises when the cylinder is located in the vicinity of one of the cooled walls of the enclosure.

Framed in this general background, a comprehensive numerical study on buoyancy-driven convection of alumina-water nanofluids inside a cooled square cavity containing a heated circular cylinder is executed by the way of a two-phase model based on the double-diffusive approach accounting for the effects of the Brownian diffusion and thermophoresis.

This paper aims to address the flow of Sisko nanofluid by an unsteady curved surface. Non-uniform heat source/sink is considered for heat transfer analysis.

Numerical solutions are constructed using bvp4c procedure.

Pressure profile inside boundary region is increased when A and K are enhanced.

No such analysis is yet presented.

The purpose of this study is to analyze the heat transfer and flow enhancement of an Al₂O₃-water nanofluid filling an inclined channel whose lower wall is embedded with periodically placed discrete hydrophobic heat sources. Formation of a thin depletion layer of low viscosity over each hydrophobic heated patch leads to the velocity slip and temperature jump condition at the interface of the hydrophobic patch.

The mixed convection of the nanofluid is analysed based on the two-phase non-homogeneous model. The governing equations are solved numerically through a control volume approach. A periodic boundary condition is adopted along the longitudinal direction of the modulated channel. A velocity slip and temperature jump condition are imposed along with the hydrophobic heated stripes. The paper has validated the present non-homogeneous model with existing experimental and numerical results for particular cases. The impact of temperature jump condition and slip velocity on the flow and thermal field of the nanofluid in mixed convection is analysed for a wide range of governing parameters, namely, Reynolds number (50 ≤ Re ≤ 150), Grashof number ( 103≤Gr≤5×104), nanoparticle bulk volume fraction ( 0.01≤φb≤0.05), nanoparticle diameter ( 30≤dp≤60) and the angle of inclination ( −60°≤σ≤60°).

The presence of the thin depletion layer above the heated stripes reduces the heat transfer and augments the volume flow rate. Consideration of the nanofluid as a coolant enhances the rate of heat transfer, as well as the entropy generation and friction factor compared to the clear fluid. However, the rate of increment in heat transfer suppresses by a significant margin of the loss due to enhanced entropy generation and friction factor. Heat transfer performance of the channel diminishes as the channel inclination angle with the horizontal is increased. The paper has also compared the non-homogeneous model with the corresponding homogeneous model. In the non-homogeneous formulation, the nanoparticle distribution is directly affected by the slip conditions by virtue of the no-normal flux of nanoparticles on the slip planes. For this, the slip stripes augment the impact of nanoparticle volume fraction compared to the no-slip case.

This paper finds that the periodically arranged hydrophobic heat sources on the lower wall of the channel create a significant augmentation in the volume flow rate, which may be crucial to augment the transport process in mini- or micro-channels. This type of configuration has not been addressed in the existing literature.

The purpose of the current article is to explore the rotational behavior on nanofluid flow over an exponentially stretching surface. Heat and mass flux are formulated upon Cattaneo–Christov theory.

Effect of thermophoretic, Brownian motion and thermally convective conditions is further retained. Novel boundary layer approximations are applied to transform the governing equations of continuity, momentum, energy and nanoparticle volume fraction. Convergent series solutions are obtained to manage the rotating flow with the aid of homotopy analysis method (HAM).

Depending on the several dimensionless parameters including the local rotation parameter the Prandtl number Pr, the thermophoresis parameter, the Brownian motion parameter, the Lewis number Le, Biot number Bi, Deborah number in terms of heat flux relaxation parameter and Deborah number in terms of mass flux relaxation parameter with the dimensionless physical quantities are deliberated through graphs. Present results are also likened with the foregoing results in significance.

No such assumptions have been made for the development of analytical solution so far.

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 investigate a mathematical model with numerical simulation for bacterial growth in the heart valve.

For antibacterial activities and antibodies properties, nanoparticles have been used. As antibiotics are commonly thought to be homogeneously dispersed through the blood, therefore, non-Newtonian fluid of Casson micropolar blood flow in the heart valve for two dimensional with variable properties is used. The heat transfer with induced magnetic field translational attraction under the influence of slip is considered for the resemblance of the heart valve prosthesis. The numeral results have been obtained by using the Chebyshev pseudospectral method.

It is proven that vascular resistance decreases for increasing blood velocity. It is noted that when the magnetic field will be induced from the heart valve prosthesis then it may cause a decrease in vascular resistance. The unbounded molecules and antibiotic concentration that are able to penetrate the bacteria are increased by increasing values of vascular resistance. The bacterial growth density cultivates for upswing values of magnetic permeability and magnetic parameters.

To the best of the authors’ knowledge, this is the first study to investigate a mathematical model with numerical simulation for bacterial growth in the heart valve.

The purpose of this study is to analyze the nonhomogeneous model on the mixed convection of Al2O3–Fe3O4 Bingham plastic hybrid nanofluid in a ventilated enclosure subject to an externally imposed uniform magnetic field. Entropy generation and the pressure drop are determined to analyze the performance of the heat transfer. The significance of Joule heating arising due to the applied magnetic field on the heat transfer of the yield stress fluid is described.

The ventilation in the enclosure of heated walls is created by an opening on one vertical wall through which cold fluid is injected and another opening on the opposite vertical wall through which fluid can flow out.

This study finds that the inclusion of Fe₃O₄ nanoparticles with the Al₂O₃-viscoplastic nanofluid augments the heat transfer. This rate of enhancement in heat transfer is higher than the rate by which the entropy generation is increased as well as the enhancement in the pressure drop. The yield stress has an adverse effect on the heat transfer; however, it favors thermal mixing. The magnetic field, which is acting opposite to the direction of the inlet jet, manifests heat transfer of the viscoplastic hybrid nanofluid. The horizontal jet of cold fluid produces the optimal heat transfer.

The objective of this study is to analyze the impact of the inclined cold jet of viscoplastic electrically conducting hybrid nanofluid on heat transfer from the enclosure in the presence of a uniform magnetic field. The combined effect of hybrid nanoparticles and a magnetic field to enhance heat transfer of a viscoplastic fluid in a ventilated enclosure has not been addressed before.