Stability analysis for the Walters-B model saturated with permeable nanofluid is taken under study including cross diffusion effects. The porous medium is defined using modified Darcy model, and the nanofluid is considered to have the impact of thermophoresis and Brownian motion. The thermal energy equation includes the effects of diffusion and also cross diffusion. For the study of linear theory, normal mode procedure is applied and to understand the nonlinear theory, the method of minimal representation of double Fourier series is utilized. The effects of nondimensional parameters such as concentration Rayleigh number, Lewis number, Soret and Dufour parameters, Solutal Rayleigh number, elastic parameter, Prandtl number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are represented graphically. The effect of time on transient Nusselt numbers is also taken under investigation. It is concluded that when time is small, the three Nusselt numbers oscillate for all the governing parameters and approach to steady-state as time increases.

The mixed convective heat transfer of a micropolar nanofluid in a square lid-driven cavity has been numerically studied. The lid is thermally insulated, the side walls are kept cold, and the bottom wall is kept hot with sinusoidally thermal boundary condition. The governing equations were solved by finite volume method using the SIMPLE algorithm. The effect of Grashof number (10 2 –10 5 ), the volume fraction of nanoparticles (0.0–0.1), and micropolarity (0.0–2.0) has been investigated on the heat transfer of Al 2 O 3 –water nanofluid. Also, the variable model was used to calculate fluid viscosity and thermal conductivity coefficient of the nanofluid. The results showed that an increase in Grashof amplifies the buoyancy force and enhances the Nusselt number. Also, an increase in vortex viscosity at low Grashof numbers strengthens the forced convection and increases the Nusselt number over the bottom wall. However, at Gr = 10 5 , the increase in vortex viscosity up to K = 1.0 leads to a decrease in the amount of heat transfer, but its further increase entails the increase in heat transfer. Although the addition of nanoparticles to the fluid improves heat transfer rate, the extent of improvement at nonzero K values is lower than that in the Newtonian fluid. The comparison of the average Nusselt number computed on the hot wall under two different states of temperature-depended thermo-physical properties and constant thermo-physical properties reveals that their difference is more significant for the Newtonian fluid especially at higher volume fraction.

Turbulent characteristics of Czochralski melt flow are presented using the unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence modeling approach. Three-dimensional, transient computations were performed using the Launder and Sharma low-Re k-ε model and Menter shear stress transport (SST) k-ω model on an idealized Czochralski setup with counterrotating crystal and crucible. A comparative assessment is performed between these two Reynolds-averaged Navier–Stokes (RANS) models in capturing turbulent thermal and flow behaviors. It was observed that the SST k-ω model predicted a better resolution of the Czochralski melt flow capturing the near wall thermal gradients, resolving stronger convective flow at the melt free surface, deciphering more number of characteristics Czochralski recirculating cells along with predicting large number of coherent eddy structures and vortex cores distributed in the melt and hence a larger level of turbulent intensity in the Czochralski melt compared with that by Launder and Sharma low-Re k-ε model.

This paper presents an investigation of a three-phase oscillating heat pipe (3P OHP). The working fluid in the OHP consists of phase change material (PCM) and water. During the operation, the PCM changes the phase between solid and liquid, and water changes phase between liquid and vapor. The OHP investigated herein contains three phases: solid, liquid, and vapor. Erythritol was selected as the PCM with an instant cooling effect when dissolved in water due to the high fusion heat of 340 J/g. When the working fluid flows into the evaporator section, the PCM solid phase of the working fluid can become liquid phase in the evaporator, and the PCM liquid phase of the working fluid become solid phase in the condenser. The effects of heat input ranging from 100 to 420 W, and the erythritol concentration ranging from 1 to 50 wt % on the slug oscillations, and the OHP thermal performance was investigated. Experimental results show that while the erythritol can help to increase the heat transfer performance of an OHP, the heat transfer performance depends on the erythritol concentration. With a range of 1–5 wt % concentration of erythritol/water mixtures, a maximum 10% increase in the thermal performance was observed. When the erythritol concentration of erythritol/water mixtures was increased to a range of 10–50 wt %, the thermal performance of OHPs was lower than pure water-filled OHP, and the thermal performance decreased as the erythritol concentration was further increased. In addition, visualization results showed that slug oscillation amplitudes and velocities were reduced in the OHPs with erythritol solution compared with water-filled OHP.

This article presents a numerical study of particle deposition in two fluids, i.e., liquid and droplet flow in a single row tube bundle heat exchanger. The tubes in the heat exchanger are modeled as heating sources. Two level-set functions are used to capture the liquid-droplet interface and the liquid-deposit front. The effects of different parameters, including Damköhler number, thermal conductivity of the deposit, viscosity of the liquid, and the heating power of the tube on the flow and heat transfer, are investigated. The deposit profiles on the tube surface are analyzed. Comparison is made for the averaged Nusselt number for the case without and with deposition. It is found that the tube surface has a thicker deposit at the upstream facing side compared with that of the downstream facing side. Generally, the heat transfer rate reduces with the growth of the deposit. Under certain conditions, heat transfer can be increased because of the increase in fluid velocity due to blockage of the flow area by the deposit. The averaged Nusselt number oscillated temporally in response to the droplet movement across the tube. Generally, the temperature at the liquid-deposit front decreases with thicker deposit formed. The averaged Nusselt number along the liquid-deposit front increases to a critical value initially, and it starts to decrease with the growth of the deposit.

In this study, the influence of the applied magnetic field is investigated for magneto-micropolar fluid flow through an inclined channel of parallel porous plates with constant pressure gradient. The lower plate is maintained at constant temperature and the upper plate at a constant heat flux. The governing motion and energy equations are coupled while the effect of the applied magnetic field is taken into account, adding complexity to the already highly correlated set of differential equations. The governing equations are solved numerically by explicit Runge–Kutta. The velocity, microrotation, and temperature results are used to evaluate second law analysis. The effects of characteristic and dominate parameters such as Brinkman number, Hartmann Number, Reynolds number, and micropolar viscosity parameter are discussed on velocity, temperature, microrotation, entropy generation, and Bejan number in different diagrams. The results depicted that the entropy generation number rises with the increase in Brinkman number and decays with the increase in Hartmann Number, Reynolds number, and micropolar viscosity parameter. The application of the magnetic field induces resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the presence of magnetic field tends to increase the contribution of fluid friction entropy generation to the overall entropy generation; in other words, the irreversibilities caused by heat transfer reduced. Therefore, to minimize entropy, Brinkman number and Hartmann Number need to be controlled.

Steam-assisted gravity drainage (SAGD) process has been an optimized method to explore heavy oil reservoirs in the world. The oil viscosity reduction and gravity force near the interface of steam–chamber are the main development mechanisms. In classical models, conductive heat transfer plays the only or dominant role in the heat transmission from high-temperature steam to low-temperature oil sands. Although some mathematical studies have paid attention to the convective heat transfer, the role of heat transfer by flowable oil normal to the steam–chamber interface has been given little attention. In SAGD, the viscosity of bitumen can be reduced by several orders of magnitude by the release of latent heat from injected steam. In this study, an analytical model is developed for the heat transfer process induced by flowable oil. Also, in order to accurately simulate the oil viscosity characteristics in steam–chamber, a correlation between oil viscosity and pressure is proposed. Results indicate that the oil mobility plays an important role on the flow normal to interface when the distance is smaller than 6 m. Even under the most extreme circumstances ( μ w = 0.1127 cp), the flowing of oil normal to steam–chamber interface also cannot be ignored. Comparing to Irani and Ghannadi model, it can be easy to draw the conclusion that the new model consists with the underground test facility (UTF) field data much better. This new analytical model will benefit to understanding the convective heat transfer mechanism in SAGD process.

In this paper, the effect of magnetic field on natural convection of Al 2 O 3 /water nanofluid in an enclosure containing twin protruding heat sources placed on top and bottom walls arranged in-line and staggered manner is presented. For this purpose, coupled equations governing fluid flow and heat transfer are solved in Cartesian framework using streamline upwind/Petrov–Galerkin (SUPG) finite element method. Numerical computations are performed to predict the fluid flow, heat transfer, and entropy generation for a wide range of Hartmann number (0.0 ≤ Ha ≤ 100.0), Rayleigh number ( 10 3 ≤ Ra ≤ 10 6 ), and nanoparticle volume fraction ( 0.0 ≤ ϕ ≤ 0.1 ). The simulated results indicate that, for both in-line and staggered arrangement, the entropy generation due to heat transfer is significant along isothermal surfaces, whereas entropy generation due to fluid friction is higher at no-slip walls and along the regions of contact between adjacent recirculation cells. For both in-line and staggered arrangement, increase in global total entropy generation and average Nusselt number along top and bottom heat sources is obtained with decreasing Ha and increasing Ra. Furthermore, for both in-line and staggered arrangement, variation in global total entropy generation and average Nusselt number along top and bottom heat sources with increasing nanoparticle volume fraction, depend on both Ha and Ra.

A mathematical model has been constructed for determining the effects of variable viscosity and thermal conductivity on unsteady Jeffery flow over a stretching sheet in the presence of magnetic field and heat generation. The governing partial differential equations are transformed into a set of nonlinear coupled ordinary differential equations and then solved numerically by using the Runge–Kutta–Fehlberg method with shooting technique. A critical analysis with earlier published papers is done and the results are found to be in accordance with each other. Numerical solutions are then obtained and investigated in detail for different physical parameters such as skin-friction coefficient and reduced Nusselt number as well as other parametric values such as the velocity and temperature.

In this study, the influences of the applied magnetic field and fluid elasticity were investigated for a nonlinear viscoelastic fluid obeying the Carreau equation between concentric annulus where the inner cylinder rotates at a constant angular velocity and the outer cylinder is stationary. The governing motion and energy balance equations are coupled while viscous dissipation is taken into account, adding complexity to the already highly correlated set of differential equations. The numerical solution is obtained for the narrow gap limit and steady-state base flow. Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow was investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effects of the Hartmann number, the Brinkman number, the Deborah number, and the fluid elasticity on the stability of the flow were investigated. The application of the magnetic field induces a resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the study shows that the presence of magnetic field tends to slowdown the fluid motion and thus increases the fluid temperature. However, the total entropy generation number decreases as the Hartmann number and fluid elasticity increase and it increases with increasing Brinkman number.

The thermal characteristics of Bingham plastic fluid flows are analyzed in circular microchannels under uniform wall heat flux condition. The analytic approach presented here reveals that the governing parameters are Bingham number, dimensionless radius of the plug flow region, and Brinkman number. The results demonstrate that there is a strong influence of viscous dissipation on heat transfer and entropy generation for Brinkman numbers greater than a specific value. With increasing the Brinkman number and dimensionless radius of the plug flow region, entropy generation is increased, while the Nusselt number is decreased. The influence of these parameters on the entropy generation from heat transfer is strongly higher than the entropy generation from fluid friction. The average dimensionless total entropy shows that the Bingham plastic fluids generate entropy more than Newtonian fluids; also, an increase in the dimensionless radius of the plug flow region results in increasing the average dimensionless total entropy generation. By letting the dimensionless radius of the plug flow region equal to zero, the generalized expressions and results will be simplified to Newtonian fluids.

The convective heat transfer coefficient and pressure drop of silver-water nanofluids is measured in a counter flow heat exchanger from laminar to turbulent flow regime. The experimental results show that the convective heat transfer coefficient of the nanofluids increases by up to 69% at a concentration of 0.9 vol. % compared with that of pure water. Furthermore, the experimental results show that the convective heat transfer coefficient enhancement exceeds the thermal conductivity enhancement. It is observed that the measured heat transfer coefficient is higher than that of the predicted ones using Gnielinski equation by at least 40%. The use of the silver nanofluid has a little penalty in pressure drop up to 55% increase 0.9% volume concentration of silver nanoparticles.

In the search for new, more effective coolant fluids, nanoparticle suspensions have shown promise due to their enhanced thermal conductivity. However, there is a concomitant increase in the viscosity, requiring an increase in pumping power to achieve the same flow rate. Studies of flow cooling in simple geometries indicate that there is a benefit to using nanofluids, but it is difficult to justify extending these results to the far more complicated geometries. Moreover, with the variability of property measurements found in literature, it is possible to show conflicting results from the same set of flow-cooling data. In this work we present a self-contained study of the properties and effectiveness of an alumina in water nanofluid. Flow-cooling is studied in an off-the-shelf fluid cooling package for electronics to examine the effects of the particulates in a practical scenario. We measure the thermal conductivity and viscosity of the same suspensions to assure consistent interpretation of our results. We find that, while there is no anomalous enhancement of the thermal properties or transport, there is a benefit to using a low volume fraction alumina nanoparticle suspension over using the base fluid alone. In fact, there is an optimal volume fraction (1%) for this nanofluid and electronics cooling system combination that maximizes the heat dissipated. However, we find that this benefit decreases as the volume fraction, and hence the viscosity, increases. Understanding where the trade-off between viscosity increase and thermal conductivity increase occurs is critical to designing an electronics cooling system using a nanofluid as a coolant.