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Natural convection in a square cavity filled with electrically conducting nanofluid that is driven by a periodic temperature profile along on of the vertical wall is studied numerically. The top and bottom horizontal walls are kept adiabatic. The right wall is maintained at low temperature while the temperature of the opposing vertical wall varies sinusoidally with time about a mean temperature. Flow and heat transfer performance through the enclosure is examined over a wide range of oscillation amplitudes and frequencies, Hartmann number, Rayleigh number and solid volume fraction at Prandtl number Pr = 6.2. The results show that oscillation amplitude, A, and frequency, f, of the vertical wall significantly affect the response of heat transfer inside the cavity. For A > 0.5, the forcing frequency is found to remain almost constant at f = 2.5, while it shifts towards a higher frequency f = 5 for A ≤ 0.5. At low Rayleigh number, Nusselt number is found to be independent of Rayleigh and Hartman numbers, while at higher Rayleigh number, convective flow dominates, and Nusselt number becomes independent of Hartmann number. In this regime, the Nusselt scaling with Rayleigh number agrees well with the exponent predicted by theory of natural convection in a cavity without magnetic field or nanoparticles, with a value of 1/4. With the increase of solid volume fraction, the heat transfer rate may increase or decrease depending on the values of Hartmann and Rayleigh numbers.

The heat transfer from the side-wall of a duct through which an electrically conducting fluid flows within a strong transverse magnetic field is numerically investigated using high-resolution numerical simulation. Parameter ranges considered are 0 ≤ H a ≤ 2400 and 100 ≤ R e ≤ 3000 for a constant blockage ratio of 1 / 4 . The gain in the heat transfer using obstacles of different geometric shapes are compared. For H a = 320 , a maximum heat transfer enhancement of 78 % is obtained when using the square cylinder at a modes R e = 1000 , while the triangular cylinder outperformed the various other vortex promoter geometries at Re = 2000 yielding a 75% improvement.. However, at a higher Hartmann number of H a = 2400 , a maximum heat transfer augmentation of 16 % and 40 % is obtained for the triangular cylinder at R e = 1000 and 2000, respectively. This suggests that for a duct flow under the influence of a strong magnetic field, the triangular obstacle is a superior heat transfer promoter geometry compared to the square or circular cylinders. A further net power analysis reveals that the heat transfer enhancement dominates over the pumping power to produce net benefits for even a modest heat transfer enhancement.

Repeated flow-facing wedge-shaped protrusions are explored as a means to enhance the heat transfer behaviour in a quasi-two-dimensional magnetohydrodynamic duct flow. Quasi-two-dimensionality is achieved under a strong magnetic field which are prevalent in the cooling blankets of fusion reactors. Ranges of Hartmann friction parameters (50 ≤ H ≤ 500) and Reynolds numbers (1300 ≤ R e ≤ 3000) are investigated. The effect of blockage β (wedge height to duct height), pitch γ (distance between wedges) and wedge angle ϕ on heat transfer ratio HR and efficiency η are considered. A monotonic increase in HR with β is observed in the range of β investigated. It is possible to further improve HR by changing the geometric parameter to an optimal pitch and optimal wedge angle. Corresponding to each H there exists an optimal β , γ and ϕ where maximum η could be achieved. In contrast to the optimal β which showed a monotonic increase with H , optimal γ and ϕ showed a reversal in the trend after a critical H . Effectiveness of surface modification on the heated wall is also established through a net power analysis.

The fluid dynamics and heat transfer characteristics of magnetohydrodynamic duct flow often degrade the laminarization caused by the magnetic field. The present work evaluates the performance of a system featuring alternating current injection from a point electrode as a vortex promoter for enhancement of the thermal-hydraulic characteristics. It is found that the vortices generated by the current injection alone generally induce a greater thermal-hydraulic performance with a significantly smaller additional pressure loss than configurations featuring a physical obstacle. A maximum overall efficiency index of 1.83 was recorded within the parameter space investigated.

The effect of rotation on horizontal convection in a cylindrical enclosure is investigated numerically. The thermal forcing is applied radially on the bottom boundary from the coincident axes of rotation and geometric symmetry of the enclosure. First, a spectral element method is used to obtain axisymmetric basic flow solutions to the time-dependent incompressible Navier–Stokes equations coupled via a Boussinesq approximation to a thermal transport equation for temperature. Solutions are obtained primarily at Rayleigh number $\mathit{Ra}=10^{9}$ and rotation parameters up to $Q=60$ (where $Q$ is a non-dimensional ratio between thermal boundary layer thickness and Ekman layer depth) at a fixed Prandtl number $\mathit{Pr}=6.14$ representative of water and enclosure height-to-radius ratio $H/R=0.4$. The axisymmetric solutions are consistently steady state at these parameters, and transition from a regime unaffected by rotation to an intermediate regime occurs at $Q\approx 1$ in which variation in thermal boundary layer thickness and Nusselt number are shown to be governed by a scaling proposed by Stern (1975, Ocean Circulation Physics. Academic). In this regime an increase in $Q$ sees the flow accumulate available potential energy and more strongly satisfy an inviscid change in potential energy criterion for baroclinic instability. At the strongest $Q$ the flow is dominated by rotation, accumulation of available potential energy ceases and horizontal convection is suppressed. A linear stability analysis reveals several instability mode branches, with dominant wavenumbers typically scaling with $Q$. Analysis of contributing terms of an azimuthally averaged perturbation kinetic energy equation applied to instability eigenmodes reveals that energy production by shear in the axisymmetric mean flow is negligible relative to that produced by conversion of available potential energy from the mean flow. An evolution equation for the quantity that facilitates this exchange, the vertical advective buoyancy flux, reveals that a baroclinic instability mechanism dominates over $5\lesssim Q\lesssim 30$, whereas stronger and weaker rotations are destabilised by vertical thermal gradients in the mean flow.

The design of vortex promoters in a heated-wall duct is often limited by the considerations of practicality, especially in complex systems such as fusion blankets. The present study investigates the use of current injection to invoke a street of vortices in quasi-two-dimensional high transverse magnetic field magnetohydrodynamic duct flows to enhance instability behind a cylinder. The intent is to generate intensive flow vorticity parallel to a magnetic field downstream of a field-aligned cylinder. Electric current enters the flow through an electrode embedded in one of the Hartmann walls, radiates outward, imparting a rotational forcing around the electrode due to the Lorentz force. The quasi-two-dimensional nature of these flows then promotes a vortical rotation across the interior of the duct with axis aligned to the magnetic field. The hot and cold walls are parallel to the magnetic field. Electric current amplitude and pulse width, excitation frequency and electrode position are systematically varied to explore their influences on the convective heat transport phenomenon. This investigation builds on a recommendation from previous work of Bühler (J. Fluid Mech., vol. 326, 1996, pp. 125–150) dedicated to understanding of the flow stability in a similar configuration. This study provides supportive evidence for the use of current injection as an alternative to the conventional mechanically actuated turbuliser, with heat transfer almost doubled for negligible additional pumping power requirements.

We demonstrate that instability in enclosed horizontally driven convection is due to a convective buoyancy-driven transverse-roll instability resembling the classical Rayleigh–Benard convection in the thermal forcing boundary layer rather than a shear instability in the corresponding kinematic boundary layer. Instability growth is weakly sensitive to the local velocity profile, with velocity shear acting to select a transverse roll mode in preference to longitudinal rolls. The convectively unstable region grows from the hot end of the forcing boundary with increasing Rayleigh number two orders of magnitude lower than the natural onset of unstable horizontal convection. This analysis highlights the importance of the thermal boundary layer to the instability dynamics of horizontal convection, elucidating the path towards an understanding of turbulence and heat transport scaling in horizontal convection at oceanic Rayleigh numbers.

Heat transfer efficiency from a duct side-wall in which an electrically conducting fluid flows under the influence of a transverse magnetic field is investigated. A quasi-two-dimensional magnetohydrodynamic model is employed to model the flow using high-resolution numerical simulation. The gap height and angle of attack of a rectangular cylinder, with aspect ratio α = 1 / 2 and blockage ratio β = 1 / 4 , are independently varied to establish relationships between obstacle configuration and heat transfer efficiency. The heat transfer efficiency is measured through an efficiency index given by the ratio of heat transfer enhancement to pressure drop penalty in comparison to an empty duct case. At gap height ratios 1.15 ⩽ G / L c 2 for an upright cylinder above a heated lower wall, thermal enhancement and efficiency can be improved; with a peak thermal efficiency of η = 1.6 occurring at G / L c = 1.5 . Additional increases in thermal efficiency for an obstacle at the duct centre-line ( G / L c = 2 ) can be achieved through inclining the cylinder at γ = - 7.5 ° , γ = - 37.5 ° and 0 ° γ ⩽ 22.5 ° . However, these configurations offered no improvement over simply offsetting an upright cylinder at a gap height ratio of G / L c = 1.5 . For a cylinder offset at G / L c = 1.5 , varying the incidence angle through - 37.5 ° γ ⩽ 22.5 ° , - 7.5 ° ⩽ γ 0 ° and 0 ° γ ⩽ 15 ° can lead to additional thermal efficiency benefits; with a global peak efficiency of η = 1.7 occurring at γ = - 37.5 ° . The streamwise distribution of the local time-averaged Nusselt number and the effect of Hartmann dampening for 100 ⩽ Ha ⩽ 2000 on heat transfer and flow dynamics are also investigated. A net power balance analysis reveals that in fusion applications the heat transfer enhancement dominates over the pumping power cost to produce net benefits for even modest heat transfer enhancement.

Horizontal convection has been used as an idealised model of the ocean overturning circulation, where some non-uniform buoyancy forcing profile is imposed along a horizontal boundary. Several different driving temperature profiles have been chosen for past numerical and laboratory studies, likely for convenience, yet the effect of the shape of the chosen profile on the resulting horizontal convection flow remains unexplored. Here high order numerical simulation is used to investigate this problem. Time independent, periodic and chaotic regimes are identified as functions of Rayleigh number (Ra) and profile shape, with a step temperature profile being found to be more unstable than a linear temperature profile. Using a nonlinear Stuart–Landau analysis, the primary instability is consistently found to occur through a supercritical (non-hysteretic) bifurcation. This research highlights the importance of the horizontal buoyancy forcing profile in determining the thermal forcing required to produce instability in horizontal convection. In addition, Nusselt number scales to R a 1 / 5 in the fully convective regime, with scaling exponents elevating beyond R a ≈ 10 10 . This elevated scaling was more pronounced for the linear thermal boundary profile than for the step profile over the computed Rayleigh numbers range.

The effect of rotation on horizontal convection flow in a free-surface cylindrical enclosure driven by a radially increasing temperature profile along the base is investigated numerically and theoretically. The governing equations of mass, momentum and energy subject to Boussinesq approximation applied to gravity term, have been discretised using a spectral-element method for velocity and temperature fields. Results of a scaling analysis are compared with numerical simulations at a fixed Prandtl number Pr = 6.14 , Reynolds numbers up to 3200, and Rayleigh number up to 3.2 × 10 11 in an enclosure with height-to-radius ratio H / R = 0.4 . The results show that heat transfer in rotating horizontal convection is significantly affected by rotation, and where rotation effects are significant, Nusselt number scalings adapted from Park and Whitehead and Stern describe the behaviour at moderate and high rotation rates, respectively. A scaling analysis is conducted to describe the suppression of convective flow at high rotation rates. Flows are characterised in terms of a rotation parameter and are divided into three regimes: a diffusive regime with Nusselt number independent of thermal forcing and rotation, a rotation-affected convective regime, and a convective regime unaffected by rotation at sufficiently high Rayleigh number.

The heat transfer from the side-wall of a duct through which an electrically conducting fluid flows within a strong transverse magnetic field is investigated. A circular cylinder aligned with the magnetic field is offset from the duct centerline. In this configuration the flow is well described by a quasi-two-dimensional model and is therefore solved on a two-dimensional domain. The effects of blockage ratio, gap ratio and Reynolds number on the flow and heat transfer are considered. An optimal cylinder position is determined using an efficiency index defined as the ratio of heat transfer enhancement to pressure drop penalty resulting from insertion of the cylinder in the channel. Cylinder placement with gaps to the heated wall of between 0.83 and 1.4 diameters performed best, achieving at least 95% of the peak efficiency indices for each blockage ratio. These gap ratios corresponded to the periodic shedding of alternating-sign vortices into the wake which interacted with the heated side-wall boundary layer to form counter-rotating vortex pairs carrying hot fluid into the duct interior. By offsetting the cylinder from the wake centreline, heat transfer enhancement of up to 48% compared to the centreline placement is achieved with only a modest increase in the pressure head losses from cylinder drag.

The fluid flow and heat transfer of a liquid metal past a circular cylinder in a rectangular duct (width-to-height aspect ratio of 2) under a strong transverse magnetic field is studied numerically using a quasi-two-dimensional model. Transition from steady to unsteady flow regimes is determined as a function of Hartmann number and blockage ratio, as are Strouhal number, and the heat transfer from the heated wall to the fluid. Downstream cross-stream mixing induced by the cylinder wake was found to increase heat transfer by more than a factor of two in some cases.

A vortex decay model for predicting spatial evolution of peak vorticity in a wake behind a cylinder is presented. For wake vortices in the stable region behind the formation region, results have shown that the presented model has a good capability of predicting spatial evolution of peak vorticity within an advecting vortex across 0.1 ≤ β ≤ 0.4, 500 ≤ H ≤ 5000, and 1500 ≤ ReL ≤ 8250. The model is also generalized to predict the decay behaviour of wake vortices in a class of quasi-two-dimensional magnetohydrodynamic duct flows. Comparison with published data demonstrates remarkable consistency.

An approach is studied for side-wall heat transfer enhancement in the magnetohydrodynamic flow of fluid in a rectangular duct that is damped by a strong transverse magnetic field. The mechanism employs the rotational oscillation of a cylinder placed inside the duct to encourage vortex shedding, which promotes the mixing of fluid near a hot duct wall with cooler fluid in the interior. The effectiveness of the heat transfer enhancement is investigated over a wide range of oscillation amplitudes and forcing frequencies. The motivation for exploring this mechanism is inspired by the transient growth response of this flow, which indicates that the optimal disturbances feeding the vortex shedding process are localized near the cylinder, and are characterized by an asymmetrical disturbance with respect to the wake centreline. The results show that a considerable increase in heat transfer from the heated channel wall due to rotational oscillation of the cylinder can be achieved, with the maximum enhancement of mo...