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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.

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 wakes behind cylinders having an equilateral triangular cross-section are studied numerically for various cylinder inclinations and Reynolds numbers. For steady flows, the development of the recirculation region near the onset of flow separation is described, and the separation Reynolds numbers mapped for different cylinder inclinations. Cylinder inclinations that are not reflection symmetric about the horizontal centreline produce asymmetric recirculation regions which persist until the flow becomes unstable. Flow separation is observed to initiate on the rear-face of the cylinder and develops in size with increasing Reynolds numbers until the separation points become defined at the triangular cross-section's vertices where they remain even at higher Reynolds numbers. Using the Stuart–Landau equation, the critical Reynolds numbers of the different flow cases are quantified. The inclination of the cylinder is seen to strongly affect the location of the separation points, the dimensions of the recirculation region, and ultimately the critical Reynolds numbers. Increasing the Reynolds number past the instability threshold, a Benard–von Karman vortex street is initially observed before the downstream region of the wake re-aligns to a bi-layered vortex structure. Beyond this regime, the vortex street is observed to develop variously. At most cylinder inclinations ( α 30 ° and α ≳ 42 ° ), the bi-layered wake re-assembles into a secondary vortex street further downstream. For a small range of cylinder inclinations ( 30 ° ≤ α ≲ 38 ° ), the shedding vortices interact to form a vortex street similar to that produced by the 2P shedding mode for oscillating circular cylinders, while inclinations 38 ° ≲ α 54 ° describe the development of a P+S-like vortex street. The formation of these unsteady wakes are attributed to vortex interactions in the wake. The drag and lift force coefficients for various cylinder inclinations and Reynolds numbers are also summarised. Phase trajectories of the force coefficients reveal that the transition from the bi-layered wake to the 2P-like wake alters its profile significantly, while the transitions to the other vortex streets observed did not incur such changes.

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.

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...