Differentially Heated Research Articles

Influence of tilt angles and different models of fluid viscosity on coupled natural convection in a differentially heated closed square cavity with a partition

This article investigates the behavior of various viscosity models under conjugated natural convection in a square cavity with a conductive baffle at various angles of inclination and differential heating of the side walls. Numerical simulations were performed using the finite volume method for a fluid having viscous properties similar to those of a non-Newtonian fluid. The slope angle of the computational domain and the choice of the non-Newtonian fluid model were considered as the main parameters. The inclination of the hull took on the values 0°, 30°, 45°, 60° and 90°. The received data illustrate that the increase in the velocity of convection flows is strongly influenced by the angles of inclination of 30° and 60°. By analyzing various non-Newtonian fluid models, the power low viscosity model predicted velocities more than other viscosity models. Whereas in the Herschel-Bulkley viscosity model, only the heat transfer process mainly occurred. Analysis of the obtained local Nusselt number showed that the values were higher on the cold wall. This is explained by more intense heat transfer due to convection on this wall. It should also be noted from the data obtained that when the region is tilted at α = 90° for the Carreau viscosity model, one can notice the complete absence of the convection process, and when using the Herschel–Bulkley viscosity model, no flow mixing occurred, which led to heat exchange solely due to heat transfer for different tilt angles.

No Glycation Required: Interference of Casein in AGE Receptor Binding Tests.

For the determination of the binding of heated cow’s milk whey proteins such as β-lactoglobulin to the receptors expressed on immune cells, inhibition ELISA with the soluble form of the receptor for advanced glycation end products (sRAGE) and scavenger receptor class B (CD36) has been successfully used in the past. However, binding to heated and glycated caseins in this read-out system has not been tested. In this study, inhibition ELISA was applied to measure the binding of cow’s milk casein alone, as well as all milk proteins together, which underwent differential heat treatment, to sRAGE and CD36, and we compared those results to a dot blot read out. Moreover, binding to sRAGE and CD36 of differentially heated milk protein was measured before and after in vitro digestion. Casein showed binding to sRAGE and CD36, independent from the heat treatment, in ELISA, while the dot blot showed only binding to high-temperature-heated milk protein, indicating that the binding is not related to processing but to the physicochemical characteristics of the casein. This binding decreased after passage of casein through the intestinal phase.

Swirling Flows Characteristics in a Cylinder Under Effect of Buoyancy

Thermal buoyancy, induced by injection or by differential heating of a tiny rod is explored to control breakdown in the core of a helical flow driven by the lid rotation of a cylinder. Three main parameters are required to characterize numerically the flow behavior; namely, the rotational Reynolds number Re, the cavity aspect ratio and the Richardson number Ri. Warm injection/rod, Ri > 0, is shown to prevent on-axis flow stagnation while breakdown enhancement is evidenced when Ri < 0. Results revealed that a bubble vortex evolves into a ring type structure which may remain robust, as observed in prior related experiments or, in contrast, disappear over a given range of parameters (Λh, Re, Ri > 0). Besides, the emergence of such a toroidal mode was not found to occur under thermal stratification induced by a differentially heated rod. Moreover, three state diagrams were established which provide detailed flow characteristics under the distinct and combined effects of buoyancy strength, viscous effects and cavity aspect ratio.

Differential Heating Drives Downslope Flows that Accelerate Mixed‐Layer Warming in Ice‐Covered Waters

AbstractIn ice‐covered lakes, penetrative radiation warms fluid beneath a diffusive boundary layer, thereby increasing its density and providing energy for convection in a diurnally active, deepening mixed layer. Shallow regions are differentially heated to warmer temperatures, driving turbulent gravity currents that transport warm water downslope and into the basin interior. We examine the energetics of these processes, focusing on the rate at which penetrative radiation supplies energy that is available to drive fluid motion. Using numerical simulations that resolve convective plumes, gravity currents, and the secondary instabilities leading to entrainment, we show that advective fluxes due to differential heating contribute to the evolution of the mixed layer in waterbodies with significant shallow areas. A heat balance is used to assess the relative importance of differential heating to the one‐dimensional effects of radiative heating and diffusive cooling at the ice‐water interface in lakes of varying morphologies.

Unsteady Natural Convection in a Differentially Heated Rectangular Enclosure Possessing Sinusoidal Corrugated Side Walls Loaded with Power Law Non-Newtonian Fluid

This research is a numerical analysis exhaustively investigating two-dimensional (2D) transient convective heat transfer in a differentially heated rectangle, possessing sinusoidal corrugated side walls at constant temperatures. The quadrilateral space is filled with a power-law non-Newtonian fluid, plus the right and left walls are uniformly cooled and heated, respectively. The top and bottom walls are retained as adiabatic and the side walls are recast exploiting sinusoidal corrugated shape. The governing equations of the problem are solved using the finite volume method. The evaluation of fluid flow and heat transfer is conducted in such a manner that the power law index n varies from 0.6 to 1.4, the Rayleigh number Ra from 103 to 107, the corrugation amplitude CA from 0.1 to 0.5, and the corrugation frequency CF of the sinusoidal side walls is in the range of 1 to 5. The results are studied at different values of Ra, n, CA, and CF; they are presented in the form of streamlines, isotherms, and average Nusselt numbers ( $$\overline{\rm{Nu}}$$ ) of the hot side wall. Further, the heat transfer characteristics are presented and the effect of sudden differential heating, as well as its consequential transient behavior, on the fluid flow, velocity, and temperature plots are demonstrated in accordance with the scope of the governing parameters.

Experimental Investigation on Heat Losses From Differentially Heated Cylindrical Cavity Receiver Used in Paraboloid Concentrator

In the present study, an experimental testing facility is created to analyze the heat losses from the cylindrical solar cavity. Tests are carried out under the temperature range from 225 °C to 425 °C for a cavity inclination from θ = 0–90 deg in steps of 30 deg. It is observed that for off-flux investigation of solar cavity receiver, near isothermal wall temperature condition can be realized with the differential heating arrangement. The total loss is found to be the highest when the cavity aperture is positioned at sideways (θ = 0 deg). It decreases by 43–51% when the cavity is inclined (θ = 90 deg). The conduction loss is found to be accounted for up to 32–34% of the total heat loss, whereas the cavity radiative loss is estimated to be 13%, 16%, and 20% of the total heat loss, respectively, for cavity wall temperature 225 °C, 325 °C, and 425 °C. The investigation of convective losses showed significant change with cavity tilt angles. It is 46–54% of the total heat loss when the cavity aperture is facing sideways (θ = 0 deg), whereas its value reduces up to 4% of the total heat loss when the cavity aperture is facing downward (θ = 90 deg). A Nusselt number correlation has been developed for predicting the convective heat loss from a open cavity. The Nusselt number correlation correlates 100% of data within ± 20% deviation.

Transient air flow and heat transfer due to differential heating on inclined walls and heat source placed on the bottom wall in a partitioned attic shaped space

Numerical simulations are carried out to study the unsteady air flow and heat transfer in a partitioned triangular cavity of differentially heated from inclined walls and heat source placed at the bottom wall. The finite volume numerical method has been employed to solve the governing equations. The grid sensitivity test has been carried out and obtained results have been validated against experimental results. The dependency of several parameters on fluid flow and heat transfer is studied including Rayleigh number from 103 to 106, heater size from 0.2 to 0.6, heater position from 0.3 to 0.7 and aspect ratio from 0.2 to 1.0 with a fixed Prandtl number of 0.72 (air). A conductive partition of infinite conductivity is placed at the middle of the enclosure, which means that only heat can freely transfer between two fluid zones through the partition. Results are presented as a form of isotherms and streamlines. Also, heat transfer is presented as a form of Nusselt number. Both transient and steady states of solutions are presented in this study.

Natural convection due to differential heating of inclined walls and heat source placed on bottom wall of an attic shaped space

Numerical investigation of free convection heat transfer in an attic shaped enclosure with differentially heated two inclined walls and filled with air is performed in this study. The left inclined surface is uniformly heated whereas the right inclined surface is uniformly cooled. There is a heat source placed on the right side of the bottom surface. Rest of the bottom surface is kept as adiabatic. Finite volume based commercial software ANSYS 15 (Fluent) is used to solve the governing equations. Dependency of various flow parameters of fluid flow and heat transfer is analyzed including Rayleigh number, Ra ranging from 103 to 106, heater size from 0.2 to 0.6, heater position from 0.3 to 0.7 and aspect ratio from 0.2 to 1.0 with a fixed Prandtl number of 0.72. Outcomes have been reported in terms of temperature and stream function contours and local Nusselt number for various Ra, heater size, heater position, and aspect ratio. Grid sensitivity analysis is performed and numerically obtained results have been compared with those results available in the literature and found good agreement.

Multiple Zonal Jets in a Differentially Heated Rotating Annulus

AbstractA laboratory experiment of multiple baroclinic zonal jets is described, thought to be dynamically similar to flow observed in the Antarctic Circumpolar Current. Differential heating sets the overall temperature difference and drives unstable baroclinic flow, but the circulation is free to determine its own structure and local stratification; experiments were run to a stationary state and extend the dynamical regime of previous experiments. A topographic analog to the planetary β effect is imposed by the gradient of fluid depth with radius supplied by a sloping bottom and a parabolic free surface. New regimes of a low thermal Rossby number (RoT ~ 10−3) and high Taylor number (Ta ~ 1011) are explored such that the deformation radius Lρ is much smaller than the annulus gap width L and similar to the Rhines length. Multiple jets emerge in rough proportion to the smallness of the Rhines scale, relatively insensitive to the Taylor number; a regime diagram taking the β effect into account better reflects the emergence of the jets. Eddy momentum fluxes are consistent with an active role in maintaining the jets, and jet development appears to follow the Vallis and Maltrud phenomenology of anisotropic wave–turbulence interaction on a β plane. Intermittency and episodes of coherent meridional jet migration occur, especially during spinup.

Heating uniformity and differential heating of insects in almonds associated with radio frequency energy

Radio frequency (RF) treatments have potential as alternatives to chemical fumigation for phytosanitary disinfestation treatments in the dried nut industry. To develop effective RF treatment protocols for almonds, it is desirable to determine heating uniformity and the occurrence of RF differential heating of insects. This study compared heating uniformity in almonds (Nonpareil) heated by RF and by forced hot air. A mathematical model suggested a 4.7 and 6.0 °C RF preferential heating of the target pest navel orangeworm (Amyelois transitella [Walker]) over almonds at heating rates of 5 and 10 °C min−1, respectively, for the loss factor ratio of 183 at 27.12 MHz, when the heat transfer coefficient between insects and almonds was set at 500 W m−2 °C−1. To validate the model, a gellan gel with dielectric properties similar to those of the target pest was used as a model insect. When almond kernels were heated at 27.12 MHz from 21 °C to 55 °C, the model insects were differentially heated about 4.6 °C and 5.6 °C higher than the kernel temperatures at heating rates of 5 and 10 °C min−1, respectively. These values corresponded to a heating rate for the model insect of 1.2 times greater than that for almond kernels. Slight preferential heating of insects in almonds using RF energy would improve the efficacy of large-scale RF treatments.

Uneven Cooling: The influence of atmospheric dynamics on the thermal evolution of gas giants

AbstractPlanets cool and contract as they age, with a cooling rate that depends on the efficiency with which they can transport heat out to space, first through the convective interior and then radiatively out through the atmosphere. The bottleneck for this cooling is the radiative-convective boundary (RCB), where the heat transport is the least efficient. Due to differential heating and atmospheric dynamics, the depth of the RCB can vary with latitude and longitude, meaning that the actual global cooling rate may differ from what would be calculated assuming a spherically symmetric RCB, as in 1D evolutionary models. Here we present models of the deep atmosphere of a generic hot Jupiter, calculate inhomogeneity in the RCB, and determine the resulting effect on the global thermal evolution. Although this issue can apply to any differentially heated gas giant, we focus on the hot Jupiter class of planet because: 1) the thick radiative zones above their deep RCBs can have a stronger influence on deforming the surface of the RCB than would generally be the case for a less-irradiated planet, and 2) an uneven RCB should increase the cooling rate, potentially exacerbating the mismatch between the large radii measured for some hot Jupiters and the smaller radii expected from evolutionary models.

The primary flow transition in a differentially heated rotating channel of fluid with O(2) symmetry

The primary flow transition in a periodic differentially heated rotating channel of fluid with O(2) symmetry is studied. This transition occurs when a time-independent flow that is uniform along the channel bifurcates to a stationary wave flow. The fluid is modelled using the Navier–Stokes equations in the Boussinesq approximation and the flow transition is found using linear stability analysis. The computation of the flow transition curve is performed efficiently by replacing the relevant eigenvalue problem with an equivalent bordered linear system, and by implementing a pseudoarclength continuation strategy that is appropriate for large-scale systems. The dynamics of the fluid near the transition are deduced by applying centre manifold reduction and normal form theory. The reduction produces analytical expressions for the normal form coefficients in terms of functions that must be computed numerically.The results indicate that the transition to stationary wave flow occurs via a supercritical pitchfork bifurcation to a group orbit, sometimes referred to as a pitchfork of revolution. Furthermore, at several points along the transition curve two such pitchfork bifurcations occur simultaneously, which physically corresponds to the interaction of two stationary wave modes. An analysis of the normal form equations that are associated with the steady-state mode interactions shows the possibility of bistability and hysteresis of the stationary waves. Many of the results obtained in the channel model show a remarkable quantitative similarity to those of theoretical and experimental studies of analogous experiments using a cylindrical annulus, even though the difference in the symmetries of the systems ensure certain qualitative differences. This suggests that the dynamics of the fluid are dominated by the differential heating and the rotation, and not by the curvature of the system.

Transient Mixed Convection Coupled with Surface Radiation inside a Square Cavity with Different Configurations - A Critical Study

The conjugate heat transfer within differentially heated enclosure in presence of surface radiation is a complex phenomenon, which has become a research topic because of its practical relevance. The flow and heat transfer depends on the orientation of source of buoyancy and shear force. Buoyancy driven flow depends on the terminal temperature difference between the walls and its orientation. Similarly, the shear driven flow depends on the wall movement and its direction. The interaction between the shear induced flow with the buoyancy induced flow caused due to different orientation of differential heating of walls in presence of surface radiation is studied in the present article. The governing equations of mass, momentum and energy are solved using modified MAC method. The unsteady flow and heat transfer characteristics significantly vary with the magnitude of velocity and the direction of wall movement. The relative importance of different influencing parameters such as Rayleigh number (Ra), emissivity (ε) and Richardson number (Ri) has been analyzed in the present study. It is noticed that direction of wall movement and Rayleigh number affect both steady and unsteady flow patterns and heat transport processes in the cavity. Presence of surface radiation significantly changes the flow structures in case of vertical wall movement compared to horizontal wall movement for bottom heated cavity. Period of transience for shear dominated regimes (Ri << 1) is less compared to buoyancy dominated regimes (Ri >> 1). This study finds its application in industrial convection ovens and uninterrupted-flow in bakery systems, in food processing industries.

Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls

Numerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 105 to 108 with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed except for the density where Boussinesq’s approximation has been considered. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh number with corrugation amplitude and frequency.

High Rayleigh Number Laminar-Free Convection in Cavities: New Benchmark Solutions

The fully matrix-inversion-free artificial compressibility (AC), characteristic based split (CBS) algorithm is used to produce a stable and accurate solution for high Rayleigh number natural convection in rectangular cavities. Two benchmark problems are solved using the AC-CBS scheme: the classical differentially heated (DH) cavity, and a cavity subject to temperature boundary conditions on its sides, which is proposed here as a new benchmark. For the DH cavity problem, the dependence of the solution on the computational grid is highlighted, and it is shown how the horizontal velocity is more sensitive than the other calculated quantities. For the newly proposed benchmark, the numerical results are compared to experimental data that has recently appeared in the open literature.

Preferential Heating and Acceleration ofαParticles by Alfvén-Cyclotron Waves

Preferential heating and acceleration of heavy ions in the solar wind and corona represent a long-standing theoretical problem in space physics, and are distinct experimental signatures of kinetic processes occurring in collisionless plasmas. We show that fast and slow ion-acoustic waves (IAW) and transverse waves, driven by Alfvén-cyclotron wave parametric instabilities can selectively destroy the coherent fluid motion of different ion species and, in this way lead to their differential heating and acceleration. Trapping of the more abundant protons by the fast IAW generates a proton beam with drift speed of about the Alfvén speed. Because of their larger mass, alpha particles do not become significantly trapped and start, by conservation of total ion momentum, drifting relative to the receding bulk protons. Thus the resulting core protons and the alpha particles are differentially heated via pitch-angle scattering.

An investigation of reversing numerical dynamos driven by either differential or volumetric heating

We present a study of reversing Boussinesq dynamos driven thermally in a rotating spherical shell. For differentially heated dynamos, we investigate the Ekman number dependence of the strong/weak field transition. It is demonstrated that several non-asymptotic features emerge at high Ekman number E > 1 × 1 0 − 3 . At lower E < 1 × 1 0 − 3 , it is shown that reversing dynamos are in weak field states with little influence of the Lorentz force on the flow. A non-magnetic investigation of the onset of convection inside the tangent cylinder (TC) highlights this transition to the lower E regime. Based on these results we choose to study the detailed reversal mechanisms of a dynamo at E = 3.16 × 1 0 − 4 as a compromise between low- E features and numerical expense. For this case comparison with known visual interpretation has been made. We have developed a filtering method where the Lorentz force is being damped consistently in selected regions of the shell. It is demonstrated that upwelling plumes at the inner core boundary (ICB) inside the TC destabilise the magnetic dipole to some extent. However, the induction processes in the main part of the TC interior, in particular at the core-mantle boundary (CMB), stabilise the dipole. The net effect of the TC interior is dipole stabilisation. The polar TC-surface and the equatorial CMB region also contribute to dipole stabilisation. Equatorial upwelling plumes at the ICB outside the TC are necessary to the strong/weak field transition at this Ekman number and act as pronounced reversal builders/triggers. The filtering method highlights the ICB plumes as promoters of dipole instability. For comparison we have therefore also investigated volumetrically heated dynamos where buoyancy is stronger at the CMB. In contrast to the above solutions, these dynamos may be in strong field reversing states. The latter require sufficiently high magnetic Prandtl number Pm. For lower Pm we find solutions with a weak, erratically reversing dipole. The dependence on the inner core size has been determined showing that the erratic dipole dynamos extend to higher Pm for smaller inner cores. A non-magnetic investigation of the onset of convection suggests that these results should be close to the case without an inner core. The filtering method shows that the dipole position of the erratic dipole dynamos is destabilised by flow fluctuations anywhere in the shell. Like for differentially heated dynamos, the reversing strong field dynamos are stabilised by the flow inside the TC where the CMB region reinforces the stabilisation. In sharp contrast, however, the ICB region plays no role to reversals. In fact, the equatorial CMB region contains the processes that build/trigger reversals.

Turbulence, waves, and jets in a differentially heated rotating annulus experiment

We report an analog laboratory study of planetary-scale turbulence and jet formation. A rotating annulus was cooled and heated at its inner and outer walls, respectively, causing baroclinic instability to develop in the fluid inside. At high rotation rates and low temperature differences, the flow became chaotic and ultimately fully turbulent. The inclusion of sloping top and bottom boundaries caused turbulent eddies to behave like planetary waves at large scales, and eddy interaction with the zonal flow then led to the formation of several alternating jets at mid-depth. The jets did not scale with the Rhines length, and spectral analysis of the flow indicated a distinct separation between jets and eddies in wavenumber space, with direct energy transfer occurring nonlocally between them. Our results suggest that the traditional “turbulent cascade” picture of zonal jet formation may be an inappropriate one in the geophysically important case of large-scale flows forced by differential solar heating.

Role of ‘Bejan’s heatlines’ in heat flow visualization and optimal thermal mixing for differentially heated square enclosures

Heat flow patterns in the presence of natural convection have been analyzed with Bejan’s heatlines concept. Momentum and energy transfer are characterized by streamfunctions and heatfunctions, respectively such that streamfunctions and heatfunctions satisfy the dimensionless forms of momentum and energy balance equations, respectively. Finite element method has been used to solve the velocity and thermal fields and the method has also been found robust to obtain the streamfunction and heatfunction accurately. The unique solution of heatfunctions for situations in differential heating is a strong function of Dirichlet boundary condition which has been obtained from average Nusselt numbers for hot or cold regimes. The physical significance of heatlines have been demonstrated for a comprehensive understanding of energy distribution and optimal thermal management via analyzing three cases. Case 1 involves the uniform and non-uniform heating of bottom wall with cooled side walls. The studies illustrate that the heat flow primarily occurs from the central regime of the bottom wall to a very small regime of the top portion of side walls. A large portion of central regime of cold side walls do not receive significant amount of heat. In order to maximize the thermal energy distribution, the distributed heating at the middle portions of the bottom and side walls have been considered in case 2 and heatlines clearly depict the distributions of heat from the hot walls to the large regimes of the cold wall. Further case 3 illustrates the enhanced heat flows in presence of heated bottom and left side walls. Heatline is found as an effective numerical tool to visualize energy distribution in order to establish a suitable heating strategy.

On the boundary layer structure of differentially heated cavity flow in a stably stratified porous medium

This paper considers two-dimensional flow generated in a stably stratified porous medium by monotonic differential heating of the upper surface. For a rectangular cavity with thermally insulated sides and a constant-temperature base, the flow near the upper surface in the high-Darcy–Rayleigh-number limit is shown to consist of a double horizontal boundary layer structure with descending motion confined to the vicinity of the colder sidewall. Here there is a vertical boundary layer structure that terminates at a finite depth on the scale of the outer horizontal layer. Below the horizontal boundary layers the motion consists of a series of weak, uniformly stratified counter-rotating convection cells. Asymptotic results are compared with numerical solutions for the cavity flow at finite values of the Darcy–Rayleigh number.