Convective Heat Transport Research Articles

Compuational study on transport of thermal energy and mass species in power law rheological fluid with hybrid nanostructures in the presence of chemical reaction

Power law rheological model is used for mathematical modeling of simultaneous transport of heat and energy via hybrid nanoparticles distributed in heat generating fluid exposed to magnetic field. Governing conservation laws, correlation between thermos-physical properties fluid, solid particles, suitable no-slip momentum and temperature boundary conditions are provided system of boundary value problems which are solved numerically using finite element method (FEM). The FEM simulations are used in capturing the dynamics of physical parameters on the momentum transport and heat energy transfer under the influence of non-uniformly moving surface which is being heated in non-uniform manner. Power law fluid flow experiences retardation as intensity of magnetic field is increased. Hybrid nanofluid is more heat generative than mono nanofluid and power law index causes a decrease in flow. Consequently, convective transport of heat is compromised. Generative and destructive chemical reactions have opposite trend on transport of species in power law fluid.

Fully developed entropy-optimized MHD nanofluid flow by a variably thickened rotating surface

Entropy generation analysis for three-dimensional (3D) magnetohydrodynamic (MHD) flow of viscous fluid through a rotating disk is addressed in this article. Entropy generation is explored as a function of temperature and velocity. The modeling of the considered problem is performed through Buongiorno model. Conservation of energy comprises dissipation, convective heat transport and Joule heating. Flow under consideration is because of nonlinear stretching velocity of disk. Transformations used lead to the reduction of partial differential equations into ordinary differential equations. Total entropy generation rate is scrutinized. Non-linear computations have been carried out. Domain of convergence for the obtained solutions is identified. Radial, axial and tangential velocities are interpreted. Entropy equation is studied in the presence of dissipation, Brownian diffusion and thermophoresis effects. Velocity and temperature gradients are discussed graphically. Meaningful results are summed up in the concluding section.

Natural convection of mathrm {Al}_{2}mathrm {O}_{3}-water nanofluid in a non-Darcian wavy porous cavity under the local thermal non-equilibrium condition

This study investigates thermal natural convective heat transfer in a nanofluid filled-non-Darcian porous and wavy-walled domain under the local thermal non-equilibrium condition. The considered cavity has corrugated and cold vertical walls and insulated horizontal walls except the heated part positioned at the bottom wall. The transport equations in their non-dimensional model are numerically solved based on the Galerkin finite-element discretization technique. The dimensionless governing parameters of the present work are the nanoparticle in volume concentration, the Darcy number, number of undulations, modified heat conductivity ratio, dimensionless heated part length, and location. Comparisons with other published theoretical and experimental results show good agreement with the present outcomes. The findings indicate that the heater length, its position, and the waves number on the side vertical walls as well as the nanoparticles concentration can be the control parameters for free convective motion and heat transport within the wavy cavity.

Connections between nonrotating, slowly rotating, and rapidly rotating turbulent convection transport scalings

In this paper, we investigate and develop scaling laws as a function of external nondimensional control parameters for heat and momentum transport for nonrotating, slowly rotating, and rapidly rotating turbulent convection systems, with the end goal of forging connections and bridging the various gaps between these regimes. Two perspectives are considered, one where turbulent convection is viewed from the standpoint of an applied temperature drop across the domain and the other with a viewpoint in terms of an applied heat flux. While a straightforward transformation exists between the two perspectives, indicating equivalence, it is found the former provides a clear set of connections that bridge between the three regimes. Our generic convection scalings, based upon an inertial-Archimedean balance, produce the classic diffusion-free scalings for the nonrotating limit and the slowly rotating limit. This is characterized by a free-falling fluid parcel on the global scale possessing a thermal anomaly on par with the temperature drop across the domain. In the rapidly rotating limit, the generic convection scalings are based on a Coriolis-inertial-Archimedean (CIA) balance, along with a local fluctuating-mean advective temperature balance. This produces a scenario in which anisotropic fluid parcels attain a thermal wind velocity and where the thermal anomalies are greatly attenuated compared to the total temperature drop. We find that turbulent scalings may be deduced simply by consideration of the generic nondimensional transport parameters—local Reynolds Reℓ=Uℓ/ν; local Péclet Peℓ=Uℓ/κ; and Nusselt number Nu=Uϑ/(κΔT/H)—through the selection of physically relevant estimates for length ℓ, velocity U, and temperature scales ϑ in each regime. Emergent from the scaling analyses is a unified continuum based on a single external control parameter, the convective Rossby number, RoC=gαΔT/4Ω2H, that strikingly appears in each regime by consideration of the local, convection-scale Rossby number Roℓ=U/(2Ωℓ). Thus we show that RoC scales with the local Rossby number Roℓ in both the slowly rotating and the rapidly rotating regimes, explaining the ubiquity of RoC in rotating convection studies. We show in non-, slowly, and rapidly rotating systems that the convective heat transport, parametrized via Peℓ, scales with the total heat transport parameterized via the Nusselt number Nu. Within the rapidly rotating limit, momentum transport arguments generate a scaling for the system-scale Rossby number, RoH, that, recast in terms of the total heat flux through the system, is shown to be synonymous with the classical flux-based CIA scaling, RoCIA. These, in turn, are then shown to asymptote to RoH∼RoCIA∼RoC2, demonstrating that these momentum transport scalings are identical in the limit of rapidly rotating turbulent heat transfer.Received 22 February 2020Accepted 7 September 2020Corrected 30 March 2021DOI:https://doi.org/10.1103/PhysRevResearch.2.043115Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAstrophysical fluid dynamicsGeophysical fluid dynamicsRayleigh-Bénard convectionRotating geophysical flowsScaling laws of complex systemsTurbulenceNonlinear DynamicsFluid DynamicsInterdisciplinary Physics

Application of different hybrid nanofluids in convective heat transport of Carreau fluid

Abstract Herein, the numerical investigation is carried out to study the flow and heat transfer analysis through a hybrid nanofluid flow over a porous medium. The governing partial differential equations are transformed into ordinary differential equations with the help of similarity transformations. The resulting ODEs are solved by a numerical technique using RKF-45 Method. Through graphs, the impacts of pertinent parameters on energy and velocity field were deliberated. Indeed, the outcomes were quite promising. It is noticed that, the surface drag force in terms of Hartman number changes has inverse relation to x -axis and directly relation to y-axis. Furthermore, the rate of heat transfer is more in MoS_2-Ag hybrid nanofluid is more than that of TiO_2-CuO hybrid nanofluid.

Influence of flow pulsations and yield stress on heat transfer from a sphere

In this work, the momentum and heat transfer characteristics of a time-dependent flow of Bingham plastic fluid over a heated isothermal sphere have been investigated numerically over wide ranges of conditions: Reynolds number, 5 ≤ Re ≤ 120, Bingham number, 0.1 ≤ Bn ≤ 100, Prandtl number, 0.7 ≤ Pr ≤ 100, frequency, π/4 ≤ ω* ≤ π and amplitude, 0 ≤ A ≤ 0.8. The influence of the fluid yield stress and inertia due to the imposed flow pulsations on the flow and thermal fields have been examined in detail. Detailed structure of the flow and temperature fields are analysed in terms of the instantaneous streamlines, isothermal contours, yielded/unyielded zones, surface pressure profiles, time-average drag coefficient and surface- and time-average Nusselt number. The influence of the frequency and amplitude of pulsations on the size of yielded (fluid-like) and unyielded (solid-like) zones is considered in order to understand convective heat transport. The size of yielded zones is seen to be in phase with the imposed pulsating velocity. However, the yield stress effects suppress the influence of flow pulsations. The temporal evolution of the drag coefficient and Nusselt number lag the imposed pulsating flow by different degrees thereby indicating the inherently different evolution of the momentum and thermal boundary layers. Broadly, the pulsating flow conditions may lead to up to 20% augmentation in heat transfer provided there is a moderate degree of advection and/or when the fluid yield stress effects are weak, i.e., small Bingham numbers. Thus, the maximum benefits of pulsating flow accrue in Newtonian fluids only. Finally, the present values of the time-average Nusselt number have been consolidated in the form of a predictive expression.

Heat and mass transport analysis of the drying of freshwater fishes by a forced convective air‐dryer

AbstractThe drying behavior of different freshwater fishes (with/without scales) is investigated using a simple convective heated air dryer. Drying processes are analyzed to study the kinetics of drying, shrinkage dependent variable effective diffusivity, convective heat and mass transport, and the energy aspect of drying. Among the drying kinetic models, Hasibuan–Daud and Haghi–Angiz‐I models produce the best fit for fishes with scales and Hii model produces the best fit for fish without scales. Diffusion analysis performed based on simplified solution of Fick's diffusion equation shows higher effective diffusivity for fish without scales, proving additional barrier from scales (for fish with scales) that need to be considered during dryer design. Calculated instantaneous heat and mass transfer coefficients (different for fish with or without scales) also agree with this observation, accentuating the difference based on scales. Drying process for all fishes obeys the heat‐mass transfer correlation. Estimated parameters such as effective diffusivity (0.2–1 × 10−9 m2/s) and convective heat and mass transfer coefficients (7–14 W/m2/K and 2.8–4.5 × 10−6 m/s, respectively) can be utilized in designing different fish drying systems. Average and instantaneous total energy consumption, specific moisture extraction ratio, and specific energy consumption are evaluated in order to provide a comprehensive picture of the drying process.Practical ApplicationsFresh‐ and salt‐water fishes account for major sources of protein‐rich food for substantial parts of the population in underdeveloped and developing nations. To circumvent the wastage associated with microbial contaminations during prolific seasons, fish drying has been widely employed as a way of preserving this perishable food. Convective drying of agricultural products as well as marine foods is a commonly employed drying method for food preservation. This study investigates the drying behavior of three different freshwater fishes using an in‐house constructed forced convective air dryer. The experimental drying characteristics and estimated parameters by model fitting during fish drying will be particularly applicable in the wide field of fish drying. The outcome of this study can also be utilized for more effectively designing and evaluating low‐cost convective fish dryers.

Convective heat transport in a heat generating MHD vertical layer saturated by a non-Newtonian nanofluid: a bidirectional study

PurposeIn this framework, the three dimensional (3D) flow of hydromagnetic Carreau nanofluid transport over a stretching sheet has been addressed by considering the impacts of nonlinear thermal radiation and convective conditions.Design/methodology/approachInfinite shear rate viscosity impacts are invoiced in the modeling. The heat and mass transport characteristics are explored by employing the effects of a magnetic field, thermal nonlinear radiation and buoyancy effects. Rudimentary governing partial differential equations (PDEs) are represented and are transformed into ordinary differential equations by the use of similarity transformation. The nonlinear ordinary differential equations (ODEs), along with the boundary conditions, are resolved with the aid of a Runge-Kutta-Fehlberg scheme (RKFS) based on the shooting technique.FindingsThe impact of sundry parameters like the viscosity ratio parameter (β*), nonlinear convection parameters due to temperature and concentration (βT, βC), mixed convection parameter (α), Hartmann number (M2), Weissenberg number (We), nonlinear radiation parameter (NR), and the Prandtl number (Pr) on the velocity, temperature and the concentration distributions are examined. Furthermore, the impacts of important variables on the skin friction, Nusselt number and the Sherwood number have been scrutinized through tables and graphical plots.Originality/valueThe velocity distribution is suppressed by greater values of the Hartmann number. The velocity components in the tangential and axial directions of the fluid are raised with the viscosity ratio parameter and the tangential slip parameter, but these components are reduced with concentration to thermal buoyancy forces ratio and stretching sheet ratio.

Effect of horizontal pressure gradient on Rayleigh–Bénard convection of a Newtonian nanoliquid in a high porosity medium using a local thermal non‐equilibrium model

AbstractA study of linear and weakly nonlinear stability analyses of Darcy–Brinkman convection in a water–alumina, nanoliquid‐saturated porous layer for stress‐free isothermal boundaries, when the solid and nanoliquid phases are in local thermal nonequilibrium, is conducted. The critical eigenvalue is found using the Galerkin approach. The effect of the pressure gradient, thermal conductivity ratio, interphase heat transfer coefficient, inverse Darcy number, and Brinkman number on the heat transport and onset of convection is examined and represented graphically. The critical values of wavenumber and nanoliquid Rayleigh number are found for different problem parameter values. The effect of increasing the porosity‐modified ratio of thermal conductivity advances the onset of convection and increases the amount of heat transport, whereas the remaining parameters have the opposite impact on the onset of convection and amount of heat transport. The classical results of the local thermal equilibrium case and Darcy–Bénard convection in the presence of pressure gradient are obtained as a limiting case of the present problem.

Entropy analysis of Powell–Eyring hybrid nanofluid including effect of linear thermal radiation and viscous dissipation

Hybrid nanofluids are introduced as heat transfer fluids with greater surface stability, diffusion and dispersion capabilities compared to traditional nanofluids. In this work, flow, convective heat transport and volumetric entropy generation in Powell–Eyring hybrid nanofluid are investigated. Hybrid nanofluid occupies the space over the uniform horizontal porous stretching surface with velocity slip at the interface. Effect of viscous dissipation and linear thermal radiation are also included in the simplified model. Mathematical equations for conservation of mass, momentum, energy and entropy are simplified under assumptions of boundary layer flow of Powell–Eyring hybrid nanofluid. Similarity solutions are obtained by transformation of governing partial differential equations to ordinary differential equations, using similarity variables. Keller box finite difference scheme is then adopted to find the approximate solutions of reduced ordinary differential equations. Numerical computations are performed for alumina–copper water ( $${\mathrm{Al}}_2{\mathrm{O}}_3$$ – $${\mathrm{Cu/H}}_{2}{\mathrm{O}}$$ ) hybrid nanofluid and conventional copper water ( $${\mathrm{Cu}}$$ – $${\mathrm{H}}_{2}{\mathrm{O}}$$ ) nanofluid. Graphs are produced for velocity, temperature and entropy profiles to study the effect of governing parameters. Skin friction factor and the local Nusselt number are also calculated at the boundary. The notable findings indicate that the hybrid Powell–Eyring nanofluid is better thermal conductor when compared with the conventional nanofluid. The rate of heat transfer at the boundary is greatest for smallest value of the shape factor parameter. The increase in Reynolds number and Brinkman number increases the overall entropy of the system.

Sources and transport of fluid and heat at the newly-developed Theistareykir Geothermal Field, Iceland

Successful management of geothermal energy requires detailed understanding of physical and chemical conditions within the field prior to exploitation. It is thus crucial to identify fluids involved and their residence times, as well as the heat source, so as to assess the potential of the resource in terms of energy production. To this end, a geochemical study of relatively undisturbed fluids from the newly-developed Theistareykir geothermal field, Northern Volcanic Zone, Iceland was carried out on production wells, fumaroles, and mud pots. Noble gas (He, Ne, Ar, Kr, and Xe) elemental and isotopic abundances and stable isotopes (δ18O and δ2H) were measured to determine the system fluid sources and dynamics as exploitation proceeds. Results of this study, together with previously published data, show that four fluid sources are present: modern and local meteoric water (48.9%); sub-modern meteoric water from regional highlands precipitation (10.6%); pre-Holocene glaciated meteoric water (40.4%) with strongly depleted δ2H values of −127‰, calculated 40K-40Ar* fluid residence times from 57 ± 20 ka to 92 ± 30 ka and a (U/Th)-4He fluid residence times from 96 ± 50 ka to 160 ± 80 ka; and, finally, 3He-rich magmatic fluids. Concomitant enrichment in 18O and radiogenic 4He suggests that some fluids reside a long time in the reservoir, exchanging O and He with reservoir rocks. Maximum estimated helium isotopic ratios, 3He/4He (R), of 11.45 Ra (Ra = atmospheric ratio) show that the magma beneath Theistareykir is a depleted mid-ocean ridge basalt (MORB) mantle (DMM), with less influence (8.7 to 12.7%) of the Icelandic mantle plume source. Calculated heat (Q)/3He ratios plotted vs. R/Ra and 4He/36Ar ratios suggest that convective heat transport dominates the eastern part of the field where the magmatic heat source is located, while in other parts of the field, heat conduction seems to be dominant. Boiling and phase separation exists in the field, as indicated by δ18O values which fall to the left of the Global Meteoric Water Line in a δ18O vs. δ2H plot, but Q/3He ratios indicate that boiling affects only 1–10% of the fluid reservoir. With this obtained knowledge, any subsequent changes in the field conditions during the exploitation phase of Theistareykir can be better understood, helping to sustainably manage the resource.

Buoyancy-driven melting and heat transfer around a horizontal cylinder in square enclosure filled with phase change material

This work primarily focuses on designing a cost effective method yielding high rate of heat transfer from a heated object to ensure the faster melting of the phase change material (PCM). A numerical investigation has been performed on the laminar natural convection from a two-dimensional heated circular cylinder confined in a square enclosure filled with a phase change material, namely, the lauric acid. In particular, the coupled momentum and energy equations are solved to delineate the influence of the geometric position of the cylinder within the square enclosure on the melt and heat transfer characteristics of the phase change material. The solid-liquid phase change is formulated using the enthalpy–porosity technique. The detailed velocity and temperature fields are visualized in terms of velocity vectors, isotherm contours, melt fraction contours, melting rate, energy storage and surface averaged Nusselt number. The results reported herein are restricted to the six distinct geometrical positions (i.e., four symmetric and two asymmetric) of the cylinder within the enclosure. The rate of convective heat transport and hence the melt fraction is found to decrease with the increasing distance of the cylinder from the base of the enclosure. In addition, the influence of the mushy zone parameter (Amush) on the melting behaviour has also been explored. The reported numerical results for the melt fraction have been correlated as a function of the melting time and the geometric positions of the heated cylinder. Finally, one can conclude that it is possible to realize an enhanced rate of melting and energy storage simply by adjusting the location of the cylinder under confinement and thus the performance of a thermal energy storage (TES) system can remarkably be improved.

Infrared imaging of the cooling fin equation

A simple experiment based on thermal imaging is devised to observe and measure, along a cooling fin in contact with a hot spot, the temperature profile determined by conductive and convective heat transport. By using a simple theoretical approach, the cooling fin equation is justified and applied to describe, in an educational framework and perspective, the experimental results. Both the experimental setup and the theoretical model discussed in this work are suited for undergraduate physics students.

Numerical simulation of mixed convective 3D flow of a chemically reactive nanofluid subject to convective Nield's conditions with a nonuniform heat source/sink

AbstractThe present investigation aims to explore the influence of a mixed convection and nonuniform heat source/sink on unsteady flow of a chemically reactive nanofluid driven by a bidirectionally expandable surface. Convective heat transport phenomenon is used to maintain the temperature of the surface. Moreover, zero mass flux is also accounted at the surface such that the fraction of nanomaterial maintains itself on strong retardation. The governing nonlinear set of partial differential equations is transformed into a set of ordinary differential equations via a suitable combination of variables. The Keller‐Box scheme has been incorporated to make a numerical inspection of the transformed problem. The spectacular impacts of the pertinent constraints on thermal and concentration distributions are elucidated through various plots. Graphical outcomes indicate that the thermal state of nanomaterial and nanoparticles concentration are escalated for elevated amounts of Biot number, porosity parameter and nonuniform heat source/sink constraints. Furthermore, it is also seen that escalating amounts of unsteady parameter, temperature controlling indices, Prandtl number, and expansion ratio parameter reduce the thermal and concentration distributions. Numerical results for the rate of heat transference have been reported in tabular form. The grid independence approach is used to verify the convergence of the numerical solution and the CPU run time is also obtained to check the efficiency of the numerical scheme adopted for finding the solution.

True Science for Government Leaders and Educators: The Main Cause of Global Warming

Government leaders and educators ought to be able to rely on scientists to tell the truth about climate change, but science has been tainted by politics. Real science, unlike politics, is all about telling the truth, truth that is securely anchored to the properties of matter and radiation. The current, high-profile, politically-driven, climate-change debate centers on two disparate ideas, namely, either global warming is caused by carbon dioxide or is not occurring at all. Neither is correct. Evidence from World War II indicates that particulate pollution, not carbon dioxide, is the cause of global warming. The difference between daily high and nightly low temperature data, tracked over time over a large geographic area, provide evidence that global warming is in fact occurring, which is independent of carbon dioxide. Particles in the lower atmosphere (troposphere) are heated by solar radiation and by radiant heat from the Earth, and transfer that heat to atmospheric gases by molecular collisions. The resultant heating increases atmospheric temperature, and reduces the temperature difference relative to air near the surface, which reduces atmospheric convection, and concomitantly reduces convective heat transport from the surface. This is the mechanism whereby particulate pollution causes global warming.

Detection of groundwater flux changes in response to two large earthquakes using long-term bedrock temperature time series

Heat as a groundwater tracer has potential application in identifying earthquake-induced changes in fluid flow. Since convective heat transport modifies the phase and amplitude of periodic oscillations under pure heat conduction condition, temporal variation of groundwater flux can thus be derived from multi-depth periodic temperature signals. Here we present groundwater flux changes after two large earthquakes nearby, determined from in situ bedrock temperature measurements in the Xianshuihe fault zone, at the eastern margin of the Tibetan Plateau. Five-year temperature time series at six different locations are recorded by high sensitivity temperature sensors (10−4 K) installed at various depths ranging from 0 to 20 m. Groundwater fluxes are estimated through time-varying amplitudes and phases of the annual oscillations, extracted from the Dynamic Harmonic Regression technique. Results show different hydrological responses to these two earthquakes. After the 2013 Ms 7.0 Lushan earthquake, sustained rise in upward flux was revealed at all locations in the intermediate-field, contradicting to the modeled coseismic static dilatational strains. However, groundwater flux patterns after the 2014 Ms 6.3 Kangding earthquake are consistent with the coseismic volumetric strain distribution of a quadrantal pattern of this event. We propose that enhanced hydraulic permeability by dynamic stress might cause the increased upward fluid flux after the Lushan earthquake in the intermediate-field, while coseismic static volumetric strain may account for the hydrological changes after the Kangding earthquake in the near-field. This is the first time that temperature–time series are used to quantify continuous earthquake-related changes in groundwater fluxes. In situ temperature monitoring can provide insights into earthquake-driven hydrologic responses, and also offer additional information to identify temporal changes in crustal strain or hydraulic properties.

A Critical Review of the Physics and Modeling of Deteriorated Heat Transfer in Supercritical Fluids

Abstract Modeling of deterioration of heat transfer (DHT) observed in fluid flows at supercritical pressure remains a challenge due to incomplete understanding of the underlying physics. Given the challenges involved in the experimental and computational study of this phenomenon, it is crucial that the growing collective experimental and computational data be periodically analyzed in a comparative manner through critical reviews. This paper aims to provide such a critical review. The experimental and computational evidence continues to support the postulate that streamwise acceleration of the lower density, near-wall fluid layer relative to the higher density bulk flow promotes reduced turbulent mixing and hence reduced convective heat transport. At lower mass flowrates, this may be driven by buoyancy force, whereas at higher thermal loading, the dominant driver may be the increased favorable streamwise pressure gradient prompted by the bulk flow acceleration. A discussion of these physical mechanisms and an assessment of related semi-empirical models constitute the scope of this review.

Theoretical and analytical analysis of convective heat transport of radiated micropolar fluid over a vertical plate under nonlinear Boussinesq approximation

PurposeIn heat transfer problems, if the temperature difference is not sufficiently so small then the linear Boussinesq approximation is not adequate to describe thermal analysis. Also, nonlinear density variation with respect to temperature/concentration has a significant impact on heat and fluid flow characteristics. Because of this reason, the impact of nonlinear density variation in the buoyancy force term cannot be neglected. Therefore in this paper, the unsteady flow and heat transfer of radiating magneto-micropolar fluid by considering nonlinear Boussinesq approximation is investigated analytically.Design/methodology/approachThe flow is fully developed and time-dependent. Heat and mass flux boundary conditions are also accounted in the analysis. The governing equations of transport phenomena are treated analytically using regular perturbation method. To analyze the tendency of the obtained solutions, a parametric study is performed.FindingsIt is established that the velocity field is directly proportional to the nonlinear convection parameter and the same trend is observed with the increase of the value of Grashof number. The micro-rotational velocity profile decreases with increase in the nonlinear convection parameter. Further, the temperature profile increases due to the presence of radiative heat aspect.Originality/valueThe effectiveness of nonlinear Boussinesq approximation in the flow of micropolar fluid past a vertical plate in the presence of thermal radiation and magnetic dipole is investigated for the first time.

Rayleigh–Bénard convection of a viscoplastic liquid in a trapezoidal enclosure

The objective of this paper is to clarify the role of sloping walls on convective heat transport in Rayleigh–Bénard convection within a trapezoidal enclosure filled with viscoplastic fluid. The rheology of the viscoplastic fluid has been modeled with Bingham fluid model. The system of coupled nonlinear differential equations was solved numerically by Galerkin's weighted residuals scheme of finite element method. The numerical experiments are carried out for a range of parameter values, namely, Rayleigh number (5.103 ≤ Ra ≤ 105), yield number (0 ≤ Y ≤ Yc), and sidewall inclination angle (ϕ = 0, π/6, π/4, π/3) at a fixed Prandtl number (Pr = 500). Effects of the inclination angle on the flow and temperature fields are presented. The results reveal that inclination angle causes a multicellular flow and appears as the main parameter to govern heat transfer in the cavity. The heat transfer rate is found to increase with the increasing angle of the sloping wall for both Newtonian and yield stress fluids. On the other hand, the plug regions also found to increase with increasing φ, which is unusual but perhaps not unexpected behavior. In the yield stress fluids, the flow becomes motionless above a critical yield number Yc because the plug regions invade the whole cavity. The critical yield number Yc is also affected by the change of inclination angle and increases significantly with the increase of φ.

Thermal radiation in Rayleigh-Bénard convection experiments.

An important question in turbulent Rayleigh-Bénard convection (RBC) is the effectiveness of convective heat transport, which is conveniently described via the scaling of the Nusselt number (Nu) with the Rayleigh (Ra) and Prandtl (Pr) numbers. In RBC experiments, the heat supplied to the bottom plate is also partly transferred by thermal radiation. This heat transport channel, acting in parallel with the convective and conductive heat transport channels, is usually considered insignificant and thus neglected. Here we present a detailed analysis of conventional far-field as well as strongly enhanced near-field radiative heat transport occurring in various RBC experiments. A careful inclusion of the radiative transport appreciably changes the Nu=Nu(Ra) scaling inferred in turbulent RBC experiments near ambient temperature utilizing gaseous nitrogen and sulfur hexafluoride as working fluids. On the other hand, neither the conventional far-field radiation nor the strongly enhanced near-field radiative heat transport appreciably affects the heat transport law deduced in cryogenic helium RBC experiments.