Variable Surface Heat Research Articles

Observed Diurnal Cycles of Near‐Surface Shear and Stratification in the Equatorial Atlantic and Their Wind Dependence

AbstractThe diurnal cycles of near‐surface velocity and temperature, also known as diurnal jet and diurnal warm layer (DWL), are ubiquitous in the tropical oceans, affecting the heat and momentum budget of the ocean surface layer, air‐sea interactions, and vertical mixing. Here, we analyze the presence and descent of near‐surface diurnal shear and stratification in the upper 20 m of the equatorial Atlantic as a function of wind speed using ocean current velocity and hydrographic data taken during two trans‐Atlantic cruises along the equator in October 2019 and May 2022, data from three types of surface drifters, and data from Prediction and Research Moored Array in the Tropical Atlantic (PIRATA) moorings along the equator. The observations during two seasons with similar mean wind speeds but varying surface heat fluxes reveal similar diurnal jets with an amplitude of about 0.11 m s−1 and similar DWLs when averaging along the equator. We find that higher wind speeds lead to earlier diurnal peaks, deeper penetration depths, and faster descent rates of DWL and diurnal jet. While the diurnal amplitude of stratification is maximum for minimal wind speeds, the diurnal amplitude of shear is maximum at 6 m depth for moderate wind speeds of about 5 m s−1. The inferred wind dependence of the descent rates of DWL and diurnal jet is consistent with the earlier onset of deep‐cycle turbulence for higher wind speeds. The DWL and the diurnal jet not only trigger deep‐cycle turbulence but are also observed to modify the wind power input and thus the amount of energy available for mixing.

Convective heat loss from a modified solar cavity receiver with vertical plate fins: An experimental assessment

AbstractExperimental investigations have been conducted to study the convective heat transfer from a cylindrical solar cavity receiver with vertical fins. The experiments were performed under varying surface heat flux levels and at seven inclination angles, ranging from −90° (upward facing) to +90° (downward facing) at 30° intervals. The impact of fins on the heat transfer process was studied by conducting experiments in two scenarios, namely, finned and unfinned cavities. The findings of the study showed that with an increase in cavity inclination, the magnitude of convective heat loss decreased in both finned and unfinned cavities, while the cavity surface temperature increased. At +90° inclination, the convective heat loss and Nusselt number were observed to have the lowest value, while the surface temperature had the highest value. For a downward‐facing cavity, the fins reduced convective heat loss, leading to an increase in cavity surface temperature. The finned cavity performed better for a vertically downward‐facing inclination (+90°) as it had a contribution of only 11% for convection heat loss compared with the unfinned cavity, which had a contribution of 21% for the same. Furthermore, an empirical model was developed based on the experimental results for the Nusselt number, which correlates experimental data with an error margin of ±15%. This model can be used to predict the Nusselt number for different inclination angles and surface heat flux levels. The presence of vertical fins in the cavity was found to be effective in reducing convective heat loss, especially for downward‐facing cavities. Understanding the influence of fin and cavity inclination on convective heat transfer can lead to enhanced efficiency and performance of solar receivers, thereby increasing the overall energy output of the system.

Stratification and temporal evolution of mixing regimes in diurnally heated river flows

Direct numerical simulations of stratified open channel flows subject to a varying surface heat flux are performed. The influence of the diurnal heating time on the spatial and temporal variation of mixing in the flow and the characteristics of the mean flow state are examined. The control parameters are the bulk stability parameter lambda_{B}, defined through the ratio of the channel height delta and a bulk Obukhov length scale mathscr{L}_{B}, and the diurnal time scale hat{t}, defined as the ratio of the heating time to an eddy turnover time. The Prandtl number Pr and Reynolds number Re_{tau} have values of 1 and 400. Simulations are performed over hat{t} = 1 to 24 and lambda_{B} = 0.6 to 26. Two key flow features are used to classify the flow regimes observed, namely the laminar layer depth (LLD) and stratified layer depth (SLD) where the LLD is defined as the depth from the free surface when the buoyancy Reynolds number Re_{B} approx 7 and the SLD is the depth from the free surface when the turbulent Froude number Fr approx 1. This study attempts to characterise how these length scales vary across the diel cycle. The LLD is a viscous length scale and a regime map of a viscous parameter, the bulk Obhukov Reynolds number Re_mathscr{L}, and hat{t} is presented to classify the LLD behaviour. A regime map of lambda _{B} and hat{t} is presented to classify the behaviour of the SLD. Three classifications for each layer depth behaviour within a diel cycle form the basis of the regime maps for this paper: a neutral flow where the LLD or SLD does not exist (denoted by NL and NS), a stratified flow where the LLD or SLD are diurnally varying (denoted as DL and DS) and a persistent layer of the LLD or SLD (denoted as PL and PS). The transition between the NL to DL is hat{t} propto Re_{mathscr{L}}^{4.5}, DL to PL is hat{t} propto Re_{mathscr{L}}^{- 0.5}, NS to DS is hat{t} propto lambda _{B}^{0} and DS to PS is hat{t} propto lambda _{B}^{1}. The regime maps may be used as a predictive tool to determine when suppressed mixing regimes occur in rivers. At each flow depth, the flow sweeps though a range of mixing states across the diel cycle. The local mixing efficiency are briefly assessed and found to scale well with the instantaneous Fr number according to the regimes proposed by Garanaik and Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323-333).

An experimental inverse problem in determining spatially varying surface heat flux using measured temperature readings

An experimental investigation to estimate the unknown spatially dependent surface heat flux of a flat plate based on the surface temperature readings taken by a thermography camera and the conjugate gradient method (CGM) is examined in this study. In the present three-dimensional inverse problem, the functional form of the heat flux is considered to be initially unknown; thus, the functional form of the heat flux is classified as the category of function estimation. In addition, air velocity is specified as the working condition, not the heat transfer coefficient; therefore, it is defined as an inverse heat conduction-convection conjugated problem (IHCCCP). The experimental study for estimating the unknown spatially dependent surface heat flux has not been examined previously in the IHCCCP. The estimations of the inverse solutions are conducted experimentally with two designed plate heaters and various inlet air velocities and plate thicknesses, and the total heat losses are found to be approximately 5% of the original design heating power. The experimental results indicated that for a uniform heating design (Design A), the estimated heat fluxes are always very accurate if the heat losses are deducted from the design power. For the nonuniform heating design (Design B), due to the existence of two discontinuities in the heating power, the estimated relative errors for heat fluxes are found to be between 16% and 18% using 6 to 8 iterations, reflecting the nature of the inverse problem, i.e., a small measurement error will amplify the error of the estimates; in addition, the estimated heat flux becomes less accurate as the plate thickness increases. Finally, numerical simulations with errorless measurements are performed, and the results reveal that the estimated errors for heat fluxes can be decreased to approximately 8% with 150 iterations for Design B.

Reprint of: Surface temperature of a multi-layer thermal barrier coated wall subject to an unsteady heat flux

A one-dimensional analytical method of determining the surface temperature of a thermal barrier coated plane wall subjected to an arbitrarily time-varying heat flux was developed. The method allows fast computation, enabling it to be embedded in combustion simulation software to correctly calculate wall heat transfer, which is important for reciprocating engine applications with thin, low thermal inertia coatings that have large temperature swings. The method relies on superposition of the response to successive step changes in heat flux, obtained by discretizing the heat flux history, to compile the solution. The embedded problem of a step-change in heat flux is addressed using the one-dimensional heat diffusion equation in conjunction with the matrix method in the Laplace domain, assuming the lateral conduction is neglected. For a two-layer wall (one coating layer on top of the metal wall) in the limit where kρc of the coating is small relative to that for the wall material, an analytical inversion to the time domain can be derived. For modest values of this parameter or for more than one coating layer, the residue theorem is invoked to invert to the time domain, with the poles and residues found numerically. The analytical inversion, however, provided the impetus for defining a set of non-dimensional parameters that uniquely characterize the surface temperature swing for arbitrary periodic heat flux to the wall. Non-dimensional results are given for a sinusoidially varying surface heat flux.

Surface temperature of a multi-layer thermal barrier coated wall subject to an unsteady heat flux

A one-dimensional analytical method of determining the surface temperature of a thermal barrier coated plane wall subjected to an arbitrarily time-varying heat flux was developed. The method allows fast computation, enabling it to be embedded in combustion simulation software to correctly calculate wall heat transfer, which is important for reciprocating engine applications with thin, low thermal inertia coatings that have large temperature swings. The method relies on superposition of the response to successive step changes in heat flux, obtained by discretizing the heat flux history, to compile the solution. The embedded problem of a step-change in heat flux is addressed using the one-dimensional heat diffusion equation in conjunction with the matrix method in the Laplace domain, assuming the lateral conduction is neglected. For a two-layer wall (one coating layer on top of the metal wall) in the limit where kρc of the coating is small relative to that for the wall material, an analytical inversion to the time domain can be derived. For modest values of this parameter or for more than one coating layer, the residue theorem is invoked to invert to the time domain, with the poles and residues found numerically. The analytical inversion, however, provided the impetus for defining a set of non-dimensional parameters that uniquely characterize the surface temperature swing for arbitrary periodic heat flux to the wall. Non-dimensional results are given for a sinusoidially varying surface heat flux.

Nearshore natural convection induced by a periodic thermal forcing at the water surface

Field observations reveal that under calm weather conditions, natural convection resulting from spatial variations in the temperature field plays a significant role in promoting exchanges and mixings in lakes and reservoirs. The present investigation is concerned with natural convection generated by a periodically varying surface temperature within a reservoir model consisting of a sloping nearshore section and a flat offshore section. Three approaches, including derivation of analytical solution, numerical simulation, and scaling analysis, are integrated to reveal the variation of flow response with the intensity of the thermal forcing. The analytical solution reveals that for a sinusoidally varying surface temperature, a cosinusoidally varying surface heat flux is imposed if the duration of the period is sufficiently long. Numerical results show dramatic differences in flow response between conduction-dominated and convection-dominated thermal flow. The former is in phase with the cosinusoidal variation of surface heat flux, whereas the latter is in phase with the sinusoidal variation of surface temperature. The thermal forcing for conduction-dominated and convection-dominated flow is prescribed by surface heat flux and surface temperature, respectively. An evident phase lag is observed shortly after the thermal forcing switches sign. For convection-dominated flow with a Rayleigh number of 2 × 107, the maximum velocity during the cooling phase is significantly larger than that during the heating phase owing to the occurrence of flow instability during the cooling phase, which agrees with field observations. The scales for flow velocity and phase lag are derived by scaling analysis and verified by the results of numerical simulations.

Heat flow, heat production, and crustal temperatures in the Archaean Bundelkhand craton, north‐central India: Implications for thermal regime beneath the Indian shield

AbstractHeat flow and heat production data sets constrain the crustal thermal structure in the 2.5–3.5 Ga Bundelkhand craton, the oldest cratonic core in northern Indian shield, for the first time and allow comparisons with the southern Indian shield. Temperature measurements carried out in 10 boreholes at five sites in the craton, combined with systematic thermal conductivity measurements on major rock types, yield low heat flow in the range of 32–41 mW m−2, which is distinct from the generally high heat flow reported from other parts of the northern Indian shield. Radioelemental measurements on 243 samples of drill cores and outcrops reveal both large variability and high average heat production for the Neo‐Archaean to Palaeo‐Proterozoic granites (4.0 ± 2.1 (SD) μW m−3) relative to the Meso‐Archaean tonalite‐trondhjemite‐granodiorite (TTG) gneisses (2.0 ± 1.0 (SD) μW m−3). On the basis of new heat flow and heat production data sets combined with available geological and geophysical information, a set of steady state, heat flow‐crustal heat production models representative of varying crustal scenarios in the craton are envisaged. Mantle heat flow and Moho temperatures are found to be in the range of 12–22 mW m−2 and 290–420°C, respectively, not much different from those reported for the similar age Dharwar craton in southern India. This study reveals similar mantle thermal regimes across the northern and southern parts of the Indian shield, in spite of varying surface heat flow regimes, implying that much of the intraprovince and interprovince variations in the Indian shield are explained by variations in upper crustal heat production.

Solution of inverse radiation-conduction problems using a Kalman filter coupled with the recursive least–square estimator

This paper presents a non–intrusive inverse heat transfer procedure for predicting the time–varying heat flux on the surface of semitransparent media. Inverse radiation–conduction problems were analyzed using a Kalman filter coupled with a recursive least–square estimator (KF–RLSE). Since its unique capability to make fast predictions, KF–RLSE can be easily integrated to existing real–time control systems of industrial facilities. The performance of KF–RLSE was examined thoroughly in a series of numerical simulations in two semitransparent materials (i.e. the glass with black coating and the ceramic of zirconium dioxide ZrO2) to extract the time–varying surface heat flux on–line from the measured temperature history at boundary. Results showed that the proposed method can predict the unknown boundary flux with an acceptable error. The influence of different parameters on the accuracy and stability of the predicted heat flux was also investigated. Results indicated that the sensor location, process noise covariance and absorption coefficient exerted stronger effects on retrieval results compared with other parameters.

An evaluation of gas transfer velocity parameterizations during natural convection using DNS

AbstractDirect numerical simulations (DNS) of free surface flows driven by natural convection are used to evaluate different methods of estimating air‐water gas exchange at no‐wind conditions. These methods estimate the transfer velocity as a function of either the horizontal flow divergence at the surface, the turbulent kinetic energy dissipation beneath the surface, the heat flux through the surface, or the wind speed above the surface. The gas transfer is modeled via a passive scalar. The Schmidt number dependence is studied for Schmidt numbers of 7, 150 and 600. The methods using divergence, dissipation and heat flux estimate the transfer velocity well for a range of varying surface heat flux values, and domain depths. The two evaluated empirical methods using wind (in the limit of no wind) give reasonable estimates of the transfer velocity, depending however on the surface heat flux and surfactant saturation. The transfer velocity is shown to be well represented by the expression, , where is a constant, is the buoyancy flux, is the kinematic viscosity, is the Schmidt number, and the exponent depends on the water surface characteristics. The results suggest that and and for slip and no‐slip boundary conditions at the surface, respectively. It is further shown that slip and no‐slip boundary conditions predict the heat transfer velocity corresponding to the limits of clean and highly surfactant contaminated surfaces, respectively.

Free convection in MHD micropolar fluid with radiation and chemical reaction effects

In this paper, the effects of radiation and first order chemical reaction on free convection heat and mass transfer in a micropolar fluid is considered. A uniform magnetic field is applied normal to the plate. The plate is maintained with variable surface heat and mass fluxes. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The dimensionless velocity, microrotation, temperature, concentration and heat and mass transfer rates are presented graphically for various values of coupling number, magnetic parameter, radiation parameter, chemical reaction parameter. The numerical values of the skin friction and wall couple stress for different values of governing parameters are also tabulated.

Effects Of Changing Surface Heat Flux On Atmospheric Boundary-Layer Flow Over Flat Terrain

We examine the unsteady response of a neutral atmospheric boundary layer (ABL) of depth h and friction velocity u * when a uniform surface heat flux is applied abruptly or decreased rapidly over a time scale t thetas less than about h /(10u *). Standard Monin–Obukhov (MO) relationships are used for the perturbed eddy viscosity profile in terms of the changes to the heat flux and mean shear. Analytical solutions for changes in temperature, mean wind and shear stress profile are obtained for the surface layer, when there are small changes in h /|LMO| over the time scale tMO~|L MO|/(10u*) (where L MO and t MO are the length and time scales, respectively). They show that a maximum in the wind speed profile occurs at the top of the thermal boundary layer for weak surface cooling, i.e. a wind jet, whereas there is a flattening of the profile and no marked maximum for weak surface heating. The modelled profiles are approximately the same as those obtained from the U.K. Met Office Unified Model when operating as a mesoscale model at 12-km horizontal resolution. The theoretical model is modified when strong surface heating is suddenly applied, resulting in a large change in h /|L MO| (>>1), over the time scale t MO. The eddy structure is predicted to change significantly and the addition of convective turbulence increases the shear turbulence at the ground. A low-level wind jet can form, with convective turbulence adding to the mean momentum of the flow. This was verified by our laboratory experiment and direct numerical simulations. Additionally, it is shown that the effects of Coriolis acceleration diminish (rather than as suggested in the literature, amplify) the formation of the wind jets in the situations considered here. Hence, only when the surface heat flux changes over time scales greater than 1/f (where f is the Coriolis parameter) does the ABL adjust monotonically between its equilibrium states. These results are also applicable to the ABL passing over spatially varying surface heat fluxes.

Finite difference analysis of unsteady natural convection MHD flow past an inclined plate with variable surface heat and mass flux

A numerical solution of the transient free convection MHD flow of an incompressible viscous fluid past a semi-infinite inclined plate with variable surface heat and mass flux is presented here. The non-dimensional governing equations of the flow are unsteady, coupled and non-linear integro partial differential equations. The governing equations are solved by an efficient, more accurate and unconditionally stable implicit finite difference scheme. Velocity, temperature and concentration of the flow have been presented for various parameters such as Prandtl number, Schmidt number, the buoyancy ratio parameter, Grashof number, inclination angle φ and the magnetic parameter. The local and average skin friction, Nusselt number and Sherwood number are also presented graphically.

Entrainment and Decoupling Relations for Cloudy Boundary Layers

An idealized model of the relationship between entrainment in cloud-topped boundary layers, circulation structure, and the degree of decoupling between the cloud and subcloud layers is developed based on simple turbulent flux distributions and the premise that the entrainment rate, both at cloud top and across cloud base when some stability exists there, is controlled by the large-eddy structure for quasi-steady buoyantly driven conditions. Layers are classified in three regimes depending on whether the cloud-top entrainment rate is ultimately limited by the transport of eddies spanning the full boundary layer (I), the cloud layer (II), or the subcloud layer (III). Algebraic relations are derived for the boundaries between, and entrainment fluxes in, each regime as a function of a convenient set of physical input parameters. The transition from regime II into III, representing the decoupling transition leading to a cumulus coupled layer, is emphasized. The model predicts that decoupling is promoted by a decrease in Bowen ratio or increase in cloud-top humidity to temperature jump ratio, and, depending on the point in parameter space, either promoted or inhibited by an increase in cloud-top radiative cooling or an increase in cloud depth. In spite of the complex cloud-layer dynamics involving cumulus plumes, a simple prediction is given for the quasi-steady cloud-top entrainment rate in regime III based on the subcloud dynamics. The model is compared with results from an extensive set of large-eddy simulations varying surface heat and moisture fluxes, cloud-top humidity and temperature jumps, and relative cloud depth. Good agreement is found with the predicted entrainment rates, the qualitative layer structure, and location of the decoupling boundary in the parameter space varied.

Inverse Convection Problem for Determining Wall Heat Flux in Annular Duct Flow

An inverse problem for unsteady forced convection in an annular duct is presented. The simulated temperature data taken at the outer wall are used to estimate the time-dependent axially varying surface heat flux distribution at the inner wall of the annular passage. No prior information on the functional form of the unknown wall heat flux is needed in the inverse method. The effects of the functional form of the wall heat flux, the number of the measurement points, and the measurement errors on the accuracy of the estimation are investigated. It is shown that the reconstruction of the timewise and spatial variations of the wall heat flux is satisfactory even if the estimated function is not smooth. [S0022-1481(00)01003-3]

Analytical solutions of transient heat conduction in semi-infinite solid with time varying boundary conditions by means of similarity transformation

An anlytical solution to the transient one dimensional linear heat conduction with time varying boundary conditions is obtained by means of similarity transformation via one-parameter groups. Two types of time varying boundary conditions are considered. These are; time varying surface temperature and time varying surface heat flux boundary conditions. In the analysis, thermal conductivity and thermal diffusivity, are assumed to be constant. The solution is generalized for a general polynomial type of time varying boundary conditions.

Ｎｉで汚染したＳｉ表面の再配列構造

Ni-contaminated surfaces of coverages less than 0.1 ML (monolayer) were studied by low-energy electron diffraction (LEED), Auger-electron spectroscopy (AES) and ion channeling and blocking spectroscopy with varying surface heat treatment. The reconstructed structures of Ni-contaminated surfaces of Si vary with the Ni-concentration in the surface, which changes depending on the heat treatment.The surface reconstructed structures on Ni-contaminated surfaces for Si (110), (100) and (111) have been discussed on the basis of our experimental results of LEED with referring to other results of scanning tunneling microscopy (STM) .

Transient temperatures from periodic surface heat flux for slabs, cylinders, and spheres

The transient temperatures resulting from a periodically varying surface heat flux boundary condition have numerous applications. In this work, explicit, analytic solutions are presented for the transient surface and medium temperatures due to periodically varying step changes in surface heat flux for geometries such as a slab, cylinder, and sphere. The nonlinear case allowing for the added effects of radiation from the surface into an external ambient are studied numerically.

Free convection from a vertical plate with nonuniform surface heat flux and embedded in a porous medium

An analysis is presented for the calculation of heat transfer due to free convective flow along a vertical plate embedded in a porous medium with an arbitrarily varying surface heat flux. By applying the appropriate coordinate transformations and the Merk series, the governing energy equation is expressed as a set of ordinary differential equations. Numerical solutions are presented for these equations which represent universal functions and several computational examples are provided.

Synopsis of Analytic Solutions for the Temperature Distribution in a River Downstream From a Dam or Reservoir

A synopsis of analytic solutions for river temperature downstream from a dam is presented. Transient, convective, and diffusive effects are considered as well as periodic and spatially varying surface heat exchange. Two new solutions of the transient equation for heat transport in a river with fluctuating surface heat exchange have been developed. The first describes the transient‐convective temperature response in a river subjected to a combination of fluctuating and spatially varying surface heat transfer. The second new solution represents a complete transient‐convective‐diffusive solution to the equation for river temperature when surface heat exchange is dependent upon periodically varying meteorological conditions. The parameters determining the amplitude of the river response, as well as the lag between atmospheric forcing and river response, are delineated.