scholarly journals Stochastic analysis of field-scale heat advection in heterogeneous aquifers

2012 ◽  
Vol 16 (3) ◽  
pp. 641-648 ◽  
Author(s):  
C.-M. Chang ◽  
H.-D. Yeh
Keyword(s):  
Temperature Field ◽  
Heat Transport ◽  
Stochastic Analysis ◽  
Transport Model ◽  
Field Scale ◽  
Heat Advection ◽  
Rate Of Growth ◽  
Second Moments ◽  
Mean Temperature ◽  
The Mean

Abstract. Owing to the analogy between the solute and heat transport processes, it can be expected that the rate of growth of the spatial second moments of the heat flux in a heterogeneous aquifer over relatively large space scales is greater than that predicted by applying the classical heat transport model. The motivation of stochastic analysis of heat transport at the field scale is therefore to quantify the enhanced growth of the field-scale second moments caused by the spatially varying specific discharge field. Within the framework of stochastic theory, an effective advection-dispersion equation containing effective parameters (namely, the macrodispersion coefficients) is developed to model the mean temperature field. The rate of growth of the field-scale spatial second moments of the mean temperature field in the principal coordinate directions is described by the macrodispersion coefficient. The variance of the temperature field is also developed to characterize the reliability to be anticipated in applying the mean heat transport model. It is found that the heterogeneity of the medium and the correlation length of the log hydraulic conductivity are important in enhancing the field-scale heat advection, while the effective thermal conductivity plays the role in reducing the field-scale heat advection.

scholarly journals Stochastic analysis of field-scale heat advection in heterogeneous aquifers

2011 ◽  
Vol 8 (6) ◽  
pp. 10311-10331
Author(s):  
C.-M. Chang ◽  
H.-D. Yeh
Keyword(s):  
Temperature Field ◽  
Heat Transport ◽  
Stochastic Analysis ◽  
Transport Model ◽  
Field Scale ◽  
Heat Advection ◽  
Rate Of Growth ◽  
Second Moments ◽  
Mean Temperature ◽  
The Mean

Abstract. Owing to the analogy between the solute and heat transport processes, it can be expected that the rate of growth of the spatial second moments of the heat flux in a heterogeneous aquifer over relatively large space scales is greater than that predicted by applying the classical heat transport model. The motivation of stochastic analysis of heat transport at the field scale is therefore to quantify the enhanced growth of the field-scale second moments caused by the spatially varying specific discharge field. Within the framework of stochastic theory, an effective advection-dispersion equation containing effective parameters (namely, the macrodispersion coefficients) is developed to model the mean temperature field. The rate of growth of the field-scale spatial second moments of the mean temperature field in the principal coordinate directions is described by the macrodispersion coefficient. The variance of the temperature field is also developed to characterize the reliability to be anticipated in applying the mean heat transport model. It is found that the heterogeneity of the medium and the correlation length of the log hydraulic conductivity are important in enhancing the field-scale heat advection, while the effective thermal conductivity plays the role in reducing the field-scale heat advection.

scholarly journals The Rapid Warming of the North Atlantic Ocean in the Mid-1990s in an Eddy-Permitting Ocean Reanalysis (1982–2013)

2016 ◽  
Vol 29 (15) ◽  
pp. 5417-5430 ◽  
Author(s):  
Chunxue Yang ◽  
Simona Masina ◽  
Alessio Bellucci ◽  
Andrea Storto
Keyword(s):  
Atlantic Ocean ◽  
Heat Transport ◽  
North Atlantic ◽  
North Atlantic Ocean ◽  
Ocean Reanalysis ◽  
The North ◽  
Mean Temperature ◽  
The Mean ◽  
The North Atlantic ◽  
Mean State

Abstract The rapid warming in the mid-1990s in the North Atlantic Ocean is investigated by means of an eddy-permitting ocean reanalysis. Both the mean state and variability, including the mid-1990s warming event, are well captured by the reanalysis. An ocean heat budget applied to the subpolar gyre (SPG) region (50°–66°N, 60°–10°W) shows that the 1995–99 rapid warming is primarily dictated by changes in the heat transport convergence term while the surface heat fluxes appear to play a minor role. The mean negative temperature increment suggests a warm bias in the model and data assimilation corrects the mean state of the model, but it is not crucial to reconstruct the time variability of the upper-ocean temperature. The decomposition of the heat transport across the southern edge of the SPG into time-mean and time-varying components shows that the SPG warming is mainly associated with both the anomalous advection of mean temperature and the mean advection of temperature anomalies across the 50°N zonal section. The relative contributions of the Atlantic meridional overturning circulation (AMOC) and gyre circulation to the heat transport are also analyzed. It is shown that both the overturning and gyre components are relevant to the mid-1990s warming. In particular, the fast adjustment of the barotropic circulation response to the NAO drives the anomalous transport of mean temperature at the subtropical/subpolar boundary, while the slowly evolving AMOC feeds the large-scale advection of thermal anomalies across 50°N. The persistently positive phase of the NAO during the years prior to the rapid warming likely favored the cross-gyre heat transfer and the following SPG warming.

Turbulent free convection above a heated plate inclined at a small angle to the horizontal

1963 ◽  
Vol 16 (2) ◽  
pp. 282-312 ◽  
Author(s):  
D. J. Tritton
Keyword(s):  
Temperature Field ◽  
Velocity Field ◽  
Small Angle ◽  
Large Scale ◽  
Temperature Fluctuations ◽  
Platinum Resistance ◽  
Heated Plate ◽  
Lower Edge ◽  
Mean Temperature ◽  
The Mean

An investigation has been made of the structure of the motion above a heated plate inclined at a small angle (about 10°) to the horizontal. The turbulence is considered in terms of the similarities to and differences from the motion above an exactly horizontal surface. One effect of inclination is, of course, that there is also a mean motion.Accurate data on the mean temperature field and the intensity of the temperature fluctuations have been obtained with platinum resistance thermometers, the signals being processed electronically. More approximate information on the velocity field has been obtained with quartz fibre anemometers. These results have been supplemented qualitatively by simultaneous observations of the temperature and velocity fluctuations and also by smoke experiments.The principal features of the flow inferred from these observations are as follows. The heat transfer and the mean temperature field are not much altered by the inclination, though small, not very systematic, variations may result from the complexities of the velocity field. This supports the view that the mean temperature field is largely governed by the large-scale motions. The temperature fluctuations show a systematic variation with distance from the lower edge and resemble those above a horizontal plate when this distance is large. The largescale motions of the turbulence start close to the lower edge, but the smaller eddies do not attain full intensity until the air has moved some distance up the plate. The mean velocity receives a sizable contribution from a ‘through-flow’ between the side-walls. Superimposed on this are developments that show that the momentum transfer processes are complex and certainly not capable of representation by any simple theory such as an eddy viscosity. On the lower part of the plate there is surprisingly large acceleration, but further up the mixing action of the small eddies has a decelerating effect.

Experimental Study on Convective Heat Transfer for Turbulent Flow in a Square Duct With a Ribbed Rough Wall (Characteristics of Mean Temperature Field)

1994 ◽  
Vol 116 (2) ◽  
pp. 332-340 ◽  
Author(s):  
M. Hirota ◽  
H. Fujita ◽  
H. Yokosawa
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Turbulent Flow ◽  
Cross Section ◽  
Rough Wall ◽  
Turbulent Shear ◽  
Turbulent Heat ◽  
Square Duct ◽  
Mean Temperature ◽  
The Mean

This paper presents experimental results concerning a time-mean temperature field obtained in forced convection heat transfer for a turbulent flow through a square duct with a ribbed rough bottom wall. The secondary flow pattern in the duct is reflected in the distribution of the local Nusselt number, the values of which on the smooth walls of the rough duct are 1.71~1.97 times those of the smooth duct. In the upper half cross section near the upper smooth wall opposite the bottom ribbed rough wall, the profile of the mean temperature distribution is similar to that of the primary flow velocity distribution, and the validity of the temperature inner law was confirmed. However, in the lower half cross section near the bottom ribbed rough wall, the dissimilarity between the mean velocity and the mean temperature fields becomes pronounced, and the inner law is not valid for mean temperature distributions. The mechanism of the heat transfer near the ribbed rough wall was examined based on the transport equations of turbulent shear stress and turbulent heat flux.

Spatial Variability of Physical Parameters and Processes in Two Field Soils

1991 ◽  
Vol 22 (5) ◽  
pp. 327-340 ◽  
Author(s):  
K. Høgh Jensen ◽  
J. C. Refsgaard
Keyword(s):  
Transport Model ◽  
Flow Direction ◽  
Measurement Data ◽  
Flow Simulation ◽  
Solute Concentration ◽  
Conclusive Evidence ◽  
Physical Parameters ◽  
Effective Parameters ◽  
The Mean ◽  
Tracer Experiments

A numerical analysis of solute transport in two spatially heterogeneous fields is carried out assuming that the fields are composed of ensembles of one-dimensional non-interacting soil columns, each column representing a possible soil profile in statistical terms. The basis for the analysis is the flow simulation described in Part II (Jensen and Refsgaard, this issue), which serves as input to a transport model based on the convection-dispersion equation. The simulations of the average and variation in solute concentration in planes perpendicular to the flow direction are compared to measurements obtained from tracer experiments carried out at the two fields. Due to the limited amount of measurement data, it is difficult to draw conclusive evidence of the simulations, but reliable simulations are obtained of the mean behaviour within the two fields. The concept of equivalent soil properties is also tested for the transport problem in heterogeneous soils. Based on effective parameters for the retention and hydraulic conductivity functions it is possible to predict the mean transport in the two experimental fields.

scholarly journals Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach

2021 ◽  
Vol 5 (2) ◽  
pp. 51
Author(s):  
Ashraf M. Tawfik ◽  
Mohamed Mokhtar Hefny
Keyword(s):  
Molecular Species ◽  
Transport Model ◽  
Mean Square Displacement ◽  
Telegraph Equation ◽  
Reaction Model ◽  
Simulation Techniques ◽  
Experimental Works ◽  
The Mean ◽  
Classical Transport ◽  
Fractional Reaction

In recent years, different experimental works with molecular simulation techniques have been developed to study the transport of plasma-generated reactive species in liquid layers. Here, we improve the classical transport model that describes the molecular species movement in liquid layers via considering the fractional reaction–telegraph equation. We have considered the fractional equation to describe a non-Brownian motion of molecular species in a liquid layer, which have different diffusivities. The analytical solution of the fractional reaction–telegraph equation, which is defined in terms of the Caputo fractional derivative, is obtained by using the Laplace–Fourier technique. The profiles of species density with the mean square displacement are discussed in each case for different values of the time-fractional order and relaxation time.

Influence of rotating magnetic field on Maxwell saturated ferrofluid flow over a heated stretching sheet with heat generation/absorption

2019 ◽  
Vol 20 (5) ◽  
pp. 502 ◽  
Author(s):  
Aaqib Majeed ◽  
Ahmed Zeeshan ◽  
Farzan Majeed Noori ◽  
Usman Masud
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
Velocity Field ◽  
Differential Equations ◽  
Heat Transport ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
The Impact

This article is focused on Maxwell ferromagnetic fluid and heat transport characteristics under the impact of magnetic field generated due to dipole field. The viscous dissipation and heat generation/absorption are also taken into account. Flow here is instigated by linearly stretchable surface, which is assumed to be permeable. Also description of magneto-thermo-mechanical (ferrohydrodynamic) interaction elaborates the fluid motion as compared to hydrodynamic case. Problem is modeled using continuity, momentum and heat transport equation. To implement the numerical procedure, firstly we transform the partial differential equations (PDEs) into ordinary differential equations (ODEs) by applying similarity approach, secondly resulting boundary value problem (BVP) is transformed into an initial value problem (IVP). Then resulting set of non-linear differentials equations is solved computationally with the aid of Runge–Kutta scheme with shooting algorithm using MATLAB. The flow situation is carried out by considering the influence of pertinent parameters namely ferro-hydrodynamic interaction parameter, Maxwell parameter, suction/injection and viscous dissipation on flow velocity field, temperature field, friction factor and heat transfer rate are deliberated via graphs. The present numerical values are associated with those available previously in the open literature for Newtonian fluid case (γ 1 = 0) to check the validity of the solution. It is inferred that interaction of magneto-thermo-mechanical is to slow down the fluid motion. We also witnessed that by considering the Maxwell and ferrohydrodynamic parameter there is decrement in velocity field whereas opposite behavior is noted for temperature field.

scholarly journals First Benedicks Effect in Gas-Free Mercury, as Influenced by the Mean Temperature

Nature ◽  
1940 ◽  
Vol 145 (3665) ◽  
pp. 148-148
Author(s):  
C. BENEDICKS ◽  
P. SEDERHOLM
Keyword(s):  
Mean Temperature ◽  
The Mean
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