Heat Transfer Scheme Research Articles

Rigorous evaluation of a soil heat transfer model for mesoscale climate change impact studies

The influence of Climate Change on plant development as well as on carbon and nitrogen cycling in soils is an important research topic for Global Change impact assessment at the regional scale. These changes affect the availability and quality of ground and surface waters and accordingly the future productivity of agriculturally used landscapes. The integrated assessment of these changes requires a robust prediction of the potential future characteristics of soil temperature and moisture based on scale-appropriate, process-oriented models. Hence, we present the Soil Heat Transfer Module (SHTM) used as a component of the mesoscale decision support system DANUBIA, which is developed by the multi-disciplinary research project GLOWA-Danube (www.glowa-danube.de). DANUBIA is applied on the Upper Danube catchment to assess the future changes in water availability, quality and use based on Global Change scenarios.In order to cover the temporal and spatial resolution (1h, 1×1km) of the main model as well as the desired investigation period of 50 years, SHTM combines a variable time step conductive heat transfer algorithm with an analytical lower boundary condition to react to long-term climate change with minimal model drift. Changes in soil moisture and soil freezing are explicitly taken into account. The ground heat flux at the soil surface is computed by iterative closure of the energy balance including radiative, latent and sensible energy fluxes. Validation of the heat transfer scheme shows that the variable time step solution improves computational efficiency while imposing only minimal RMSE and phase shift errors. Furthermore, the analytical lower boundary stabilizes the long term heat balance and induces a rather small potential model drift in the order of 0.001Wm−2. Then the results of the full land surface model including SHTM are compared to measurements at 25 agrometeorological sites. Without site-specific parameterisation other than land cover type, we show that the model performs well (RMSE about 2K) in reproducing daily and annual top soil temperature dynamics over long simulation periods. The analysis of systematic model errors reveals that about 75% of the RMSE is attributable to uncertainties in meteorological input, canopy parameters and snow processes.

A two-dimensional study on natural convection and heat transfer in the enclosure with heat transfer and radiation coupled in natural convection

Numerical investigation using SIMPLE algorithm with QUICK scheme for natural convection and heat transfer in the enclosure bounded by a solid wall and with heat transfer and radiation coupled in natural convection has been conducted. The various parameters are: Rayleigh number (from 103 to 105), dimensionless conductivity of bounding wall (from 0 to 100), dimensionless wall thickness (from 0 to 0.6) and radiation emissivity of all surfaces (from 0 to 1). The results suggest that flow and heat transfer are influenced by radiation. Radiation is a dominant action on flow and heat transfer. With increase of the thermal conductivity of wall, flow and heat transfer turn stronger. The temperature distribution changes obviously. When the thermal conductivity of wall is over a certain critical number, the increasing trend of flow and heat transfer may disappear. With increase of enclosure wall thickness, flow and heat transfer turn slighter. When the enclosure wall thickness is over a certain critical number, the flow and heat transfer will turn slow.

Multifunctional design of two-dimensional cellular materials with tailored mesostructure

Two-dimensional cellular materials (prismatic honeycombs) provide a range of properties that make them suitable for multifunctional applications involving heat dissipation and structural performance. In this paper we present two-scale homogenization-based finite element scheme for convective heat transfer and structural characterization of 2-D cellular metals with uniform and graded cell sizes of various topologies as well as with mixed cell-topologies. For convective heat transfer analysis, the cells are modeled implicitly as temperature-dependent sinks modeling the out-of-plane fluid convection through the cells; the sink strength is determined via a micromechanics problem of heat transfer in a cell. For structural analysis, the cellular material is represented as a micropolar continuum with linear elastic constitutive equations obtained via micromechanics solution of a representative unit cell. The analyses are then used in conjunction with an optimization algorithm to design cellular materials with functionally tailored mesostructures. The analysis and design framework enables tailoring cellular materials with graded cell structures of a given topology as well as with cell structures that combine multiple topologies.

2D finite element analysis of thermal balance for drained aluminum reduction cells

Based on the principle of energy conservation, the applicable technique for drained cell retrofitted from conventional one was analyzed with 2D finite element model. The model employed a 1D heat transfer scheme to compute iteratively the freeze profile until the thickness variable reached the terminating requirement. The calculated 2D heat dissipation from the cell surfaces was converted into the overall 3D heat loss. The potential drop of the system, freeze profile and heat balance were analyzed to evaluate their variation with technical parameters when designing the 150 kA conventional cell based drained cell. The simulation results show that the retrofitted drained cell is able to keep thermal balance under the conditions that the current is 190 kA, the anodic current density is 0.96 A/cm2, the anode-cathode distance is 2.5 cm, the alumina cover is 16 cm thick with a thermal conductivity of 0.20 W/(m·°C) and the electrolysis temperature is 946 °C.

Three-dimensional simulation using fixed coarse-grid thermal-fluid scheme and conduction heat transfer scheme in distinct element method

Three-dimensional simulation using particle–thermal-fluid coupling scheme with a mixed Lagrangian–Eulerian approach is presented and the scheme is described by extending author's previous research [Y. Shimizu, 2004. “Fluid Coupling in PFC2D and PFC3D”, numerical modeling in micromechanics via particle methods—2004, Proceeding of 2nd International PFC Conference, Balkema, 2004, pp. 281–287]. The scheme solves the continuity, Navier–Stokes (N–S) and thermal energy equations numerically in Eulerian Cartesian coordinates, then derives pressure, velocity vectors and temperature for each fixed cell by considering particle existence. On the other hand, driving forces and thermal energy from fluid are applied to the particles as external body forces and a source term in the force–displacement law and the heat transfer calculations, respectively. This paper describes the thermal scheme for both fluid and particles. Results of two- and three-dimensional simulations involving forced convective heat transfer by fluid and conduction heat transfer within particles are presented.

The improved ladder production for the Belle silicon vertex detector (SVD2.1)

In autumn 2003 data taking with the new silicon vertex detector SVD2 in Belle started at the KEK-B energy-asymmetric e/sup +/e/sup -/ collider in Tsukuba, Japan. The detector works as expected, however, it was decided to produce replacement ladders for the inner two layers of the vertex detector which are most exposed to the high radiation doses from the beam. The new ladders are not merely reproducing the existing design but include some significant improvements. The readout electronics is designed in a FR4 hybrid board with a new heat transfer scheme in order to dissipate the heat produced in the VA1TA front-end readout chips. The flex circuits that connect the double-sided silicon sensors (DSSD's) with the hybrid boards were redesigned using a 2-layer technique which improved the production quality and lowered their costs significantly. Production and testing will be finished by the end of 2004 and will provide Belle with spare ladders as well as new expertise for possible future projects like e.g. developments for a high luminosity B-factory.

A Numerical Study of the Enhancement of Chip Cooling via a Flow-Disturbing Obstruction Block

Two-dimensional convection heat transfer on a chip with a flow-disturbing obstruction block above it, as induced by natural coupling between flow and structure, was investigated numerically. The effects of various induced trajectories of the obstruction block on chip cooling were investigated. A numerical algorithm PISO, a conjugate heat transfer scheme for fluid-solid thermal interactions with moving grids was used to solve a coupled system of governing equations. The study shows that the induced trajectories of the obstruction block, as a result of natural coupling between the block and the flow, have a noticeable impact on chip cooling. The present study successfully simulated the motion of an obstruction block on a heated chip and the associated “lock-in” phenomenon due to natural coupling. When lock-in occurs, the trajectory of the block movement follows the shape of an oval. If this occurs, the cross-stream movement is much larger than the stream-wise movement. Passively induced disturbance of the flow field for the case with a large oval trajectory yields an enhancement of heat dissipation from the chip. In general, the vibration of the block as induced by an unbalanced pressure field around the chip would disturb the thermal boundary above the chip. Hence, the induced vibration enhances heat dissipation from the chip. It is concluded in this study that a vibrating obstruction block with a lock-in mode of oscillation is a vital condition for achieving an enhancement of heat dissipation as can be observed by an increase of Nusselt number on the chip top surface.

TWO FINITE-ELEMENT SCHEMES FOR STEADY CONVECTIVE HEAT TRANSFER WITH SYSTEM ROTATION AND VARIABLE THERMAL PROPERTIES

ABSTRACT We develop standard and mixed finite-element schemes for steady convective heat transfer with system rotation, temperature-dependent density and viscosity. Existence and convergence are proven for the two schemes. They are shown to be globally convergent and capable of capturing both nonsingular and singular solutions. The convergence rate is found to be optimal in H1-norm and L2-norm for nonsingular solutions.

A diffusion model for drying of a heat sensitive solid under multiple heat input modes

To obtain optimal drying kinetics as well as quality of the dried product in a batch dryer, the energy required may be supplied by combining different modes of heat transfer. In this work, using potato slice as a model heat sensitive drying object, experimental studies were conducted using a batch heat pump dryer designed to permit simultaneous application of conduction and radiation heat. Four heat input schemes were compared: pure convection, radiation–coupled convection, conduction–coupled convection and radiation–conduction–coupled convection. A two-dimensional drying model was developed assuming the drying rate to be controlled by liquid water diffusion. Both drying rates and temperatures within the slab during drying under all these four heat input schemes showed good accord with measurements. Radiation–coupled convection is the recommended heat transfer scheme from the viewpoint of high drying rate and low energy consumption.

Revisiting bulk heat transfer on Peyto Glacier, Alberta, Canada, in light of the OG parameterization

AbstractA scheme for katabatic turbulent heat transfer proposed by Oerlemans and Grisogono (2002), here referred to as the OG parameterization, is compared with bulk heat-transfer estimates on Peyto Glacier, Alberta, Canada. Automatic weather stations (AWSs) provide off-glacier data to drive the parameterization and glacier data for bulk estimates. Micrometeorological datasets are used to assess two schemes that employ the Monin-Obukhov stability parameter, z/L, to modify logarithmic, or neutral, bulk heat-transfer equations to allow for stability. Both schemes fail at >1 m above the surface, where the AWS sensors are located, unless a modified approach is used in which the stability correction is constant for z/L ≥1/3. Then the bulk sensible-heat-flux density falls to ≈0.93 of its neutral estimate at all measurement levels, thus providing a basis for comparison with the parameterization. The results of the comparison are very good, indicating that a one-to-one relationship between bulk and parameterized values can be achieved by optimizing the fit with a background exchange coefficient and, because there is only one off-glacier AWS, using a sinusoidal function to model the diurnal variation of the potential temperature lapse rate.

A Nonstandard Finite Difference Scheme for Nonlinear Heat Transfer in a Thin Finite Rod

A nonstandard finite difference scheme is constructed to solve an initial-boundary value problem involving a quartic nonlinearity that arises in heat transfer involving conduction with thermal radiation. It is noted that the positivity condition is equivalent to the usual linear stability criteria and it is shown that the representation of the nonlinear term in the finite difference scheme, in addition to the magnitudes of the equation parameters, has a direct bearing on the scheme's stability. Finally, solution profiles are plotted and avenues of further inquiry are discussed.

An efficient parallel-computing method for modeling nonisothermal multiphase flow and multicomponent transport in porous and fractured media

This paper presents an efficient massively parallel scheme for modeling large-scale multiphase flow, multicomponent transport and heat transfer in porous and fractured reservoirs. The new scheme is implemented into a parallel version of the TOUGH2 code and the numerical performance is tested on a Cray T3E-900 (a distributed-memory parallel computer with 692 processors) and IBM RS/6000 SP (a distributed-memory parallel computer with 3328 processors). The efficiency and robustness of the parallel-computing algorithm are demonstrated by completing three over-million-cell simulations using site-specific data for site characterization. The first application is the development of a three-dimensional unsaturated zone numerical model simulating flow of moisture in the unsaturated zone of Yucca Mountain, Nevada; the second problem is the modeling of flow of moisture, gas, and heat at the same site. The third application is the study of flow-focusing phenomena through fractures for the same site. Simulation results show that the parallel-computing technique enhances modeling capability by several orders of magnitude in speedup of computing times for large-scale modeling studies.

Stiffness problem in modeling wave flows of heterogeneous media with a three‐temperature scheme of interphase heat and mass transfer

The numerical modeling of wave flows of heterogeneous media with a three‐temperature scheme of interphase heat and mass transfer involves the problem of equation stiffness. A discrete model of improved stability was developed to describe these processes. Test calculations of the interaction of a shock wave with a bounded layer of a mixture of a gas and droplets assuming a discrete model over a wide range of initial data showed that the stability conditions do not depend on the rate of interphase interaction (C‐stability).

Parallel Numerics and Applications

Parallel Numerics and Applications

An Unstructured hp Finite-Element Scheme for Fluid Flow and Heat Transfer in Moving Domains

This paper presents the formulation, validation, and application of a spectral/hp algorithm for numerical solution of the Navier–Stokes and heat/scalar transport equations in arbitrarily moving complex geometries. The new spectral element algorithm is based on the arbitrary Lagrangian Eulerian formulation and utilizes modal expansion of Jacobi polynomials in mixed triangular and quadrilateral elements in two dimensions. Time integration is performed by stiffly stable schemes and can deliver up to third-order time accuracy for transient problems. Test cases with sufficiently smooth solutions demonstrate spectral convergence and low phase/dissipation error. Preliminary simulation results for micro-mixers and micro-heat spreaders are also presented.

A comparative study on the performance of two time stepping schemes for convection in a fluid saturated porous medium

A comparative study has been carried out to investigate the performance of two different time stepping schemes for convective heat transfer and flow in a fluid saturated porous medium. Both the schemes are based on the velocity correction procedure. The first scheme is a semi‐implicit one in which the linear and non‐linear porous medium terms of the momentum equation are treated implicitly but solution of the simultaneous equation system is avoided by lumping the mass. The second procedure (quasi‐implicit) treats the porous medium and viscous terms implicitly and a simultaneous equation system is constructed to solve the equations of momentum conservation. Two numerical examples have been considered and both the schemes are tested for various parameters governing the flow and heat transfer in these problems. Results show that, at smaller Rayleigh numbers and on fine meshes, the quasi‐implicit scheme gives faster convergence to steady state in both Darcy and non‐Darcy regimes than that of the semi‐implicit scheme. At higher Rayleigh numbers, the semi‐implicit scheme is faster in the Darcy regime. Also, the semi‐implicit scheme is faster than that of the quasi‐implicit scheme on a coarse mesh used in this study. In general both the schemes predict transient cyclic developments well.

A CONSERVATIVE ADAPTIVE-MESH ALGORITHM FOR UNSTEADY, COMBINED-MODE HEAT TRANSFER USING THE DISCRETE ORDINATES METHOD

Adaptive mesh refinement (AMR) permits a computational algorithm to allocate additional grid resolution when and where it is most needed. A block-structured AMR scheme provides this capability without sacrificing the numerical and computational efficiencies associated with regular meshes. In this article we describe an AMR implementation of the discrete ordinates method for radiative transfer, coupled with an existing projection method for low-Mach-number flows. The complete algorithm constitutes a conservative scheme for unsteady combined-mode heat transfer. Results for two-and three-dimensional examples are shown.

A new time marching BE scheme for transient heat transfer with a thermal moving boundary

In this article, the BEM solution of the diffusion equation with a moving boundary is discussed. It is shown that the analytical time integration both for the 0- and 1-order modes lead to a special exponent–integral function and the reference time parameter τ will be important to the computational efficiency. In this article, the local time-dependent solution is used so that a series matrix computation can be reduced. Hence a new time marching scheme which is suitable to a moving boundary case is presented with some successful numerical tests.

A New Discrete Ordinates Quadrature Scheme for Three-Dimensional Radiative Heat Transfer

A New Discrete Ordinates Quadrature Scheme for Three-Dimensional Radiative Heat Transfer

High Heat Flux Absorption Utilizing Porous Materials With Two-Phase Heat Transfer

By combining two-phase heat transfer with forced convective flow through a porous material, a new heat transfer scheme emerges with the ability to absorb high heat fluxes without the corresponding temperature increase encountered in single-phase systems. In general, flow-through sintered metals are characterized by high thermal conductivity due to the metallic media, and a fluid flow which on the macro scale can be described as slug flow in nature. These same characteristics are exhibited by liquid metal flow cooling systems. To predict the heat transfer attributes of this two-phase flow process, a semi-analytical model was developed using the conservation equations of mass, momentum, and energy along with the apparent physical properties of the composite material. The results indicate that when a heat flux is applied to one side of the bounding surface and adiabatic conditions exist on the remaining sides, the surface temperature asymptotically approaches the same value regardless of the mass flow rate. In addition to the analytical results, definitions for the convection coefficient and Nusselt number for flow-through porous materials with phase change are presented.