Three-dimensional multi-scale plate assembly for maximum heat transfer rate density

This paper extends the design concept for generating multi-scale structures in forced convection for a finite-size flow system to a three-dimensional heat-generating plate with the objectives of maximising heat transfer rate density, or the heat transfer rate per unit volume. The heat-generating plates, arranged in a stack form channels in which the fluids are forced through by an applied pressure difference. The first stage of this work consists of numerical simulation of the flow and heat transfer in a large number of flow configurations, to determine the optimum plate spacing, and the maximum heat transfer rate density. In the subsequent stages, shorter plates are inserted in the centers at adjacent (longer) plates in the entranced region were the boundary layer are thin and there is a core of unused fluid. The heat transfer density is further increased by progressively inserting another set of even shorter plates between the plates and then optimizing the whole structure. The resulting structure is an optimized multi-scale and multi channel structure with horizontal equidistant heated plates of decreasing lengths scales. Further more the effects of plate thickness and dimensionless pressure drop number on the multi-scale structure was investigated. The numerical results are found to be in good agreement with predicted analytical results.     

Dendritic constructal heat exchanger with small-scale crossflows and larger-scales counterflows

This paper describes the constructal route to the conceptual design of a two-stream heat exchanger with maximal heat transfer rate per unit volume. The flow structure has multiple scales. The smallest (elemental) scale consists of parallel-plates channels the length of which matches the thermal entrance length of the small stream that flows through the channel. This feature has two advantages: it eliminates the longitudinal temperature increase (flow thermal resistance) that would occur in fully developed laminar flow, and it doubles the heat transfer coefficient associated with fully developed laminar flow. The elemental channels of hot fluid are placed in crossflow with elemental channels of cold fluid. The elemental channel pairs are assembled into sequentially larger flow structures (first construct, second construct, etc.), which have the purpose of installing (spreading) the elemental heat transfer as uniformly as possible throughout the heat exchanger volume. At length scales greater than the elemental, the streams of hot and cold fluid are arranged in counterflow. Each stream bathes the heat exchanger volume as two trees joined canopy to canopy. One tree spreads the stream throughout the volume (like a river delta), while the other tree collects the same stream (like a river basin). It is shown that the spacings of the elemental and first-construct channels can be optimized such that the overall pumping power required by the construct is minimal. The paper concludes with a discussion of the advantages of the proposed tree-like (vascularized) heat exchanger structure over the use of parallel small-scale channels with fully developed laminar flow.     

Constructal multi-scale cylinders in cross-flow

This paper reports a new concept for maximizing heat transfer density in assemblies of cylinders in cross-flow: the use of cylinders of several sizes, and the optimal placement of each cylinder in the assembly. The heat transfer is by laminar forced convection with specified overall pressure difference. The resulting flow structure has multiple scales that are distributed nonuniformly through the available volume. Smaller cylinders are placed closer to the entrance to the assembly, in the wedge-shaped flow regions occupied by fluid that has not yet been used for heat transfer. The paper reports the optimized flow architectures and performance for structures with 1, 2 and 3 cylinder sizes, which correspond to structures with 1, 2 and 4 degrees of freedom. The heat transfer rate density increases (with diminishing returns) as the optimized structure becomes more complex. The optimized cylinder diameters are relatively robust, i.e., insensitive to changes in complexity and flow regime (pressure difference). The optimized spacings decrease monotonically as the driving pressure difference increases. The multi-scale flow architectures optimized in this paper have features and qualities similar to tree-shaped (dendritic) designs, where the length scales are numerous, hierarchically organized, and nonuniformly distributed through the available space.     

Heat transfer between two parallel plates with laminar pulsating flow

The problem of heat transfer from two parallel plates of infinite width is formulated for the case where the flow between these plates consists of a periodic motion imposed on a fully developed laminar steady flow. The results indicate an increase in the heat transfer rate with pulsation. This increase is proportional to the amplitude of pulsation and inversely proportional to the Prandtl number.     

Combustion and heat transfer in model two-dimensional porous burners

A two-dimensional model of two simple porous burner geometries is developed to analyze the influence of multidimensionality on flames within pore scale structures. The first geometry simulates a honeycomb burner, in which a ceramic is penetrated by many small, straight, nonconnecting passages. The second geometry consists of many small parallel plates aligned with the flow direction. The Monte Carlo method is employed to calculate the viewfactors for radiation heat exchange in the second geometry. This model compares well with experiments on burning rates, operating ranges, and radiation output. Heat losses from the burner are found to reduce the burning rate. The flame is shown to be highly two-dimensional, and limitations of one-dimensional models are discussed. The effects of the material properties on the peak burning rate in these model porous media are examined. Variations in the flame on length scales smaller than the pore size are also present and are discussed and quantified.     

Entrance region heat transfer in a channel downstream of an impinging jet array

An experimental investigation is carried out on the entrance region heat transfer in a parallel plate channel downstream of a jet array located in one of the plates. The jet impingement surface is kept isothermal while the opposing surface, containing the jet array, is adiabatic. The focus of the investigation is the systematic study of the effect of flow rate and array geometric parameters on local Nusselt numbers in the entrance region of the channel immediately downstream of the array. To place these results in context, Nusselt numbers opposite the array and in the fully developed region downstream of the channel entrance are also included. In the entrance region, the ratio of the local to fully developed Nusselt number is independent of the channel Reynolds number, and the effects of some jet array geometric parameters are significant. These effects become negligible within 10 hydraulic diameters from the channel entrance. The entrance length is about 21 hydraulic diameters. The fully developed Nusselt numbers agree well with previous measurements. Empirical correlations are developed to fit the observations.     

Development of bipolar plates with different flow channel configurations for fuel cells

Bipolar plates include separate gas flow channels for anode and cathode electrodes of a fuel cell. These gases flow channels supply reactant gasses as well as remove products from the cathode side of the fuel cell. Fluid flow, heat and mass transport processes in these channels have significant effect on fuel cell performance, particularly to the mass transport losses. The design of the bipolar plates should minimize plate thickness for low volume and mass. Additionally, contact faces should provide a high degree of surface uniformity for low thermal and electrical contact resistances. Finally, the flow fields should provide for efficient heat and mass transport processes with reduced pressure drops. In this study, bipolar plates with different serpentine flow channel configurations are analyzed using computational fluid dynamics modeling. Flow characteristics including variation of pressure in the flow channel across the bipolar plate are presented. Pressure drop characteristics for different flow channel designs are compared. Results show that with increased number of parallel channels and smaller sizes, a more effective contact surface area along with decreased pressured drop can be achieved. Correlations of such entrance region coefficients will be useful for the PEM fuel cell simulation model to evaluate the affects of the bipolar plate design on mass transfer loss and hence on the total current and power density of the fuel cell.     

Constructal multi-scale cylinders with natural convection

This paper shows that in a space filled with assemblies of cylinders cooled by natural convection the heat transfer density can be increased progressively by the use of cylinders of several sizes, and the optimal placement of each cylinder in the assembly. Smaller cylinders are placed closer to the entrance to the assembly, in the wedge-shaped flow regions occupied by fluid that has not yet been used for heat transfer. The paper reports the optimized flow architectures and performance for structures with one and two cylinder sizes, which correspond to structures with one and two degrees of freedom. The heat transfer rate density increases as the optimized structure becomes more complex. The optimized cylinder diameters are relatively robust, i.e., insensitive to changes in complexity and flow regime (Rayleigh number). The optimized spacings decrease monotonically as the Rayleigh number increases. The structure performance can be improved by endowing the cylinder assemblies with more degrees of freedom.     

Laminar Forced Flow and Heat Transfer in Cross-Corrugated Triangular Ducts

The fluid flow and heat transfer characteristics in a cross-corrugated triangular channel are studied under laminar forced flow and uniform wall temperature conditions. Both the local and the periodic mean values of friction factor and wall Nusselt numbers in the hydro and thermally developing entrance region are investigated. It is found that at higher Reynolds numbers, recirculations in the lower wall valleys are a dominant factor for flow and heat transfer, while at lower Reynolds numbers, parallel flows in the upper wall corrugation are the predominant factor. Compared with a parallel flat plates duct, the Nusselt numbers in a cross-corrugated triangular duct can be enhanced, and can be even higher at higher Reynolds numbers. The growth of steady recirculations and the concomitant periodic disruption and thinning of the boundary layer promote enhanced transport of heat as well as momentum. Effects of heat transfer enhancement are more obvious under higher Reynolds numbers. Two correlations are proposed to predict the periodic mean values of Nusselt numbers and friction factors for Reynolds numbers from 10 to 2000.     

Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.     

Heat transfer characteristics of a partially insulated tube with an impulsive temperature rise

The heat transfer for a laminar forced convection inside a two dimensional planar symmetric duct is analyzed. The fluid passage is formed by two parallel plates, and flow is fully developed and incompressible. Flow is isothermal to a position x_o = 0, where the wall temperature jumps impulsively to T₁ > T₀ and remains at this value up to the position x₁, where it jumps back T₀. The problem is considerably simplified by introducing a transformation to reduce the heat transfer problem to the standard thermal entrance region problem for flow between parallel plates. Various heat transfer characteristics for different values of Prandtl and Nusselt numbers are analyzed and found to be physically realistic.     

APPLICATION OF GROOVED FINS TO ENHANCE FORCED CONVECTION TO TRANSVERSE FLOW

A numerical study is performed to investigate the heat transfer characteristics of a two-dimensional forced convection over a plate with protruded transverse groove fins. The study is made for four geometries, five different Reynolds numbers, and for more groove fins with smaller size. Numerical analysis is carried out to investigate the flow patterns, isotherms, heat transfer rates, and the effectiveness of the increased grooves. Local Nusselt number and total heat transfer rate are calculated and the average Nusselt number is correlated as a function of Reynolds and Prandtl numbers. Protruded grooves yield a much larger heat transfer rate than a flat plate owing to flow penetration into the groove. Grooved fins with protruded mounting are suitable for heat transfer enhancement, and the total length is recommended not to exceed the reattachment length significantly. The derived correlations and physical considerations may be used when designing grooved plates to enhance heat transfer.     

Vascularization with line-to-line trees in counterflow heat exchange

Here we report the heat and fluid flow characteristics of counterflow heat exchangers with tree-shaped line-to-line flow channels. The flow structures of the hot and cold sides are sequences of point-to-line trees that alternate with upside-down trees. The paper shows under what conditions the tree vascularization offers greater heat flow access than corresponding conventional designs with parallel single-scale channels. The analytical part is based on assuming fully developed laminar flow in every channel and negligible longitudinal conduction in the solid. The numerical part consists of simulations of three-dimensional convection coupled with conduction in the solid. It is shown that tree vascularization offers greater heat flow access (smaller global thermal resistance) than parallel channels when the number of pairing levels increases and the available pumping power or pressure drop is specified. When the solid thermal conductivity increases, the heat transfer effectiveness decreases because of the effect of longitudinal heat conduction. The nonuniformity in fluid outlet temperature becomes more pronounced when the number of pairing levels increases and the pumping power (or pressure drop number) increases. The nonuniformity in outlet fluid temperature decreases when the solid thermal conductivity increases.     

Heat transfer of a parallel flow two-layered microchannel heat sink

A numerical study is conducted to predict the thermal performance of a parallel flow two-layered microchannel heat sink on heat transfer and compared to the case of counterflow for various channel aspect ratios. Findings reveal that the parallel flow configuration leads to a better heat transfer performance except for high Reynolds number and high channel aspect ratio. Further study on the horizontal rib thickness shows that lower thermal resistance can be achieved in a parallel flow two-layered microchannel heat sink with smaller thickness of middle rib.     

Viscous dissipation effects on parallel plates with constant heat flux boundary conditions

This paper investigates basic analytical expressions for Nusselt number with the effect of viscous dissipation on the heat transfer between infinite fixed parallel plates, where the focus is on hydro-dynamically and thermally fully developed flow of a Newtonian fluid with constant properties, neglecting the axial heat conduction. Thermal boundary conditions considered are: both the plates kept at different constant heat fluxes, both the plates kept at equal constant heat fluxes, and one plate insulated. From the analysis, new expressions for Nusselt numbers have been found, as a function of various definitions of the Brinkman number.     

Turbulent Heat Transfer in the Entrance Region of a Tube

Correlation of the data for heat transfer between a fluid in turbulent flow and the entrance region of a tube is made for the entrance shapes normally used in heat exchangers. Equations representing the variation of the “average heat transfer” with tube length, Reynolds number, and Prandtl number are suggested.     

MODELING OF CONJUGATE HEAT TRANSFER BETWEEN PARALLEL PLATES SEPARATED BY A HYDRODYNAMICALLY DEVELOPED LAMINAR FLOW BY THE QUADRUPOLE METHOD

The thermal quadrupole method allows the quasi-analytical modeling of heat transfer through a hydrodynamically developed laminar flow between two parallel plates. It is a meshless method based on an integral transform technique. The principle consists of calculating the transfer matrix linking temperature and flux density between the two walls of the channel. The convection-diffusion equation which governs heat transfer in the flow is solved analytically. The interest of this “fluid quadrupole” is to allow the modeling of the conjugate heat transfer between the channel and thick walls through the analytical formalism of the quadrupole method. It is cheked, in the case of mini-microchannels, that the local convective heat transfer coefficient h is rather strongly dependent on the wall nature.     

Comparison of parallel and counter flow coil absorber performance

This study concentrates on the absorber used in the vapor absorption systems using water–lithium bromide solution with water as the refrigerant and investigates the simultaneously occurred heat and mass transfer during the absorption process. The heat and mass transfer equations were applied to simulate this process and solved using a computer program written in Delphi 7 for the parallel and counter flow absorbers. The simulation results were compared with the results of the past studies. The solution and cooling water temperatures, the overall heat transfer coefficient, the heat transferred and the mass absorbed were calculated for the parallel and counter flow absorbers. It is concluded that the counter flow absorber presents better performance for all conditions. For smaller number of coils, the difference is smaller, however if the number of coils is bigger, the counter flow absorber presents much better performance than the parallel flow absorber. When the number of coils is 20 and 120, the counter flow absorber provides 1.7% and 26% higher heat and mass transfer than the parallel flow absorber respectively.     

Heat transfer enhancement in a channel with a built-in square cylinder

A two dimensional numerical investigation of the unsteady laminar flow pattern and forced convective heat transfer in a channel with a built-in square cylinder is presented. The channel in the entrance region has a length to plate spacing of ten. The computations were made for several Reynolds number and two square cylinder sizes. Hydrodynamic behavior and heat transfer results are obtained by solution of the complete Navier-Stokes and energy equation. The results show that these flow exhibits laminar self-sustained oscillations for Reynolds numbers above the critical one. This study shows that oscillatory separated flows result in a significant heat transfer enhancement but also in a significant pressure drop increase.     

Svelteness, freedom to morph, and constructal multi-scale flow structures

This paper reviews recent progress on constructal theory and design. The emphasis is on the development of multi-scale, nonuniformly distributed flow structures that offer increased compactness (e.g., heat transfer density). Examples are counterflow heat exchangers with tree-shaped hot and cold streams, and tree architectures on a disc. Every flow system has a property called svelteness (Sv), which is the ratio between its external (global) length scale and its internal length scale (V^1/3), where V is the volume occupied by all the ducts. Emphasis is placed on the development of simple strategies for decreasing the computational cost required by the development of such structures. The generation of multi-scale flow configurations is a process that can be projected on a diagram having global performance on the abscissa and degrees of freedom on the ordinate. This process rules the development (evolution) of all flow configurations for systems with global objective, global constraints and freedom to morph.