Constant wall heat flux boundary conditions in porous media under local thermal non-equilibrium conditions

Boundary conditions for constant wall heat flux in the absence of local thermal equilibrium conditions are analyzed in this work. Effects of variable porosity and thermal dispersion are also analyzed. Different forms of constant heat flux boundary conditions found in the literature were investigated in this work. The effects of pertinent parameters such as porosity, Darcy number, Reynolds number, inertia parameter, particle diameter and solid-to-fluid conductivity ratio were analyzed. Quantitative and qualitative interpretations of the results are utilized to investigate the prominent characteristics of the models under consideration. Limiting cases resulting convergence or divergence of the models are also considered. Results are presented in terms of the fluid, solid and total Nusselt numbers.     

Adiabatic-isothermal mixed boundary conditions in heat transfer

Mixed boundary conditions of the adiabatic-isothermal type often arise in the mathematical modeling of heat transfer phenomena. Under certain circumstances, the mixed condition gives rise to singular behavior which cannot be adequately treated by numerical means alone. The numerical procedure must be supplemented by an asymptotic analysis for the local behavior near the singularity. In the special case of a mixed boundary condition on a straight boundary, the strength of the singularity is given in terms of a path-independent integral, the value of which can be determined from the numerical solution for the far-field behavior. Implications of overlooking the singular behavior due to the mixed boundary condition are discussed.     

Unsteady conjugated heat transfer in thick walled pipes involving two-dimensional wall and axial fluid conduction with uniform heat flux boundary condition

Transient conjugated heat transfer in thick walled pipes for thermally developing laminar flow is investigated involving two-dimensional wall and axial fluid conduction. The problem is solved numerically by a finite-difference method for hydrodynamically developed flow in a two-regional pipe, initially isothermal in which the upstream region is insulated and the downstream region is subjected to a suddenly applied uniform heat flux. A parametric study is done to analyze the effects of four defining parameters namely, wall thickness ratio, wall-to-fluid thermal conductivity ratio, wall-to-fluid thermal diffusivity ratio and the Peclet number. The results are given by non-dimensional interfacial heat flux values, and it is observed that, heat transfer characteristics are strongly dependent on the parameter values.     

Laminar flow and heat transfer in plate-fin triangular ducts in thermally developing entry region

Laminar forced flow and heat transfer in plate-fin isosceles triangular ducts encountered in compact heat exchangers is investigated. The flow is hydrodynamically fully developed, but developing thermally under uniform temperature conditions. Heat conduction in the fin of finite conductance and convection in the fluid are analyzed simultaneously as a conjugate problem. The study covers a wide range of apex angles from 30° to 120°, and fin conductance parameters from 0 to infinitely large. Nusselt numbers in the developing and fully developed regions for various apex angles and fin conductance parameters are obtained, which can be used in estimation of heat transfer characteristics in plate-fin compact heat exchangers with fins of various conductivities and thickness.     

Improvement in heat transfer performance by employing unique screen inserts in a horizontal heat pipe under small heat flux conditions

Two kinds of screen mesh inserts were produced with unique cross-sectional shapes (NW2 and NW3) to improve heat transfer in a horizontal evaporating tube under small heat flux conditions. These inserts were expected to supply liquid from the thick bottom layer to the upper (top) part of a heated horizontal round tube, which is the most difficult part to wet. In the present work, heat transfer performances were investigated experimentally by using a horizontal heat pipe with a visual observation capability. The experimental results showed that NW2 and NW3 worked well if the heat flux was less than 8 kW/m². This improvement was confirmed by comparison with both the data for an ordinary screen-mesh wick and calculated results based on an analytical model. © 1998 Scripta Technica, Heat Trans Jpn Res, 26(8): 529–540, 1997     

Bimaterial problems with an interfacial cavity for some boundary conditions subjected to uniform heat flux normal to the interface

Abstract

Stress analysis is carried out for a bimaterial infinite plane with an interfacial cavity. Uniform heat flux applies to the normal to the interface. Four combinations of boundary conditions are considered, that is, isothermal and adiabatic boundary conditions for heat flux analysis, and external force and displacement boundary conditions for stress analyses. The infinite plane consists of two bonded dissimilar materials of a half plane with a single notch. To achieve analytical solutions, a rational mapping function and a complex variable method are used. By changing the mapping function, other geometries for the notch can be analyzed. Complex stress functions for isothermal and external boundary conditions can be only achieved for stress calculation. The stress intensities of debonding are investigated for various debonding lengths for some elliptical holes, and for the debonding extensions. Complex stress functions for isothermal and displacement boundary conditions can be expressed by an infinite series and stress components et al. cannot be calculated. However, a solution of interfacial rigid inclusion can be solved. Complex stress functions for the adiabatic boundary are achieved by the integral forms for external force and displacement boundary conditions, and the integral cannot be carried out, and therefore, stress components cannot be achieved.     

Convective Heat and Mass Transfer in Water at Super—Critical Pressures under Heating or Cooling Conditions in Vertical Tubes

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Convective heat transfer equation for turbulent flow in tubes applied to internal combustion engines operated under motored conditions

An equation developed for the case of turbulent flow in tubes was applied for the study of convective heat transfer in internal combustion engines. Calculated average heat flux values under motored conditions were compared to measurements, results available in the literature obtained by using a computational fluid dynamics (CFD) code and the correlations of Woschni and Annand. Cumulative heat flux values for the four models were also compared to measurements at the end of the compression stroke and start of expansion. Average heat transfer rates were found to be predicted with reasonable accuracy by the proposed model. The major advantage of this equation compared to the correlations of Woschni and Annand is that it does not require any corrections for specific engine characteristics or working conditions. The proposed model was found to correctly predict higher heat transfer rates as engine speed, load and compression ratio were increased. Accuracy at the end of the compression stroke was found to be within acceptable limits for the cumulative heat flux, comparable to that of the CFD code, except for one case of the seven different engines investigated. Therefore, this model can be used to predict spatial average convective heat flux values with fairly good accuracy under motored conditions, when limited information on engine geometry is available, or when computing resources are required to be minimal.     

Analytical Solution of Coupled Laminar Heat-Mass Transfer in a Tube with Uniform Heat Flux

Analytical solution is obtained of coupled laminar heat-mass transfer in a tube with uniform heat flux. This corresponds to the case when a layer of sublimable material is coated on the inner surface of a tube with its outer surface heated by uniform heat flux and this coated material will sublime as gas flows throught the tube.     

Time and space resolved wall temperature and heat flux measurements during nucleate boiling with constant heat flux boundary conditions

The lack of time and space resolved measurements under nucleating bubbles has complicated efforts to fully explain pool-boiling phenomena. In this work, time and space resolved temperature and heat flux distributions under nucleating bubbles on a constant heat flux surface were obtained using a 10 × 10 microheater array with 100 μm resolution along with high-speed images. A numerical simulation was used to compute the substrate conduction, which was then subtracted from the heater power to obtain the wall-to-liquid heat transfer. The data indicated that most of the energy required for bubble growth came from the superheated layer around the bubble. Microlayer evaporation and contact line heat transfer accounted for not more than 23% of the total heat transferred from the surface. The dominant heat transfer mechanism was transient conduction into the liquid during bubble departure. Bubble coalescence was not observed to transfer a significant amount of heat.     

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.     

Convective heat transfer in foams under laminar flow in pipes and tube bundles

The present study reports experimental data and scaling analysis for forced convection of foams and microfoams in laminar flow in circular and rectangular tubes as well as in tube bundles. Foams and microfoams are pseudoplastic (shear thinning) two-phase fluids consisting of tightly packed bubbles with diameters ranging from tens of microns to a few millimeters. They have found applications in separation processes, soil remediation, oil recovery, water treatment, food processes, as well as in fire fighting and in heat exchangers. First, aqueous solutions of surfactant Tween 20 with different concentrations were used to generate microfoams with various porosity, bubble size distribution, and rheological behavior. These different microfoams were flowed in uniformly heated circular tubes of different diameter instrumented with thermocouples. A wide range of heat fluxes and flow rates were explored. Experimental data were compared with analytical and semi-empirical expressions derived and validated for single-phase power-law fluids. These correlations were extended to two-phase foams by defining the Reynolds number based on the effective viscosity and density of microfoams. However, the local Nusselt and Prandtl numbers were defined based on the specific heat and thermal conductivity of water. Indeed, the heated wall was continuously in contact with a film of water controlling convective heat transfer to the microfoams. Overall, good agreement between experimental results and model predictions was obtained for all experimental conditions considered. Finally, the same approach was shown to be also valid for experimental data reported in the literature for laminar forced convection of microfoams in rectangular minichannels and of macrofoams across aligned and staggered tube bundles with constant wall heat flux.     

Heat transfer in HCCI multi-zone modeling: Validation of a new wall heat flux correlation under motoring conditions

The present study focuses on the development and a preliminary validation of a heat transfer model for the estimation of wall heat flux in HCCI engines via multi-zone modeling. The multi-zone model describes heat flow between zones and to the combustion chamber wall. Mass, species and enthalpy transfer, which affect the temperature field within the combustion chamber, are also considered between zones, accounting for the convective heat transfer terms. The multi-zone heat transfer model presented herein has been developed for HCCI combustion simulation and although it has been used in the past, its validation was based on cylinder pressure data under firing conditions. In the present study a more accurate validation of the model is conducted. This is achieved by comparing the multi-zone model heat loss rate predictions to the corresponding predictions of a validated CFD code. The cases examined correspond to actual motoring cases, against which the CFD code has been validated in a previous work. Moreover, a sensitivity analysis is presented, to assess the effect of the zone configuration, i.e. zone thickness and number, on the predicted heat loss rate and temperature profiles. In addition, a comparison is made between the results obtained from the proposed heat flux correlation and one in which the temperature gradient at the wall is approximated via finite differences.     

Free convection heat transfer of non Newtonian nanofluids under constant heat flux condition

Two different kinds of non-Newtonian nanofluids were prepared by dispersion of Al₂O₃ and TiO₂ nanoparticles in a 0.5 wt.% aqueous solution of carboxymethyl cellulose (CMC). Natural convection heat transfer of non-Newtonian nanofluids in a vertical cylinder uniformly heated from below and cooled from top was investigated experimentally. Results show that the heat transfer performance of nanofluids is significantly enhanced at low particle concentrations. Increasing nanoparticle concentration has a contrary effect on the heat transfer of nanofluids, so at concentrations greater than 1 vol.% of nanoparticles the heat transfer coefficient of nanofluids is less than that of the base fluid. Indeed it seems that for both nanofluids there exists an optimum nanoparticle concentration that heat transfer coefficient passes through a maximum. The optimum concentrations of Al₂O₃ and TiO₂ nanofluids are about 0.2 and 0.1 vol.%, respectively. It is also observed that the heat transfer enhancement of TiO₂ nanofluids is higher than that of the Al₂O₃ nanofluids. The effect of enclosure aspect ratio was also investigated. As expected, the heat transfer coefficient of nanofluids as well as the base fluid increases by increasing the aspect ratio.     

Scaling for the Prandtl number of the natural convection boundary layer of an inclined flat plate under uniform surface heat flux

An improved scaling analysis and direct numerical simulations are performed for the unsteady natural convection boundary layer adjacent to a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages: a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as the numerical results. Previous scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings perform very well with Rayleigh number and aspect ratio dependency. In this study, a modified Prandtl number scaling is developed using a triple-layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the modified scaling performs considerably better than the previous scaling.