Convective heat transfer for laminar flows in a multi-passage circular pipe subjected to an external uniform heat flux

Convective heat transfer properties of an hydrodynamically and thermally fully-developed flow in a multi-passage circular tube subjected to an external uniform heat flux are analyzed. The significant dimensionless parameters affecting the problem have been determined. The expressions of Nusselt numbers on the inner and the outer wall are obtained. The limiting cases are correlated with the existing values. The representative curves illustrating the variation of Nusselt numbers with the pertinent parameters are plotted.     

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     

Effect of uniform heat flux on stress distribution around a triangular hole in anisotropic infinite plates

The presence of a hole in an anisotropic plate under uniform heat flux causes thermal stress around the hole. In this study, on the basis of two-dimensional thermoelastic theory and using Lekhnitskii’s complex variable technique, the stress analysis of an anisotropic infinite plate with a circular hole under a uniform heat flux is developed to the plate containing a triangular hole. For this purpose, an infinite plate containing a triangular hole is mapped to the outside of a unit circle using a conformal mapping function. Stress and displacement distributions around the triangular holes in an anisotropic infinite plate are investigated in thermal steady-state condition. The plate is under uniform heat flux at infinity and Neumann boundary conditions and thermal-insulated condition on the hole boundary are considered. The rotation angle of the hole, fiber angle, the angle of heat flux, bluntness, and the aspect ratio of hole size are investigated in the present study. The accuracy of the analytical results is also confirmed by finite element analysis.     

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 transfer in horizontal cylinder

A stationary heat crossflow through a horizontal cylindrical cavity filled with water has been investigated depending on the flow direction in a gravity field in the interval of Grashof's numbers ranging from 15 to 5 × 10⁶.     

Viscous non-newtonian forced convection heat transfer in semi-circular and equilateral triangular ducts: an experimental study

An experimental study was made of the steady developing laminar convective heat transfer to distilled water and viscous non-Newtonian fluids described by the power law model flowing in straight channels of uniform semi-circular and equilateral triangular cross-sections. Local axial Nusselt number distributions are presented for ducts with the horizontal bottom plane subjected to uniform heat flux while the rest of the channel is well-insulated. The measured Nusselt number distribution for Carbopol 934 solutions compared very well with the numerical predictions using the Galerkin finite element method to solve the governing conservation equations. The effect of Rayleigh number on the heat transfer is discussed. It is shown at high Rayleigh numbers the local Nusselt number shows local minima and maxima whose magnitude depends on the Rayleigh number.     

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.     

Laminar tube flow heat transfer in non-newtonian fluids under arbitrary wall heat flux

Analytical solutions are developed for the wall temperature profile of a power law fluid in laminar flow in a circular tube. This profile is first developed for the boundary condition involving uniformly constant heat flux at the wall. This is next extended for the boundary condition involving an arbitrarily varying heat flux at the wall. The computed results are finally compared with measured values obtained from a horizontal recirculating flow experimental unit.