Constant Wall Heat Flux Research Articles

Graetz problem with non-linear viscoelastic fluids in non-circular tubes

A numerical investigation of the Graetz problem in straight pipes of circular and non-circular cross-sections is carried out to analyze the influence of the rheological parameters on the heat transfer enhancement with negligible axial heat conduction and viscous dissipation for a class of non-linear viscoelastic fluids constitutively represented by the simplified Phan-Thien–Tanner (SPPT) model. The analysis considers both constant wall heat flux and constant wall temperature thermal boundary conditions and concludes that the combined elastic and shear-thinning effects represented by the parameter ɛWe2 lead to heat transfer enhancement for low values of the parameter of order O(1) whereas values of the parameter ɛWe2 > O(10) lead to a decrease in the heat transfer rate in the case of constant wall heat flux. Nusselt number distributions in the entrance region of tubes of equilateral triangular, square and rectangular cross-sections as well as Nusselt numbers Nu = f(ɛWe2) for the fully developed flow in these non-circular tubes are reported for the first time for non-linear viscoelastic fluids of the SPPT type. It is concluded that for small values of elasticity (We), the computations based on the methods included in the Polyflow software are in full agreement with analytical results when available and that discrepancies exist for high values of We. Such limitations may not exist with pseudo-spectral methods.

Numerical simulation of the pressure drop and heat transfer of two phase slug flows in microtubes using moving frame of reference technique

Enhancement in heat transfer using two phase slug flow in microtubes and microchannels has encouraged researchers to focus on this topic as one of the potential methods for miniaturizing heat sinks and exchangers. Numerical simulation of two phase slug flow is time consuming, so some researchers conduct their numerical studies using the moving frame of reference technique for a unit cell consisting of only one slug, i.e. a single phase study, in order to accelerate the simulation process. Both single phase and two phase simulation methods have been performed in the present study and results have been compared. This shows to what extent the moving frame of reference assumption is valid in the case of two phase flow in hydrophilic microtubes when a thin liquid film exists around moving gas bubbles. The present comparison has been conducted for pressure drop and heat transfer for two thermal boundary conditions i.e. constant wall temperature and constant wall heat flux. It has been shown that the moving frame of reference method overpredicts pressure drop and heat transfer and possible reasons have been discussed. This also shows that in a slug flow with no film around bubbles more heat transfer could be achieved.

A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids

In this work, we propose an approximate methodology to estimate the Nusselt number and friction factor in fully developed non-Newtonian laminar flow in circular pipes for a constant wall heat flux. The methodology was tested using several constitutive equations, including generalized Newtonian fluids and viscoelastic models such as the simplified Phan-Thien–Tanner (sPTT), Herschel–Bulkley, Bingham, Casson, and Carreau–Yasuda constitutive equations. The error of the approximate methodology was found to be smaller than 3.2%, except for the fluids with yield stress for which the maximum error increased to about 8% for the cases analyzed, which cover a wide range of shear viscosity curves.

Heat Transfer with Axial Conduction in Triangular Ducts Filled with Saturated Porous Materials

The study reports the contribution of axial conduction in heat transfer to flow passing through triangular porous passages. The problem under consideration uses the H2 boundary condition; that is, locally constant wall heat flux. Because of the geometrical asymmetry, nonorthogonal boundary conditions can exist and this makes the determination of heat transfer more demanding. The porous medium is fully saturated and the placement of porous materials can enhance the transfer of heat to a flowing fluid. A fully developed flow is considered for the velocity field in the presence of a thermally developing temperature field. The weighted residual method is used throughout the calculations.

Convective Heat Transfer in Microchannels of Noncircular Cross Sections: An Analytical Approach

Analytical solutions are presented for velocity and temperature distributions of laminar fully developed flow of Newtonian, constant property fluids in micro/minichannels of hyperelliptical and regular polygonal cross sections. The considered geometries cover several common shapes such as ellipse, rectangle, rectangle with round corners, rhombus, star-shape, and all regular polygons. The analysis is carried out under the conditions of constant axial wall heat flux with uniform peripheral heat flux at a given cross section. A linear least squares point matching technique is used to minimize the residual between the actual and the predicted values on the boundary of the channel. Hydrodynamic and thermal characteristics of the flow are derived; these include pressure drop and local and average Nusselt numbers. The proposed results are successfully verified with existing analytical and numerical solutions from the literature for a variety of cross sections. The present study provides analytical-based compact solutions for velocity and temperature fields that are essential for basic designs, parametric studies, and optimization analyses required for many thermofluidic applications.

Numerical analysis of laminar heat transfer performance of in-plane spiral ducts with various cross-sections at fixed cross-section area

A numerical approach is carried out to investigate the heat transfer performance of in-plane spiral ducts with various cross sections – rectangular, square, triangular, trapezoidal, circular and half circular. Simulations were carried out at a constant inlet Reynolds number at fixed cross section area for both constant wall temperature and constant wall heat flux conditions. Results are compared to straight ducts of the same cross sections and at the same length as the coiled ducts. The effects of Reynolds number and Prandtl number are also discussed for various geometries. The results are presented and are aimed to determine the advantages, limitations and effects of in-plane spiral ducts of various cross sections on the flow and heat transfer characteristics when the cross section area is fixed.

Numerical Investigation on Laminar Microconvective Liquid Flow With Entrance Effect and Graetz Problem due to Variation in Thermal Properties

This work deals with the analysis of forced convection in single-phase laminar flow of liquid through microsized circular geometry with a diameter of 100 × 10−6 m. The problem with hydrodynamically and thermally developing flow in the entrance region with no-slip, no-temperature jump and constant wall heat flux boundary condition is numerically studied. Two-dimensional (with axisymmetry) simulation is carried out to understand the effect of fluid property variations on flow development and heat transfer. Pure continuum-based governing equations are solved to predict the significance of momentum and energy transport due to temperature-dependent viscosity and thermal conductivity variation, respectively. The radial inward flow is induced due to temperature-dependent density variation that sharpens the axial velocity profile. The investigation also analyzes the change in Nusselt number with locations in the channel for Graetz problem with uniform heating condition. The flattening of axial velocity profile, radial temperature profile, and inward radial flow influences the heat flow characteristics. The investigations in computational domain show that Nusselt number in thermal entrance region deviates from constant properties solution due to scaling effects.

An Experimental Study on Heat Transfer and Entropy Generation in Circular Tube Fitted with Trapezium-Nozzles

Heat transfer, friction factor and entropy generation from the inside surface of a horizontal circular tube fitted with trapezium - nozzle have been investigated experimentally. The heat transfer test section is heated electrically imposing axially and circumferentially constant wall heat flux. Three different pitch ratios (PR) of trapezium -nozzle arrangements in the test tube are introduced with PR=2, 4, and 7. The experiments covered a range of Reynolds numbers from 8000 to16000. Heat transfer and friction factor analyses are presented for different conditions of pitch ratios (PR) and Reynolds number. The results indicate that the trapezium - nozzle of different pitch ratios has a great effect on the results of heat transfer coefficient and friction factor. The Nusslet number increases with an increase in Reynolds number and it decreases with an increase in pitch ratios. It is found that using the trapezium -nozzle results in increasing the heat transfer rate compared with the plain tube. The maximum gain in Nusslet number is obtained for the smallest pitch ratio used, PR=2. This indicates that the effect of the reverse/re-circulation and surface flows can improve the heat transfer rate in the circular tube. For fixed Reynolds number, the friction factor increases with the decrease in pitch ratio for the circular tubes with trapezium -nozzle. The entropy generation number increases with increase Reynolds number at all cases, whereas the entropy generation number shows its highest value at pitch ratio of 2. From these results, it was found that the average enhancement in Nusselt number for circular tube fitted with trapezium - nozzle at pitch ratio (PR=2) is in the range of 202% to 257% compared with the plain circular tube for all tested conditions. Correlations of the Nusselt number and friction factor with Reynolds number and pitch ratio are presented. Key words : Enhancement heat transfer; Circular tube; Re-circulation/Reverse flow; Turbulator; Entropy generation; Trapezium –nozzle

Flow and Heat Transfer Characteristics of Turbulent Gas Flow in Microtube with Constant Heat Flux

Local friction factors for turbulent gas flows in circular microtubes with constant wall heat flux were obtained numerically. The numerical methodology is based on arbitrary-Lagrangian-Eulerian method to solve two-dimensional compressible momentum and energy equations. The Lam-Bremhorst's Low-Reynolds number turbulence model was employed to calculate eddy viscosity coefficient and turbulence energy. The simulations were performed for a wide flow range of Reynolds numbers and Mach numbers with different constant wall heat fluxes. The stagnation pressure was chosen in such a way that the outlet Mach number ranged from 0.07 to 1.0. Both Darcy friction factor and Fanning friction factor were locally obtained. The result shows that the obtained both friction factors were evaluated as a function of Reynolds number on the Moody chart. The values of Darcy friction factor differ from Blasius correlation due to the compressibility effects but the values of Fanning friction factor almost coincide with Blasius correlation. The wall heat flux varied from 100 to 10000 W/m2. The wall and bulk temperatures with positive heat flux are compared with those of incompressible flow. The result shows that the Nusselt number of turbulent gas flow is different from that of incompressible flow.

Effects of Natural Convection from an Open Square Cavity Containing a Heated Circular Cylinder

The problem of natural convection heat transfer in a square open cavity containing a heated and conducting circular cylinder at the centre is analyzed in this paper. As boundary conditions of the cavity, the left vertical wall is kept at a constant heat flux, bottom and top wall are kept at different high and low temperature respectively. The remaining side is open. Two dimensional laminar steady state natural convection is considered. This configuration is related in the design of electronic devices, solar energy receivers, uncovered flat plate solar collectors geothermal reservoirs etc. The fluid is concerned with different Prandtl numbers, Grashof numbers and the properties of the fluid are assumed to be constant. The development of Mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by employing Galerkin weighted finite element method. Flow field and heat transfer were predicted for fluid with Pr = 0.72 , 1.0 ,7.0; Gr = 103, 104, 105 ,106; inclination angles of the cavity are ? = 0°, 15°, 30°, 45° and diameter ratio dr = 0.2.The average Nusselt number increases as the increases of inclination angle of the cavity for lower Pr and lower temperature at bottom wall. The average Nu increases mainly for higher inclinations and for higher Gr. Various vortices and recirculations are formed into the flow field for higher Pr and higher temperature at the bottom wall. DOI: http://dx.doi.org/10.3329/bjsir.v47i1.10718Bangladesh J. Sci. Ind. Res. 47(1), 19-28, 2012

The study of laminar convective heat transfer of CuO/water nanofluid through an equilateral triangular duct at constant wall heat flux

AbstractThe present paper focuses on the heat transfer of an equilateral triangular duct by employing the CuO/water nanofluid in a laminar flow and under constant heat flux condition. The triangular ducts were used due to their ease of creation and high compaction. They have less pressure drop when compared to the circular and non‐circular ducts and their other attributes are very useful in industrial applications. These reasons cause their heat transfer characteristics to be very important. In this paper, to improve the heat transfer of an equilateral triangular duct, a CuO/water nanofluid was employed. The nanofluid was conducted through an equilateral triangular duct with a constant wall heat flux. Results show that the experimental heat transfer coefficient of the CuO/water nanofluid is more than that of distilled water. Also, the experimental heat transfer coefficient of a CuO/water nanofluid is greater than the theoretical one. The heat transfer enhancement of the equilateral triangular duct increases with the nanofluid volume concentration as well as the Peclet number. So a 41% enhancement in the convective heat transfer coefficient for a 0.8% CuO/water nanofluid can be seen when compared to pure water. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21011

Chemically Reacting Hydromagnetic Unsteady Flow of a Radiating Fluid Past a Vertical Plate with Constant Heat Flux

The combined effects of thermal radiation absorption and magnetic field on an unsteady chemically reacting convective flow past an impulsively started vertical plate is studied in the presence of a constant wall heat flux. Boundary layer equations are derived and the resulting approximate nonlinear partial differential equations are solved numerically using a semi-discretization finite difference technique. A parametric study of all parameters involved is conducted, and a representative set of numerical results for the velocity, temperature, and concentration profiles as well as the skin-friction parameter and Sherwood number are illustrated graphically to show typical trends of the solutions. Further validation with previous works is carried out and an excellent agreement is achieved.

Heat Transfer in Turbulent Liquid-solid Flow Considering the Interparticle Collision Effect

A turbulent liquid-solid suspension upward flow in a vertical pipe is simulated numerically using the Eulerian-Lagrangian approach. Particle-particle and particle-wall collisions are simulated based on the deterministic approach. The model considers the thermal turbulent field characteristics and includes k θ-τθ equation model, in addition to the k-τ model for two-phase flow. Numerical model validation was performed for an upward pipe liquid-solid flow with constant wall heat flux. Variations of the heat transfer coefficient by the loading ratio, the particle density, and the particle diameter are studied. It is observed that particle to liquid density has a dominant effect on turbulence and heat transfer characteristics.

A dispersion model for predicting the heat transfer performance of TiO2–water nanofluids under a laminar flow regime

Nanofluids are a suspension of particles with ultrafine size in a conventional base fluid that increases the heat transfer performance of the original base fluid. They show higher thermal performance than base fluids especially in terms of the thermal conductivity and heat transfer coefficient. During the last decade, many studies have been carried out on the heat transfer and flow characteristics of nanofluids, both experimentally and theoretically. The purpose of this article is to propose a dispersion model for predicting the heat transfer coefficient of nanofluids under laminar flow conditions. TiO2 nanoparticles dispersed in water with various volume fractions and flowing in a horizontal straight tube under constant wall heat flux were used. In addition, the predicted values were compared with the experimental data from He et al. [14]. In the present study, the results show that the proposed model can be used to predict the heat transfer behaviour of nanofluids with reasonable accuracy. Moreover, the results also indicate that the predicted values of the heat transfer coefficient obtained from the present model differ from those obtained by using the Li and Xuan equation by about 3.5% at a particle volume fraction of 2.0%.

Gas flow and heat transfer in nanotube and nanowire arrays

Gas flow through arrays of nanotube or nanowire structures is modeled by combining the one-dimensional equations for conservation of mass, momentum, and energy with the linearized free-molecular drag and heat transfer for a cylinder. The results show that the pressure gradient, temperature, and local velocity of the gas are governed by coupled ordinary differential equations. Three cases are considered: an isothermal system, a constant wall temperature, and a constant wall heat flux. While the coupled momentum, heat transfer, and continuity equations are nonlinear, the relatively low velocities encountered in these systems cause the nonlinear portions of pressure drops and thermal phenomena to be relatively small.

Fluid flow and heat transfer characteristics of spiral coiled tube: Effects of Reynolds number and curvature ratio

Numerical analysis was performed to investigate flow and heat transfer characteristics in spiral coiled tube heat exchanger. Radius of curvature of the spiral coiled tube was gradually increased as total rotating angle reached 12π. As the varying radius of curvature became a dominant flow parameter, three-dimensional flow analysis was performed to this flow together with different Reynolds numbers while constant wall heat flux condition was set in thermal field. From the analysis, centrifugal force due to curvature effect is found to have significant role in behavior of pressure drop and heat transfer. The centrifugal force enhances pressure drop and heat transfer to have generally higher values in the spiral coiled tube than those in the straight tube. Even then, friction factor and Nusselt number are found to follow the proportionality with square root of the Dean number. Individual effect of flow parameters of Reynolds number and curvature ratio was investigated and effect of Reynolds number is found to be stronger than that of curvature effect.

Laminar convective heat transfer for in-plane spiral coils of noncircular cross sections ducts: A computational fluid dynamics study

The objective of this study was to carry out a parametric study of laminar flow and heat transfer characteristics of coils made of tubes of several different cross-sections e.g. square, rectangular, half-circle, rectangular and trapezoidal. For the purpose of ease of comparison, numerical experiments were carried out base on a square-tube Reynolds number of 1000 and a fixed fluid flow rate while length of the tube used to make coils of different diameter and pitch was held constant. A figure of merit was defined to compare the heat transfer performance of different geometry coils; essentially it is defined as total heat transferred from the wall to the surroundings per unit pumping power required. Simulations were carried out for the case of constant wall temperature as well as constant heat flux. In order to allow reasonable comparison between the two different boundary conditions - constant wall temperature and constant wall heat flux - are tested; the uniform heat flux boundary condition was computed by averaging the heat transferred per unit area of the tube for the corresponding constant wall temperature case. Results are presented and discussed in the light of the geometric effects which have a significant effect on heat transfer performance of coils.

Extended exergo-economic performance evaluation criteria for enhanced heat transfer duct with constant wall heat flux

Comprehensive performance evaluation criteria for enhanced duct in comparison with smooth duct subjected to constant wall heat flux have been proposed under various design constraints. The net profit value (NPV) and the total cost value (TCV) have been derived from the perspectives of exergy recovery and exergy destruction respectively. By taking spirally corrugated duct as an example, the evaluation results reveal that the exergo–economic performance of enhanced duct is inconsistent from different perspectives under various design constraints and largely dependent on Reynolds number (Rea) and dimensionless wall heat flux (Nq).

BOUNDARY CONDITION EFFECTS ON NATURAL CONVECTION OF BINGHAM FLUIDS IN A SQUARE ENCLOSURE WITH DIFFERENTIALLY HEATED HORIZONTAL WALLS

Natural convection of Bingham fluids in square enclosures with differentially heated horizontal walls has been numerically analyzed for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for different values of Bingham number Bn (i.e., nondimensional yield stress) for nominal Rayleigh and Prandtl numbers ranging from 10 to 10 and from 0.1 to 100, respectively. A semi-implicit pressure-based algorithm is used to solve the steady-state governing equations in the context of the finite-volume methodology in two dimensions. It has been found that the mean Nusselt number Nu increases with increasing Rayleigh number, but Nu is found to be smaller in Bingham fluids than in Newtonian fluids (for the same nominal values of Rayleigh and Prandtl numbers) due to augmented flow resistance in Bingham fluids. Moreover, Nu monotonically decreases with increasing Bingham number irrespective of the boundary condition. Bingham fluids exhibit nonmonotonic Prandtl number Pr dependence on Nu and a detailed physical explanation has been provided for this behavior. Although variation of Nu in response to changes in Rayleigh, Prandtl, and Bingham numbers remains qualitatively similar for both CWT and CWHF boundary conditions, Nu for the CWHF boundary condition for high values of Rayleigh number is found to be smaller than the value obtained for the corresponding CWT configuration for a given set of values of Prandtl and Bingham numbers. The physical reasons for the weaker convective effects in the CWHF boundary condition than in the CWT boundary condition, especially for high values of Rayleigh number, have been explained through a detailed scaling analysis. The scaling relations are used to propose correlations for Nu for both CWT and CWHF boundary conditions and the correlations are shown to capture Nu satisfactorily for the range of Rayleigh, Prandtl, and Bingham numbers considered in this analysis.

Free convection from a truncated cone subject to constant wall heat flux in a micropolar fluid

The paper studies the problem of free convection about a vertical frustum of a cone in a micropolar fluid. It is assumed that the flow is laminar, steady and the wall is subjected to a constant heat flux and the angle of the frustum of the cone is large enough so that the transverse curvature effects are negligible. Under these assumptions, the governing boundary layer equations subject to appropriate boundary conditions are transformed into a set of equations of parabolic type, that are solved using the local non-similarity method. The space of parameters contains the Prandtl number Pr, the micropolar parameter Δ and the microrotation parameter n. Numerical solutions are obtained by varying Pr from 6.7 to 100, Δ from 0 (Newtonian fluid) to 2 and considering two values of n with physical significance (0 and 0.5). Flow and heat transfer characteristics are determined and are shown in graphs. The results are discussed and compared at some extent with those reported by the present author in a previous study (Postelnicu in Int. J. Eng. Sci. 44:672–682, 2006) on the isothermal case.