Uniform Wall Temperature Boundary Condition Research Articles

CONVECTIVE HEAT TRANSFER INSIDE A ROTATING HELICAL PIPE FILLED WITH SATURATED POROUS MEDIA

In this paper, we study the hydrothermal characteristics of flow inside a rotating helical pipe filled with saturated homogeneous porous medium. The analysis is being carried out for the case of small curvature and torsion. Using the perturbation approach, velocity and temperature fields are solved for both uniform wall heat flux and uniform wall temperature boundary conditions. Perturbation expansion up to the third order is carried out to investigate the effect of rotation on the flow. The influence of rotation on velocity is noticed as early as the first order, and on temperature solution, it has an effect in the third order. The influence of rotation on the Nusselt number does not appear till third order, and it is discovered that the Nusselt number grows as dimensionless curvature increases. Moreover, the theoretical results have been verified against experimental data from existing literature for the special case of zero rotation and curvature of the pipe. The available experimental data align well with and support the theoretical results in this limiting case.

Natural Convective Heat Transfer from Vertical Isothermal Polygonal Cylinders

A numerical study was undertaken on the laminar convective heat transfer from vertical polygonal cylinders with an uncovered top surface for a relatively small polygons area. The polygonal cylinders were perpendicularly placed on a flat adiabatic base plate, and uniform wall temperature boundary conditions were assumed. The governing equations for geometrical evaluation were solved numerically in terms of dimensionless variables using FLUENT. The numerical model has been validated with the existing experimental and empirical correlation equations. From the results obtained, mean Nusselt numbers from the polygonal cylinders were calculated using parameters such as the Rayleigh number ; the polygon area ; the number of sides of the polygon, ; and the Prandtl number . Results were obtained only for . Values of in the range , values of in the range to , and values of in the range 0.08 to 1 were considered. The effects of , and on the mean Nusselt number for the combined and for the individual surfaces of the polygonal cylinder are presented. Correlation equations for the mean Nusselt numbers for the side and top surfaces of the polygonal cylinders were developed.

The mechanism of laminar convective heat transfer enhancement enforced by twisting of elliptical tube

Nusselt number has unique characteristics under uniform wall temperature (UWT) and uniform wall heat flux (UWHF) thermal boundary conditions in twisted elliptical tube. Twisting of elliptical tube produces larger local Nusselt number under UWT than that under UWHF in some regions. In order to discover the mechanisms to form such characteristics in twisted elliptical tube, the velocity contribution and velocity gradient contribution to the transport of the heat flux defined by Fourier's law, q, are numerically investigated in this paper. Velocity gradient under UWHF contributes more greatly to the transport of the heat flux under UWHF than under UWT, which results larger local Nusselt number under UWHF than under UWT in straight elliptical tube. Velocity and its gradient contributions to the transport of the heat flux nearly normal to the wall surface have larger values under UWHF than under UWT in most regions, which produces larger local Nusselt number in twisted elliptical tube under UWHF than under UWT in these regions. In some regions velocity and its gradient contributions to the transport of the heat flux nearly normal to the wall surface have larger values under UWT than under UWHF produces larger local Nusselt number in twisted elliptical tube under UWT than under UWHF in these regions.

Viscous heating effects on heat transfer characteristics of laminar compressible channel flow

The present paper investigates viscous heating effects on heat transfer characteristics of laminar Newtonian compressible channel flow. At first, incompressible Poiseuille flow case is addressed analytically by including viscous dissipation term in energy conservation equation. Temperature distributions in the channel cross-section and local Nusselt numbers are derived as functions of the Brinkman number, highlighting the role of the viscous term. The analysis is numerically supported by a set of CFD simulations. Additional CFD results are employed to extend the analysis to compressible flow case resulting in dedicated local Nusselt number correlations, function of Brinkman and Mach numbers, and expansion-altered temperature profiles. The study assumes no-slip flow and no temperature-jump boundary conditions at the channel wall (Knudsen number Kn<10−3), and addresses both fluid heating and cooling, both uniform heat flux (UHF) and uniform wall temperature (UWT) boundary condition (BC), and both circular (CR) and parallel-plate (PP) channel cross-section.

Comparison of urban airflow between solar-induced thermal wall and uniform wall temperature boundary conditions by coupling CitySim and CFD

Previous studies investigated the urban wind airflow under the isothermal condition, solar-induced thermal wall and uniform wall temperature boundary conditions. The differences in spatially-averaged airflow properties among those three boundary conditions have not been investigated yet. This study investigated different scenarios to identify: (1) whether the solar-induced non-uniform wall temperatures could be replaced by the uniform wall temperatures (average of all wall temperatures from solar-induced scenario) in the analysis of urban wind airflow and (2) the wind conditions that the wall thermal boundary conditions might be neglected. In this study, urban energy model, CitySim, was employed to calculate the solar-induced walls’ temperatures of an idealized 5 × 5 building array, which were set as thermal boundary conditions in computational fluid dynamic (CFD) simulations. The simulation results were compared to those obtained from cases with uniform wall temperatures and isothermal conditions. The results showed that excluding wall thermal boundary conditions underestimated the spatially-averaged flow properties when reference wind speed (Uref) was lower than 2.0 m s−1 under the designed scenarios and noticeable difference of airflow pattern was observed between isothermal and non-isothermal conditions. The solar-induced wall temperature condition might be replaced by uniform wall temperature condition with Uref of 3.0 m s−1 under parallel wind condition, and with Uref of 5.0 m s−1 under oblique wind conditions. Meanwhile, the airflow structures of the street canyons inside the three-dimensional building array differed significantly from the previous results obtained from isolated street canyon model.

Heat transfer correlation for circular and non-circular ducts in the transition regime

A new model to predict the Nusselt number in the entry region of smooth non-circular ducts and channels is developed, for both uniform heat flux and uniform wall temperature boundary conditions. The model, valid for the laminar, transition, turbulent and fully turbulent regimes, is developed using the asymptotic results for both laminar and turbulent flow in circular and non-circular ducts. The proposed model is valid for fluids with Prandtl numbers between 0.7 and 78, Reynolds numbers in the range of 890 to 248,800, and a ratio of the length of the duct to the square root of the cross-section area in the range of 0.001 to 0.03. Comparisons are made with several existing databases for circular and non-circular ducts, showing that the proposed correlation has an overall root mean square error equal to 10.0%, which is smaller than the other literature correlations. This correlation is shown to provide good predictions against the entire database, for both boundary conditions. One of the major accomplishments of this work is the versatility of the proposed equation, where for calculating the Nusselt number on circular and most common noncircular ducts a unique equation is necessary.

Simulative analysis of turbulent flow through a circular conduit with uniform wall temperature and constant heat flux boundary conditions

PurposeThis study aims to investigate numerically a two-dimensional fully developed mean turbulent fluid flow, and heat transfer in a circular duct is numerically investigated using FORTRAN 95 code that applies the finite difference method to solve the thermal problem for the two thermal boundary conditions, constant surface temperature, constant heat and steady, axisymmetric flow. Several important results have been drawn and discussed from thermal analysis. Finally, the numerical results of the model developed in the document have been validated in good accuracy by comparing them with some correlation results available in the specialized literature.Design/methodology/approachThe methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas' algorithm, a program in FORTRAN version 95 was developed to numerically solve the discretized form of the system of equations describing the problem.FindingsThe profiles of the solutions are provided from which the authors infer that the numerical and literature correlation agreed very well. Another result that they obtained from this study is the number of Nusselt in the thermal entrance region to which a parametric study based on Reynolds and Peclet numbers, and the longitudinal coordinate, was carried out and discussed well for the impact of the scientific contribution.Originality/valueThe novelty of the work is the application of the finite difference method programed on the FORTRAN code, as a sequential numerical method of an ODEs system, to determine the number of Nusselt in both uniform wall temperature and wall heat flux uniform.

Analysis of fully developed flow and heat transfer through n-sided polygonal ducts with round corners using the Galerkin weighted residual method

The Galerkin weighted residuals method is extended solve the laminar, fully developed flow and heat transfer of Al2O3-water nanofluid inside polygonal ducts with round corners for the constant heat flux and uniform wall temperature boundary conditions. Using the method, semi-analytical, closed-form solutions are obtained for the friction coefficient and the Nusselt number in terms of the radius of the round corners for the triangular, rectangular, hexagonal, and octagonal ducts. The effects of varying the radius of the round corners and the volume fraction of the nanoparticles on the friction coefficient and the Nusselt number are analyzed. The results show that the friction factor and the average Nusselt number increase with increasing the radius of the round corners. The study indicates that the Galerkin weighted residuals method is an accurate and efficient technique to obtain closed-form solutions for the flow and temperature fields in ducts with complex cross sectional shapes.

Effects of the Random Distributions on the Laminar Flow and Heat Transfer in a Quasi-Counter Flow Parallel-Plate Membrane Channel

ABSTRACTAn internally cooled parallel-plate membrane contactor has been employed for liquid desiccant air dehumidification. The contactor is comprised of a series of quasi-counter flow parallel-plate membrane channels (QCPMC). The processing air and the liquid desiccant (solution) streams are separated by the membranes. Cooling tubes are installed in the solution channel to take away the absorption heat. The laminar flow and heat transfer in the QCPMC with the cooling tubes in the solution side (QCPMCC) are studied based on a unit cell containing the sandwiched domain outside the cooling tubes between two neighboring membranes. This paper is focused on the effects of the random distributions in the height direction on the transport phenomena in the QCPMCC. The governing equations of the momentum and thermal transports are built up together with a uniform wall temperature boundary condition. The product of the mean friction factor and Reynolds number and the mean Nusselt number are then calculated. Effects of the various random distributions in the height direction on the product of the mean friction factor and Reynolds number and the mean Nusselt number are analyzed. Compared to the regular arrangement, the mean Nusselt number for the random distribution is larger than that for the regular one when the Reynolds number is less than 68.5. However when the Reynolds number is larger than 68.5, the mean Nusselt number for the random distribution is smaller than that for the regular one.

Laminar flow and heat transfer in an internally-cooled hexagonal parallel-plate membrane channel (IHPMC)

A internally-cooled hexagonal parallel-plate membrane contactor has been proposed and employed for liquid desiccant air dehumidification, which contains a series of internally-cooled hexagonal parallel-plate membrane channels (IHPMC) for the liquid desiccant stream. Several cooling tubes are installed in the solution channel to take away the absorption heat swiftly. The friction factors and heat transfer coefficients in the complex IHPMC are necessary for the structural design and energy analysis. This study will be focused on the influences of the channel structural parameters on the product of mean friction factors and Reynolds number (fRe)m and Nusselt numbers (Num) in the IHPMC, instead of on the coupled heat and mass transports. The laminar flow and heat transfer in the solution channel are studied based on a unit cell containing the sandwiched domain outside the cooling tubes between two neighboring membranes. The momentum and thermal transport governing equations are built up together with a uniform wall temperature boundary condition and solved by a finite volume approach. The mean (fRe)m and Nusselt numbers (Num) are calculated and analyzed. Influences of the tube numbers (N), tube outer diameters (do), tube distributions, Reynolds number (Re), and tube shapes on the (fRe)m and Num are studied. It can be found that when the do is equal to 0.002m, the (fRe)m rises with an increase in the N, while the Num decrease with the N increasing. When the N is fixed as 3, the (fRe)m increase with the do increasing, and the Num decrease with the do increasing. The results are useful for the performance evaluation, structural design of the membrane contactors formed by the IHPMC used for liquid desiccant air dehumidification.

Laminar flow and heat transfer in a quasi-counter flow parallel-plate membrane channel in the solution side with cooling tubes

An internally-cooled parallel-plate membrane contactor has been proposed, designed, and used for liquid desiccant air dehumidification. It is comprised of a series of side in and out parallel-plate membrane channels (QCPMC). The processing air and the liquid desiccant (solution) streams are separated by the membranes. Cooling tubes are installed in the solution channel to take away the absorption heat. The friction factors and heat transfer coefficients in the complex QCPMC with the cooling tubes in the solution side (QCPMCC) are necessary for the structural design and energy analysis. Therefore the laminar flow and heat transfer in the solution channel are studied based on a unit cell containing the sandwiched domain outside the cooling tubes between two neighboring membranes. The momentum and thermal transport governing equations are built up together with a uniform wall temperature boundary condition and solved by a finite volume approach. The mean (fRe) and Nusselt numbers (Num) are then calculated. Influences of the Reynolds numbers (Re), tube number (Ntube), tube outer diameters (douter), tube arrangements, and connection types of tubes on the (fRe)m and Num are analyzed. It can be found that when douter=0.003m, the (fRe)m rises with an increase in the Ntube. However the Num decrease with the Ntube increasing. When Ntube=4, the (fRe)m rise with an increase in the douter. However the larger the douter are, the smaller the Num are.

Laminar flow and heat transfer in plate membrane channels: Effects of the deformation heights

Membrane channels have been extensively used for air humidity control and energy recovery. The membranes are commonly parallel-plate type. However they probably are deformed because of their weak mechanical strengths and fluid pressure. Effects of the deformation heights (Δh) on the laminar flow and heat transfer in the plate membrane channels are studied based on two unit cells. Each one of them includes two neighboring membranes and a channel sandwiched by the membranes. The equations governing the momentum and heat transports are established together with a uniform wall temperature boundary condition and numerically solved by a finite volume approach. The mean (fRe) and Nusselt number (Num) are obtained. The influences of the deformation heights (Δh), aspect ratios (b/a), and Reynolds numbers (Re) on the (fRe)m and Num are calculated. It can be found that when the b/a is less than or equal to 25, the Num rises with the Δh increasing for the air channel. However the Num firstly rises, and then decreases with the Δh increasing when the b/a ranging from 30 to 40. For the water/LiCl solution channels, the Num for the LiCl solution is about 40%–56% larger than that for the water stream.

Entropy generation analysis of laminar flow of a nanofluid in a circular tube immersed in an isothermal external fluid

This paper is an analytical study of entropy generation in the laminar flow of nanofluids in a circular tube. The tube is immersed in an isothermal external fluid – which is the most general thermal boundary condition but has not been studied in much detail in literature. Two nanofluids, namely – water–Al2O3 and ethylene glycol–Al2O3 have been chosen for this study. The effects of the external Biot number, non-dimensional temperature difference and volume fraction on the entropy generation characteristics of the flow have been shown through graphs and the physical reasoning behind the observed trends has been discussed threadbare. It is shown that the addition of nanoparticles is beneficial only at smaller Reynolds number and for less viscous base fluids. Most importantly, it is proved that the entropy generated in the case of a tube immersed in an isothermal external fluid is bounded by those for uniform heat flux and uniform wall temperature boundary conditions.

Laminar flow and heat transfer in a quasi-counter flow parallel-plate membrane channel (QCPMC)

A parallel-plate membrane contactor with side inlets and side outlets has been designed and used for air humidity control. The contactor is comprised of a series of quasi-counter flow parallel-plate membrane channels (QCPMC). The laminar flow and heat transfer in the QCPMC are investigated based on a unit cell including one membrane and half of the channel. The equations governing the momentum and heat transports are established together with a uniform wall temperature boundary condition and numerically solved by a finite volume difference approach. The mean product of friction factor and Reynolds number (fRe) and Nusselt number (Num) are then obtained and numerically validated by those taken from other well-known publications. Influences of the Reynolds numbers (Re), entrance ratios (xin/x0), aspect ratios (x0/H), and various fluids with different Prandtl numbers (Pr) on the (fRe)m and Num are obtained and analyzed. It can be found that a distinct vortex is generated for the water stream flowing through the QCPMC when the Re is greater than 100. Further, for the same x0/H, the Num of the LiCl stream is the largest, and next the water stream, the least the air stream.

Free stream flow and forced convection heat transfer across rotating circular cylinder in steady regime: effects of rotation, Prandtl number and thermal boundary condition

Free stream flow and forced convection heat transfer across a rotating circular cylinder have been investigated numerically for the range of Reynolds number between 5 and 40 (5 ≤ Re ≤ 40). The non-dimensional rotation rate, α is employed upto a maximum value of 5. The governing equations namely, continuity, momentum, and energy equations have been solved in 2D steady laminar flow regime for the range of Prandtl number between 0.7 and 67 (0.7 ≤ Pr ≤ 67). Uniform heat flux (UHF) and constant wall temperature (CWT) boundary conditions have been considered, separately, for the range of afore mentioned parameters. New results are presented depicting the behavior of temperature field around the cylinder rotating in a high Pr environment (Pr ≥ 33) with non-dimensional rotation rate in the range between 0 and 5 (0 ≤ α ≤ 5). It is noted that the heat transfer across the cylinder becomes increasingly independent of the thermal boundary condition i.e. UHF or CWT.

Optimal solution of nonlinear heat and mass transfer in a two-layer flow with nano-Eyring–Powell fluid

This paper deals with the fully-developed two-layer Eyring–Powell fluid in a vertical channel divided into two equal regions. One region is filled with the clear Eyring–Powell fluid and other with the nano-Eyring–Powell fluid. The flow is observed under the uniform wall temperature and concentration boundary conditions for combined heat and mass transfer. The governing coupled nonlinear ordinary differential equations (ODEs) of the flow in each layer are analytically solved by using optimal homotopy analysis method (OHAM) based on the homotopy analysis method (HAM). HAM is an efficient analytical approximation method to solve highly nonlinear problems. The effect of Brownian motion parameter on Eyring–Powell fluid is also observed and the influence of significant parameters is presented for their different values.

Experimental and numerical study of fluid flow and heat transfer in a twisted square duct

Heat transfer and friction factor characteristics of air flow inside twisted square duct are studied experimentally and through three-dimensional numerical simulations. Experiments were conducted for air with uniform wall temperature boundary condition, twist ratio of 11.5 and 16.5, and Reynolds number 600–70,000. Laminar to turbulent flow transition point was identified. The results show considerable enhancement in heat transfer and pressure drop in both laminar and also in turbulent flow regimes till Reynolds number of 9500. Twist ratio of 11.5 shows relatively higher heat transfer and pressure drop compared to straight square duct. Three-dimensional analysis of steady fully-developed laminar flow inside twisted duct of square cross section flow area is carried out for Reynolds number range of 100–100,000 using commercially available software. The numerical study is conducted for a uniform wall temperature case, twist ratio of 2.5, 5, 10 and 20, for Prandtl number range of 0.7 to 20. The maximum value for product of friction factor and Reynolds number is observed for a twist ratio of 2.5 and a Reynolds number of 3000. The maximum Nusselt number is observed for the same values for Prandtl number of 20. Correlations for friction factor and Nusselt number are developed involving swirl parameter in the laminar flow regime. Correlations are also provided for the entire range of turbulent regime. Local distribution of friction factor ratio and Nusselt number across a cross-section is presented. Based on constant pumping power criteria, enhancement factor is defined to compare twisted ducts with straight ducts. Selections of twisted square duct are presented in terms of enhancement factor. It is found that twisted duct performs well in laminar and also to some extent in turbulent flow regime due to strong presence of secondary flow. It is recommended to use twisted square duct in laminar flow regime for entire range of Prandtl number studied. Maximum enhancements factor of 10.5 is obtained with twist ratio of 2.5, Prandtl number of 20 and Reynolds number of 3000. Guidelines are provided for selection of twisted square duct in terms of Reynolds number and Prandtl number. Comparison with twisted elliptic tube and twisted tape are discussed. These results would help in the design and development of compact heat exchanger.

Second Law Analysis of Laminar Flow in a Circular Pipe Immersed in an Isothermal Fluid

Entropy generation and pumping power to heat transfer ratio (PPR) of a laminar flow, for a circular tube immersed in an isothermal fluid, are studied analytically in this paper. Two different fluids, namely, water and ethylene glycol, are chosen to study the influence of fluid properties on entropy generation and PPR. The expressions for dimensionless entropy generation, Bejan number and PPR are derived in a detailed way and their variations with Reynolds number, external Biot number, and the dimensionless temperature difference are illustrated. The results of the analysis are compared with those for a laminar flow in a circular tube with uniform wall temperature boundary condition. Finally, a criterion is established to determine which type of thermal boundary conditions is more suitable for a particular fluid, with respect to its influence on entropy generation.

A Simple Method of Determining Entropy Generation Rate in Viscous Fluid Flow Through Ducts

Entropy generation rate in a flow channel is associated with a number of parameters including the geometry of the channel, the thermal boundary conditions, and the thermo-physical properties of the fluid. Accurate determination of the overall rate of entropy generation in a duct may take considerable computational time, especially when two- or three-dimensional modeling is required as a result of geometry and complex relationship between the convection heat transfer and fluid flow parameters involved. In this paper, a simple yet accurate method of estimation for the total rate of entropy generation in a duct is presented. Consequently, a representative temperature, the “Log Mean Temperature”, at which the convection heat transfer and fluid flow properties are evaluated for the determination of total rate of entropy generation, is introduced. It is shown that the approximate Log Mean Temperature method provides considerably accurate values of total rate of entropy generation in a duct for both uniform wall heat flux and uniform wall temperature boundary conditions. Water and glycerol (highly viscous fluid at around room temperature) are used to assess the accuracy of the approximate Log Mean Temperature method. The assessment is done within the coverage of laminar flow (Re < 3,000) and single phase fluid (i.e., no phase change). It is shown that the error in using the approximate Log Mean Temperature method in evaluating the total rate of entropy generation in a duct stays within less than 1 % for the entire practical range of Re numbers and temperature changes considered.

Twist parameter Influence on Heat Transfer Coefficient Augmentation for a square Twisted Tube

Heat transfer augmentation due to twisting parameter was investigated in atwisted tube of square cross sectional area. Twisting parameter is defined as the ratio of the length of the tube where it completed twisting of360 degrees to its hydraulic diameter. Four twist parameters were chosen;5, 10, 25 and 50, and a comparison is made with a straight untwisted duct. Two sets of Reynolds numbers were considered for laminar and transient flow. The laminar flow is performed at Re=500,1000,1500 and 2000. While for transient flow the range of Reynolds number are Re=5000,6000,7000,8000 and 9000.Theinfluence of twist parameter on convective heat transfer coefficient in laminar and transient flow was investigated. Numerical simulations were performed for three-dimensional, steady state incompressible flow in body-fitted coordinate using finite volume method and standard k-ε turbulence model. For the heat transfer problem the uniform wall temperature (UWT) boundary condition at tube wall is considered. It was observed that the heat transfer coefficient increases with decreasing twist parameter. This is interpreted to the nature of span wise swirling flow generated. The swirling increases cross flow velocity vectors as it becomes far from tube center towards walls. At tube wall the thickness of boundary layer becomes thinner as near wall velocity become larger which leads to a boundary layer of good thermal characteristics. Also swirling increases internal mixing process which enhances internal thermal equilibrium. The heat transfer coefficient also increases as Reynolds number increased as velocity components are increased