Colburn Heat Transfer Factor Research Articles

Three-dimensional CFD study on thermo-hydraulic behaviour of finned tubes in a heat exchange system for heat transfer enhancement

Abstract The present study performs a three-dimensional CFD analysis to investigate the hydrodynamic and thermal properties of annular finned tubes in a heat exchange system. All computations are performed in the turbulent flow regime (4330 ≤ Re ≤ 8790), and the Transition SST model is applied for turbulence modelling. The impact of Prandtl number (0.7 ≤ Pr ≤ 50) on the various parameters, such as the heat transfer coefficient, heat transfer rate, and pressure drop, are considered. The results indicate that the thermo-hydraulic behaviour is significantly affected by incrementing both Reynolds and Prandtl numbers. The fin’s surface temperature distribution is examined to get a better insight into its thermal performance, and it is observed that the rear portion of the fin contributes the least to heat transfer. Other important parameters like the fin efficiency and Colburn heat transfer factor are found to significantly impact the performance of the heat exchange system for the above range of settings. The velocity contours show the horseshoe vortex formation near the fin-tube junction, and the channelling effect is observed between consecutive tubes. Different fluids are compared based on the j/f factor for enhanced heat transfer at the minimum possible flow resistance.

Numerical simulation on flow and heat transfer performances of serrated and wavy fins in plate-fin heat exchanger for hydrogen liquefaction

In order to test the applicability of the existing correlations of the flow and heat transfer performances (FHTPs) of the high-efficiency fins to the plate-fin heat exchanger (PFHE) for hydrogen liquefaction, a numerical model is established to investigate the FHTPs of hydrogen in the serrated fin (SF) and wavy fin (WF). The results show that the existing correlations can be applied to the conditions of the low-pressure hydrogen in 30–300 K and the high-pressure hydrogen in 40–300 K. However, the FHTPs of the high-pressure hydrogen in 30–40 K are obviously different from the existing correlations and need the new correlations for calculation. The high-pressure and low-temperature condition leads the low velocity in the fin channel, resulting in that the serrated locations of the SF and the wave crest and wave trough of the WF are the keys to affect the FHTPs. On the basis, a series of data points reflecting the relationships between the FHTPs and the operational and structural parameters are extracted from the response surfaces to establish the new correlations. For the SF, the new correlations of the Colburn heat transfer factor (j) and the Fanning friction factor (f) have a good consistency with the original data, with the fitting goodness of 96.4% and 92.4% and the average relative deviations of 8.3% and 9.7% respectively. And the fitting goodness and average relative deviations of the new correlations of the WF are 96.5% and 99.0%, and 7.9% and 9.3% respectively. The new correlations of the SF and WF can be used to guide the design of the PFHE in 30–40 K for hydrogen liquefaction.

Study on performance comparison of different fin combinations of catalyst filled plate fin heat exchanger for hydrogen liquefaction

A mathematical model of catalyst filled plate fin heat exchanger (CFPFHE) is established to compare different fin models and analyze fin performance of different fin combinations. The results show that the single-layer fin model inadequately reflects the double-layers fin model from flow distribution and fin performance. The indexes of ortho-para hydrogen conversion (YYpH2) of different fin combinations are all about 0.95, meeting the requirement of the CFPFHE. The plain_serrated fin has the best fin performance among four fin combinations. Compared with the plain_plain, the Colburn heat transfer factor (j factor) and thermal enhancement factor (TEF) of cool and hot sides of the plain_serrated fin are increased by 68.0∼51.0% and 28.5∼13.6%, 8.5∼6.1% and 8.4%∼6.1% at Rehot = 500∼1500, respectively. Further, the fin combinations of high-efficiency fin and plain respectively used in cool and hot sides have excellent overall fin performance, which provides a theoretical guidance for fin selection of the CFPFHE.

Study on continuous cooling process coupled with ortho-para hydrogen conversion in plate-fin heat exchanger filled with catalyst

A mathematical model of the plate-fin heat exchanger filled with catalyst (CFPFHX) is established to investigate the continuous cooling process coupled with ortho-para hydrogen conversion at 42–70 K. The flow and heat transfer performance and the efficiency of ortho-para hydrogen conversion in the CFPFHX are quantitatively evaluated, and the effects of the structural parameters on the flow and heat transfer coupled with ortho-para hydrogen conversion are analyzed. The results show that the Elovich model is the best existing kinetic models of ortho-para hydrogen conversion with an average relative deviation of 1.8%. The Colburn heat transfer factor (j factor) of the hot side of the CFPFHX is 4.3 times that of the plate-fin heat exchanger (PFHX), and the thermal enhancement factor (TEF) of the hot side is 37.7% of that of the PFHX. Meanwhile, for the CFPFHX, the j factor and the TEF of the hot side under different structural parameters are always about 8–10 times and 68%–93% of that of the cold side respectively. Therefore, the CFPFHX can ensure the flow and heat transfer performance and realize the ortho-para hydrogen continuous conversion. And a fin with the larger flow area (high fin height, wide fin spacing and small fin thickness) has a better flow and heat transfer performance and ortho-para hydrogen conversion. The outlet para-hydrogen ratio youtp-H2 and the mass space velocity vm in the CFPFHX have an approximate linear trend. When mass space velocity vm ≤ 0.6589 kg/(m3·s), the outlet para-hydrogen ratio youtp-H2 can meet the requirement at 42–70 K. Above all, the mechanism of flow and heat transfer coupled with ortho-para hydrogen conversion is revealed for the first time in this study, which can provide a theoretical guidance for the application of the integrated technology in large scale hydrogen liquefaction process.

Numerical investigation on serrated fin of sub-atmosphere plate-fin heat exchanger used in superfluid helium system

A mathematical model is developed to investigate the effects of working media, operating conditions and fin structural parameters on the flow and heat transfer performance of sub-atmospheric and low-temperature helium in serrated fin. For helium, nitrogen and air, when the Reynolds number (Re) is less than 2500, the Colburn heat transfer factor (j factor) of helium is in the middle, while that is the lowest when Re is higher than 2500. The Fanning friction factor (f factor) of helium under the working condition is much higher than those of air and nitrogen under corresponding working conditions. The results show that short fin height is selected for high Re and high fin height is selected for low Re. The overall performance can be improved by increasing the fin spacing and decreasing the fin thickness. Small fin length can improve the overall performance, but the effect is poor at high Re. The Kriging response surface is used to fit the flow and heat transfer correlations of serrated fin. The fitting degrees of j and f factors are 0.963 and 0.978 respectively, and the average relative errors are 4.31% and 8.79% respectively. The two correlations have good prediction performance, which can provide a theoretical reference for the design of sub-atmospheric and low-temperature plate-fin heat exchanger.

Building a MATLAB applicaton for preliminary design and optimization of shell and tube heat exchangers

Designing shell and tube heat exchangers is a complex and time-consuming procedure. Since they are one of the most common process units in process industry, great effort should be made to improve their design and to facilitate the design procedure. Therefore, in this study, an easy-to-use MATLAB application for shell and tube heat exchanger preliminary design and optimization was developed. The application enables users to select operating parameters manually and test their effect on heat transfer area and pressure drop. Moreover, the application helps users to optimize the preliminary design, in terms of finding the minimal heat transfer area required to meet the process requirements. The validity of the application was tested on the example from the literature, where the heat transfer area was 61.91 m2. During the proposed optimization procedure, different parameter values were tested and an optimal combination of parameters was found within 5 seconds (for all combinations), resulting in the heat transfer area of 53.27 m2. The application has a great feature of displaying the impact of baffle cut value and baffle spacing on most important design parameters: heat transfer area, tube-side pressure drops and shell-side pressure drops. Also, new correlations were developed for the calculation of the Colburn heat transfer factor and friction factor as a function of Reynolds number and baffle cut value. Overall, the application has proven to be useful for the preliminary design of shell and tube heat exchangers, and can represent the foundation for the development of advanced heat exchanger design applications.

Non-Newtonian power-law fluid’s thermal characteristics across periodic array of circular cylinders

The thermal characteristics of incompressible non-Newtonian power-law fluids across periodic array of circular cylinders have been examined using the finite volume-based numerical solver ANSYS-FLUENT for the following ranges of physical parameters: Reynolds number; 1 ≤ Re ≤ 40: Prandtl number; 1 ≤ Pr ≤ 100: power-law index; 0.40 ≤ n ≤ 1.8; and fluid volume fractions ranging from 0.70 to 0.99. The thermal features have been described via isotherm patterns, local and average Nusselt numbers and the Colburn heat transfer factor and found to be strongly dependent over the above physical parameters. It was observed that the dense isotherms with the increasing inertial and viscous diffusion suggest an improvement in the rate of heat transfer across the periodic cylinders. An increase in local Nusselt number was seen with the increasing values of Re and/or Pr across all the fluid volume fractions. Further, the different behavior of the average Nusselt number was noticed because of the shear-thinning and shear-thickening natures. An enhancement of about 97% was noticed in the shear-thinning region between the extreme fluid volume fractions for the highest value of Pr and the lowest values of Re and n. However, in many cases, the enhancement was noticed to be even more than 100%. An empirical correlation for the average Nusselt number and the Colburn heat transfer factor (jH) has been developed to give the additional physical insight of the results. Finally, the comparison was made with the available literature which displayed a good agreement with the present results.

Numerical Investigation of Heat Transfer of Non-Newtonian Power-Law Fluids Around a Triangular Prism in Time-Periodic Regime

Laminar heat transfer characteristics of non-Newtonian power-law fluids from a long (heated) triangular prism in the time-periodic regime have been explored. Momentum and energy equations were solved using finite volume methodology over the range of non-dimensional control parameters: Reynolds number (Re) = 50–150, Prandtl number (Pr) = 1–50 and power-law index (n) = 0.4–1.8. For the fixed Pr, the local and the time-averaged Nusselt numbers increase with rising Re irrespective of n. However, the local and the time-averaged Nusselt numbers decrease as the fluid nature alters from pseudo-plastic (n 1) for the fixed Re and Pr. Maximum enhancements in the values of time-averaged Nusselt numbers for Pr = 10, 20 and 50 with respect to Pr = 1 are observed to be approximately 180, 273 and 438%, respectively. Further, it is observed that for the fixed n and Pr, the Colburn heat transfer factor (or the jh factor) decreases with rising Re. Finally, the various values of the jh factor at different Re, n and Pr have been correlated via a simple expression, thus enabling its estimation in a new application.

Methodology of heat transfer and flow resistance measurement for matrices of rotating regenerative heat exchangers

Abstract The theoretical basis for the indirect measurement approach of mean heat transfer coefficient for the packed bed based on the modified single blow technique was presented and discussed in the paper. The methodology of this measurement approach dedicated to the matrix of the rotating regenerative gas heater was discussed in detail. The testing stand consisted of a dedicated experimental tunnel with auxiliary equipment and a measurement system are presented. Selected experimental results are presented and discussed for selected types of matrices of regenerative air preheaters for the wide range of Reynolds number of gas. The agreement between the theoretically predicted and measured temperature profiles was demonstrated. The exemplary dimensionless relationships between Colburn heat transfer factor, Darcy flow resistance factor and Reynolds number were presented for the investigated matrices of the regenerative gas heater.

Opposing buoyancy characteristics of Newtonian fluid flow around a confined square cylinder at low and moderate Reynolds numbers

ABSTRACTThe influence of opposing-buoyancy mixed convection from a square cylinder in a vertical channel has been studied at Reynolds numbers (Re) = 1–100, Richardson numbers (Ri) = 0 to −1, and blockage ratios (β) = 10–50% for air as a working fluid. The onset of a steady to a time-periodic regime is found for Ri = 0 (at Re = 35, 65, 74, and 62), Ri = −0.5 (at Re = 12, 39, 48, and 54), and Ri = −1 (at Re = 9, 30, 39, and 50) for β = 10%, 25%, 30%, and 50%, respectively. The initiation of flow separation is also determined. Finally, the correlations of Strouhal number, drag coefficient, and the Colburn heat transfer factor were obtained.

Shape optimization of water-to-water plate-fin heat exchanger using computational fluid dynamics and genetic algorithm

In the design calculation of a plate-fin heat exchanger, the convective heat transfer coefficients of the plate and fin are often simplified to the same value. Further, in the calculation of the convective heat transfer coefficient, the Colburn heat transfer factor and Fanning friction factor are generally obtained using empirical equations. In this work, to obtain more precise results, the convective heat transfer coefficients of the plate and fin are defined as independent parameters. The Colburn factor and Fanning factor are obtained according to the results of computational fluid dynamics. The fin height, fin pitch, fin thickness, and fin length are considered as four design parameters. A modified number of entropy production units (Ns) is adopted. Ns due to friction (NsΔP), Ns due to heat transfer (NsΔT), and NsTotal are considered as three objective functions. The optimal structural parameters of a water-to-water plate-fin heat exchanger applied to an air-conditioning system are obtained using genetic algorithm by single objective optimization and multi-objective optimization.

Transition to periodic unsteady and effects of Prandtl and Richardson numbers on the flow across a confined heated trapezoidal prism

The effects of wall confinements (β) and of Prandtl numbers (Pr) on the laminar flow around a heated trapezoidal prism are investigated numerically for Pr = 0.71–100 and β = 12.5–50 % at low Reynolds numbers (Re). The critical value of the Reynolds number (i.e., the transition from a steady to a time-periodic regime) is calculated and it exists between Re = (36 and 37), (60 and 61) and (91 and 92) for the blockage ratios of 12.5, 25 and 50 %, respectively. The average Nusselt number increases with increasing Re and/or Pr and/or blockage ratio. The variation of local Nusselt number on each surface of the obstacle and the representative isotherm contours are presented to elucidate the role of Pr and blockage ratio on the heat transfer from the trapezoidal prism. The maximum heat transfer enhancement with respect to a square prism on the basis of equal projected area is found to be approximately 31 and 45 % for the blockage ratios of 12.5 and 25 %, respectively, for Pr = 0.71 and Re = 1. The Colburn heat transfer factor correlations are also obtained for the preceding range of settings. Finally, the influence of Richardson number (Ri = 0–1) on the flow and heat transfer characteristics has been studied for air as working fluid.

Power-law shear-thinning flow around a heated square bluff body under aiding buoyancy at low Reynolds numbers

Power-law shear-thinning fluid flow over a heated square bluff body is numerically investigated under aiding buoyancy mixed convection at low Reynolds numbers. Semi-explicit finite volume code is developed to solve the governing equations along with the appropriate boundary conditions. Both aiding buoyancy and shear-thinning natures are found to augment the heat transfer rate from the surface of the long square bar. In aiding buoyancy, the total drag coefficient is found to be more for the square cylinder than that of the circular cylinder, whereas the average cylinder Nusselt number for the square cylinder is found to be lower than the circular one on equal side/diameter basis. Maximum augmentation in heat transfer is found to be approximately 20% with respect to forced convection. Finally, a heat transfer correlation is established by using the Colburn heat transfer factor.

Heat transfer in Bingham plastic fluids from a heated elliptical cylinder

The forced convection heat transfer characteristics in Bingham plastic fluids from a heated elliptical cylinder of various aspect ratios E(=a/b) have been investigated numerically. The momentum and energy equations have been solved here by using the finite element method over wide ranges of rheological and kinematic parameters as: 0.01⩽Bn⩽100 (Bingham number), 0.01⩽Re⩽40 (Reynolds number), 1⩽Pr⩽100 (Prandtl number) and 0.1⩽E⩽10 (aspect ratio) thereby approaching the limiting conditions of a plate aligned with and transverse to the direction of mean flow. Furthermore, the influence of the type of thermal boundary condition, i.e., constant wall temperature (CWT) and constant heat flux (CHF) prescribed on the surface of the elliptical cylinder has also been examined. Extensive numerical results are reported herein in terms of the isotherm contours, variation of the Nusselt number on the surface of the cylinder for the two above-noted thermal boundary conditions and finally, the overall results are presented in terms of the surface averaged Nusselt number. Irrespective of the boundary condition prescribed on the surface of the cylinder, the Nusselt number shows a positive dependence on the both Reynolds number and Prandtl number while the effect of Bingham number is somewhat dependent on the Reynolds number range. The average Nusselt number has also been interpreted and correlated in terms of the Colburn heat transfer factor (j). Empirical correlations for the Colburn factor as functions of the Bingham number and aspect ratio have been proposed based on the present numerical results.

Analysis of heat transfer and pressure drop characteristics in an offset strip fin heat exchanger

A steady-state three-dimensional numerical model was used to study the heat transfer and pressure drop characteristics of an offset strip fin heat exchanger. Water was the heat transfer medium, and the Reynolds number Re dh ranged from 10 to 3500. Variations in the Fanning friction factor f and the Colburn heat transfer factor j relative to Re dh were observed. General correlations for the f and j factors were derived, and these could be used to analyze fluid flow and heat transfer characteristics of offset strip fins in the laminar, transition, and turbulent regions. Finally, three performance criteria ( j/ f, j/ f 1/3, and JF) were adopted, and the best performance criteria for the cases Pr = 7 and Pr = 50 were chosen to be JF and j/ f 1/3, respectively.

Forced convection heat transfer from an elliptical cylinder to power-law fluids

Forced convection heat transfer to incompressible power-law fluids from a heated elliptical cylinder in the steady, laminar cross-flow regime has been studied numerically. In particular, the effects of the power-law index (0.2⩽n⩽1.8), Reynolds number (0.01⩽Re⩽40), Prandtl number (1⩽Pr⩽100) and the aspect ratio of the elliptic cylinder (0.2⩽E⩽5) on the average Nusselt number (Nu) have been studied. The average Nusselt number for an elliptic cylinder shows a dependence on the Reynolds and Prandtl numbers and power-law index, which is qualitatively similar to that for a circular cylinder. Thus, heat transfer is facilitated by the shear-thinning tendency of the fluid, while it is generally impeded in shear-thickening fluids. The average Nusselt number values have also been interpreted in terms of the usual Colburn heat transfer factor (j). The functional dependence of the average Nusselt number on the dimensionless parameters (Re,n,Pr,E) has been presented by empirically fitting the numerical results for their easy use in process design calculations.

Heat transfer from immersed surfaces in liquid fluidised beds

Heat transfer data were obtained using a small electrically-heated simulated plate immersed in a liquid—fluidised bed. For steel balls and for spherical and cylindrical particles of glass fluidised by dimethyl phthalate, two correlations valid over the voidage range 0.40–0.85 were obtained; one was based on the Reynolds number ( Re 0), involving the particle diameter and its terminal falling velocity, and the other on a modified Reynolds number ( Re m ) incorporating the interstitial velocity and the volume: surface ratio of the voids. ▪ and ▪ In the above eqns, St is the Stanton number, J h the Colburn heat transfer factor and e the voidage. K is a constant depending on the properties of the solid particles.

Heat and momentum transfer in the flow of gases through packed beds

AbstractHeat and momentum transfer studies have been made for the flow of gases through fixed beds consisting of randomly packed, solid metallic particles. The experimental technique employed in these studies made possible for the first time the procurement of gas‐film heat transfer data under steady state conditions and in the absence of mass transfer effects. Electric current passed through the metallic particles of the bed created within the particles a steady generation of heat, which was continuously removed by gases flowing through the bed. Several direct temperature measurements of both gases and solids within the bed made possible the direct calculation of the heat transfer coefficient for the gas film to produce the Colburn heat transfer factor jh, which has been found to correlate with the modified Reynolds number, Reh = √ ApG/[µ(1 – ∈)φ]. The shape factor φ was established in these studies for cubes and cylinders and was found to be identical to their respective sphericities.Pressure‐drop measurements produced a friction factor fk of the Blake type, which yielded separate curves for each shape when correlated with the modified Reynolds number Rem. No simple relationship was found to exist between the heat transfer and friction factors. A single correlation of the pressure‐drop data was obtained for the modulus fkoφn when correlated with a Reynolds number of the type Rem = √ ApG/[µ(1 – ∈)]. The exponent n varies with the particle shape.Experimental runs have been carried out for 3/16, 1/4, 5/16‐in. spheres, 1/4 and 3/8‐in. cubes, and regular cylinders using hydrogen and carbon dioxide to extend the range of molecular weights beyond that of air, used for the majority of these runs. A particle‐size, column‐diameter effect was found to exist for both heat and momentum transfer. This effect becomes significant in the low Reynolds region.