Development of colburn ‘j’ factor and fanning friction factor ‘f’ correlations for compact heat exchanger plain fins by using CFD

A numerical model has been developed for plain fin of plate fin heat exchanger. Plain fin performance has been analyzed with the help of CFD by changing the various parameters of the fin, Colburn ‘j’ and fanning friction ‘f’ factors are calculated. These values compared with the standard values. The correlations have been developed between Reynolds number Re, fin height h, fin thickness t, fin spacing s, Colburn factor ‘j’ and friction factor ‘f’.     

Effect of fin thickness on air-side performance of herringbone wavy fin-and-tube heat exchangers

In the present study, the effects of fin thickness on the heat transfer and friction characteristics of fin-and-tube heat exchangers having herringbone wavy fin configuration are experimentally investigated. The experimental apparatus consists essentially of a well insulated open wind tunnel and herringbone wavy fin-and-tube heat exchangers made from aluminium plate finned, copper tube. Air and water are used to be working fluids in air-side and tube-side, respectively. A total of 10 samples of the fin-and-tube heat exchangers are tested. The experimental procedures are conducted by keeping the inlet water temperature at a pre-selected value, adjusting the water volumetric flow rate at a specific value and varying the air velocity. The results are presented as plots of the Colburn factor and friction factor against the Reynolds number based on the fin collar outside diameter (Re_Dc). From the results, it is found that for number of tube rows (N) = 2, the Colburn factor increases with increasing fin thickness. For N 4, the Colburn factor decreases with increasing fin thickness when Re_Dc < 1800, and increases with increasing fin thickness when Re_Dc > 2500. The friction factor increases with increasing fin thickness when fin pitch (F_p) 1.81 mm.     

Intensity of convective mass/heat transfer in a rotary regenerator rotor with the transverse needle-fins

A forced convective mass transfer coefficient was electrochemically measured for a cylindrical bundle of transverse needle-fins ?1 × 10.9, applied as the rotor porous matrix of a rotary heat regenerator. The baffle inside the rotor was present. The technique based on the ferricyanide–ferrocyanide redox reaction controlled at the cathode, in the presence of a sodium hydroxide based electrolyte, was used in this experiment. A set of the six neighbouring fins, connected in parallel, was the cathode. The distribution of the mass transfer coefficient according to different static rotor angle position and the mean mass transfer Chilton–Colburn coefficient correlation j _M  = j _M (Re) for rotation numbers, Ro: 0, 0.8, 1.6 and 2.0 were stated in the mean Reynolds number, Re, range 180–985. The comparison was made between the convective heat fluxes of the pin-fins and the sheet rotor, for Ro = 0.     

3D Numerical heat transfer and fluid flow analysis in plate-fin and tube heat exchangers with electrohydrodynamic enhancement

Three-dimensional laminar fluid flow and heat transfer over a four-row plate-fin and tube heat exchanger with electrohydrodynamic (EHD) wire electrodes are studied numerically. The effects of different electrode arrangements (square and diagonal), tube pitch arrangements (in-line and staggered) and applied voltage (V_E=0–16 kV) are investigated in detail for the Reynolds number range (based on the fin spacing and frontal velocity) ranging from 100 to 1,000. It is found that the EHD enhancement is more effective for lower Re and higher applied voltage. The case of staggered tube pitch with square wire electrode arrangement gives the best heat transfer augmentation. For V_E=16 kV and Re = 100, this study identifies a maximum improvement of 218% in the average Nusselt number and a reduction in fin area of 56% as compared that without EHD enhancement.     

Air-side performance of louver-finned flat aluminum heat exchangers at a low velocity region

The heat transfer and pressure drop characteristics of heat exchangers having louver fins were experimentally investigated. The samples had small fin pitches (1.0–1.4 mm), and experiments were conducted up to a very low frontal air velocity (as low as 0.3 m/s). Below a certain Reynolds number (critical Reynolds number), the fall-off of the heat transfer coefficient curve was observed. The critical Reynolds number was insensitive to the louver angle, and decreased as the louver pitch to fin pitch ratio (L _p /F _p ) decreased. Existing correlations on the critical Reynolds number did not adequately predict the data. The heat transfer coefficient curves crossed over as the Reynolds number decreased. Possible explanation is provided considering the louver pattern between neighboring rows. Different from the heat transfer coefficient, the friction factor did not show the fall-off characteristic. The reason was attributed to the form drag by louvers, which offsets the decreased skin friction at low Reynolds numbers. The friction factor increased as the fin pitch decreased and the louver angle increased. A new correlation predicted 92% of the heat transfer coefficient and 94% of the friction factor within ±10%.     

Experimental and numerical investigation on air-side performance of fin-and-tube heat exchangers with various fin patterns

Air-side heat transfer and friction characteristics of five kinds of fin-and-tube heat exchangers, with the number of tube rows (N = 12) and the diameter of tubes (D_o = 18 mm), have been experimentally investigated. The test samples consist of five types of fin configurations: crimped spiral fin, plain fin, slit fin, fin with delta-wing longitudinal vortex generators (VGs) and mixed fin with front 6-row vortex-generator fin and rear 6-row slit fin. The heat transfer and friction factor correlations for different types of heat exchangers were obtained with the Reynolds numbers ranging from 4000 to 10000. It was found that crimped spiral fin provides higher heat transfer and pressure drop than the other four fins. The air-side performance of heat exchangers with the above five fins has been evaluated under three sets of criteria and it was shown that the heat exchanger with mixed fin (front vortex-generator fin and rear slit fin) has better performance than that with fin with delta-wing vortex generators, and the slit fin offers best heat transfer performance at high Reynolds numbers. Based on the correlations of numerical data, Genetic Algorithm optimization was carried out, and the optimization results indicated that the increase of VG attack angle or length, or decrease of VG height may enhance the performance of vortex-generator fin. The heat transfer performances for optimized vortex-generator fin and slit fin at hand have been compared with numerical method.     

Estimating heat transfer rates from mass transfer studies on plate heat exchanger surfaces

Tests were conducted on surfaces for plate heat exchangers, of the cross-corrugated type, to determine local and overall mass transfer rates. Analogous heat transfer data was obtained by the method described by Chilton and Colburn using the j-factor method.     

Experimental investigation of heat transfer and flow pattern from heated horizontal rectangular fin array under natural convection

This paper presents results of the experimental study conducted on heated horizontal rectangular fin array under natural convection. The temperature mapping and the prediction of the flow patterns over the fin array with variable fin spacing is carried out. Dimensionless fin spacing to height (S/H) ratio is varied from 0.05 to 0.3 and length to height ratio (L/H) = 5 is kept constant. The heater input to the fin array assembly is varied from 25 to 100 W. The single chimney flow pattern is observed from 8 to 12 mm fin spacing. The end flow is choked below 6 mm fin spacing. The single chimney flow pattern changes to sliding or end flow choking at 6 mm fin spacing. The average heat transfer coefficient (h_a) is very small (2.52–5.78 W/m² K) at 100 W for S = 5–12 mm. The h_a is very small (1.12–1.8 W/m² K) at 100 W for 2–4 mm fin spacing due to choked fin array end condition. The end flow is not sufficient to reach up to central portion of fin array and in the middle portion there is an unsteady down and up flow pattern resulting in sliding chimney. The central bottom portion of fin array channel does not contribute much in heat dissipation for S = 2–4 mm. The h_a has significantly improved at higher spacing as compared to lower spacing region. The single chimney flow pattern is preferred from heat transfer point of view. The optimum spacing is confirmed in the range of 8–10 mm. The average heat transfer results are compared with previous literature and showed similar trend and satisfactory agreement. An empirical equation has been proposed to correlate the average Nusselt number as a function of Grashof number and fin spacing to height ratio. The average error for this equation is ?0.32 %.     

The effects of span position of winglet vortex generator on local heat/mass transfer over a three-row flat tube bank fin

The naphthalene sublimation method was used to study the effects of span position of vortex generators (VGs) on local heat transfer on three-row flat tube bank fin. A dimensionless factor of the larger the better characteristics, JF, is used to screen the optimum span position of VGs. In order to get JF, the local heat transfer coefficient obtained in experiments and numerical method are used to obtain the heat transferred from the fin. A new parameter, named as staggered ratio, is introduced to consider the interactions of vortices generated by partial or full periodically staggered arrangement of VGs. The present results reveal that: VGs should be mounted as near as possible to the tube wall; the vortices generated by the upstream VGs converge at wake region of flat tube; the interactions of vortices with counter rotating direction do not effect Nusselt number (Nu) greatly on fin surface mounted with VGs, but reduce Nu greatly on the other fin surface; the real staggered ratio should include the effect of flow convergence; with increasing real staggered ratio, these interactions are intensified, and heat transfer performance decreases; for average Nu and friction factor (f), the effects of interactions of vortices are not significant, f has slightly smaller value when real staggered ratio is about 0.6 than that when VGs are in no staggered arrangement. A cross section area of flow passage [m²] - A _mim minimum cross section area of flow passage [m²] - a width of flat tube [m] - b length of flat tube [m] - B _pT lateral pitch of flat tube: B _pT = S ₁/T _p - d _h hydraulic diameter of flow channel [m] - D _naph diffusion of naphthalene [m²/s] - f friction factor: f = pd _h/(Lu ² _max/2) - h mass transfer coefficient [m/s] - H height of winglet type vortex generators [m] - j Colburn factor [–] - JF a dimensionless ratio, defined in Eq. (23) [–] - L streamwise length of fin [m] - L _PVG longitudinal pitch of vortex generators divided by fin spacing: L _pVG = l _VG/T _p - l _VG pitch of in-line vortex generators [m] - m mass [kg] - m mass sublimation rate of naphthalene [kg/m²·s] - Nu Nusselt number: Nu = d _h/ - P pressure of naphthalene vapor [Pa] - p non-dimensional pitch of in-line vortex generators: p = l _VG/S ₂ - Pr Prandtl number [–] - Q heat transfer rate [W] - R universal gas constant [m²/s²·K] - Re Reynolds number: Re = ·u _max·d _h/ - S ₁ transversal pitch between flat tubes [m] - S ₂ longitudinal pitch between flat tubes [m] - Sc Schmidt number [–] - Sh Sherwood number [–]: Sh = hd _h/D _naph - Sr staggered ratio [–]: Sr = (2Hsin – C)/(2Hsin) - T _p fin spacing [m] - T temperature [K] - u _max maximum velocity [m/s] - u average velocity of air [m/s] - V volume flow rate of air [m³/s] - x,y,z coordinates [m] - z sublimation depth[m] - heat transfer coefficient [W/m²·K] - heat conductivity [W/m·K] - viscosity [kg/m²·s] - density [kg/m³] - attack angle of vortex generator [°] - time interval for naphthalene sublimation [s] - fin thickness, distance between two VGs around the tube [m] - small interval - C distance between the stream direction centerlines of VGs - p pressure drop [Pa] - 0 without VG enhancement - 1, 2, I, II fin surface I, fin surface II, respectively - atm atmosphere - f fluid - fin fin - local local value - m average - naph naphthalene - n,b naphthalene at bulk flow - n,w naphthalene at wall - VG with VG enhancement - w wall or fin surface     

A Taguchi approach for determination of optimum design parameters for a heat exchanger having circular-cross sectional pin fins

The present work submits an investigation about the optimal values of design parameters and performance analysis for a heat exchanger having cylindrical pin fins positioned in a rectangular channel. The experiments covered the following range: Reynolds number 13,500–42,000, the clearance ratio (C/H) 0, 0.33 and 1, the interfin spacing ratio (S _y /D) 1.208, 1.944 and 3.417. In the experimentation, Taguchi method was employed, and Nusselt number and friction factor were considered as performance parameters. While the optimum parameters were determined, due to the goals (above aims) more than one being, the trade-off among goals was considered. First of all, each goal was optimized, separately. Then, all goals were optimized together, considering the priority of goals, and the optimum results were found to be Reynolds number of 42,000, fin height of 50 mm and pitch of 3.417. The performance analysis also was made under a constant pumping power constraint, and the results showed that the use of cylindrical pin fins may lead to an advantage on the basis of heat transfer enhancement.     

Wing-type vortex generators for fin-and-tube heat exchangers

The effect of wing-type vortex generators on heat transfer and pressure drop of a fin-and-tube heat exchanger element was investigated. Local heat transfer was measured by liquid crystal thermography on the fin in the Reynolds number range of 600–2700. Flow losses were estimated from the measured pressure drop of an element. Delta winglets were used as vortex generators. Four fin-and-tube configurations were tested, an inline and a staggered arrangement, each with plain fins and with fins with a pair of vortex generators behind each tube. For the inline tube arrangement the vortex generators increase the heat transfer by 55–65% with a corresponding increase of 20–45% in the apparent friction factor. Results indicate that the vortex generators have the potential to reduce considerably the size and mass of heat exchangers for a given heat load.     

Heat transfer for laminar flow in internally finned pipes with different fin heights and uniform wall temperature

An analysis is presented for fully developed laminar convective heat transfer in a pipe provided with internal longitudinal fins, and with uniform outside wall temperature. The fins are arranged in two groups of different heights. The governing equations have been solved numerically to obtain the velocity and temperature distributions. The results obtained for different pipe-fins geometries show that the fin heights affect greatly flow and heat transfer characteristics. Reducing the height of one fin group decreases the friction coefficient significantly. At the same time Nusselt number decreases inappreciably so that such reduction is justified. Thus, the use of different fin heights in internally finned pipes enables the enhancement of heat transfer at reasonably low friction coefficient.Nomenclature A_f dimensionless flow area of the finned pipe, Eq. (8) - a_f flow area of the finned pipe - C_p specific heat at constant pressure - f coefficient of friction, Eq. (12) - H₁, H₂ dimensionless fin height h₁/r_o h₂/r_o - h₁, h₂ fin heights - average heat transfer coefficient at solid-fluid interface - KR fin conductance parameter, k_s/k_f - k_f thermal conductivity of fluid - k_s thermal conductivity of fin - l pipe length - mass flow rate - N number of fins - Nu Nusselt number, Eqs. (15) and (16) - P pressure - Q total heat transfer rate at solid fluid interface - Q_f1, Q_f2 heat transfer rate at fin surface - q_w average heat flux at pipe-wall, Q/(2 r_ol) - R dimensionless radial coordinate r/r_o - Re Reynolds Number, Eq. (13) - r radial coordinate - r_o radius of pipe - r₁, r₂ radii of fin tips - T temperature - T_b bulk temperature - U dimensionless velocity, Eq. (2) - U_b dimensionless bulk velocity - u_z axial velocity - z axial coordinate - angle between the flanks of two adjacent fins - half the angle subtended by a fin - angle between the center-lines of two adjacent fins - angular coordinate - dynamic viscosity - density - dimensionless temperature, Eq. (6) - _b dimensionless bulk temperature     

Mixed convection heat transfer from a horizontal channel with protruding heat sources

A numerical investigation is carried out to study fluid flow and heat transfer characteristics of conjugate mixed convection from a two dimensional horizontal channel with four protruding heat sources mounted on one of the finite thick channel walls. The flow is assumed as laminar, hydrodynamically and thermally developing. Water and FC70 are the fluids under consideration. The geometric parameters such as spacing between the channel walls (S), size of protruding heat sources (L_h×t_h), thickness of substrate (t) and spacing between heat sources (b) are fixed. Results are presented to show the effect of parameters such as Re_S, Gr_S^*, Pr, k_p/k_f and k_s/k_f on fluid flow and heat transfer characteristics. Using the method of asymptotic expansions, correlations are also presented for the maximum temperature of heat source.     

Three-dimensional numerical investigation of heat transfer for plate fin heat exchangers

In the present study, the potential of rectangular fins with 30° and 90° angle and 10 mm offset from the horizontal direction for heat transfer enhancement in a plate fin heat exchanger is numerically evaluated with conjugated heat transfer approach. The rectangular fins are mounted on the flat plate channel. The numerical computations are performed by solving a steady, three-dimensional Navier–Stokes equation and an energy equation by using Fluent software program. Air is taken as working fluid. The study is carried out at Re = 400 and inlet temperatures, velocities of cold and hot air are fixed as 300, 600 K and 1.338, 0.69 m/s, respectively. Colburn factor j versus Re design data is presented by using Fluent. The results show that the heat transfer is increased by 10 % at the exit of channel with fin angle of 30° when compared to channel without fin for counter flow. The heat transfer enhancement with fins of 30° and 90° for different values of Reynolds number with 300, 500 and 800 and for varying fin heights, fin intervals and also temperature distributions of fluids on the top and bottom surface of the channel are investigated for parallel and counter flow.     

Experimental study of augmented heat transfer and friction in solar air heater with different orientations of W-Rib roughness

Artificial roughness in the form of ribs is a convenient method for enhancing thermal performance of solar air heaters. This paper presents the experimental investigation of heat transfer and friction factor characteristics of a rectangular duct roughened with W-shaped ribs arranged at an inclination with respect to the flow direction on its underside on one broad wall. W ribs have been tested both pointing in downstream W-down and upstream W-up to the flow. The range of parameters for this study has been decided on the basis of practical considerations of the system and operating conditions. The duct has a width to height ratio (W/H) of 8.0, relative roughness pitch (p/e) of 10, relative roughness height (e/D_h) of 0.03375 and angle of attack of flow (α) of 30-75°. The air flow rate corresponds to Reynolds number between 2300-14,000. The heat transfer and friction factor results have been compared with those for smooth duct under similar flow and thermal boundary condition and thermo-hydraulic performance has been investigated. Thermo-hydraulic performance comparison for different angle of attack of flow shows that W-down arrangement with angle of attack of flow as 60° gives best thermo-hydraulic performance. In addition heat transfer and friction factor correlations have been developed.     

Experimental study of convective heat transfer from a rotating finned tube in transverse air flow

 The convective heat transfer from fins to air has been evaluated using rotating annular fins subjected to an air flow parallel to the fins. The fin cooling is studied using infrared thermography. The thermal balance in a fin during its cooling process allows us to obtain the heat transfer coefficient from the temperature time evolution of the fin. Moreover, Particle Image Velocimetry allows us to obtain the flow field in the mid-plane between two fins. The influence of the fin spacing on the convective heat transfer is studied for various velocities of the superposed air flow and various fin rotational speeds. These tests were carried out for air flow Reynolds numbers (based on the shaft diameter and the velocity of the superposed air flow) between 2550 and 18200 and rotational Reynolds numbers (based on the shaft diameter and the peripheral speed) between 800 and 2.9 × 10⁴, for different fin spacings. Received: 14 May 1999/Accepted: 8 October 1999     

A review on transient test techniques for obtaining heat transfer design data of compact heat exchanger surfaces

Accurate and reliable dimensionless heat transfer characteristic is very essential for the analysis of heat exchangers. It is also required for the rating and sizing problems of heat exchangers. One of the important experimental methods used to determine the heat transfer coefficient between the heat transfer surface of the heat exchanger and the flowing fluid is transient test techniques. The transient test techniques are usually employed to establish Colburn factor versus Reynolds number characteristics of a high NTU heat exchanger surfaces like compact or matrix heat exchangers. In those situations, a single-blow test, where only one fluid is used, is employed to conduct the transient test. The transient technique may have the fluid inlet temperature having a step change, periodic or an arbitrary rise/drop. In this paper, various transient test techniques that are used for the determination of heat transfer characteristics of high NTU heat exchanger surfaces are discussed.     

The optimum fin spacing of circular tube bank fin heat exchanger with vortex generators

In real application, once the pattern of fin is determined, fin spacing of tube bank fin heat exchanger can be adjusted in a small region, and air flow velocity in the front of the heat exchanger is not all the same. Therefore, the effects of fin spacing on heat transfer performance of such heat exchanger are needed. This paper numerically studied the optimal fin spacing regarding the different front flow velocities of a circular tube bank fin heat exchanger with vortex generators. To screen the optimal fin spacing, an appropriate evaluation criterion JF was used. The results show that when front velocity is 1.75 m/s, the optimal fin spacing is 2.25 mm, when front velocity is 2.5 m/s, the optimal fin spacing is 2 mm, and when front velocity is higher than 2.5 m/s, the optimal fin spacing is 1.75 mm.     

Heat and mass transfer characteristics of simulated high moisture flue gases

The heat transfer process occurring in a condensing heat exchanger where noncondensible gases are dominant in volume is different from the condensation heat transfer of the water vapor containing small amount of noncondensible gases. In the process the mass transfer due to the vapor condensation contributes an important part to the total heat transfer. In this paper, the Colburn-Hougen method is introduced to analyze the heat and mass transfer process when the water vapor entrained in a gas stream condenses into water on the tube wall. The major influential factors of the convective-condensation heat transfer coefficient are found as follows: the partial pressure of the vapor p _v , the temperature of the outer tube wall T _w , the mixture temperature T _g , Re and Pr. A new dimensionless number Ch, which is defined as condensation factor, has been proposed by dimensional analysis. In order to determine the relevant constants and investigate the convection-condensation heat and mass transfer characteristics of the condensing heat exchanger of a gas fired condensing boiler, a single row plain tube heat exchanger is designed, and experiments have been conducted with vapor-air mixture used to simulate flue gases. The experimental results show that the convection-condensation heat transfer coefficient is 1.52 times higher than that of the forced convection without condensation. Based on the experimental data, the normalized formula for convention-condensation heat transfer coefficient is obtained. A heat transfer area m² - Ch condensation factor - c _p specific heat at constant pressure, J/(kg·K) - G mass flux Kg/(m²·s) - h heat transfer coefficient W/(m²·K) - J J-factor - Nu Nusselt number - pa pressure - Pr Prandtl number - Q heat transfer rate - q heat flux W/m² - r latent heat, kJ/kg - Re Reynolds number - Sc Schmidt number - T temperature, C or K - heat conductivity m W/(m·K) - density, kg·m³ - g gas - h moistened hot air - i interface - v vapor - w water     

Numerical simulation and experimental validation of heat transfer within rotating flows for three‐dimensional non‐axisymmetric,turbulent conditions

A control volume type numerical methodology for the analysis of steady three‐dimensional rotating flows with heat transfer, in both laminar and turbulent conditions, is implemented and experimentally tested. Non‐axisymmetric momentum and heat transfer phenomena are allowed for. Turbulent transport is alternatively represented through three existing versions of the k–ε model that were adjusted to take into account the turbulence anisotropy promoted by rotation, streamline curvature and thermal buoyancy. Their relative performance is evaluated by comparison of calculated local and global heat balances with those obtained through measurements in a laboratory device. A modified version of the Lam and Bremhorst, low Reynolds number model is seen to give the best results. A preliminary analysis focused on the flow structure and the transfer of heat is reported. Copyright © 2002 John Wiley & Sons, Ltd.