CFD Analysis of Steady Laminar Natural Convection Heat Transfer from a Pin Finned Isothermal Vertical Plate

Heat transfer behavior with both the conductive and nonconductive fins have been analyzed by examining variations of the local and average Nusselt numbers in two‐dimensional flow. The main objective of this study is to quantify and compare the natural convection heat transfer enhancement of fin array with different fin aspect ratio and at different angles of inclination. It is found that significant heat transfer augmentation is obtained for both conductive and nonconductive fins. For conductive fins 20% higher augmentation factor is obtained when the fin aspect ratio is 6, angle of inclination is 60° and the pitch‐to‐length ratio is 0.2. For nonconductive fins, 10% higher augmentation factor is obtained when fin aspect ratio is 8, angle of inclination is 45° and pitch‐to‐length ratio at 0.5. A general correlation has been developed to predict the average Nusselt number and heat transfer augmentation factor for conductive and nonconductive fin arrays as a function of different fin configurations.     

Numerical validation of natural convection heat transfer with horizontal rectangular fin array using straight knurling patterns on fins—correlation for Nusselt number

Natural convection heat transfer from horizontal rectangular fin array with various knurling patterns has been studied experimentally by the present authors to investigate the effect of knurl‐produced surface roughness of fin on the heat transfer rate. The parameters like knurling height from base, knurling depth, fin spacing, and supply wattage were considered for parametric study. In the present paper, numerical method (CFD) is used to simulate natural convection phenomena with knurled fins and results are validated with the experimental data available from literature. The numerical results show similar trends compared with experimental data and one can use this method to study various fin configurations for knurling patterns. The flow patterns from experiments and numerical method are compared for different supply wattages and fin spacing to back up the conclusion. It is also observed that the variation in nondimensional roughness depth and spacing (D _kn/H and S/H) have more effect on Nusselt number than roughness height parameter (H _kn/H). Further, the method is extended to study numerically large number of fin configurations with knurling patterns to gather sufficient data for Nusselt number with respect to fin geometric parameters as above and establish correlation for heat transfer coefficient for such type of fins.     

Thermal performance analysis of a tube finned surface

The present work submits an experimental work on the heat transfer and friction loss characteristic, employing a tube finned heating surface kept at a constant temperature in a rectangular channel. The tube fins attached on the surface (o.d.=29 mm) were arranged as either in‐line or staggered. The parameters for the study were Reynolds number (3700–30 000), depending on hydraulic diameter, the distance between the tube fins in the flow direction (S_y/D=1.72–3.45) and the fin arrangement. The change in the Nusselt number with these parameters was determined. For both tube fin arrangements, it was observed that increasing Reynolds number increased Nusselt number, and maximum heat transfer occurred at S_y/D=2.59. Thermal performances for both arrangements were also determined and compared with respect to heat transfer from the same surface without fins. With staggered array, a heat transfer enhancement up to 25 per cent for S_y/D=3.45 in staggered array was achieved in constant pumping power. Copyright © 2002 John Wiley & Sons, Ltd.     

NATURAL CONVECTION AND ENTROPY GENERATION FROM A CYLINDER WITH HIGH CONDUCTIVITY FINS

The problem of laminar natural convection from a horizontal cylinder with multiple equally spaced high conductivity fins on its outer surface was investigated numerically. The effect of several combinations of number of fins and fin height on the average effective Nusselt number was studied over a wide range of Rayleigh numbers. The results showed that there was an optimal combination of number of fins and fin height for maximum heat transfer from the cylinder for a given value of Rayleigh number. A high number of short fins slightly decreased the heat transfer from the cylinder. The calculated velocity and temperature profiles also were used to study the total entropy generation. The total entropy production was dominated by entropy generation due to thermal effects. The exception was at Ra _D = 10³ and a large cylinder diameter where entropy generation was dominated by entropy generation due to viscous effects. This information can be used to access the changes in the thermodynamic efficiency due to the addition of fins to enhance the natural convection heat transfer from a horizontal cylinder.     

Optimum design parameters of a heat exchanger

In this study, the effects of the longitudinal and lateral seperations of consecutively enlarged-contracted arranged fin pairs, widths of the fins, angle of attack, heights of fins and flow velocity on the heat and pressure drop characteristics were investigated using the Taguchi experimental-design method. Nusselt number and friction factor were considered as performance parameters. An L₁₈(2¹13⁷) orthogonal array was selected as an experimental plan for the eight parameters mentioned above. First of all, each goal was optimized, separately. Then, all the goals were optimized together, considering the priority of the goals, and the optimum results were found to be fin width of 15 mm, angle of attack of 15°, fin height of 100 mm, span-wise distance between fins of 20 mm, stream-wise distance between fins of 10 mm, span-wise distance between slices of 20 mm, stream-wise distances between slices of 20 mm at a flow velocity of 4 m/s.     

Mixed Convection from a Cylinder with Highly Conductive Fins in Cross Flow

The problem of laminar mixed convection from an isothermal cylinder with highly conductive fins in cross flow was solved numerically. The average Nusselt number was calculated at different combinations of number of fins (0–17), fin height (0–2), Reynolds number (10–200), and buoyancy parameter (0–5). The fins were most effective at low Reynolds numbers and low buoyancy. The addition of short fins at high values of the Reynolds number and buoyancy parameter resulted in a slight reduction in the Nusselt number. There was an optimal number of fins beyond which additional fins did not increase or even reduce the average Nusselt number. This number was Reynolds number- and buoyancy parameter-dependent. When using a small number of long fins at low buoyancy, an even number of fins was better than an odd number of fins.     

Development of Colburn j Factor and Fanning Friction Factor Correlations for Compact Surfaces of the Triangular Perforated Fins Using CFD

The necessity of increased heat transfer surface area has resulted in the development of compact heat exchangers, which are widely used in the aerospace and automobile industries. Hence perforations are made on triangular plain fins to study the effects on the heat transfer coefficient. A numerical model has been developed for the perforated fin of a triangular plate fin heat exchanger. Perforated fin performance has been analyzed with the help of computational fluid dynamics (CFD) by changing the various parameters of the fin. The Colburn j factor and the Fanning friction factor are calculated for different Reynolds numbers. The values of the Colburn j factor and the Fanning friction factor are validated for known geometric fins with available data in the literature and extended to triangular perforated fins. The correlations have been developed between Reynolds number, Colburn j factor, and Fanning friction factor by taking into account fin height, fin thickness, and fin spacing. The present numerical analysis is carried out for air media.     

The influence of internal fins on mixed convection inside horizontal tubes

Results of a numerical analysis of fully developed, laminar, mixed convection in horizontal tubes with two vertically oriented fins are presented. Fins are found to suppress the free convective currents and thus the enhancements in Nusselt number and friction factor decrease as the fin height increases. For all values of Grashof number and relative fin height considered, the percentage rise in Nusselt no. due to free convection exceeded the percentage increase in friction factor.     

Experimental investigation for optimization of design parameters in a rectangular duct with plate-fins heat exchanger by Taguchi method

This study presents the determination of optimum values of the design parameters in a heat exchanger with a rectangular duct by using Taguchi method. The heat exchanger has plate-fins containing periodically interrupted diverging and converging channel flow domains. The experimental investigation for the established heat exchanger involves short rectangular fins attached in 8 × 8 arrays to a surface having various inclination angles. The effects of the six design parameters such as the ratio of the duct channel width to height, the ratio of the winglets length to the duct channel length, inclination angles of winglets, Reynolds number, flow velocity and pressure drop are investigated. In the Taguchi experimental design method, Nusselt number and friction factor are considered as performance parameters. An L₂₅ (5⁶) orthogonal array is chosen as an experimental plan for the design parameters. The analysis of Taguchi method conducted with an optimization process to reach minimum pressure drop (friction factor) and maximum heat transfer (Nusselt number) for the designed heat exchanger. Experimental results validated the suitability of the proposed approach.     

Enhancement of natural convection heat transfer from a vertical heated plate using inclined fins

An enhancement technique is developed for natural convection heat transfer from a vertical heated plate with inclined fins, attached on the vertical heated plate to isolate a hot air flow from a cold air flow. Experiments are performed in air for inclination angles of the inclined fins in the range of 30° to 90° as measured from a horizontal plane, with a height of 25 to 50 mm, and a fin pitch of 20 to 60 mm. The convective heat transfer rate for the vertical heated plate with inclined fins at an inclination angle of 60° is found to be 19% higher than that for a vertical heated plate with vertical fins. A dimensionless equation on the natural convection heat transfer of a vertical heated plate with inclined fins is presented. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 334–344, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20168     

Optimum design-parameters of a heat exchanger having hexagonal fins

In the present study, the effects of the heights and widths of the hexagonal fins, streamwise and spanwise distances between fins, and flow velocity on the heat and pressure-drop characteristics were investigated using the Taguchi experimental-design method. Nusselt number and friction factor were considered as performance statistics. An L₁₈(2¹13⁷) orthogonal array was selected as the experimental plan for the five parameters mentioned above. While the optimum parameters were determined, the trade-off among goals was considered. First of all, each goal was optimized, separately. Then, all the goals were optimized together, considering the priority of the goals, and the optimum results were found to be a fin width of 14 mm, a fin height of 150 mm, spanwise distance between fins of 20 mm, and streamwise distance between fins of 20 mm for a flow velocity of 4 m/s.     

Maximization of heat transfer density from radially finned tubes in cross-flow using the constructal design method

The maximization of volumetric heat transfer density from radially finned tubes in cross-flow is investigated in this study based on the constructal design method. A row of radially finned tubes is placed in cross-air flow. The tubes and the radial fins are heated at uniform temperatures and cooled by the air cross-flow. The cross-air flow is generated by a finite pressure difference. Two dimensionless pressure differences (Bejan number) are considered (Be = 10³ and Be = 10⁵). The objective function, the degrees of freedom, and the constraints in the constructal design method should be identified. The objective function is the maximization of the heat transfer density from the finned tubes. The degrees of freedom are; the fin tip-to-fin tip spacing, the number of fins, the tube diameter, the fin thickness, and the angle between the fins. The constraints are the length and height of the space occupied by the finned tubes. The pressure-driven flow and energy equations (steady, two-dimensional, and incompressible) are solved by means of the finite volume method. The ranges of the dimensionless fin tip-to-fin tip spacing are (0.2 ≤ S ≤ 1 for Be = 10³ and 0.05≤ S ≤ 0.3 for Be = 10⁵). The number of fins is changed as (N = 2, 4, 6, 8, 10, and 12). The dimensionless tube diameter is changed as (D = 0.25, 0.5, and 0.75). The dimensionless fin thickness is changed as (T = 0.001, 0.01, and 0.05). The results showed that for both (Be = 10³) and (Be = 10⁵), the highest value of the maximum volumetric heat transfer density is for (N = 2) and decreases as the number of fins increases. In addition, the minimum values of the maximum volumetric heat transfer density occur when the vertical fins exist at (N = 4, 8, and 12).     

Experimental investigation on heat-transfer enhancement due to a gap in an inclined continuous rib arrangement in a rectangular duct of solar air heater

Artificial roughness in the form of repeated ribs has been proposed as a convenient method for enhancement of 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 repeated square cross-section split-rib with a gap, on one broad wall arranged at an inclination with respect to the flow direction. The duct has a width to height ratio (W/H) of 5.84, relative roughness pitch (P/e) of 10, relative roughness height (e/D_h) of 0.0377, and angle of attack (α) of 60°. The gap width (g/e) and gap position (d/W) were varied in the range of 0.5–2 and 0.1667–0.667, respectively. The heat transfer and friction characteristics of this roughened duct have been compared with those of the smooth duct under similar flow condition. The effect of gap position and gap width has been investigated for the range of flow Reynolds numbers from 3000 to 18,000. The maximum enhancement in Nusselt number and friction factor is observed to be 2.59 and 2.87 times of that of the smooth duct, respectively. The thermo-hydraulic performance parameter is found to be the maximum for the relative gap width of 1.0 and the relative gap position of 0.25.     

Characteristics of forced convection heat transfer in vertical internally finned tube

This work presents a numerical investigation of a vertical internally finned tube subjected to forced convection heat transfer. The governing equations were solved numerically using the control volume technique. Nusselt number, Nu, and friction factor multiplied by Reynolds number, fRe, are influenced greatly by the height and number of the radial fins. The velocity and temperature distributions inside the tube depend on the number and height of the radial fins. This paper suggests that for best heat transfer to be achieved there is an optimum combination of fin numbers and height.     

Free Convective Heat Transfer in Tilted Longitudinal Open Cavity

Heat transfer experiments were performed to investigate the effects of inclination and channel height-to-gap ratio on free convection in a simulated fin-passage with a strategic aim of devising a criterion for selecting the optimal fin length that could provide the maximum free convective capability. The ranges of parameters investigated include the Grashof number, up to 500,000; channel height-to-gap ratios of 1, 2, and 3; and tilt angles of 0°, 30°, 60°, 90°, 120°, 150°, and 180°. Selections of local and spatially averaged Nusselt number results demonstrate the manner by which the Grashof number, tilt angle, and channel height-to-gap ratio interactively affect the heat transfer. In conformity with the experimentally revealed heat transfer physics, the correlation of a spatially-averaged Nusselt number over two parallel walls and the bottom surface of an open-ended channel is derived that permits the individual and interactive effects of the Grashof number, tilt angle, and channel height-to-gap ratio on heat transfers to be evaluated. A criterion for selecting the optimal height-to-gap ratio of the fin channel is subsequently formulated as a design tool for maximizing the convective capability of a free convective fin assembly.     

Experimental study of forced convective heat transfer in a different arranged corrugated channel

In this study, heat transfer rate for sinusoidal corrugated channel has been experimentally investigated. Three different type sharp corrugation peak fins and a plain surface were used in the experiment. Results were carried out for constant heat flux of 616 W/m², varied Reynolds number Re 1500 to 8000 for the corrugation angle (27, 50 and 22/60°) and channel height of 5 and 10 mm. Nusselt number (Nu), convection heat transfer coefficient (h), Colburn factor (j) and enhancement ratio (E) against Reynolds number (Re) have been studied. The effects of the wavy geometry and channel height have been discussed. The increase of corrugated angle gave rise to a heat transfer rate.     

Natural-convection characteristics of a horizontally-based vertical rectangular fin-array in the presence of a shroud

The steady-state natural convective cooling of horizontally-based, vertical rectangular fins, when in close proximity to an adiabatic horizontal shroud, situated adjacent to and above the horizontal fin-tips, was investigated experimentally. The resuls are of significance for the designers of electronic arrays, the components of which should be maintained at temperatures less than 65°C in order to ensure operational reliability. The optimal fin separation, which corresponds with the maximum rate of heat loss from the fin-array, has been deduced for various combinations of fin protrusions and distances of the shroud above the vertical fins, when the fins' base was maintained at a uniform temperature of 40 ± 0·5°C above that of the environment (21·0 ± 0·5°C). For a constant temperature-difference between the fin-base and the environment, lower optimal fin separations and higher steady-state heat-dissipation rates ensued when the shroud clearance to the fin height ratio was increased from zero to unity. Increasing the fin protrusion above the horizontal base also resulted in higher heat-dissipation rates from the fin-array. However, the fin-array with maximum shroud clearance is a much more favourable configuration (e.g. with respect to requiring less material) for achieving heat-transfer enhancement, than the fin array which employs large fin protrusions. For an open-ended duct of approximately the dimensions considered in this project (i.e. of maximum rectangular section 240 mm × 180 mm), the fins should protrude to less than half the internal height of the duct in order that a high convective performance of the fins is achieved. There is an optimal value of the shroud clearance to fin height ratio which exceeds unity for each specific operation, i.e. the exact optimal ratio being dependent upon the geometry and temperatures involved.

Average Nusselt numbers, evaluated from the experimental data, are correlated non-dimensionally with respect to the fin-array geometry and the Grashof number. This correlation indicates that variations of the shroud clearance to fin height ratio produce only marginal variations in the average Nusselt number.     

Sensitivity analysis for MHD effects and inclination angles on natural convection heat transfer and entropy generation of Al2O3-water nanofluid in square cavity by Response Surface Methodology

The natural convection heat transfer and entropy generation of Al₂O₃-water nanofluid, in a square cavity with inclination angle θ and the presence of a constant axial magnetic field B₀ are examined in this paper. The governing equations are solved numerically by finite volume method. Also an effective parameters analysis was performed by using of the Response Surface Methodology (RSM). The effects of the Rayleigh number (10³, 10⁴, 10⁵ and 10⁶), Hartmann number (0, 10, 30 and 50) and also inclination angles (0°, 30°, 60° and 90°) are investigated. It is observed that the mean Nusselt number and the total entropy generation increase when the Rayleigh number increases. It is also found that, regardless of the Ha parameter, by increasing of the inclination angles, the mean Nusselt number and entropy generation rate increase until inclination angle 30° and then they decrease. Also, for low Ra numbers, by increasing the Ha parameter, the mean Nusselt number increases until Ha = 10 and then decreases. The analysis showed that the sensitivity of the Nusselt number and the entropy generation to Ha parameter was too small, and as a result it was negligible. Also, the sensitivity of the mean Nusselt number and the entropy generation to inclination angle, θ, increases by increasing of this angle. It is also observed that the mean Nusselt number and the entropy generation were more sensitive to the inclination angle θ than the Ha parameter.     

Optimization of short micro pin fins in minichannels

Finned minichannels are modeled in order to optimize microstructure geometry and maximize heat transfer dissipation through convection from a heated surface. Six pin fin shapes – circle, square, triangle, ellipse, diamond and hexagon – are used in a staggered array and attached to the bottom heated surface of a rectangular minichannel and analyzed. Also, using square pin fins, different channel clearance over fins are investigated to optimize the fin height of the fins with respect to that of the channel. Fin width and spacing are investigated using a ratio of fin width area to the channel width. Fin material is then varied to investigate the heat dissipation effects. Triangular fins with larger fin height, smaller fin width, and spacing double the fin width maximizes the number of fins in each row and yields better performance. Correlations describing the Nusselt number and the Darcy friction factor are obtained and compared to previous ones from recent studies. These correlations only apply to short fins in the laminar regime. Completely understanding the effects of micro pin fins in a minichannel is essential to maximizing the performance in small scale cooling apparatuses to keep up with future electronic advancements.     

Numerical investigation of semiempirical relations representing the local Nusselt number magnitude of a pin fin heat sink

Heat transfer augmentation study using air jet impingement has recently attained great interest toward electronic packaging systems and material processing industries. The present study aims at developing a nondimensional semiempirical relation, which represents the cooling rate (Nu) in terms of different geometric and impinging parameters. The spacing of the fin (S/d_p) and the fin heights (H/d_p) are the geometric parameters, while the impinging Reynolds number (Re) and nozzle‐target spacing (Z/d) are the impinging parameters. During the plot of the Nusselt profile, three vital secondary peaks are observed due to local turbulence of air over the heat sink. To incorporate this nonlinear behavior of the Nusselt profile in developing nondimensional empirical relations, the Nusselt profiles are divided into different regions of secondary rise and fall. Four different sets of the semiempirical relation using regression analysis are proposed for Z/d ≤ 6, H/d_p ≤ 4.8 with S/d_p ≤ 1.58, S/d_p > 1.58 and for Z/d > 6, H/d_p > 4.8 with S/d_p ≤ 1.58, S/d_p > 1.58. These empirical relations benefit the evaluation of the cooling rate (Nu) without any experimentation or simulation.