Parametric study of natural convection heat transfer from horizontal rectangular fin arrays

A systematic theoretical investigation of the effects of fin spacing, fin height, fin length and temperature difference between fin and surroundings on the free convection heat transfer from horizontal fin arrays was carried out. The three-dimensional elliptic governing equations were solved using a finite volume based computational fluid dynamics (CFD) code. Preliminary simulations were made for cases reported in the literature. After obtaining a good agreement with results from the literature a large number of runs were performed for a detailed parametric study. It has been shown that it is not possible to obtain optimum performance in terms of overall heat transfer by only concentrating on one or two parameters. The interactions among all the design parameters must be considered. Results are presented in graphical form together with optimum values and correlations, and compared with available experimental data from the literature.     

Numerical analysis of natural convection heat transfer from rectangular shrouded fin arrays on a horizontal surface

The main aim of this investigation is to discover the effects of clearance parameters on the steady-state heat transfer. In order to solve the three-dimensional elliptic governing equations, a finite volume based CFD code was used. The clearance gap between fin tips and shroud, the base and fin temperatures and the size and configuration of the finned surfaces were varied during the parametric study. The numerical results have been compared to existing experimental values from the literature and the comparison shows a good agreement. It is found that the heat transfer coefficient increases with the increase in the clearance parameter and it approaches to the value of heat transfer coefficient obtained for unshrouded fin arrays.     

Forced convection and flow friction characteristics of air-cooled horizontal equilateral triangular ducts with ribbed internal surfaces

Experimental studies have been conducted to examine the forced convection and flow friction characteristics of air-cooled horizontal equilateral triangular ducts whose internal surfaces have been fabricated with uniformly spaced square ribs. Effects of duct geometry (i.e. relative rib height (H/D) and relative rib-to-rib spacing (S/W)) as well as the hydraulic-diameter based Reynolds number (Re_D) on heat transfer coefficient and friction factor of a fully developed turbulent air flow in a horizontal triangular duct with ribbed internal surfaces have been fully investigated. The ranges of experimental parameters under consideration are: H/D from 0.11 to 0.21, S/W from 3.41 to 13.93, and Re_D from 4000 to 23,000. Optimum relative rib height and relative rib-to-rib spacing corresponding to maximum thermal performance of this system have been determined, which are equal to 0.18 and 7.22, respectively. Flow friction in the triangular duct increases rather linearly with the relative rib height, but a maximum flow friction factor is obtained at the relative rib-to-rib spacing of 7.22. Non-dimensional expressions for prediction of average Nusselt number and friction factor in terms of Re_D, H/D and S/W have been developed correspondingly, which correlate well with the experimental data with maximum deviations of ±3.5% and ±8.7%, respectively.     

Forced heat convection heat transfer from shrouded staggered fin arrays

The heat transfer characteristics of staggered, frontally shrouded fin arrays have been studied experimentally, in the case of forced convection of air. Nusselt number and Colburn number are given, for the range of Reynolds numbers from 2000 to 12000. The local Nusselt number distributions signal the existence of the periodically developed temperature field. Average Colburn number values are found to be in agreement, from an engineering standpoint, with correlations predicted for offset strip-fin heat exchangers.     

Forced convection of flow past two tandem rectangular cylinders in a channel

This work performed the first numerical investigation on the forced convection of flow past two tandem rectangular cylinders in a channel at Re?=?100. The aspect ratio (AR) and gap ratio (GR) of the two cylinders are chosen at AR?=?1(1)4 and GR?=?1(1)8, respectively. The objective of the present work is to explore the effects of AR and GR on the characteristic flow and heat transfer quantities for the rectangular geometry that has not been studied before. The effects of the two parameters are presented by the instantaneous flow pattern, characteristic aerodynamic and heat transfer quantities, local heat transfer rate, flow patterns in the gap and near wake, and temperature distribution on the channel walls. Both time-averaged and fluctuating quantities are analyzed and presented. Numerical results reveal that for cylinders of all ARs, there are two flow regimes categorized based on the GR: the steady flow regime at GR?≤?3, where the gap flow is steady, and the unsteady flow regime at GR?≥?4. The characteristic aerodynamic and heat transfer quantities abruptly change as the flow transits from steady to unsteady regime especially for the downstream cylinder. The time-averaged and maximum fluctuating local heat transfer rate for the upstream cylinder almost does not vary with the GR, whereas they substantially vary for the downstream cylinder. The AR affects the magnitude of the quantities but not their variation trends. For flows in the unsteady regime, the recovery of the wake flow after the downstream cylinder is much more rapidly than those of steady flows due to the acceleration arising from the instability brought by the incoming shedding vortices. The violent shedding also effectively enhances heat transfer and increases the temperature of the channel walls.     

Forced convection in horizontal porous channels with hydrodynamic anisotropy

This paper presents an exact solution for fully developing forced convective flow in parallel-plate horizontal porous channels with an anisotropic permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. A constant heat flux is applied on the channel side walls. Basing this analysis on the generalized Brinkman-extended Darcy model which allows the satisfaction of the no-slip boundary condition on solid wall, it is found that anisotropic parameters K^* and ? have a strong influence on the flow fields and heat transfer rate, in the limiting case of low porosity media (Da→0). The results indicate that a maximum (minimum) heat transfer rate is reached when the orientation of the principal axis with higher permeability of the anisotropic porous matrix is parallel (perpendicular) to the vertical direction.     

Experimental investigation of mixed convection heat transfer from longitudinal fins in a horizontal rectangular channel

Mixed convection heat transfer from longitudinal fins inside a horizontal channel has been investigated for a wide range of modified Rayleigh numbers and different fin heights and spacings. An experimental parametric study was made to investigate effects of fin spacing, fin height and magnitude of heat flux on mixed convection heat transfer from rectangular fin arrays heated from below in a horizontal channel. The optimum fin spacing to obtain maximum heat transfer has also been investigated. During the experiments constant heat flux boundary condition was realized and air was used as the working fluid. The velocity of fluid entering channel was kept nearly constant (0.15 ? w_in ? 0.16 m/s) using a flow rate control valve so that Reynolds number was always about Re = 1500. Experiments were conducted for modified Rayleigh numbers 3 × 10⁷ < Ra¹ < 8 × 10⁸ and Richardson number 0.4 < Ri < 5. Dimensionless fin spacing was varied from S/H = 0.04 to S/H = 0.018 and fin height was varied from H_f/H = 0.25 to H_f/H = 0.80. For mixed convection heat transfer, the results obtained from experimental study show that the optimum fin spacing which yields the maximum heat transfer is S = 8–9 mm and optimum fin spacing depends on the value of Ra¹.     

Forced convection heat transfer to water with air injection in a rectangular duct

A study was made of forced convection heat-transfer to water and air-water mixtures in a horizontal rectangular duct with air injection through one porous heated wall. The main independent variables are the rate of air injection through the porous wall, the superficial liquid velocity in the duct, and the amount of air mixed with the water upstream of the heated test section; the method of mixing the upstream air and water is also varied. The dependent variables reported are the heat-transfer coefficient, over a range of approximately 60:1, and the flow pattern, extending from bubble flow through to annular flow.     

Natural convection heat transfer between horizontal concentric rectangular pipes

Natural convection heat transfer between concentric rectangular pipes was studied numerically. It has been found that rolls of even numbers form in the region on the top surface of the inner pipe. The number of rolls depends on both the Rayleigh number and the aspect ratio. An oblong circulation of flow forms in the region between the side surface of the inner pipe and the surface of the outer pipe. The aspect ratio does not have much effect on the average Nusselt number at the side surface of the inner pipe. The relation between the Nusselt and Rayleigh numbers at the top surface resembles that of the Rayleigh-Bénard convection obtained by Silveston (Chandrasekhar, S. 1961. Hydrodynamic and Hydromagnetic Stability, Oxford University Press, 68). The average Nusselt number at the bottom surface of the inner pipe decreases with increasing aspect ratio because the region where heat transfer is affected significantly by convection is limited. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(4): 271–283, 1998     

Natural convection and radiation from vertically-based arrays of vertical, rectangular fins: a numerical model

A two-dimensional numerical model has been developed for the prediction of natural convection and radiation losses from the surfaces of a vertical rectangular fin array protruding perpendicularly outwards from a vertical rectangular base. The individual contributions of the natural convection and radiation were first estimated separately and then summed to give the overall steady-state rate of heat dissipation through the heat exchanger to the ambient air. The theoretical predictions obtained using this model have been compared with experimental observations from previous investigations.     

Forced steady-state convections from pin-fin arrays

The steady-state thermal and air-flow resistance performances of horizontally-based pin-fin assemblies have been investigated experimentally. The effects of varying the geometrical configurations of the pin-fins and the air-flow rates have been studied. The optimal pin-fin separation S_xopt in the span-wise direction, to achieve a maximum rate of heat transfer from the assembly, is 1·0 ± 0·2 mm ≤ S_x ≤ 3·0 ± 0·2 mm for the pin-fins arranged either in the in-line or the staggered array. The optimal pin-fin separations in the stream-wise direction for these two arrays are 7·6 ± 0·2 mm and 7·8 ± 0·2 mm respectively. The general correlation of the data is:

     

Mixed convection heat transfer in horizontal rectangular ducts with radiation effects

The study of mixed convection heat transfer in horizontal ducts with radiation effects has been numerically examined in detail. This work is primarily focused on the interaction of the thermal radiation with mixed convection for a gray fluid in rectangular horizontal ducts. The vorticity–velocity method is employed to solve the three-dimensional Navier–Stokes equations and energy equation simultaneously. The integro-differential radiative transfer equation was solved by the discrete ordinates method. The attention of the results is focused on the effects of thermal buoyancy and radiative transfer on the development of temperature, the friction factor and the Nusselt number. Results reveal that radiation effects have a considerable impact on the heat transfer and would reduce the thermal buoyancy effects. Besides, the development of temperature is accelerated by the radiation effects.     

Experimental investigation of forced and mixed convection heat transfer in a foam-filled horizontal rectangular channel

An experimental study was performed to investigate the heat transfer characteristics of the mixed convection flow through a horizontal rectangular channel where open-cell metal foams of different pore densities (10, 20 and 30 PPI) were situated. A uniform heat flux was applied at all of the bounding walls of the channel. For each of three values of the uniform heat flux, temperatures were measured on the entire surfaces of the walls. Results for the average and local Nusselt numbers are presented as functions of the Reynolds and Richardson numbers. The Reynolds number based on the channel height of the rectangular channel was varied from 600 to 33000, while the Richardson number ranged from 0.02 to 103, extending over forced, mixed and natural convection. Second important parameter that influences the heat transfer is the aspect ratio of the foams. Three different aspect ratios (AR) as 0.25, 0.5 and 1 are tested. Based on the experimental data, new empirical correlations have been constructed to link the Nusselt number. The results of all cases were compared to that of the empty channel and the literature. We found that our results were in agreement with those that are mentioned in the literature.     

Forced convection in a wavy-wall channel

The rates of heat transfer for flow through a sinusoidally curved converging-diverging channel has been analyzed using a simple coordinate transformation method and the spline alternating-direction implicit method. The effects of the wavy geometry, Reynolds number and Prandtl number on the skin-friction and Nusselt number have been studied. Results show that the amplitudes of the Nusselt number and the skin-friction coefficient increase with an increase in the Reynolds number and the amplitude-wavelength ratio. The heat transfer enhancement is not significant at smaller amplitude wavelength ratio, however, at a sufficiently larger value of amplitude wavelength ratio the corrugated channel will be seen to be an effective heat transfer device, especially at higher Reynolds numbers.     

Forced convection about a rotating sphere

Laminar forced convection about a rotating sphere that is subjected to a uniform stream in the direction of the axis of rotation has been numerically investigated. The boundary-layer equations governing this case have been solved by means of a finite-difference scheme for a fluid of Pr=0·7 over wide ranges of Reynolds number (Re) and Taylor number (Ta). Both the isothermal and constant-heat-flux thermal boundary conditions have been considered. A comparison with data available in the literature has been made. Results not available in the literature, at considerably large values of the spin parameter (Ta/Re²), are presented for the local and average Nusselt numbers.     

Experimental study of free convection from a pair of vertical arrays of horizontal cylinders at very low Rayleigh numbers

Steady laminar free convection from a pair of vertical arrays of equally-spaced uniformly heated horizontal cylinders set in free air is studied experimentally. A specifically developed experimental facility is used to perform heat flux and temperature measurements and thermal field visualization by means of Schlieren technique. Experiments are performed for pairs of tube-arrays consisting of five circular cylinders, for center-to-center horizontal and vertical spacing ranging from 2 to 145 cylinder-diameters and from 4 to 12 cylinder-diameters respectively, and for values of the Rayleigh number based on the cylinder-diameter in the range between 2.4 and 11.9. It is found that any cylinder may exhibit either enhanced or reduced Nusselt numbers with respect to the case of single array, depending on its location in the array, on the geometry of the array, as well as on the Rayleigh number. The visualization has allowed to relate a number of observed effects to the fact that side-by-side placement of the arrays produces a lateral air suction into the space between them.     

Free convection about a rectangular prismatic crystal growing from a solution

Sodium chlorate crystals growing from unstirred aqueous solutions were observed by schlieren techniques. Growth rate data were best correlated by Sh = 0.48 Ra^0.25 with finite interface kinetics and a characteristic length L equal to the crystal height plus the inverse reciprocal sum of the horizontal dimensions. The growth rate was slightly higher when the plume was laminar than when it was irregular. The horizontal growth rate was greater than the vertical growth rate, with the ratio tending to decrease with increasing plume instability. The threshold Grashof number for plume instability was greatly decreased with decreasing height for crystals with the same horizontal dimensions. The frequency of eddy emission was proportional to L⁻²Ra^0.8. The velocity of the eddies approached a constant value with increasing distance above the crystal surface, the terminal value being roughly proportional to Ra^1/2/L.