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 %.     

Computation of conjugate natural convection heat transfer from a rectangular fin on a partially heated horizontal base

In this study, a numerical investigation has been carried out to reveal the mechanism of fluid flow and heat transfer from a vertical rectangular fin attached to a partially heated horizontal base. The problem is a conjugate conduction-convection heat transfer problem with open boundaries. The governing equations for the problem are the conservation of mass, momentum and energy equations for the fluid and the heat conduction equation for the fin. The control volume technique based on the SIMPLEC algorithm with a nonstaggerred grid arrangement is employed to solve the governing equations. The effect of the heated base, on the mechanism of the fluid flow and heat transfer, is numerically investigated. Temperature distribution and flow patterns around the fin are plotted to support the discussion. Results are obtained for air at laminar and steady flow. Received on 15 May 1997     

Transient natural convection in a rectangular enclosure with one heated side wall

This paper describes a numerical and theoretical study of the transient natural convection heating of a two-dimensional rectangular enclosure filled with fluid. The heating is applied suddenly along one of the side walls, while the remaining three walls are maintained insulated. It is shown that the process has two distinct phases, an early period dominated by conduction and a late period dominated by convection. The scaling laws for the heat transfer rate and the effectiveness (energy storage fraction) are determined based on scale analysis. These theoretical results are confirmed by numerical experiments conducted in the domain Ra = 10³−10⁶, Pr = 7, A = 1, where Ra is the Rayleigh number based on height and initial temperature difference, Pr is the Prandtl number, and A is the height/length ratio of the enclosure. Correlations for heat transfer rate and effectiveness are constructed by comparing the theoretical scaling laws with the numerical results.     

Thermodynamic optimization of contact melting of phase change material inside a horizontal cylindrical capsule

Finite time thermodynamic analysis is applied to the contact melting process of phase change material inside a horizontal cylindrical capsule. With the minimum entropy generation in given time as the objective function the quadratic nonlinear ordinary differential equation that the optimal melting process should be satisfied is derived. The dimensionless liquid height, melt liquid film thickness, Nusselt number, melting rate, optimal wall temperature and entropy generation are obtained by the numerical method. The optimal results are discussed and compared with the unoptimizable analytical results under the condition of constant wall temperature. It is found that the heat transfer and thermodynamics performance of the optimal melting process is better than that of the melting with constant wall temperature.     

The onset of natural convection in a horizontal air layer heated from below

In this work, the beginning of the instability (onset of convection) of an air layer of infinite width and depth heated from underneath with a constant heat flux is studied. In the theoretical part, the instability is studied using the quasi-static assumption. The functional relationship of Rayleigh number vs. horizontal wave number of the disturbance is obtained in a digital computer using Green's Fonctions for the case of Prandtl number equal to one. Furthermore in order to make a comparison with similar investigations, limiting cases of infinite and very small Prandtl numbers are also taken into consideration.-In the experimental part, Rayleigh numbers corresponding to the onset of manifest convection based on visual observations are investigated by optical methods under various heat fluxes. The average value measured is found to be 145.     

Natural convection of non-Newtonian power law fluids in a shallow horizontal rectangular cavity uniformly heated from below

Analytical and numerical study is conducted for two-dimensional steady-state buoyancy driven flow of a non-Newtonian power law fluid confined in a shallow rectangular horizontal cavity uniformly heated from below, while its short vertical rigid sides are considered adiabatic. The effect of the non-Newtonian behaviour on the onset of convection, fluid flow, temperature field, and heat transfer is examined. A closed approximate analytical solution is developed on the basis of the parallel flow assumption and the obtained results are validated numerically by solving the full governing equations.     

Numerical simulation of natural convection of latent heat phase-change-material microcapsulate slurry packed in a horizontal rectangular enclosure heated from below and cooled from above

A two-dimensional numerical simulation of natural convection in a rectangular enclosure heated from below and cooled from above has been conducted with non-Newtonian phase-change-material (PCM) microcapsulate slurry with latent heat capacities. The formulation of the mathematical model in dimensionless co-ordinates and discretization of the governing equations have been done using the finite volume method. Both natural convection and heat transfer characteristics are discussed about natural convection with PCM microcapsulate slurry, which exhibits the pseudoplastic non-Newtonian fluid behavior and a peak value in the specific heat capacity with latent heat. The viscosity of the present PCM microcapsulate slurry is assumed to follow the Ostwald-de Waele power law fluid model with the power-law index n and the consistency coefficient K. The effects of phase-change material, the mass concentration, and the aspect ratio Ar on the natural convection heat transfer are described, respectively. By comparing with the results of microcapsule slurry without phase change, the enhancement in heat transfer is found in microcapsule slurry with phase change during the phase change temperature range. Numerical simulations are performed in the following parametric ranges: the width–height aspect ratio of the enclosure Ar from 2 to 20, the mass concentrations C _m of the slurry from 10 to 40%, power law index n of the slurry from 0.89 to 1.0 and Rayleigh numbers Ra ranges from 10³ to 10⁷.     

Experimental investigation of free convection above a heated horizontal wire

Results are presented of an experimental investigation of the convective plume above a fine horizontal wire, heated by a constant current in air and in water. The temperature distribution in the plume was investigated using the IAB-451 shadow instrument in the diffraction interferometry method. The experimental results are in good agreement with laminar convection theories above a linear heat source. In the air, a comparison was made with the experimental results of other authors.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhicheskoi Fiziki, Vol. 11, No. 2, pp. 169–173, March–April, 1970.The author wishes to express his indebtedness to V. D. Zimin and N. V. Eyzhanov for their assistance with numerical solutions of Eqs. (1.3).     

The onset of manifest convection from suddenly heated horizontal cylinders

Experimental data are presented for the onset of manifest convection in water around a heated horizontal cylinder. Thin nickel coatings were applied to three plexiglass cylinders of different diameters. The nickel surface was used as a heater and observations were made by a holographic interferometer. Initially, conduction prevailed within the system, in agreement with other time-dependent investigations of heating or cooling from a surface. After a period of time the manifest convection was detected around the cylinder. The critical Rayleigh number which defines the onset of convection was 20–30 for cylinders with 15, 25 and 40 mm diameters.     

Natural convection heat transfer in a uniformly heated horizontal pipe

Natural convection heat transfers inside horizontal pipes were measured. The Rayleigh numbers were varied from 6.8 × 10⁸ to 1.5 × 10¹², while the Prandtl number was fixed at 2,094. Based on the analogy concept, a copper sulfate electroplating system was adopted to measure mass transfer rates in place of heat transfer rates. Test results using single-piece electrodes were in good agreement with the work of Sarac and Korkut. The angle-dependent mass transfer rates, measured using piecewise electrodes, were compared with the results of studies on natural convection in concentric annuli, and showed similar trends. The experiments were expanded to the turbulent region, and a transition criterion was proposed. Angle-dependent natural convection heat transfer correlations for the laminar and turbulent regions were derived.     

Visualization of natural convection inside shallow solar stills

 Visualization techniques are employed to contribute to the understanding of the mechanisms responsible for heat and mass flow between the water basin and the condensing cover inside a shallow solar still. Laser sheets and tracers were employed to record images, where the dominant nature of convection in cell patterns was observed. Received: 1 February 1997/Accepted: 2 February 1998     

Laminar natural convection between partially heated vertical parallel plates

A numerical analysis has been performed to examine the characteristics of laminar natural convection in vertical channel with unheated entry and unheated exit. The heated section is subjected to uniform wall temperature (UWT) or uniform heat flux (UHF). Theoretical results for average Nusselt number and induced volume flow rateQ were derived under fully developed condition. Particular attention is paid to investigating the effects of the partially heated section on the induced volume flow rate and Nusselt number for various conditions. Results show that for UWT the induced volume flow rateQ increases with decreasing unheated entry length or increasing total length of heated section and unheated exit. For a fixed unheated entry length, the channel with a longer heated section length causes a greaterQ. Additionally, for both UWT and UHF, the average Nusselt number under fully-developed condition increases with increasing value ofE ₁/E ₂.

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Laminare Naturkonvektion zwischen teilbeheizten senkrechten Parallelplatten

Zusammenfassung Die numerische Untersuchung soll das Verhalten einer laminaren Strömung bei natürlicher Konvektion in einem senkrechten Kanal mit unbeheiztem Ein- und Austritt klären. Der beheizte Abschnitt wird entweder mit gleichförmiger Wandtemperatur (UWT) oder gleichförmigem Wärmefluß (UHF) beaufschlagt. Bezüglich voll ausgebildeter Strömung ließen sich theoretische Ergebnisse für die mittlere Nußelt-Zahl und den induzierten VolumenstromQ gewinnen. Besonderes Interesse galt der Untersuchung des Einflusses des teilbeaufschlagten Abschnittes auf Volumenstrom und Nußelt-Zahl unter verschiedenen Nebenbedingungen. Die Ergebnisse zeigen, daß im UWT-Fall der induzierte VolumenstromQ mit abnehmender unbeheizter Einlauflänge oder zunehmender Gesamtlänge des Heizabschnittes anwächst. Bei fester unbeheizter Einlauflänge erzeugt der Kanal mit längerem Heizabschnitt einen höheren StromQ.

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Nomenclature b half channel width - E ₁ ratio of unheated exit length to channel length,l ₁/l - E ₂ ratio of heated section length to channel length,l ₂/l - E ₃ ratio of unheated entry length to channel length,l ₃/l - Gr _L Grashof number, Eq. (4) - g gravitational acceleration - k thermal conductivity - l channel length - l ₁ unheated exit length - l ₂ heated section length - l ₃ unheated entry length - L dimensionless channel length, Eq. (4) - L ₁ dimensionless unheated exit length - L ₂ dimensionless heated section length - L ₃ dimensionless unheated entry length - average Nusselt number - Nu _x local Nusselt number - p pressure defect - P dimensionless pressure defect, Eq. (4) - Pr Prandtl number,/ - q _w wall heat flux of heated section - Q dimensionless induced volume flow rate, Eq. (8) - Ra _E Rayleigh number based on the heated section length,Ra _L/E₂ - Ra _L Rayleigh number based on the full channel length,Gr _LPr - T temperature - T ₀ inlet temperature - T _w wall temperature - u, v velocity components in thex andy directions, respectively - U, V dimensionless velocity components in thex andy directions, respectively, Eq. (4) - u ₀,U ₀ dimensional and dimensionless inlet velocity, respectively - x, y coordinates in thex andy directions, respectively - X, Y dimensionless coordinates in thex andy directions, respectively, Eq. (4) - X ratio of longitudinal distance from the entrance of heated section to the heated section length,X=[X–(L–L ₁–L ₂)]/L ₂ Greek symbols thermal diffusivity - thermal expansion coefficient - kinematic viscosity - dimensionless temperature, Eq. (4) - ₀ fluid density at ambient temperature     

Mixed convection flow in a horizontal rectangular channel subjected to a horizontal thermal gradient

This paper deals with a mixed convection water flow in a horizontal rectangular duct, uniformly heated from one lateral vertical wall and thermally insulated elsewhere. The supplied heat flux induces a secondary flow, which structure is constituted of one longitudinal roll in the considered aspect ratio (Γ = 1.9), embedded into a return flow of possibly large stream wise extension (up to twenty channel heights). Such situation induces helicoidal trajectories for the fluid flow particles, which contributes to a heat transfer enhancement compared to purely forced convection flow.     

Laminar mixed convection in the entrance region of horizontal rectangular ducts

A generally applicable finite element procedure for the prediction of laminar mixed convection in horizontal straight ducts of arbitrary cross-section is presented. The procedure, based on the parabolized simplification of the complete Navier-Stokes equations and on the Boussinesq approximation of the buoyancy terms, is validated through comparisons of computed results with the available literature data for mixed convection in the entrance region of a rectangular duct of aspect ratio a=2. Uniform heating at different sides is considered as the thermal boundary condition, although the proposed formulation allows specification of most thermal boundary conditions of practical interest.     

Adjoint optimization of natural convection problems: differentially heated cavity

Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (\(Pr=0.15{-}7\)) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors’ knowledge, this behavior is illustrated here for the first time.     

Visualization of natural convection heat transfer on horizontal cylinders

Natural convection heat transfer phenomena on horizontal cylinders were investigated experimentally in order to explore the applicability of analogy experimental method using the copper electroplating system and to visualize the local heat transfer depending on the angular position and the diameter of the horizontal cylinder. The diameters of the cylinders are varied from 0.01 to 0.15 m, which correspond to the Rayleigh numbers of 1.73 × 10⁷–5.69 × 10¹¹. The measured mass transfer coefficients show good agreements with the existing heat transfer correlations. The patterns of copper plated on the aluminum cathodes for various Rayleigh numbers reveal and visualize the local heat transfer depending on the angular position and show good agreement with the works of Kitamura et al. The hydrogen bubbles produced at higher applied potential visualize the plumes appeared on top region of the cylinders.