Natural convective heat transfer of heated packed beds

Natural convection heat transfer of heated packed bed was investigated. Experiments were performed for a single heated sphere buried in unheated packed beds varying its locations and for packed beds with all heated spheres varying the heights of packed beds from 0.02 m to 0.26 m. Mass transfer experiments using a copper electroplating system were performed based upon the analogy between heat and mass transfer. The diameter of sphere was 0.006 m, which corresponds to Ra_d of 1.8 × 10⁷. For the single heated sphere cases, the measured results agreed well with the existing natural convection heat transfer correlations for packed beds and even with those for a single sphere in an open channel. For all heated sphere cases, the average heat transfers decrease with increasing packed bed heights.     

Time evolution of double-diffusive convection in a vertical cylinder with radial temperature and axial solutal gradients

The characteristics of transient double-diffusive convection in a vertical cylinder are numerically simulated using a finite element method. Initially the fluid in the cavity is at uniform temperature and solute concentration, then constant temperature and solute concentration, which are lower than their initial values, are imposed along the sidewall and bottom wall, respectively. The time evolution of the double-diffusive convection is investigated for specific parameters, which are the Prandtl number, Pr = 7, the Lewis number, Le = 5, the thermal Grashof number, Gr_T = 10⁷, and the aspect ratio, A = 2, of the enclosure. The objective of the work is to identify the effect of the buoyancy ratio (the ratio of solutal Grashof to thermal Grashof numbers: N = Gr_S/Gr_T) on the evolution of the flow field, temperature and solute field in the cavity. It is found that initially the fluid near the bottom wall is squeezed by the cold flow from the sidewall, a crest of the solute field forms and then pushed to the symmetry line. In the case of N > 0, a domain with higher temperature and weak flow (dead region) forms on the bottom wall near the symmetry line, and the area of dead region increases when N varies from 0.5 to 1.5. More crests of the solute field are formed and the flow near the bottom wall fluctuates continuously for N < 0. The frequency of the fluctuation increases when N varies from −0.5 to −1.5. Corresponding to the variety of the thermal and solutal boundary layers, the average rates of heat transfer (Nu) at the sidewall remain almost unchanged while the average rates of mass transfer (Sh) at the bottom wall change much in the cases of N = 1, 0, −1.     

Effect of cross sectional shape during condensation in a single square minichannel

The objective of this work is to present new condensation heat transfer coefficients measured inside a single square cross section minichannel, having a 1.18 mm side length, and compare them to the ones previously measured in a circular minichannel. Tests have been performed with R134a at 40 °C saturation temperature, at mass velocity ranging between 200 and 800 kg m^?2 s^?1. As compared to the heat transfer coefficients measured in the circular cross section channel, for the same hydraulic diameter, in the square minichannel the authors find a heat transfer enhancement at the lowest value of mass velocity, which must be due to the effect of surface tension. No heat transfer coefficient increase has been found at the highest values of the mass velocity where condensation is shear stress dominated.     

Direct numerical simulation of wall-normal rotating turbulent channel flow with heat transfer

Direct numerical simulation of wall-normal rotating channel flow with heat transfer has been performed for the rotation number N_τ from 0 to 0.1, the Reynolds number 194 based on the friction velocity of non-rotating case and the half-height of the channel, and the Prandtl number 1. The objective of this study is to reveal the effects of rotation on the characteristics of turbulence and heat transfer. Some statistical turbulence and heat transfer quantities, including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and turbulence structures, are investigated. Based on the present calculated results, two typical rotation regimes are identified. When 0 < N_τ < 0.06, the turbulence statistics correlated with the spanwise velocity fluctuation are enhanced since the shear rate of spanwise mean flow induced by Coriolis force increases; however, the other statistics are suppressed. When N_τ > 0.06, all the turbulence statistics are suppressed significantly. To elucidate the effects of rotation on the turbulent heat transfer, the budget terms in the transport equation of turbulent heat fluxes are analyzed. Remarkable change of the direction of near-wall streak structures of the velocity and temperature fluctuations, nearly in alignment with the absolute mean flow direction, is revealed. An attempt to evaluate the mean spacing and the direction of streaky structures near the wall has been examined based on the two-point correlations of the velocity and temperature fluctuations.     

Phemonenological model of heat transfer in an infiltrated granular bed at moderate Reynolds numbers

A model of heat transfer in an infiltrated granular bed, which allows for most important special features of the process, viz., anisotropy of thermal properties and nonuniform distribution of the porosity and gas (liquid) velocity over the cross section, has been formulated. The concepts of the filtration boundary layer and viscous sublayer have been introduced and identified. Temperature fields and values of the coefficient of heat exchange between the bed and the wall of the tube bounding it have been calculated. The latter are generalized in the form of the dimensionless correlation which is compared with the available experimental data. It is shown that at Re_∞ ⩽ 2000 the developed model describes the process of heat transfer in the granular bed well.     

Frequency-dependent heat transfer enhancement from rectangular heated block array in a pulsating channel flow

The effect of pulsating flow on convective heat transfer from periodically spaced blocks in tandem on a channel wall is experimentally investigated. The spacing l between repeated blocks varied from l/L = 0.3 to 0.6 where L is the block pitch. The experiments are carried out in the range of 10 Hz < f_F < 100 Hz and 0.2 < A < 0.3. A pulsating flow is imposed by an acoustic woofer at the channel inlet and a constant heat is generated at each protruding block. The impact of the important governing parameters such as the Reynolds number, the Strouhal number and the inter-block spacing on heat transfer rate from heated blocks is examined in detail. The experimental results show that thermal transport from the blocks is greatly affected by the frequency, the amplitude of the flow pulsation, the inter-block spacing and the Reynolds number. Thermal resonance frequency which shows a maximum heat transfer coincides well with the inverse of traveling time of a fluid parcel that can be determined from the block periodicity and the Reynolds number.     

Laminar flow and heat transfer in a periodic serpentine channel with semi-circular cross-section

Computational fluid dynamics (CFD) has been used to study fully developed laminar flow and heat transfer behaviour in periodic serpentine channels with a semi-circular cross-section. The serpentine elements are characterised by their wavelength (2L), channel diameter (d) and radius of curvature of bends (R_c), with results reported for Reynolds numbers (Re) up to 450, as well as for a range of geometric configurations (3 < L/d < 12.5, 0.525 < R_c/d < 2.25) at Re = 110. The flow in these channels is characterised by the formation of Dean vortices following each bend. As the Reynolds number is increased, more complex vortical flow patterns emerge and the flow domain becomes increasingly dominated by these vortices. Alignment of flow with vorticity leads to efficient fluid mixing and high rates of heat transfer.Constant wall heat flux (H2) and constant wall temperature (T) boundary conditions and a range of fluid Prandtl numbers (0.7 < Pr < 100) have been examined. High rates of heat transfer and low pressure loss are found relative to fully-developed flow in a straight pipe, with heat transfer enhancements greater than 10 for a Prandtl number of 100.As part of this work, we also obtain an accurate value for the Nusselt number for fully-developed flows in straight semi-circular passages with constant wall temperature, Nu_T = 3.323(±0.001).     

CFD modeling of mass transfer in annular reactors

A computational fluid dynamics (CFD) investigation of single-phase flow mass transfer prediction in annular reactors was conducted. Different hydrodynamic models including laminar, standard k–ε, realizable k–ε, Reynolds stress (RSM), and the Abe-Kondoh-Nagano (AKN) (a low Reynolds number turbulence model) were evaluated against experimental data in terms of their mass transfer predication capabilities. The laminar model predicted successfully the average mass transfer in the flows under laminar regime (Re < 1500). Among the four evaluated turbulence models, the AKN model provided a better prediction of the average mass transfer rates in the systems when operated both under transitional and turbulent conditions (3000 < Re < 11000). The RSM performed very similarly to the AKN model, except for the entrance region of the reactors where it predicted lower mass transfer rates. These results make the AKN and RSM models very attractive to be integrated in CFD-based simulations of turbulent annular reactors.     

Experimental investigation on the convective heat transfer in straight and coiled corrugated tubes for highly viscous fluids: Preliminary results

The forced convective heat transfer in straight and coiled tubes, having smooth and corrugated wall, was experimentally investigated in two ranges of the Reynolds number: a lower one (5 < Re < 13) obtained with Glycerol and a higher one (150 < Re < 1500) obtained with Ethylene Glycol. The aim of the research was to verify the effectiveness of these passive heat transfer enhancement techniques when highly viscous fluids are treated. This issue is particularly crucial in applications in which the thermal processing of high Prandtl number fluids is required, such as in the food, chemical, pharmaceutical and cosmetics industries. In the present note, preliminary results, obtained by considering a given geometrical configuration characterized by a tube diameter of 14 mm, a curvature ratio of 0.06, a corrugation depth of 1 mm and a corrugation pitch of 16 mm, are presented. The main conclusion is that the wall curvature enhances heat transfer at all Re, whereas the wall corrugation enhances heat transfer only in the higher Re range; moreover the wall corrugation is totally ineffective in the low Re range and, if helical coils are present, it also destroys the benefit induced by the wall curvature. The largest increment in heat transfer rates is thus obtained by using smooth helical coils at low Re, and corrugated helical coils at larger Re. The results, although of preliminary nature, suggest interesting applications of the passive heat transfer enhancement technique based on smooth wall coiled tubes in the very low Reynolds number values range, while the combined passive technique based on wall corrugation and curvature represents an interesting solution for Reynolds number values in the range 150–1500.     

Correlations for combined heat and mass transfer from an open cavity in a horizontal channel

Combined heat and mass transfer from a horizontal channel with an open cavity heated from below is numerically examined in this paper. Air is the fluid considered (Pr = 0.7). The main focus of the study is mass-transfer driven flows (|N| > 1). The governing parameters considered are the buoyancy ratio N, Lewis number Le, Reynolds number Re, and Grashof number Gr. Based on the scale analysis, correlations for the entire convection regime, from natural, mixed, to forced convection, were proposed.     

Experimental investigation of single-phase turbulent flow of R-134a in a multiport microchannel heat sink

This experimental study aims to investigate the heat transfer characteristics of single-phase turbulent flow of R-134a refrigerant in a rectangular multi-micro channel heat sink having 27 channels where each channel has a hydraulic diameter of 421 μm. Experimental results were obtained for inlet temperatures ranging from 24 to 33 °C, mass fluxes from 1485 to 2784 kg m^− 2 s^− 1 and wall heat fluxes from 3 to 24 kW m^− 2. The results indicate that the heat transfer coefficients are found to be higher at lower inlet temperatures than those at higher ones. In addition, when equal amount of heat supplied to the heat sink, the heat transfer coefficients increase with increasing the mass flux of refrigerant. They were also compared with 12 well-known correlations and it was seen that 4 of 12 were in good agreement with each other with the average deviation < 10%. The findings demonstrate that well-known correlations in fundamental sources can be used to predict the heat transfer coefficient of R-134a during its single phase flow in a multiport microchannel heat sink under turbulent regime.     

Effect of packing geometry on the rate of mass and heat transfer at a vertical tube imbedded in fixed bed under single and two phase flow

Rates of liquid–solid mass transfer and heat transfer (by analogy) were studied in an annular reactor with a packed annulus. Two types of inert fixed bed packing were used namely, cylinders and Raschig rings. The electrochemical technique which involves measuring the limiting current of the cathodic reduction of ferricyanide ion in a large excess of sodium hydroxide was used in the present study. Variables studied are packing geometry, packing size, gas and liquid superficial velocities and physical properties of the solution. The presence of inert fixed bed in the annulus enhanced the rate of mass transfer and the rate of heat transfer at the outer wall of the inner cylinder by a factor ranging from 1.1 to 6.1 depending on the packing geometry, particle size and both the liquid and gas superficial velocities. The present data were compared with the previous data on the packed annulus with inert spherical packing. For single phase liquid flow the mass transfer enhancement ratio increases in the order: Raschig rings > cylinders > spheres, while in the case of two phase flow, spheres gave the highest enhancement ratio. For the present range of conditions it was found that, as the particle size decreases the enhancement ratio increases. All data were correlated in the form of dimensionless equations.Possible practical applications of the present study such as design of fixed bed reactor internal cooler, prediction of the rate of diffusion controlled corrosion of vertical tube cooler imbedded in a fixed bed reactor and design of annular double tube catalytic and electrochemical reactors with a fixed bed turbulence promoter were highlighted.     

Determination of annular condensation heat transfer coefficient of steam in microchannels with trapezoidal cross sections

Experiments have been carried out to determine annular condensation heat transfer coefficient of steam in two silicon microchannels having trapezoidal cross sections with the same aspect ratio of 3.15 at 54 < G < 559 kg/m² s under 3-side cooling conditions. A semi-analytical method, based on turbulent flow boundary layer theory of liquid film with correlations of pressure drop and void fraction valid for microchannels, is used to derive the annular local condensation heat transfer coefficients. The predicted values based on the semi-analytical model are found within ±20% of 423 data points. It is shown that the annular condensation heat transfer coefficient in a microchannel increases with mass flux and quality and decreases with the hydraulic diameter.     

Optimal geometry of L and C-shaped channels for maximum heat transfer rate in natural convection

The present paper documents the geometric optimization of L and C-shaped channels in laminar natural convection subject to global constraints. The objective is to maximize the heat transfer rate from the hot wall to the coolant fluid. Three different configurations were considered: (i) an L-shaped asymmetric vertical heated channel with an adiabatic horizontal inlet, (ii) an asymmetric vertical heated channel with an adiabatic vertical outlet, and finally, (iii) a C-shaped vertical channel with horizontal inlet and outlet. The two first configurations are free to morph according to two degrees of freedom: the wall-to-wall spacing and inlet (or outlet) height. The third configuration is optimized with respect to the wall-to-wall spacing, and the heights of the inlet and outlet ports. The effect of the inlet or outlet horizontal adiabatic duct lengths is also investigated. The optimization is performed numerically by using the finite element technique, in the range 10⁵ < Ra < 10⁷ for Pr = 0.7, where Ra is the Rayleigh number based on a fixed total height H of the channel. The numerical results show that optimization is relevant, since the three degrees of freedom considered have a strong effect on the heat transfer delivered from the hot wall to the fluid. The optimal geometric characteristics obtained numerically (i.e., optimal spacing, optimal height and lengths) are reported and correlated within a 7.5% maximal disagreement range.     

Experimental study of forced convection heat transfer from a cam shaped tube in cross flows

An experimental investigation has been conducted to clarify forced convection heat transfer characteristic and flow behavior of an isothermal cam shaped tube in cross flow. The range of angle of attack and Reynolds number based on an equivalent circular tube are within 0° < α < 180° and 1.5 × 10⁴ < Re_eq < 2.7 × 10⁴, respectively.The results show that the mean heat transfer coefficient is a maximum at about α = 90° over the whole range of the Reynolds numbers. It is found that thermal hydraulic performance of the cam shaped tube is larger than that of a circular tube with the same surface area except for α = 90° and 120°. Furthermore, the effect of the diameter of the cam shaped tube upon the thermal hydraulic performance is discussed.     

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.71 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ⩽ 10⁻⁵ irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da ⩾ 10⁻⁴. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Experimental study of thermal behaviors in a rectangular channel with baffle of pores

This experimental study attempts to explore the local heat transfer in rectangular channel with baffles, and analyzes the experimental results of baffles with different heights and pores in the event of five Reynolds numbers and three heating quantities. Apart from increasing the perturbation of flow field, the channel's flow field with baffles, which is similar to a backward-facing step flow field, is very helpful to heat transfer. To obtain an optimized baffle and increase the perturbation of flow field, this experiment employed baffles with five heights (H = 10–50 mm) and different numbers of pores (N = 1–3), as well as heat flux: Q = 40–100 l/min, Reynolds number: 702–1752, and heating quantity: q_in = 90–750 W/m². In addition to measurement of overall temperature distribution, emphasis is also placed on analysis of local heat transfer coefficient. Furthermore, heat transfer distribution of channel can be applied to explain how the baffles of pores have an influence upon backward-facing step flow field, shear layer, recirculation region, reattachment region and redeveloped boundary layer. Finally, some empirical formulas derived form experimental results may provide a reference for future design.     

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.     

Experimental investigation of the forced convective boiling heat transfer of R-600a/oil/nanoparticle

In this paper an experimental study of convective boiling heat transfer of R-600a/oil/nanoparticle mixtures is investigated. The experimental setup was prepared with a smooth horizontal tube as a test section with the length and diameter of 9.5 and 103 mm, respectively, and pure R-600a was applied for evaluating the heat transfer enhancement. Six mixtures containing 1% weight fraction of R-600a/oil with different concentrations of CuO nanoparticles including 0.0, 0.5, 1.0, 1.5, 2.0 and 5.0% weight fraction of R-600a/oil/nanoparticle were used in our study.The mass velocity per cross area was considered at the range of 50–700 kg/m² s for low vapor quality (ϕ < 0.25). The results showed that the convective boiling heat transfer coefficient will be increased by increasing the mass fraction of nanoparticles up to 2%, while by increasing the mass fraction of nanoparticles up to 5% the heat transfer coefficient will be reduced.     

Bénard convection from a circular cylinder in a packed bed

Bénard convection around a circular heated cylinder embedded in a packed bed of spheres is studied numerically. The Forchheimer–Brinkman–extended Darcy momentum model with the Local Thermal Non-Equilibrium energy model is used in the mathematical formulation for the porous layer. The governing parameters considered are the Rayleigh number (10³ ≤ Ra ≤ 5 × 10⁷) and the thermal conductivity ratio (0.1 ≤ k_r ≤ 10,000). The structural properties of the packed bed are kept constant as: cylinder-to-particle diameter ratio D/d = 20 and porosity ε = 0.5, while the Prandtl number is fixed at Pr = 0.71. It is found that the presence of the porous medium suppresses significantly the strong free convection produced in the empty enclosure, and reduces considerably the high intensity of the pair of vortices generated behind the cylinder. Also, the results show that the porous medium can play the role of insulator or enhancer of heat transfer from the heat source, depending mainly on their thermal conductivities regardless of the Rayleigh number.