Combined wall-to-fluidized bed heat transfer. Bubbles and emulsion contributions at high temperature

A theoretical and experimental investigation of combined wall-to-fluidized bed heat transfer is presented. Bubble and emulsion contributions are modelled assuming both phases to be semi-transparent grey media. For a radiant bubble phase component the general situation of absorbing gases including particulate is described. Tests were performed with a two-dimensional fluidized bed column in the temperature range 500–900°C. Experimental and theoretical results emphasized that (i) a non-linear relation exists between h and T_b if the conduction-to-radiation parameter (N) is smaller than 5, indicating that radiative and conductive contributions are not independent, (ii) the dense phase radiant contribution becomes significant at temperatures higher than 700°C, (iii) at 900°C the bubble phase radiative component cannot be neglected.     

Complete heat transfer solutions of an insulated regular polyhedron by using an RPSWT model

The heat transfer characteristics for an insulated regular polyhedron (including sphere) are analyzed by using the same RPSWT model in the present study as that used by Wong and Chou previously [Energy Convers. Manage. 44 (2003) 3015]. The thermal resistance of the inner convection term and the wall conduction term in the heat transfer rate are not neglected in the present study. Thus, the complete heat transfer solution will be obtained. The present results can be applied more extensively to practical situations, such as an insulated gas tank. The results of the critical thickness t_cr and the neutral thickness t_e are independent of the values of J (generated by the effect of the inner convection term and the wall conduction term). However, the heat transfer rates are dependent on the values of J. The present study shows that the thermal resistance of the inner convection term and the body conduction term cannot be neglected in the heat transfer equation in situations of low to medium inner convection coefficients h_i and/or low to medium wall conductivities K and/or great wall thickness t₁, especially in situations with small body sizes or/and great outer convection coefficients h_o.     

Thermal characterization of turbulent tube flows over diamond-shaped elements in tandem

Experiments have been conducted to investigate the heat transfer and friction factor characteristics of the fully developed turbulent airflow through a uniform heat flux tube fitted with diamond-shaped turbulators in tandem arrangements. In the experiments, strong turbulence and recirculation flow is expected by using tandem diamond-shaped turbulators (D-shape turbulator) connected to each other by a small rod and placed inside the test tube. The parameters for this study are consisted of Reynolds number (Re) from 3500 to 16,500, the included cone angle (θ = 15°, 30° and 45°), and the tail length ratio (TR = l_t/l_h = 1.0, 1.5 and 2.0) defined as the ratio of the tail length (l_t) to the head length of turbulator (l_h). The variation of Nusselt number and friction factor with Reynolds number under the effect of those parameters are determined and presented. The experimental result reveals that the heat transfer rate increases with increasing Reynolds number and the included cone angle (θ) but decreases with the rise of the tail length ratio (TR). This is because of the mixing of the fluid in the boundary layer thereby enhancing the convective heat transfer and increasing pressure loss. For the tube with the turbulator of θ = 45°, the heat transfer enhancement is found to be 67%, 57% and 46% for tail length ratio, TR = 1.0, 1.5 and 2.0, respectively. Correlations of the Nusselt number (Nu) and friction factor (f) are developed for the evaluation of interactive effects of using the turbulators on the heat transfer and pressure loss. The good agreement between the experimental and the correlated results is obtained within 5–7% deviation. In addition, the heat transfer enhancement efficiency determined under constant pumping power is also provided.     

Experimental investigation of start-up and transient thermal performance of pumped two-phase battery thermal management system

In this study, a pumped two-phase battery thermal management system was developed, and its start-up and transient thermal performances were experimentally evaluated. The start-up behavior was characterized, and the effects of the flow rate, heat flux, and cold-source temperature on the start-up and transient thermal performances were examined. Three start-up modes were observed: fluctuating growth, temperature overshoot, and smooth growth. The fluctuating growth start-up mode appears to be suitable for battery cooling. The transient performance was improved when the flow rate was decreased, which resulted in a quicker start-up and lower average temperature (t_avg) and maximum temperature difference (∆t_max). Reducing the flow rate from 0.99 to 0.20 L/min significantly shortened the start-up time, lowered t_avg and ∆t_max, and increased the heat transfer coefficient (α) when the steady state was reached. Increasing the heat flux initially improved and then weakened the transient performance of the pumped two-phase system. Increasing the heat flux from 1.1 to 2.8 W/cm² initially reduced the start-up time and t_avg to 350 seconds and 1.5°C, respectively, but they then significantly increased to 360 seconds and 13.5°C, respectively. The transient t_avg and ∆t_max decreased with the cold-source temperature (t_cs), while the start-up time was independent of changes in t_cs.     

Influence of convective heat transfer modeling on the estimation of thermal effects in cryogenic cavitating flows

The accuracy of numerical simulations for the prediction of cavitation in cryogenic fluids is of critical importance for the efficient design and performance of turbopumps in rocket propulsion systems. One of the main remaining challenges is efficiency in modeling of the physics, handling the multi-scale properties involved and developing robust numerical methodologies. Such flows involve thermodynamic phase transitions and cavitation bubbles that are on a smaller scale than the global flow structure. Cryogenic fluids are thermo-sensitive, and therefore, thermal effects and strong variations in fluid properties can alter the cavitation properties. The aim of this work is to address the challenge posed by thermal effects. The Rayleigh–Plesset equation is modified by the addition of a term for convective heat transfer at the interface between the liquid and the bubble coupled with a bubbly flow model to assess the prediction of thermal effects. We perform a parametric study by considering several values of and models for the convective heat transfer coefficient, h_b, and we compare the resulting temperature and pressure profiles with the experimental data. Finally, the results of a 2D simulation with a commercial CFD code are presented and compared with the previous results. We note the importance of the choice of h_b for the correct prediction of the temperature drop in the cavitating region, and we assess the most efficient models, underlining that the choice of h_b estimation model in a cryogenic cavitating flow is more important in the bubble growth phase than in the bubble collapse phase.     

Heat transfer and friction factor correlations of solar air heater ducts artificially roughened with discrete V-down ribs

The heat and fluid flow characteristics of rectangular duct having its one broad wall heated and roughened with periodic ‘discrete V-down rib’ are experimentally investigated. Reynolds number (Re) has been varied from 3000-15000 with relative gap width (g/e) and relative gap position (d/w) range of 0.5-2.0 and 0.20-0.80 respectively. The respective variation in relative roughness pitch (P/e), angle of attack (α) and relative roughness height (e/D_h) have been 4-12, 30°-75° and 0.015-0.043. The effect of roughness parameters on Nusselt number (Nu) and friction factor (f) has been determined and the results obtained were compared with those of smooth duct. The maximum increase in Nu and f over that of smooth duct was 3.04 and 3.11 folds respectively. The rib parameters corresponding to maximum increase in Nu and f were d/w = 0.65, g/e = 1.0, P/e = 8.0, α = 60° and e/D_h = 0.043. Correlations for the Nu and f in terms of Re and rib parameters have been developed.     

Heat transfer enhancement of transverse ribs in circular tubes with consideration of entrance effect

The heat transfer enhancement of transverse ribs in circular tubes with a length-to-diameter ratio of 87 was experimentally investigated. The mean heat transfer and friction data were obtained for the air flow started from the entrance. An isothermal surface condition was considered. The rib pitch-to-tube diameter ratio (p/d) was in the range 0.304–5.72; the rib height-to-tube diameter ratio (e/d) was in the range 0.015–0.143; the considered Reynolds number (Re) was in the range 4608–12,936. The mean Nusselt number (Nu) and friction factor (f) were individually correlated as a function of p/d, e/d and Re. A critical e/d, equal to 0.057, was found. For e/d < 0.057, the f is proportional to e/d; for e/d ⩾ 0.057, the f is proportional to (e/d)^2.55. A performance map, indicating the corresponding heat transfer enhancement index (r₁) and efficiency index (r₂) for various p/d and e/d, was constructed. This performance map clearly indicates the ranges of p/d and e/d with a high r₂.     

Theoretical analysis of the thermal performance of all-glass evacuated tube solar collectors with absorber coating on the outside or inside of the inner tube

Theoretical efficiencies (η) and thermal behaviour of all-glass Evacuated Tube solar Collectors with an Internal Absorber Film (ETCIAF), i.e. the absorber film deposited in the inner surface of the inner tube, are compared and contrasted with the traditional design of all-glass Evacuated Tube solar Collectors with an External Absorber Film (ETCEAF), using the absorber film on the external surface of the inner tube. The values of η of the ETCIAF are unacceptably lower than that of ETCEAF for any particular value of the heat transfer coefficient (h_b) for the annular space, except in the case of a highly leaky ETCEAF, with h_b > 2.6 W/m² K. However, it is shown that the use of a transparent conductive coating with moderately low emittance 0.1−0.25 on the outside of the absorber tube of ETCIAF can offer efficiences 0.75−0.63, respectively, for f = 0.1 °C m²/K, competing well (η = 0.76) with the ETCEAF design operating under best conditions (α = 0.91, = 0.05, and h_b = 0.026 W/m² K).     

Use of porous baffles to enhance heat transfer in a rectangular channel

An experimental investigation was carried out to measure module average heat transfer coefficients in uniformly heated rectangular channel with wall mounted porous baffles. Baffles were mounted alternatively on top and bottom of the walls. Heat transfer coefficients and pressure loss for periodically fully developed flow and heat transfer were obtained for different types of porous medium (10, 20, and 40 pores per inch (PPI)) with two window cut ratios (B_h/D_h=1/3 and 2/3) and two baffle thickness to channel hydraulic diameter ratios (B_t/D_h=1/3 and 1/12). Reynolds number (Re) was varied from 20,000 to 50,000. To compare the effect of foam metal baffle, the data for conventional solid-type baffle were obtained for (B_t/D_h=1/3). The maximum uncertainties associated with module Nusselt number and friction factor were 5.8% and 4.3% respectively. The experimental procedure was validated by comparing the data for the straight channel with no baffles (B_h/D_h=0) with those in the literature [Publications in Engineering, vol. 2, University of California, Berkeley, 1930, p. 443; Int. Chem. Eng. 16 (1976) 359]. The use of porous baffles resulted in heat transfer enhancement as high as 300% compared to heat transfer in straight channel with no baffles. However, the heat transfer enhancement per unit increase in pumping power was less than one for the range of parameters studied in this work. Correlation equations were developed for heat transfer enhancement ratio and heat transfer enhancement per unit increase in pumping power in terms of Reynolds number.     

Study of the influence of the number of holes rows on the convective heat transfer in the case of full coverage film cooling: Etude de l’influence du nombre de rangées de trous sur les échanges convectifs dans le cas du refroidissement par multiperforation

The protection of the combustion wall chamber of aeronautic propeller is assumed with a full coverage film cooling. In the case of 1-9 rows of eight staggered holes, we have measured several profiles of temperature in the mainstream perturbed by jets. Variations of wall temperatures T_p have been measured simultaneously along the wall. Those experiences have been performed for three thermal cases, which are a function of the mainstream temperature T_e, the injected temperature T_i and the electrical density ?_dissi. imposed at the wall. Three blowing rates M=ρ_iU_i/ρ_eU_e are imposed too. The results are compared with the reference case without holes. The exam of the temperature profiles allows us to find a minimum number of rows to create a homogeneous cold layer. Two schemes of the convective heat transfer with two coefficients are presented and allow to represent each of the three thermal cases for the three blowing rates. Those models take into account of the three characteristic temperatures (T_e, T_i and T_p). One model is studied for 9 rows with infrared thermography. For five blowing rates, four zones of variations and an influence of M on the two coefficients are underlined.     

Computation of glass-cover temperatures and top heat loss coefficient of flat-plate solar collectors with double glazing

A set of correlations for computing the glass-cover temperatures of flat-plate solar collectors with double glazing is developed. A semi-analytical correlation for the factor f₂—the ratio of outer to inner thermal resistance of a double-glazed collector—as a function of collector parameters and atmospheric variables is obtained by regression analysis. This relation readily provides the temperature of the second (outer) glass cover (T₂). For estimating the temperature of first (inner) glass cover (T₁), another relation for the factor f₁—the ratio of thermal resistance between the two glass covers to the thermal resistance between the absorber plate and first glass cover—is developed. A wide range of variables is covered in the present analysis. The results are compared with those obtained by numerical solutions of heat-balance equations. Using the proposed relations of glass-cover temperatures, the values of top heat loss coefficient (U_t) can be computed and are found to be very close to those obtained by numerical solutions of heat-balance equations. The maximum absolute error in the calculation of U_t by the proposed method is only 1.0%, so numerical solutions of heat-balance equations for the computation of U_t are not required.     

Numerical study on in-tube laminar heat transfer of supercritical fluids

Numerical calculations were carried out for supercritical carbon dioxide flowing in miniature tubes with Re less than 1000. The heat transfer coefficient α and friction factor f were numerically studied for different values of the tube diameter, pressure, mass flux, and heat flux. When compared with the constant property flow, where Nu = 4.364 and f = 64/Re for a circular tube under a constant heat flux condition, a large divergence from the constant value was obtained for both Nu and f·Re in the vicinity of the pseudocritical temperature T_m. When cooled under a constant heat flux, Nu attained its peak value when T_b > T_m and its minimum value when T_b < T_m, while f·Re attained its peak value at T_b = T_m. With regard to the heating process, the reverse tendencies were confirmed. The variations of the specific heat with temperature were found to be the dominant factor for Nu. In addition, empirical correlations that considered the cross-sectional distribution of thermophysical properties were proposed to predict the values of Nu and f both in the near-pseudocritical temperature region and in the thermal entrance region of the tube. The proposed correlations were also verified by comparing the predicted results with numerical results obtained by using supercritical water.     

Heat transfer and friction in solar air heater duct with W-shaped rib roughness on absorber plate

Artificial roughness in form of ribs is convenient method for enhancement of heat transfer coefficient in solar air heater. This paper presents experimental investigation of heat transfer and friction factor characteristics of rectangular duct roughened with W-shaped ribs on its underside on one broad wall arranged at an inclination with respect to flow direction. Range of parameters for this study has been decided on basis of practical considerations of system and operating conditions. Duct has width to height ratio (W/H) of 8.0, relative roughness pitch (p/e) of 10, relative roughness height (e/D_h) 0.018-0.03375 and angle of attack of flow (α) 30-75°. Air flow rate corresponds to Reynolds number between 2300-14,000. Heat transfer and friction factor results have been compared with those for smooth duct under similar flow and thermal boundary condition to determine thermo-hydraulic performance. Correlations have been developed for heat transfer coefficient and friction factor for roughened duct.     

Nonhomogeneous Heat Conduction Problem and Its Thermal Deflection Due to Internal Heat Generation in a Thin Hollow Circular Disk

This article is concerned with the determination of temperature and thermal deflection in a thin hollow circular disk under an unsteady-state temperature field due to internal heat generation within it. Initially, the disk is kept at an arbitrary temperature F(r, z). For times t > 0 heat is generated within the thin hollow circular disk at a rate of g(r, z, t) Btu/hr ft³, while the boundary surfaces at (r = a), (r = b), (z = 0) and (z = h) are kept at temperatures f ₁(z, t) and f ₂(z, t), f ₃(r, t) and f ₄(r, t), respectively. The governing heat conduction equation has been solved by using a finite Hankel transform and the generalized finite Fourier transform. The results are obtained in series form in terms of Bessel's functions. As a special case, different metallic disks have been considered. The results for temperature change and the thermal deflection have been computed numerically and illustrated graphically.     

A performance evaluation plot of enhanced heat transfer techniques oriented for energy-saving

On the basis of the existing performance evaluation criteria analysis and four assumptions, a performance evaluation plot has been proposed in this paper. This plot takes the ratios of heat transfer enhancement and friction factor increase as its two coordinates. The quadrant of the coordinate where both (Nu_e/Nu₀), (f_e/f₀) are greater than 1.0 can be divided into four regions. In Region 1 heat transfer is actually deteriorated based on identical pumping power, in Region 2 heat transfer is enhanced based on identical pumping power but deteriorated based on identical pressure drop, in Region 3 heat transfer is enhanced based on identical pressure drop but the increase in friction factor is larger than the enhancement of heat transfer at identical flow rate, and in Region 4 heat transfer enhancement ratio is larger than friction factor increase ratio based on identical flow rate. For some techniques which lead to the reduction of both heat transfer rate and friction factor, the proposed plot is still applicable. Different enhanced techniques for the same reference one can be easily and clearly compared for their effectiveness when enhancement study is based on energy-saving. Five practical examples are provided to show the functions of the plot.     

Heat transfer and friction factor correlations for a duct having dimple-shape artificial roughness for solar air heaters

The heat transfer coefficient between the absorber plate and air can be considerably increased by using artificial roughness on the underside of the absorber plate of a solar air heater duct. Under the present work, an experimental study has been carried out to investigate the effect of roughness and operating parameters on heat transfer and friction factor in a roughened duct provided with dimple-shape roughness geometry. The investigation has covered the range of Reynolds number (Re) from 2000 to 12,000, relative roughness height (e/D) from 0.018 to 0.037 and relative pitch (p/e) from 8 to 12. Based on the experimental data, values of Nusselt number (Nu) and friction factor (f_r) have been determined for different values of roughness and operating parameters. In order to determine the enhancement in heat transfer and increment in friction factor values of Nusselt number and friction factor have been compared with those of smooth duct under similar flow conditions. Correlations for Nusselt number and friction factor have been developed for solar air heater duct provided such artificial roughness geometry.     

Air-side thermal hydraulic performance of offset strip fin aluminum heat exchangers

Experimental studies on the air-side heat transfer and pressure drop characteristics for 16 types offset strip fins and flat tube heat exchangers were performed. Parameters including fin space s, fin height h, fin thickness t, fin length l and flow length d, a series of tests were conducted in region of air-side Reynolds number 500–7500, at a constant tube-side water flow rate of 2.5 m³/h. The air-side thermal performance data were analyzed using the effectiveness-NTU method. The heat transfer coefficients and pressure drop data with different fin space s, fin height h, and fin length l were reported in terms of frontal air velocity. The general correlations for Colburn j-factor and Fanning fraction f-factor were derived by regression analysis and F significance test. The correlations for j and f factors can predict 95% and 90% of the experimental data within  ± 10%. And the average deviations of predictive data for the j and f factors are 0.2% and 1.2%, mean deviations are 4.2% and 5.3%.     

Heat transfer and friction behaviors in rectangular channels with varying number of ribbed walls

An experimental study of surface heat transfer and friction characteristics of a fully developed turbulent air flow in a square channel with transverse ribs on one, two, three, and four walls is reported. Tests were performed for Reynolds numbers ranging from 10,000 to 80,000. The pitch-to-rib height ratio, P/e, was kept at 8 and rib-height-to-channel hydraulic diameter ratio, e/D_h was kept at 0.0625. The channel length-to-hydraulic diameter ratio, L/D_h, was 20. The heat transfer coefficient and friction factor results were enhanced with the increase in the number of ribbed walls. The friction roughness function, R(e⁺), was almost constant over the entire range of tests performed and was within comparable limits of the previously published data. The heat transfer roughness function, G(e⁺), increased with roughness Reynolds number and compared well with previous work in this area. Both correlations could be used to predict the friction factor and heat transfer coefficient in a rectangular channel with varying number of ribbed walls. The results of this investigation could be used in various applications of turbulent internal channel flows involving different number of rib roughened walls.     

Heat transfer and friction in solar air heater duct with V-shaped rib roughness on absorber plate

In this work, results of an experimental investigation of the effect of geometrical parameters of V-shaped ribs on heat transfer and fluid flow characteristics of rectangular duct of solar air heater with absorber plate having V-shaped ribs on its underside have been reported. The range of parameters for this study has been decided on the basis of practical considerations of the system and operating conditions. The investigation has covered a Reynolds number (Re) range of 2500-18000, relative roughness height (e/D_h) of 0.02-0.034 and angle of attack of flow (α) of 30-90° for a fixed relative pitch of 10. Results have also been compared with those of smooth duct under similar flow conditions to determine the enhancement in heat transfer coefficient and friction factor. The correlations have been developed for heat transfer coefficient and friction factor for the roughened duct.     

Experimental study of forced and free convective heat transfer in the thermal entry region of horizontal concentric annuli

Forced and free convective heat transfer for thermally developing and thermally fully developed laminar air flow inside horizontal concentric annuli in the thermal entrance length has been experimentally investigated. The experimental setup consists of a stainless steel annulus having a radius ratio of 2 and an inner tube with a heated length of 900 mm subjected to a constant wall heat flux boundary condition and an adiabatic outer annulus. The investigation covers Reynolds number range from 200 to 1000, the Grashof number was ranged from 6.2 × 10⁵ to 1.2 × 10⁷. The entrance sections used were long tube with length of 2520 mm (L/D_h = 63) and short tube with length of 504 mm (L/D_h = 12.6). The surface temperature distribution along the inner tube surface, and the local Nusselt number distribution versus dimensionless axial distance Z_t were presented and discussed. It is inferred that the free convection effects tended to decrease the heat transfer at low Re number while to increase the heat transfer for high Re number. This investigation reveals that the Nusselt number values were considerably greater than the corresponding values for fully developed combined convection over a significant portion of the annulus. The average heat transfer results were correlated in terms of the relevant dimensionless variables with an empirical correlation. The local Nusselt number results were compared with available literature and show similar trend and satisfactory agreement.