Heat transfer in a pulsed bubbling fluidized bed

Surface-to-bed heat transfer and pressure measurements were carried out in a 0.17 m ID pulsed bubbling fluidized bed with glass bead and silica sand particles having mean diameters ranging from 37 μm to 700 μm to investigate the effects of flow pulsation on heat transfer and bed hydrodynamics. A solenoid valve was used to supply pulsed air to the bed at 1 to 10 Hz. The bed surface was found to oscillate with the frequency of pulsation, the oscillation's amplitude decreasing with frequency. The standard deviation of the bed pressure drop in the pulsed bed was found to be larger than that in the conventional bed due to the acceleration force imposed by pulsation. For both Geldart B and A particles, high frequency pulsation (7, 10 Hz) enhances the heat transfer compared to continuous flow, the enhancement diminishing with superficial gas velocity and particle size. For Geldart B particles, the effect of pulsation on heat transfer ceases around U_o/U_mf = 3.5, whereas 24% improvement in heat transfer coefficient was obtained for 60 μm glass bead particles (Group A) at superficial gas velocities as high as U_o/U_mf = 27. Furthermore, in the fixed bed (U_o/U_mf < 1) for Geldart B particles, 1 Hz pulsation was found to be very effective resulting in two- to three-fold increase in heat transfer coefficient compared to continuous flow at the same superficial gas velocity. The flow pulsation loses its effect on heat transfer with increasing static bed height, i.e., when H_bed/D > 0.85.     

Vertical slug flow in laminar regime in the liquid and turbulent regime in the bubble wake—Comparison with fully turbulent and fully laminar regimes

An experimental and simulation study on free bubbling vertical slug flow in laminar regime in the main liquid and turbulent regime in the near-wake bubble region is reported. A non-intrusive image analysis technique and a previously developed slug flow simulator (SFS) were used. Two aqueous glycerol solutions (0.012-0.013 and 0.022 Pa s) were studied. A single bubble-to-bubble interaction curve was obtained. Strong interaction was found for bubbles flowing less than 3-4D apart, with slight interaction persisting for longer distances. The shape of the interaction curve bridges those for fully turbulent and fully laminar regimes. The experimental average bubble velocity in undisturbed conditions was shown not to follow the correlation-based predictions for laminar regime in the liquid. Alternative fitting coefficients are proposed. An entrance length of 50-80D (or 90-170D) was obtained for normal inlet slug length distributions centred on 2-5D (or 2-6D), for superficial gas and liquid velocities up to 0.40 and 0.30 m/s, respectively. More contrasting inlet slug length distributions were found not to converge within the length of the column (6.5 m). An overall comparison between the three regimes is presented.     

Liquid re-circulation in turbulent vertical pipe flow behind a cylindrical bluff body and a ventilated cavity attached to a sparger

The turbulent flow field (Re=60024) in the wake of a cylindrical bluff body in a 0.105 m internal diameter pipe with an area blockage ratio of 82% in turbulent single-phase flow was studied using laser Doppler velocimetry (LDV). The results for the time-averaged velocity showed a toroidal vortex below the bluff body. The axial location below the bluff body where both the time-averaged radial and axial velocity components were zero (eye of the vortex) was found at approximately 0.72D. The end of the re-circulation region as defined by a stagnation point on the centreline of the pipe was found at an axial location below the bluff body of approximately 1.3D. These two locations did not change when altering the liquid superficial velocity confirming that the geometry (i.e., size) of the toroidal vortex is not dependent on the superficial liquid velocity or the speed of the vortex.Similar measurements using LDV were taken in the wake of a ventilated cavity in a vertical 0.105 m internal diameter pipe, with an area blockage ratio of 80%. The flow beneath the cavity was turbulent two-phase bubbly flow and the liquid-only flow ahead of the cavity was turbulent (Re=45618). The cavity was attached to a (central) sparger, which is a scale-up of the design used by Bacon (1995). The average gas void fraction in the wake of the cavity was 7%. The results for the time-averaged velocity confirmed the formation of a toroidal vortex remarkably similar to the vortex formed below the bluff body. The eye of the vortex and the end of the re-circulation region were found at an axial location below the ventilated cavity of 0.78 and 1.35D, respectively, i.e., almost identical to the results for the bluff body.The LDV results of the cylindrical bluff body and the ventilated cavity were compared with the fully predictive model of the velocity distribution in the vortex proposed by Thorpe et al. (2001) and good agreement was found in both cases. The model also agreed well with the data of van Hout et al. (2002) for a Taylor bubble rising in stagnant liquid in a 0.025 m internal diameter pipe. The CFX simulations of Thorpe et al. (2001) carried out for a 0.050 m internal diameter pipe, agreed well with the experimental data of the cylindrical bluff body, the ventilated cavity and the data obtained by van Hout et al. (2002) when correlating the results in the appropriate dimensionless form. Our analysis showed that the maximum axial re-circulation velocity in the centre of the vortex ring was directly proportional to the mean velocity in the annulus at the base of the cylindrical bluff body, the ventilated cavity or the Taylor bubble. The proportionality constant for all cases was found to be approximately 0.38 confirming the value proposed by Thorpe et al. (2001).     

Solids mixing behavior in a nano-agglomerate fluidized bed

The nano-particles mixing behavior in a nano-agglomerate fluidized bed (NAFB) using R972, a kind of nano-SiO₂ powder, was investigated by the nano-particle coated phosphors tracer method. The axial and radial solids dispersion coefficients in this system were two orders of magnitude lower than those in fluid catalytic cracking (FCC) catalyst systems. The axial solids dispersion coefficient increased with increasing superficial gas velocities, and ranged between 9.1 × 10^− 4 and 2.6 × 10^− 3 m²/s. There was a step increase in the axial solids dispersion coefficient between the particulate fluidization regime and bubbling and turbulent fluidization regimes. As the superficial gas velocity increased, the radial solids dispersion coefficient increased gradually, from 1.2 × 10^− 4 to 4.5 × 10^− 4 m²/s. The much smaller D_a and D_r, compared to regular fluidized systems, is mainly due to the reduced density difference between the fluidized particles and fluidizing medium. To validate this, the solids dispersion coefficients in the NABF were compared with literature values for liquid-solid particulate systems in the particulate fluidization regime and FCC systems in the bubbling and turbulent fluidization regimes. The density difference between the fluidized particles and fluidizing medium and kinetic viscosity of the fluidizing medium, and other hydrodynamic factors like the superficial velocity of the fluidizing medium and the average diameters of the fluidized particles, were the key factors in the solids mixing in the fluidized beds. Empirical correlations are given to describe the results.     

Liquid phase axial mixing in bubble columns operated at high pressures

Liquid phase axial mixing was measured in a 100 mm i.d. bubble column operated in the pressure range of 0.1-0.5 MPa. Water, ethanol and 1-butanol were used as the liquid phase and nitrogen as the gas phase. The temperature and superficial gas velocity were varied in the range of 298-323 K and 0.01-0.21 m/s, respectively. The axial dispersion coefficient increased with an increase in the gas density due to pressure. The temperature had surprisingly a small effect. A CFD model was developed for the prediction of flow pattern in terms of mean velocity and eddy diffusivity profiles. The model was further extended for the prediction of residence time distribution and hence the axial dispersion coefficient (D_L). The predictions of axial dispersion coefficient agree favorably with all the experimental data collected in this work as well as published in the literature. The model was extended for different gas-liquid systems. The predicted values of axial dispersion coefficient were found to agree very well with all the experimental data.     

Local gas–liquid slip velocity distribution in bubble columns and its relationship with heat transfer

The knowledge of the local gas–liquid slip velocity distribution can offer a better understanding for the complex transport phenomena in bubble columns. In this work, CFD–PBM simulations are carried out to investigate the effect of superficial gas velocities, axial positions, and scale of bubble columns on the time-averaged radial profiles of gas–liquid slip velocities. Furthermore, the relationship between local slip velocities and local heat transfer coefficients in pilot-scale bubble columns at superficial gas velocities of 0.05 m/s, 0.20 m/s, and 0.35 m/s is studied. The results indicate that the slip velocities decrease with the increase of r/R (r-radial position, R-column radius), while increase with increasing superficial gas velocities in general. In the fully developed region, the axial positions have small impact on the local slip velocities. A strong linear relation between heat transfer coefficients and slip velocities in the fully flow developed region is observed.     

Dimensional similitude for scale-up of hydrodynamics in a gas-liquid-(solid) EL-ALR

This study tests the scaling approach for gas-liquid-(solid) external loop airlift reactor (EL-ALR) hydrodynamics based upon geometric and dynamic similitude with a limited number (6) of dimensionless groups. A sixth dimensionless group for sparger characteristic (Scp) is developed. Scp is a convenient parameter to characterize fluid flow performance of EL-ALR and a large cold-flow 0.86 m diameter column. To our knowledge, there is more ambiguity concerning its definition for EL-ALR and a large cold-flow 0.86 m diameter column especially when different sparger structures are used. In this study, reliability of the modified Reynolds and Scp are proposed for such an EL-ALR and a large cold-flow 0.86 m diameter column used different sparger structures. The Scp is based on the pitch and angle between hole normal vector and horizontal line as the characteristic parameters. Experiments were carried out in two systems in which all six dimensionless groups were matched: a 55 wt% aqueous glycerol solution with ceramic catalyst particles in an industrially operated large cold-flow 0.86 m diameter column (system 1) and silicone oil with cylindrical aluminum particles in Taishan Scholar Lab (TSL) EL-ALR with a riser (0.47 m diameter and 2.5 m height) and two downcomers (0.08 m diameter and 2.5 m height) (system 2) with air as the gas in both cases. The micro-conductivity probe and the 3D Laser Doppler Anemometer (LDA) techniques were, respectively, implemented to measure local gas holdup (α_Gr) and Peclet number (Pe) in the riser over a wide range of operation conditions. Although Peclet number was slightly different for the two systems, trends were similar. Gas holdups were always slightly higher for system 1. The dimensionless transition velocities from dispersed to coalesced flow were similar. Differences between the two systems are significant, but generally less than 15%, so the dimensionless similitude approach gives a reasonable basis for estimating global hydrodynamic parameters under the present operating conditions. The differences between the two systems are attributed to the complex coalescence behavior of liquid mixtures and the different sparger structures chosen, suggesting that additional dimensionless groups are needed to fully characterize the local dynamic bed behavior. This agreement proves that the proposed modified dimensionless numbers can be well adapted for engineering purposes and used to compare the flow performance between the two systems.     

A simple energy balance to determine heat transfer coefficients from low temperature measurements in a fluidised bed

A bench-scale fluidised bed (105 × 200 mm) was set-up for studying bed-to-gas and wall-to-bed heat transfer. Low temperature (17-200 °C) experiments were conducted at steady state avoiding excessive instrumentation and time. Compressed dry air at ambient temperature entered the bed through a distributor of a 200-mesh brass sieve and fluidised the single charge of alumina particles with a mean diameter of approximately 250 μm. The superficial gas velocity ranged from 0.085 to 0.412 m s^− 1. A simple model was developed based on steady state energy balances, i.e. equating the electrical power input separately to the rate of heat transfer from the heater walls to the bed and from the bed to the gas. The bed-to-gas heat transfer coefficient was calculated from the model equations. Inserting this value into the relevant heat transfer equations then extracted the wall-to-bed and bed-to-gas heat transfer coefficients. The agreement between the experimental and predicted values of temperatures validated the model. The latter may be successfully used to design fluidised beds for e.g. drying or combustion.     

Local hydrodynamics and heat transfer in fluidized beds of different diameter

Heat transfer coefficients were measured in fluidization columns of 0.29 m and 1.56 m ID at fixed distance above the distributor, using an identical vertical heater, the same alumina particles and geometrically scaled bubble-cap distributors. The magnitude of the maximum heat transfer coefficients was found to be unaffected by the column diameter, but occurred at higher superficial velocities in the larger column. When the local flow structure near the heater corresponded to the turbulent flow regime of fluidization, the local heat transfer coefficients were independent of radial position in both columns.     

Mass transfer in vertical liquid-solids flow of coarse particles

Wall-to-bed mass transfer in the hydraulic transport of spherical glass particles was studied. The experiments were performed by transporting spherical glass particles 1.20, 1.94 and 2.98 mm in diameter with water in a 25.4 mm I.D. tube. The mass transfer coefficients were determined by following rate of dissolution of a segment of the transport tube prepared from benzoic acid.In the runs in hydraulic transport, the Reynolds number of the tube varied between 1826 and 27597. The loading ratio (G_p/G_f) was between 0.026 and 0.474, and the fluid superficial velocity was between 0.267 · U_t and 4.904 · U_t, where U_t represents the single particle terminal velocity. For these ratios, the voidage ranged from 0.7123 to 0.9228.Also, wall-to-bed mass transfer in the single phase flow regime was studied. In the runs without particles, the Reynolds number of the tube varied between 122 and 39132. The data for the mass transfer factor (j_D) in single phase flow are correlated for turbulent flow regime, using the Chilton-Colburn's type equations, j_D = f(Re). Those investigations were conducted in aim to compare with results for wall-to-bed mass transfer in hydraulic transport.The data for wall-to-bed mass transfer (j_D) in hydraulic transport of spherical particles were correlated by treating the flowing fluid-particle suspension as a pseudofluid, by introducing a modified suspension-wall friction coefficient (f_w) and a modified Reynolds number (Re_m). The data for wall-to-bed mass transfer in the hydraulic transport of particles show that an analogy between mass and momentum transfer exists.     

Effect of annular fins on heat transfer of a horizontal immersed tube in bubbling fluidized beds

Experiments were conducted in a bubbling air-fluidized bed to investigate the effect of annular fins of constant thickness on heat transfer. Steady state time averaged local heat transfer coefficient measurements were made by the local thermal simulation technique in a cold bubbling fluidized bed (90 mm ID, 260 mm tall) with horizontally immersed tube initially with no fin and then with three fixed annular fins of constant thickness. Silica sand of mean particle diameter 307 μm and 200 μm were used as the bed materials. The superficial velocity of air was from minimum fluidization conditions, u_mf, to approximately 3 × u_mf. The results indicate that, although the heat transfer coefficient falls with the use of fins, the total heat transfer rises as a result of the greater surface area. Increasing the particle diameter reduces the heat transfer coefficient not only for unfinned horizontal tube but also for annular finned horizontal tube at the same conditions of fluidized bed. Based on the experimental data, correlations are proposed for predicting heat transfer coefficient from fluidized bed to horizontally immersed tubes with and without fins.     

Oxygen transfer and hydrodynamics in three-phase inverse fluidized beds

Experiments were performed at ambient temperature and pressure in a 152 mm inner diameter column with air, tap water or 0.5% wt. aqueous ethanol solution, and polypropylene particles. An increase in liquid velocity and solids loading, and the presence of a surfactant reduces the gas velocity required to reach full bed expansion, which is delimited by the gas sparger. With an increase in gas velocity, solids holdups remain constant after full bed expansion, liquid holdups increase to a maximum and then decrease and gas holdups continuously increase. The addition of ethanol greatly increases the gas holdups leading to significant reductions in liquid holdups. The volumetric gas-liquid mass transfer coefficient, k_La, increases with increasing gas velocity but does not change significantly with liquid velocity. There are complex interaction effects between solids loading and surfactants as the values of k_La in the aqueous ethanol solution were greater than those in water when particles were present and smaller without particles. k_La data in water were found to be proportional to gas holdup whereas for the ethanol solution this proportionality constant first decreased with increasing gas velocity to eventually stabilize at a value smaller than for water.     

Particle motion in the CFB riser with special emphasis on PEPT-imaging of the bottom section

The riser is the key-part of a circulating fluidized bed (CFB) and its hydrodynamics are determined mainly by the combined operating superficial gas velocity, U, and solids circulation flux, G. The bottom part of the riser contributes to the total pressure drop of the riser and affects the solids residence time in the riser, due to the possible existence of a dense bed and to the presence of an acceleration zone. Positron Emission Particle Tracking (PEPT) is applied to study these phenomena by measuring the real-time particle motion in a riser of 0.09 m diameter, defining (i) the extent of the acceleration zone, including acceleration length and acceleration time; (ii) the occurrence of a bubbling/turbulent bed under specific conditions of U and G; (iii) the establishment of a fully developed flow immediately after the acceleration zone; (iv) the occurrence of core-annulus flow under specific combinations of U and G; and (v) the disappearance of the intermediate core-annulus region at high values of U and G, where riser hydrodynamics will be either dilute or dense solid up-flow.The particle upflow velocity, U_pf, after acceleration was measured and compared with the situation of dilute transport. When the solids circulation flux increases, the dilute transport mode no longer prevails, and U_pf should be calculated using an appropriate slip factor, itself a combined factor of U and G. The acceleration length and time are nearly constant, at an approximate average of 0.26 m and 0.21 s respectively, independent of U and G. The acceleration length can be modelled fairly accurately, using a C_D-factor of approximately 3.2, which is about half the value predicted by empirical equations established for dilute transport.Dense Suspension Upflow (DSU) is achieved when G exceeds ~ 130 kg m⁻ ² s^− 1.     

Simulations of chemical absorption in pilot-scale and industrial-scale packed columns by computational mass transfer

A complex computational mass transfer model (CMT) is proposed for modeling the chemical absorption process with heat effect in packed columns. The feature of the proposed model is able to predict the concentration and temperature as well as the velocity distributions at once along the column without assuming the turbulent Schmidt number, or using the experimentally measured turbulent mass transfer diffusivity. The present model consists of the differential mass transfer equation with its auxiliary closing equations and the accompanied formulations of computational fluid dynamics (CFD) and computational heat transfer (CHT). In the mathematical expression for the accompanied CFD and CHT, the conventional methods of k-ε and are used for closing the momentum and heat transfer equations. While for the mass transfer equation, the recently developed concentration variance and its dissipation rate ε_c equations (Liu, 2003) are adopted for its closure. To test the validity of the present model, simulations were made for a pilot-scale randomly packed chemical absorption column of 0.1 m ID and 7 m high, packed with 1/2^″ ceramic Berl saddles for CO₂ removal from gas mixture by aqueous monoethanolamine (MEA) solutions (Tontiwachwuthikul et al., 1992 ) and an industrial-scale randomly packed chemical absorption column of 1.9 m ID and 26.6 m high, packed with 2^″ stainless steel Pall rings for CO₂ removal from natural gas by aqueous MEA solutions (Pintola et al., 1993). The simulated results were compared with the published experimental data and satisfactory agreement was found between them in both concentration and temperature distributions. Furthermore, the result of computation also reveals that the turbulent mass transfer diffusivity D_tvaries along axial and radial directions. Thus the common viewpoint of assuming constant D_t throughout the whole column is questionable, even for the small size packed column. Finally, the analogy between mass transfer and heat transfer in chemical absorption is demonstrated by the similarity of their diffusivity profiles.     

An experimental study of flow and heat transfer of supercritical carbon dioxide in multi-port mini channels under cooling conditions

This paper presents the fluid flow and heat transfer characteristics of supercritical CO₂ in a horizontal multi-port extruded aluminum test section consisting of 10 circular channels with an inner diameter of 1.31 mm. Both local and average pressure drop and heat transfer coefficients were measured as CO₂ was cooled in the multi-port circular channels with pressures ranging from 7.4 to 8.5 MPa, inlet fluid temperatures ranging from 22 to , and mass velocity ranging from 113.7 to 418.6 kg/m² s. The results indicate that the operating pressure, the mass velocity and the temperature of CO₂ had significant effects on fluid flow and heat transfer characteristics. The pressure drop and the average heat transfer coefficient increased greatly with increasing the average temperatures of CO₂ in the near-critical region; the average heat transfer coefficient attained a peak value near the corresponding pseudocritical temperature; and the maximum heat transfer coefficient decreased as the pressure increased. Both the pressure drop and the heat transfer coefficient increased with the mass velocity, but decreased with the operating pressure. The measured average heat transfer coefficients were compared with the experimental data reported in the literatures and a large discrepancy was observed. Based on the experimental data collected in the present work, a new correlation was developed for forced convection of supercritical CO₂ in horizontal multi-port mini channels under cooling conditions.     

Dependence of particle fluctuation velocity on gas flow, and particle diameter in gas fluidized beds for monodispersed spheres in the Geldart B and A fluidization regimes

In this paper we present new experimental data on the steady-state, mean squared, fluctuation velocity, or granular temperature, of Geldart B polymer, glass, nickel, and stainless steel monodispersed spheres averaged over the wall of a gas fluidized bed, as a function of gas flow and sphere diameter. The granular temperature is obtained by Acoustic Shot Noise technology—namely power spectral analysis of the steady state vibrational energy of the wall excited by random sphere impact, and calibrated by hammer excitation over the wall. The new data extends to polymer and metallic spheres the experimental discovery of a 1996 paper of Cody et al. that the fluctuation velocity of Geldart B glass spheres when scaled to the gas superficial velocity, U_s, is inversely proportional to sphere diameter, directly proportional to a fundamental length scale, D_o^B, and is a universal function of U = (U_s / U_mf). We also demonstrate that the new data is consistent with the diameter dependence of the fluctuation velocity that can be derived from both the 1997 paper of Menon and Durian, who measured random sphere motion near the wall through the spectroscopy of scattered laser light, and the 1992 paper of Rahman and Campbell, who measured the average granular pressure of random sphere impact on a porous steel membrane. While the inverse scaling of the fluctuation velocity with sphere diameter, and the existence of a fundamental length scale for gas fluidization, D_o^B, had not been a feature of any published fundamental model, or computer simulation, of the steady state granular temperature of spheres in gas fluidized beds, we show that it is a feature of two recent dense kinetic fluidization models published in 1999, by Buyevich and Kapbasov, and Koch and Sangani. Both theories implicitly define a fundamental length scale for the fluctuation velocity, D^? = (μ_f² / ρ_p²g)^1 / 3, where ρ_p is the sphere density, μ_f is the gas viscosity, and g is the laboratory gravitational field. The new data for polymer, glass, nickel and stainless steel spheres presented in this paper, defines D_o^B = (56 ± 2)D^?. We use the Anderson-Jackson stability model to show that the length scale D_o^B, also defines a stability length scale, such that for D < D_o^B(D > D_o^B), the uniform dense phase of the fluidized bed is stable (unstable), against one dimensional, first order fluctuations in sphere concentration. The length scale, D_o^B is thus the theoretical equivalent to the empirical scaling length introduced by Geldart, D_B/A, to distinguish spheres (D > D_B/A) that bubble at fluidization, from spheres (D < D_B/A) that fluidize before bubbling. Finally, we present new experimental data, on the remarkable changes in the granular temperature, bed expansion, and bed collapse time, between Geldart B and Geldart A monodispersed glass spheres, and compare that data to granular temperature, and bed expansion, for Geldart A rough, non-spherical, log-normal dispersed diameter catalytic particles.     

Systematic mesh development for 3D CFD simulation of fixed beds: Single sphere study

To develop and validate meshes for computational fluid dynamics (CFD) simulations of transport in fixed beds, a single particle is often used as a test case. We present results for drag coefficient (C_D) and heat transfer Nusselt number (Nu) for flow past a sphere, focusing on high flow rates typical of industrial steam reformers (400 < Re < 20,000). Over this range, good predictions of C_D were obtained using large eddy simulation (LES) to capture vortex shedding and wake dynamics, with a mesh refined downstream from the sphere. The small time-steps and high cell count required make this too expensive for fixed beds. Nu can be accurately calculated using a Reynolds-averaged Navier-Stokes (RANS) method with shear-stress transport (SST) k-ω closure provided the mesh at the particle surface is fine enough and covers most of the boundary layer. Single sphere simulations of heat transfer are more useful for fixed bed mesh development than drag coefficient calculations.     

THERMAL DISPERSION AND HEAT TRANSFER IN NONISOTHERMAL BUBBLE COLUMNS†

Local axial and radial temperatures were measured at steady-state conditions in a 0.078-m-I.D. bubble column heat exchanger. Nitrogen and water superficial velocity ranges were 0-0.6 m/s and 0-0.02 m/s, respectively. Average column pressures were 3.0, 5.1, and 7.1 atm. The axial temperature profile varied significantly with all conditions encountered. Radial temperature profiles were found to be nearly constant, indicating very good radial mixing.

An axial thermal dispersion heat transfer model, capable of representing nonisothermal systems, was employed to characterize the measured bubble column temperature profiles. Thermal dispersion was apparent from large temperature changes in the entrance of the bubble column. Heat transfer coefficients depended on the gas and liquid flow rates. However, the thermal dispersion coefficients depended on linear gas velocity and were a weak function of liquid flow rates. The thermal dispersion coefficients obtained in this study were found to be consistent with other investigations. In addition, they were compared to the mass dispersion coefficients obtained by other studies and found to be in good agreement     

Thermal inefficiency model for determination of the bed-to-gas heat transfer coefficients with effectiveness factor in a fluidised bed

Process operations often involve the physical interaction of a gas and a solid phase. Fluidised bed heat transfer can be characterised by limited space–time (τ) on the basis of particle volume in the bed. As aimed in this study, a thermal inefficiency model (TIM) was developed using a pseudo-steady-state heat balance, i.e., equating the electrical power input to the rate of heat transfers from the bed to the gas. A bench-scale fluidised bed (105 × 200 mm) was operated for obtaining the gas temperature profiles. Temperature data were used for extracting the bed-to-gas heat transfer coefficients (h_BG) with effectiveness factors (η) from the TIM. Fluidised bed experiments at low temperature range (290–473 K) were conducted avoiding excessive instrumentation and time. Compressed dry air entered the bed through a distributor of a 200-mesh brass sieve and fluidised the single charge of alumina particles (1.3 kg) with a mean diameter approximately 250 μm. The superficial gas velocity was changed from 0.085 to 0.469 m s^− 1. The bed-to-gas heat transfer coefficients (h_BG0×η₀) at initial bed hight and thermal inefficiency constants (k_I) were calculated from the intercept and slope of the linear form of the TIM, respectively. The agreement between the experimental and predicted values of gas temperatures confirmed by the TIM. The latter may be successfully used to design fluidised beds for, e.g., drying or combustion.