Thermal Non-equilibrium Effects Research Articles

Investigation of Magneto-convection in Viscoelastic Fluid Saturated Anisotropic Porous Layer Under Local Thermal Non-equilibrium Condition

The problem of magneto-convection in viscoelastic fluid saturated anisotropic porous layer under local thermal non-equilibrium (LTNE) effect is investigated. Extended Darcy model with time derivative term for viscoelastic fluid of the Oldroyd type with an externally imposed vertical magnetic field is used to model the momentum equation. The entire investigation has been split into two parts: (i) linear stability analysis (ii) weakly non-linear stability analysis. We perform normal mode technique to examine linear stability analysis while truncated representation of Fourier series method is used for weakly non-linear stability analysis. The onset of convection is set in through oscillatory rather than stationary mode due to competition between the processes of thermal, magnetic effect and viscoelasticity. A comparative study between anisotropic and isotropic porous medium is made as a function of Q (Chandrasekhar number), 𝛤 (non dimensional inter phase heat transfer coefficient), 𝜆1 (Relaxation time) and λ2 (Retardation time). Apart from this, Q, 𝛤 and λ2 stabilize the system in oscillatory case while 𝜆1 destabilize the system. Furthermore 𝜉 (mechanical anisotropic parameter), 𝜂s (thermal anisotropic parameter for solid phase), destabilizes the system and 𝜂f (thermal anisotropic parameter for fluid phase) stabilizes the system. The effect of Q, 𝜆1, λ2, 𝛤, 𝜉, 𝜂f and 𝜂s on heat transfer is also examined.

Investigation of Magneto-convection in Viscoelastic Fluid Saturated Anisotropic Porous Layer Under Local Thermal Non-equilibrium Condition

The problem of magneto-convection in viscoelastic fluid saturated anisotropic porous layer under local thermal non-equilibrium (LTNE) effect is investigated. Extended Darcy model with time derivative term for viscoelastic fluid of the Oldroyd type with an externally imposed vertical magnetic field is used to model the momentum equation. The entire investigation has been split into two parts: (i) linear stability analysis (ii) weakly non-linear stability analysis. We perform normal mode technique to examine linear stability analysis while truncated representation of Fourier series method is used for weakly non-linear stability analysis. The onset of convection is set in through oscillatory rather than stationary mode due to competition between the processes of thermal, magnetic effect and viscoelasticity. A comparative study between anisotropic and isotropic porous medium is made as a function of Q (Chandrasekhar number), 𝛤 (non dimensional inter phase heat transfer coefficient), 𝜆1 (Relaxation time) and λ2 (Retardation time). Apart from this, Q, 𝛤 and λ2 stabilize the system in oscillatory case while 𝜆1 destabilize the system. Furthermore 𝜉 (mechanical anisotropic parameter), 𝜂s (thermal anisotropic parameter for solid phase), destabilizes the system and 𝜂f (thermal anisotropic parameter for fluid phase) stabilizes the system. The effect of Q, 𝜆1, λ2, 𝛤, 𝜉, 𝜂f and 𝜂s on heat transfer is also examined.

Numerical investigation of thermochemical non-equilibrium effects in Mach 10 scramjet nozzle

Abstract High-temperature non-equilibrium effects are prominent in scramjet nozzle flows at high Mach numbers. Hence, the thermochemical non-equilibrium gas model incorporating the vibrational relaxation process of molecules in the hydrocarbon-air reaction is developed to numerically simulate the flow of a hydrocarbon fuel scramjet nozzle at Mach 10. Besides, the results computed by the models of the thermally perfect gas, chemically non-equilibrium gas, and thermally non-equilibrium chemically frozen gas are applied for comparative studies. Results indicate that chemical non-equilibrium effects are more significant for the flow-field structure and parameters compared to thermal non-equilibrium effects. Meanwhile, vibrational relaxation and chemical reactions interact in the flow-field. The heat released from the chemical reactions in the flow-field of the thermochemical non-equilibrium gas model makes the thermal non-equilibrium effects weaker compared to the thermally non-equilibrium chemically frozen gas model; the chemical reactions in the thermochemical non-equilibrium gas model are more intense than in the chemically non-equilibrium gas model. Due to the slow relaxation of vibrational energy, the thermal non-equilibrium models predicted nozzle thrust lower than the thermal equilibrium models by approximately 1.11% to 1.33%; when considering the chemical reactions, the chemical non-equilibrium models predicted nozzle thrust higher than the chemical frozen models by approximately 7.30% to 7.54%. Hence, the structural design and performance study of the high Mach numbers scramjet nozzle must consider thermochemical non-equilibrium effects.

Numerical investigation on transpiration cooling with phase change based on multiphysics coupled finite element method

Transpiration cooling with phase change is an efficient active thermal protection method in aerospace. However, conducting numerical simulation of transpiration cooling with phase change is still a challenge, because porous flow, heat transfer and phase change are coupled with each other, which lead to numerical difficulties. In this article, the previous model is modified and the Zero Thickness Area Model (ZTAM) is proposed, which improves the efficiency and convergence significantly. In addition, the local thermal nonequilibrium effect and latent heat can be considered. To verify this ZTAM model, one-dimensional control equations of mass, momentum, and energy transpiration are solved using finite element method. Furthermore, the position of phase change is determined by fixed point iteration numerical algorithm, which shows good convergence. Finally, the influence on cooling effect by heat flux, coolant mass flow rate, porosity and pore diameter is investigated numerically.

An improved continuum model for hypersonic thermal nonequilibrium flow in the near-continuum regime

In this work, the rarefied Couette flow of diatomic gases with thermal nonequilibrium effects is investigated by the direct simulation Monte Carlo (DSMC) method, and a macroscopic computational model is developed to consider the local rarefaction effects for diatomic gases in the near-continuum regime. The nonlinear transport properties of the diatomic gases are studied, indicating that effective viscosity and effective translational thermal conductivity in the shear nonequilibrium state are affected by translational nonequilibrium effects, which obey the same laws for both monatomic and diatomic gases. The transport coefficients of internal energy modes are affected by both translational nonequilibrium and internal energy relaxation, therefore, the effective rotational and vibrational thermal conductivities are related to the effective viscosity through a modified Eucken relation that accounts for internal energy relaxation. Conclusively, effective constitutive relations are newly established as a function of the shear nonequilibrium parameter and the modified Eucken factors for thermal nonequilibrium flows, and these are integrated into the macroscopic two-temperature model. Subsequently, it is assessed in the simulation of hypersonic flows over flat plates and cylinders at various Knudsen numbers. The results show that the surface shear stress and heat flux obtained by the proposed model agree well with the DSMC results, indicating significantly improved performance compared to the conventional Navier–Stokes two-temperature model for hypersonic flows in the near-continuum regime.

Influence of thermochemical non-equilibrium effects on non-uniform entrance scramjet nozzle

The high Mach number scramjet nozzle flow has prominent non-uniform characteristics and high-temperature non-equilibrium effects. Thus, the thermochemical non-equilibrium gas model was developed for simulating flows in the non-uniform and uniform entrance of a Mach 10 hydrocarbon fuel scramjet nozzle. The results show that the non-uniform entrance has a higher non-uniform degree in the flow-field compared to the uniform entrance. Additionally, the expansion degree inside the nozzle is greater and the thermal non-equilibrium effects downstream of the nozzle exit are stronger. The non-uniform entrance condition has a more intense chemical reaction near the nozzle exit but has less impact on the flow parameters. For the nozzle performance, under the influence of the non-uniform entrance, the greater gas expansion degree inside the nozzle results in a lower pressure acting on the upper wall, and then the nozzle thrust decreases by 1.68%. Hence, the structural design and performance optimization of the high Mach number scramjet nozzle must consider entrance non-uniform characteristics and thermochemical non-equilibrium effects.

A modified local thermal non-equilibrium model of transient phase-change transpiration cooling for hypersonic thermal protection

Aiming to efficiently simulate the transient process of transpiration cooling with phase change and reveal the convection mechanism between fluid and porous media particles in a continuum scale, a new two-phase mixture model is developed by incorporating the local thermal non-equilibrium effect. Considering the low-pressure and high overload working conditions of hypersonic flying, the heat and mass transfer induced by capillary and inertial body forces are analyzed for sub-cooled, saturated and super-heated states of water coolant under varying saturation pressures. After the validation of the model, transient simulations for different external factors, including spatially-varied heat flux, coolant mass flux, time-dependent external pressure and aircraft acceleration are conducted. The results show that the vapor blockage patterns at the outlet are highly dependent on the injection mass flux value and the external pressure, and the reduced saturation temperature at low external pressure leads to early boiling off and vapor blockage. The motion of flying has a large influence on the cooling effect, as the inertial force could change the flow pattern of the fluid inside significantly. The comparison of the results from 2-D and 3-D simulations suggests that 3-D simulation shall be conducted for practical application of transpiration cooling, as the thermal protection efficiency may be overestimated by the 2-D results due to the assumption of an infinite width length of the porous plate.

Pathological detonation in H[formula omitted]-Cl[formula omitted] mixtures: Uncertainty quantification and thermal non-equilibrium effects

Pathological detonations are detonations with a propagation velocity higher than the classical Chapman–Jouguet velocity and which depends on the wave structure. Such a behavior has been experimentally observed in low-pressure hydrogen-chlorine mixtures and important discrepancies were reported between the experimental and the theoretical velocities. Using the steady planar detonation model, along with a state-of-the-art chemical mechanism this work aims at investigating two aspects potentially responsible for these discrepancies: (i) the impacts of uncertainties in chemical kinetics mechanisms, and (ii) thermal non-equilibrium effects. The uncertainties in the rate constants of reactions R2: 2Cl+M=Cl2+M and R3: Cl2+H=HCl+Cl are found to be the dominant sources of uncertainty for the steady propagation velocity and the induction length of the pathological detonations. The multi-temperature, thermal non-equilibrium model is found to provide generally higher detonation velocity than the experimental value and the eigenvalue solutions obtained under thermal equilibrium. Nevertheless, for specific values of the initial vibrational temperature of HCl, the results can be closer to the experimental values. This latter aspect provides the motivation for future work that relies on more comprehensive thermal non-equilibrium modeling.

Conjugate local thermal non-equilibrium heat transfer in a porous medium-filled cavity with a rotating cylinder: Analysis and insights

In this work, local thermal non-equilibrium effects are examined as they relate to conjugate natural convection heat transfer in a cavity filled with a porous medium. The investigation also considers the rotation of the central cylinder and the undulation of the cavity’s solid sides. Additionally, the analysis includes the consideration of heat transfer bifurcation occurring at the interface between the solid walls and the porous medium. The equations that govern the behavior of the fluid within the porous region and the heat transfer equations for the porous matrix and solid walls are mathematically expressed as partial differential equations. To solve these equations, the finite element method is employed. The study reports and analyzes the influence of parameters such as Darcy number, Rayleigh number, Prandtl number, and thermal conductivity ratio on flow and thermal fields. Additionally, the study examines the effect of rotational cylindrical motion on fluid flow and heat transfer via its speed rotation. The results indicate that undulated walls and rotational speed significantly impact fluid streamlines and isotherm contours within the porous space, as well as the distribution of isotherms within the solid walls. The findings of this study could have practical implications in the design and optimization of porous media-based systems involving heat transfer.

Analysis of prediction methods for non-equilibrium internal flow condensation heat transfer

Due to the climate crisis, there is a need to improve the performance of energy conversion systems and increase the use of renewable energy sources. In this context, accurate performance prediction methods for heat exchangers, including condensers, are of crucial importance. In the heat transfer process in a condenser including desuperheating and subcooling, both sensible and latent heat transfer may occur simultaneously due to thermal non-equilibrium effects. Liquid condensate may form close to the vapor saturation point of the bulk flow in the desuperheating region, while superheated vapor may penetrate beyond the liquid saturation point far into the two-phase region, and gas bubbles and subcooled mixture may exist in the subcooled region. These are complex phenomena that to a large extent affect the performance of the condenser. This paper presents an analysis of the prediction methods for non-equilibrium condensation heat transfer. First, the heat transfer mechanisms of non-equilibrium condensation are discussed. Next, state-of-the-art prediction methods developed for the target heat transfer processes are analyzed. Moreover, a database containing all data available in the open literature is built to evaluate the predictive performance of the prediction methods. Finally, a new prediction method is proposed for the subcooled condensation based on the identified heat transfer mechanisms. The results suggest that the Jacob correlation has the best predictive performance, followed by the Kondou correlation. The mean absolute percentage errors of both the Jacob and Kondou prediction methods are lower than 15 %, and more than 85 % of the experimental data points are predicted with a deviation within ± 30 %. The new prediction method proposed for the subcooled condensation is in good agreement with the experimental data, with a mean absolute percentage error of 12 %.

Influences of thermochemical non-equilibrium effects on Type III shock/shock interaction at Mach 10

Shock/shock interactions (SSIs) often lead to high thermal loads. To understand the influences of thermochemical non-equilibrium effects on the Type III SSI, four gas models based on the assumption of thermal perfect gas (TPG), thermal equilibrium chemical non-equilibrium gas (TECNG), thermal non-equilibrium chemical frozen gas (TNCFG), and thermochemical non-equilibrium gas (TCNEG) are employed to simulate the Type III SSI at Mach 10. The intersection of incident shock and bow shock is determined by dimensionless intercept of 0.05 and 0.1. It is found that the chemical non-equilibrium effects significantly lift up the impingement position of shear layer by reducing the standoff distance of bow shock. As a result, the peaks of wall pressure and heat flux calculated by TECNG and TCNEG model are higher than TPG and TNCFG model, respectively. Type IIIa SSI occur in the flows calculated by the TECNG and TCNEG model for the case with a dimensionless intercept of 0.1. The peaks of wall pressure and heat flux calculated by TECNG model are both over four times higher than those of TPG model. The thermal non-equilibrium effects slightly increase the standoff distance of bow shock and lower the impingement position of shear layer. In addition, the thermal non-equilibrium reduces the angle to the horizontal direction of shear layer by increasing the specific heat ratio.

Experimental study on the melting performance of phase change materials embedded with different material skeletons

Embedding a skeleton in an organic phase change material changes its heat transfer properties. The melting process of a composite phase change material embedded respectively with nylon, stainless steel, and aluminum alloy skeleton was investigated experimentally, and the effect of the skeleton material on the phase change process was analyzed in detail. The evolution of the phase-change interface was captured using visible-light imaging, and the temperature field distribution was obtained using an infrared camera. The temperature variations inside the composite phase change material were measured using high-precision thermocouples. The local thermal non-equilibrium effect between the skeleton and phase change material was analyzed using the difference between the temperatures of the skeleton surface and paraffin close to the surface. The results showed that the metal skeleton accelerated the migration of the phase change interface, whereas the nylon skeleton retarded the phase change process, in contrast to the pure phase change material. The complete melting time and energy storage rate of the composite phase change material with the aluminum alloy were lesser (53%) and 59.6% higher than those of the pure phase change material, respectively. The local thermal non-equilibrium effects in the melting process of composite phase change material with different material skeletons were significantly different. The larger the thermal conductivity ratio between the skeleton and phase change material, the more significant the thermal non-equilibrium effect. The maximum thermal non-equilibrium effect in the melting process of the composite phase change material with aluminum alloy skeleton was 1.59℃.

Effect of Thermal Nonequilibrium on Captured Mass Flow Rate of Scramjet Inlets

The numerical simulation of a scramjet is often based on the thermal equilibrium model, but the flow inside the inlet and isolator is likely to be in thermal nonequilibrium due to shock-based compression. The objective of this study is to investigate the effect of thermal nonequilibrium on the mass flow rate captured by the scramjet inlet. Numerical simulations based on the thermochemical nonequilibrium model (thermal nonequilibrium) and the chemical nonequilibrium model (thermal equilibrium) were adopted to study the mass flow rate of the HyShot II scramjet with the incoming flow Mach numbers ranging from 6.0 to 8.0. The results show that the maximum difference of the mass flow rate between thermal nonequilibrium and equilibrium reaches 10.7% at with . The primary cause of the mass flow rate difference is the oblique shock wave angle difference between nonequilibrium and equilibrium. The relative magnitudes of oblique shock wave angles and flow parameter ratios across the wave under equilibrium and nonequilibrium are theoretically discussed in an intuitive way. A simplified model for the HyShot II is established to predict the mass flow rate difference between thermal nonequilibrium and equilibrium. The result shows that the expression of captured mass flow rate has a significant amplification effect on the slight difference of wave angles between thermal nonequilibrium and equilibrium, which means that the effect of thermal nonequilibrium cannot be ignored for scramjet in some cases.

High temperature non-equilibrium flow characteristics of impinging shock/flat-plate turbulent boundary layer interaction at Mach 8.42

There are fewer reports on the impinging shock/boundary layer interaction in the high Mach number and high-temperature flow than that in the supersonic flow. High-temperature flow characteristics of the impinging shock/flat-plate turbulent boundary layer interaction (IS/FTBLI) at Mach 8.42 are numerically investigated by solving two-dimensional Reynolds averaged Navier–Stokes equations coupling with the thermal–chemical non-equilibrium model. An impinging shock is formed by the wedge with a 10° deflection angle. The inviscid flow parameters ahead of the cowl of a Mach 12 inlet are selected as the free-stream condition of this study. The primary emphasis of this study lies in understanding the thermal–chemical non-equilibrium effects in the IS/FTBLI. Moreover, the chemical non-equilibrium effects similar to previous reports from others are utilized for the comparative analysis. Our findings reveal that the vibrational or thermal non-equilibrium effects exhibit maximum prominence subsequent to the intersection of the impinging shock with separation shock, as well as in the convergence area of compression waves during the flow reattachment. On the other hand, the chemical non-equilibrium effects predominantly result from oxygen dissociation and atomic nitrogen production within the boundary layer; the chemical reactions are most intense within the separation zone. By comparing with a thermally perfect gas, a reduction in the flow separation is observed in the chemical non-equilibrium effects, but the flow separation is enhanced in the thermal–chemical non-equilibrium effects. The insights gained from our research are expected to contribute to the development of flow control technology in hypersonic IS/FTBLI scenarios and aid in configuring wave structures in the inner compression section of high Mach number scramjet inlets.

Experimental investigation on melting heat transfer of paraffin embedded with periodic structure metal framework

Experiments on the melting of pure paraffin and paraffin embedded with a periodic structure metal framework (PEPSMF) in a rectangular cavity are conducted to investigate the effect of the metal framework on phase change. The test section is a closed cavity composed of plexiglass and heating copper plates that is filled with pure paraffin, or PEPSMF. During experiments, constant wall temperatures (Twall = 50, 55, and 60 °C) are applied to the left sides of the test section. Visible and infrared imaging technologies are used to capture the phase fields and temperature fields. High-precision thermocouples are employed to measure the temperature at different locations inside the PEPSMF and on the surface of the heating wall. In addition, the local thermal non-equilibrium effect between the metal framework and the paraffin is analyzed thoroughly. The results reveal that the evolution of the PEPSMF's mushy zone shows unique features due to the heat conduction of the metal framework. PEPSMF has a reduced melting time and a more uniform temperature distribution than pure paraffin. The significant local thermal non-equilibrium effect is found in PEPSMF, which becomes more prominent closer to the heating wall horizontally. The local thermal non-equilibrium effect shows complex fluctuations, with a maximum value of 1.25 °C.

Numerical Simulation of Flashing Flows in a Converging–Diverging Nozzle with Interfacial Area Transport Equation

Flashing flows of initially sub-cooled water in a converging–diverging nozzle is investigated numerically in the framework of the two-fluid model (TFM). The thermal non-equilibrium effect of phase change is considered by an interfacial heat transfer model, while the pressure jump across the interface is ignored. The bubble size distribution induced by nucleation, bubble growth/shrinkage, coalescence, and breakup is described based on the interfacial area transport equation (IATE) and constant bubble number density model (CBND), respectively. The results are compared with the experimental data. Satisfactory prediction of the axial pressure distribution along the nozzle as well as the flashing inception, is achieved by the TFM-IATE coupling method. It was also found that the vapor production in the diverging section was overpredicted, and the radial gas volume fraction distribution deviated from the experiment. The radial diameter profiles exhibit opposite patterns at the nozzle throat and near the outlet, and similar trends can be observed for the superheated degree. A poly-disperse method is suggested to be introduced to describe the evolution of interfacial area concentration.

Thermochemical non-equilibrium flow characteristics of high Mach number inlet in a wide operation range

The high-temperature non-equilibrium effect is a novel and significant issue in the flows over a high Mach number (above Mach 8) air-breathing vehicle. Thus, this study attempts to investigate the high-temperature non-equilibrium flows of a curved compression two-dimensional scramjet inlet at Mach 8 to 12 utilizing the two-dimensional non-equilibrium RANS calculations. Notably, the thermochemical non-equilibrium gas model can predict the actual high-temperature flows, and the numerical results of the other four thermochemical gas models are only used for comparative analysis. Firstly, the thermochemical non-equilibrium flow fields and work performance of the inlet at Mach 8 to 12 are analyzed. Then, the influences of high-temperature non-equilibrium effects on the starting characteristics of the inlet are investigated. The results reveal that a large separation bubble caused by the cowl shock/lower wall boundary layer interaction appears upstream of the shoulder, at Mach 8. The separation zone size is smaller, and its location is closer to the downstream area while the thermal process changes from frozen to non-equilibrium and then to equilibrium. With the increase of inflow Mach number, the thermochemical non-equilibrium effects in the whole inlet flow field gradually strengthen, so their influences on the overall work performance of the high Mach number inlet are more obvious. The vibrational relaxation or thermal non-equilibrium effects can yield more visible influences on the inlet performance than the chemical non-equilibrium reactions. The inlet in the thermochemical non-equilibrium flow can restart more easily than that in the thermochemical frozen flow. This work should provide a basis for the design and starting ability prediction of the high Mach number inlet in the wide operation range.

Natural Convection in a Newtonian Nanoliquid-Saturated Porous Enclosure with Local Thermal Non-Equilibrium Effect

Buoyancy-driven convective flow and heat transfer characteristics in a Newtonian nanoliquid-saturated porous square enclosure are analyzed numerically using a local thermal non-equilibrium model. An enclosure’s horizontal walls are considered free–free and adiabatic, and the vertical walls are free–free isothermal boundaries. The dimensionless governing equations are solved using a central finite difference scheme with second-degree accuracy, and the results are in satisfactory agreement with the earlier works. The impact of various parameters on streamlines and isotherms is analyzed and depicted graphically. The effect of Darcy number, thermal Rayleigh number, and the ratio of thermal conductivities slow down the liquid flow. The temperature distribution is maximum at sidewalls and diminishes the amount of heat transport. The opposite phenomenon is observed for the solute Rayleigh number and interphase transfer coefficient of liquid-particle phases. For large values of interphase heat transfer coefficients, liquid-solid and liquid-particle are said to be in the local thermal equilibrium phase. The amount of heat transfer increases with an increasing interphase heat transfer coefficient and the ratio of the phases’ thermal conductivities. Results of local thermal equilibrium situation can be obtained as the particular case of the study. The amount of heat transfer is maximum in the local thermal non-equilibrium situation, and enhanced by 0.09% compared with the local thermal equilibrium situation. Heat transport is 0.74% less in the sparsely packed porous medium compared with the low-porosity medium.

Bio-thermal response and thermal damage in biological tissues with non-equilibrium effect and temperature-dependent properties induced by pulse-laser irradiation

Comprehension of thermal behavior underlying the living biological tissues helps successful applications of current heat therapies. The present work is to explore the heat transport properties of irradiated tissue during tis thermal treatment, in which the local thermal non-equilibrium effect as well as temperature-dependent properties arose from complicated anatomical structure, is considered. Based on the generalized dual-phase lag (GDPL) model, a non-linear governing equation of tissue temperature with variable thermal physical properties is proposed. The effective procedure constructed on an explicit finite difference scheme is then developed to predict numerically the thermal response and thermal damage irradiated by a pulse laser as a therapeutic heat source. The parametric study on variable thermal physical parameters including the phase lag times, heat conductivity, specific heat capacity and blood perfusion rate has been performed to evaluate their influence on temperature distribution in time and space. On this basis, the thermal damage with different laser variables such as laser intensity and exposure time are further analyzed.

The effect of thermal non-equilibrium on kinetic nucleation

Context. Nucleation is considered to be the first step in dust and cloud formation in the atmospheres of asymptotic giant branch (AGB) stars, exoplanets, and brown dwarfs. In these environments dust and cloud particles grow to macroscopic sizes when gas phase species condense onto cloud condensation nuclei (CCNs). Understanding the formation processes of CCNs and dust in AGB stars is important because the species that formed in their outflows enrich the interstellar medium. Although widely used, the validity of chemical and thermal equilibrium conditions is debatable in some of these highly dynamical astrophysical environments. Aims. We aim to derive a kinetic nucleation model that includes the effects of thermal non-equilibrium by adopting different temperatures for nucleating species, and to quantify the impact of thermal non-equilibrium on kinetic nucleation. Methods. Forward and backward rate coefficients are derived as part of a collisional kinetic nucleation theory ansatz. The endother-mic backward rates are derived from the law of mass action in thermal non-equilibrium. We consider elastic collisions as thermal equilibrium drivers. Results. For homogeneous TiO2 nucleation and a gas temperature of 1250 K, we find that differences in the kinetic cluster temperatures as small as 20 K increase the formation of larger TiO2 clusters by over an order of magnitude. Conversely, an increase in cluster temperature of around 20 K at gas temperatures of 1000 K can reduce the formation of a larger TiO2 cluster by over an order of magnitude. Conclusions. Our results confirm and quantify the prediction of previous thermal non-equilibrium studies. Small thermal non-equilibria can cause a significant change in the synthesis of larger clusters. Therefore, it is important to use kinetic nucleation models that include thermal non-equilibrium to describe the formation of clusters in environments where even small thermal non-equilibria can be present.