Dimensionless Mass Research Articles

Mass transfer from a sheared spherical rigid capsule

Solute mass transfer from a spherical fluid-filled rigid capsule subjected to shear flow is studied numerically, while considering unsteady, continuous, and nonuniform boundary conditions on its surface. Here, the capsule acts as a reservoir with its initially encapsulated solute concentration decaying over time. This scenario differs from the classical case study of either constant concentration or constant mass flux at the surface of the particle. The flow and the concentration field are computed using fully three-dimensional lattice Boltzmann simulations, where the fluid-structure two-way coupling is achieved by the immersed boundary method. The effects of the flow and the boundary conditions on mass transfer efficacy are quantified by the Sherwood number (the dimensionless mass transfer coefficient), which is found to increase due to the combined effects of forced convection and the rotation of the capsule. Having continuity of both the concentration and the mass flux on the capsule significantly decreases the Sherwood number as compared to the case with constant and uniform boundary condition. All the obtained results can be applied to heat transfer in the case of cooling an initially hot spherical particle, for which the concentration must be replaced by the temperature and the Sherwood number by the Nusselt number.

A solution for the quasi-one-dimensional linearised Euler equations with heat transfer

The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three variables, namely the dimensionless mass, stagnation temperature and entropy fluctuations, which are invariants of the system at zero frequency and with no heat transfer. The resulting first-order system of differential equations is then solved using the Magnus expansion method, where the perturbation parameters are the normalised frequency and the volumetric heat transfer. In this work, a measure of the flow non-isentropicity (in this case the steady heat transfer) is used for the first time as an expansion parameter. The solution method was applied to a converging–diverging nozzle with constant heat transfer for both subcritical and supercritical flow cases, showing good agreement with numerical predictions. It was observed that the acoustic and entropy transfer functions of the nozzle strongly depend on the frequency and heat transfer.

Parametric simulation of micropolar fluid with thermal radiation across a porous stretching surface

The energy transmission through micropolar fluid have a broad range implementation in the field of electronics, textiles, spacecraft, power generation and nuclear power plants. Thermal radiation's influence on an incompressible thermo-convective flow of micropolar fluid across a permeable extensible sheet with energy and mass transition is reported in the present study. The governing equations consist of Navier–Stokes equation, micro rotation, temperature and concentration equations have been modeled in the form of the system of Partial Differential Equations. The system of basic equations is reduced into a nonlinear system of coupled ODE's by using a similarity framework. The numerical solution of the problem has been obtained via PCM (Parametric Continuation Method). The findings are compared to a MATLAB built-in package called bvp4c to ensure that the scheme is valid. It has been perceived that both the results are in best agreement with each other. The effects of associated parameters on the dimensionless velocity, micro-rotation, energy and mass profiles are discussed and depicted graphically. It has been detected that the permeability parameter gives rise in micro-rotation profile.

Simulation of the pulsed outflow of air and fine powder mixture, partially filling the discharge channel

The paper studies the regularities of the pulsed outflow of air and fine powder mixture, which partially fills the ejection cylindrical channel, in both one-dimensional and two-dimensional formulations. The dynamics of a gas-dispersed medium are described in the framework of the Eulerian continuum approach with different velocities and temperatures of gas and powder particles. Analytical self-similar solutions are constructed in the equilibrium approximation. For the numerical solution of the problem, a hybrid large-particle method of the second order of accuracy in space and time is used. Comparison of exact self-similar and numerical solutions confirmed the reliability of the method. The outflow of the mixture of high-pressure gas and powder particles has a pronounced wave character, which is associated with the decomposition of the initial discontinuity, the movement, and refraction of waves at the interface of media inside the channel, as well as the reflection of waves from its bottom. The characteristic time intervals of the wave process and the corresponding distributions of gas-dynamics quantities are established. Depending on the generalized self-similar variable, the pressure, density, and velocity of the mixture are monotonic functions, and the profile of the specific (per unit cross-section) mass flow has a maximum in the critical section. Dimensionless parameters and specific mass flow of a two-phase medium in the outlet section of the discharge channel are determined. In the case of a channel limited by the size of the high-pressure chamber, a two-dimensional physical picture of the formation and evolution of a gas-dispersed mixture was studied. At the initial stage of the outflow, an “anomalous” grouping of powder particles is observed with the formation of a shock-wave structure in the subsonic mode of the carrier gas flow. After the powder layer leaves the channel, the pure gas flowing out of it accelerates to supersonic speed and an intense vortex motion develops in the wake of the gas-dispersed jet. The calculated values of the parameters allow us to justify the achievable level of technical characteristics (speed, mass flow rate) of the flow of the working gas-dispersed medium of pulsed powder devices. The proposed methodology and the results obtained are the basis for making rational decisions at the early stages of design and preparation of initial data on design and operating parameters for testing prototypes of pulsed powder technical devices.

Sizing the Thermal Energy Storage Device Utilizing Phase Change Material (PCM) for Low-Temperature Organic Rankine Cycle Systems Employing Selected Hydrocarbons

Thermal energy storage (TES) looks to be a promising technology for recovering waste heat or other intermittent heat sources, especially if it is coupled with the organic Rankine cycle (ORC) system. This system may use a variety of heat storage materials, including solids, liquids, and phase change materials (PCM). This article discusses the use of PCM as a thermal energy storage material in TES systems coupled with ORC systems. Other TES configurations may be used in ORC; however, in this article, the TES is solely used in heat exchangers, i.e., evaporator and liquid heater. The goal of this research is to establish a dimensionless storage mass parameter for sizing TES-evaporator (TES-EVA) or TES-liquid heater (TES-LH) devices for ORCs. Furthermore, the model of this system was created in the MATLAB environment using the chosen hydrocarbons as ORC working fluids. The obtained modelling results provide a novel point of view that scientists and engineers may employ while developing the TES-EVA or TES-LH utilizing PCM for ORC.

External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

This work systematically simulates the external mass transfer from/to a spherical drop and solid particle suspended in a nonlinear uniaxial extensional creeping flow. The mass transfer problem is governed by three dimensionless parameters: the viscosity ratio ( λ ), the Peclet number ( Pe ), and the nonlinear intensity of the flow ( E ). The existing mass transfer theory, valid for very large Peclet numbers only, is expanded, by numerical simulations, to include a much larger range of Peclet numbers (1 ≤ Pe ≤ 10 5 ). The simulation results show that the dimensionless mass transfer rate, expressed as the Sherwood number ( Sh ), agrees well with the theoretical results at the convection-dominated regime ( P e > 10 3 ). Only when E > 5/4, the simulated Sh for a solid sphere in the nonlinear uniaxial extensional flow is larger than theoretical results because the theory neglects the effect of the vortex formed outside the particle on the rate of mass transfer. Empirical correlations are proposed to predict the influence of the dimensionless governing parameters ( λ , Pe , E ) on the Sherwood number ( Sh ). The maximum deviations of all empirical correlations are less than 15% when compared to the numerical simulated results.

Experimental Investigation and Mathematical Modeling of Microwave Thin Layer Drying Behaviour of Apricot, Kiwi and Mint Leaves

In this study, experimental investigation and mathematical modeling of microwave drying behavior of some vegetables and fruits such as apricot, kiwi and mint leaves are performed. In this regard, a microwave oven is used for experiments and 23 thin layer drying curve equation in the literature are evaluated for mathematical modeling of drying behavior of those products. For this purpose, mass loss and drying time are measured depending on six different microwave powers (100W, 300W, 450W, 600W, 700W, and 800W) and dimensionless mass ratio, moisture content, drying rate and mass shrinkage ratio are estimated and variation of colors are observed. For comparison of equations obtained from modeling, 14 different evaluation criteria are used and the best five drying model are determined. Consequently, it is determined that the most suitable microwave powers were 300W, 600W, 700W and the best drying models are Modified Page, Midilli-Kucuk and Midilli-Kucuk for apricot, kiwi and mint leaves, respectively. Also, it is observed that when the microwave power increases, drying time significantly decreases. However, it is seen that microwave drying method is suitable for drying of kiwi and mint leaves but not suitable for drying of apricot especially at high microwave powers.

Analysis of geometric and non-geometric parameters in a Coanda device for marine applications

This numerical study comprises the geometric evaluation of turbulent, steady-state, two-dimensional, and incompressible flows over the Coanda effect-based H.O.M.E.R. (High-Speed Orienting Momentum with Enhanced Reversibility) nozzle. The main purpose is to evaluate the influence of the central septum insertion (P) and change in dimensionless mass flow rate between two inlets (m*) over the deflection angle of the mixed jet (α), velocity fields (V), and thrust forces per unit length (F) at the nozzle exit. The time-averaged conservation equations of mass and momentum have been solved using the Finite Volume Method for all simulations. Turbulence closure is solved using RANS (Reynolds-Averaged Navier–Stokes) and standard k-ε modeling. Results show the septum insertion associated with the mass flow rate difference as possible important parameters for controlling the exit jets and forces generated in the device. Moreover, higher magnitudes of m* associated with a high intruded septum (P = 11 mm) in the device led to the highest magnitudes of forces in the y-direction, while intermediate configurations of m* and P are best for maximizing forces in the x-direction. For the present conditions, the forces generated in the y-direction are almost four times higher than that generated in the x-direction, indicating that this device can be suitable for maneuverability purposes.

Experimental and theoretical study of vapor/air mixture condensation inside an inclined blind-end pipe in natural convection with considering fog formation

This study investigated the vapor condensation characteristics in an inclined pipe under natural convection conditions experimentally and numerically. The inclined blind-end concentric pipe had an inner diameter of 134 mm and a length of 680 mm, which is cooled by cooling water. The experimental pressure range was 0.2–0.6 MPa, and the dimensionless mass number range was 0.44 to 202. The fog formation phenomenon was observed in the experiment. An empirical correlation with a broad range of dimensionless mass numbers was developed based on the experimental results to predict the heat transfer coefficient (HTC). When the air mass fraction was large and the HTC was low, the effect of fog formation on the HTC had to be considered. In the numerical simulation, this study aimed to develop an HTC prediction model with broader applicability. Based on the diffusion boundary layer theory, this study improved Peterson's model by adding fog effect and wave effect. The model showed high adaptability to this experiment and other experiments in the natural convection condensation database. The improved model performed significantly better, with 96% of the data falling within an error zone of 30%. The wide range of dimensionless mass number test data might complement the natural convection condensation experimental database.

Diophantine approximation as Cosmic Censor for Kerr\u2013AdS black holes

The purpose of this paper is to show an unexpected connection between Diophantine approximation and the behavior of waves on black hole interiors with negative cosmological constant Lambda <0 and explore the consequences of this for the Strong Cosmic Censorship conjecture in general relativity. We study linear scalar perturbations psi of Kerr–AdS solving Box _gpsi -frac{2}{3}Lambda psi =0 with reflecting boundary conditions imposed at infinity. Understanding the behavior of psi at the Cauchy horizon corresponds to a linear analog of the problem of Strong Cosmic Censorship. Our main result shows that if the dimensionless black hole parameters mass {mathfrak {m}} = M sqrt{-Lambda } and angular momentum {mathfrak {a}} = a sqrt{-Lambda } satisfy a certain non-Diophantine condition, then perturbations psi arising from generic smooth initial data blow up |psi |rightarrow +infty at the Cauchy horizon. The proof crucially relies on a novel resonance phenomenon between stable trapping on the black hole exterior and the poles of the interior scattering operator that gives rise to a small divisors problem. Our result is in stark contrast to the result on Reissner–Nordström–AdS (Kehle in Commun Math Phys 376(1):145–200, 2020) as well as to previous work on the analogous problem for Lambda ge 0—in both cases such linear scalar perturbations were shown to remain bounded. As a result of the non-Diophantine condition, the set of parameters {mathfrak {m}}, {mathfrak {a}} for which we show blow-up forms a Baire-generic but Lebesgue-exceptional subset of all parameters below the Hawking–Reall bound. On the other hand, we conjecture that for a set of parameters {mathfrak {m}}, {mathfrak {a}} which is Baire-exceptional but Lebesgue-generic, all linear scalar perturbations remain bounded at the Cauchy horizon |psi |le C. This suggests that the validity of the C^0-formulation of Strong Cosmic Censorship for Lambda <0 may change in a spectacular way according to the notion of genericity imposed.

Amidation Reaction System: Kinetic Studies and Improvement by Product Removal.

The amidation reaction to produce fatty acid diethanolamide is an important unit process to produce surfactants from renewable sources rather than from petroleum sources. Amidation is a liquid-phase reaction between diethanolamine with a fatty acid methyl ester. Since the reaction is reversible, the conversion is limited by equilibrium, the side product being methanol, which is volatile. Hence, mass transfer effects need to be considered in the interpretation of kinetic data. Further, the elimination of methanol can help to shift the reaction forward. Thus, the process has the potential for process intensification. This paper provides a batch reactor model to interpret the simulation data and includes mass transfer effects analyzed using a dimensionless mass transfer parameter (αlg). Using values of this parameter greater than 4 leads to an equilibrium model where the methanol partial pressure in the bulk gas approaches that at the interface. Using this model, the kinetic and equilibrium parameters for the amidation reaction were determined using experimental data in the first part of this study. The experimental data for fitting the parameters are obtained from a closed batch reactor operated with an initial pressure of 1 bar and a temperature range of 70–80 °C. The second part of the paper examines two process-intensification concepts—viz., inert gas and vacuum stripping of methanol from the reactor—and simulates the process in the form of mass-transfer-based models. Improvement in the final conversion was demonstrated in both approaches, and predictions of the vacuum stripping model are in good agreement with the experimental results. Thus, the developed vacuum stripping model is useful for accurate analysis and design of a reactor with vacuum stripping. The novelty of the work is obtaining rate and reaction equilibrium constants, enthalpy of reaction, and liquid activity coefficient for amidation, which have no prior reporting, and providing the viability of options for side product removal. The applied modeling approaches and the experimental facilities and methods are established.

Assessment of evaporative cooling process across the mechanically driven cooling tower based on two-point boundary value problem using novel integral technique

In the present study, a novel integral technique based on a two-point boundary value problem for the evaporative cooling process occurring across the mechanically driven counter flow cooling tower is structured and solved numerically. The developed technique is validated with the experimental data reported in the literature by choosing thermal load and vaporization rate as thermal performance evaluation parameters and observed the maximum deviation to be ± 13.5%. Moreover, the effect of inlet parameters on thermal load and vaporization rate is evaluated, and it is observed that water inlet temperature and air-specific humidity has a substantial influence on the performance of the cooling tower. Unique dimensionless parameters such as characteristic thermal mass of the packed column with tower height, heat difference ratio and moisture difference ratio along the height of the packed column, and number of heat-transfer units are introduced for assessing the performance as well as transfer characteristics of the cooling tower considering air as the cooling medium and water as the working fluid. The influence of various parameters such as Lewis number, number of heat and mass transfer units, fluid flow ratio, dimensionless thermal mass of the packed column with tower height, and moisture difference ratio on cooling tower efficiency is analyzed and observed that fluid flow ratio and moisture difference ratio have a significant impact on the thermal performance of the cooling tower. Further, for the given operating range, optimal values of number of heat transfer units, fluid flow ratio, and characteristic height of the cooling tower are predicted and found to be 0.87,0.35, and 0.8 m, respectively.

Influence of the competitive effect of V-shaped slope tunnel on smoke characteristics

Numerical simulations are conducted to study the influence of the heat release rate, the fire source location, and the tunnel slope on the smoke spread characteristics of V-shaped slope tunnels. Theoretical analysis and simulation results show that the smoke movement in the V-shaped slope tunnel is affected by the competition effect on both sides, which leads to the fact that the smoke only overflows from the tunnel portal closer to the fire source, and a large amount of air flows into the tunnel from the other portal. Due to the competition effect, the downstream smoke back-layering length first decreases and then increases slightly with the increasing distance between the fire source and the grade change point (refering to the intersection point of two adjacent slope lines). As the tunnel slope increases, both the back-layering length and the influence of the fire source location on the smoke spread decrease gradually. Besides, the heat release rate has little effect on the smoke movement characteristics. Based on the back-layering length and the mass flow rate distribution, the smoke movement behaviors in the V-shaped tunnel can be divided into the double-slope control zone, the transition zone, and the single-slope control zone. When the vertical distance between the fire source and the grade change point is more than 2.1 m, the smoke movement can be classified in the single-slope control zone. The mass flow rate reaches the peak value when the fire source is located in the transition zone, and the dimensionless mass flow rate is proportional to the tunnel slope and the 0.3 power of the dimensionless heat release rate.

The Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional time‐derivative approach on transient free convection flow between two vertical parallel plates: A semi‐analytical solution

AbstractA comparative analysis on semi‐analytical solution of transient free convection flow of fractional Maxwell viscoelastic fluid between two vertical parallel plates has been investigated by employing the Caputo–Fabrizio (CF) and Atangana–Baleanus in Caputo sense (ABC) fractional time derivative. The semi‐analytical solutions for dimensionless temperature, velocity, skin friction, and mass flux are obtained using both approach (CF and ABC) and solution presented in the Laplace domain. The Riemann sum approximation was used to invert all solutions from the Laplace domain to the time domain. The influence of pertinent parameters on dimensionless temperature and velocity for both CF and ABC approach are presented graphically and in tabular form and thereafter discussed. The significant result obtained from this study is that both temperature and velocity in CF and ABC increase as the time and relaxation time parameter increases, while temperature and velocity via CF and ABC model decrease when the fractional parameter increases. It is also significant to note that, temperature, velocity, skin friction, and mass flux have a higher value in the CF model than the ABC model.

Effects of microstructural and petrophysical properties on spontaneous imbibition in tight sandstone reservoirs

Spontaneous imbibition widely occurs during the industrial development of tight reservoirs. Clarifying the spontaneous imbibition mechanisms and the key influencing factors contributes to the recovery of such reservoirs. In this study, basic tests of petrophysical properties and spontaneous imbibition experiments are conducted on 11 tight sandstone cores sampled from Dongying Sag, Bohai Bay Basin, China. The mass change and distribution of imbibed water are monitored by balance and nuclear magnetic resonance during the imbibition experiments. The petrophysical properties and fractal parameters are implemented to investigate the factors influencing imbibition in tight sandstone. The imbibition curves of 11 samples display a relatively similar shape but have differences in the final mass, the time required to reach the final mass and the slopes of the early stage. The effect of pore characteristics on imbibition process is explicated by nuclear magnetic resonance results. In the double logarithmic diagram, the imbibition curves can be divided into two regions. The main influencing factors of the final dimensionless imbibition mass are porosity, fractal dimension, and succolarity, indicating that the amount, complex characteristic, and connectivity of pores are critical for imbibition. However, no obvious relationship could be established between the permeability, lacunarity, and final dimensionless imbibition mass. The results assist with the clarification of the imbibition effect and its influencing factors during the industrial development of tight sandstone reservoirs.

Integrating multiple physical properties of microchannel gas flow to extend the Navier–Stokes equations over a wide Knudsen number range

Gas flow in microchannels can be predicted by the Navier–Stokes equations with slip boundary conditions, but only limited to a slightly rarefied flow regime. To improve that, the considerations of the effective mean free path and the volume diffusion phenomena were introduced to the non-kinetic model by previous studies separately. In this study, these two effects, along with the newly proposed wall-to-wall-collision effect, are integrated to extend the Navier–Stokes equations for the planar Poiseuille flows over a wide Knudsen number (Kn) range. The dimensionless mass flow rates calculated by the proposed model can be consistent among different working fluids or flow conditions and mostly agree with the experimental data with Kn≅0.03−57. This analysis facilitates an understanding of the mutual effects on the physical properties of microchannel gas flows and shows a promising prospect for developing a non-kinetic model for highly rarefied flows.

Unsteady conjugate model of fluid mechanics and mass transfer for butanol pervaporation process by non-porous membrane

A diffusion-convective mass transfer mathematical conjugated model of butanol recovery from a re-circulating aqueous solution by pervaporation using a polydimethylsiloxane (PDMS) membrane was developed based on computational fluid dynamics. Discretized continuity, linear momentum, and convective-diffusion mass transfer equations were solved by an in-house code based on the finite volume method for a laminar flow with a flat attached non-porous membrane. In addition, a novel numerical procedure to determine the butanol diffusivity in the PDMS membrane was developed based on the solution of the conjugate unsteady convection-diffusion model that included five coupled partial differential equations. The evolution of the distribution of the velocity profile in the fluid flow and the transient variation of butanol concentration in the feed solution and inside the PDMS membrane were determined. Variations in time and space of the dimensionless mass flux along the length of the pervaporation module were calculated from the conjugate convection-diffusion mass transfer model. The numerical predictions of the butanol mass flux in the feed solution exhibited good agreement with the experimental results with an error smaller than 3%. Understanding the mechanisms of mass and fluid transport phenomena by computational modeling can be helpful for improving the design of pervaporation processes.

Experimental investigation of the thermal performance in a single-component two-phase flow in multistream multi-fluid plate-fin heat exchangers

This paper focuses on evaluating the effects of flow rate and temperature changes of hot and cold fluid flows in multistream multi-fluid plate-fin heat exchangers with a single-component two-phase flow in the middle heat exchanger. This three-fluid heat exchanger included three layers with offset strip and wavy fin configurations. In the adjacent heat exchanger with offset strip fins, hot and cold fluids were flowing, while the middle heat exchanger with wavy fins contained a single-component two-phase flow (condensed vapor). The Nusselt number, friction factor, the thermal performance factor, and the heat transfer surface contribution of the middle heat exchanger with each of the adjacent heat exchangers, were obtained using the measured experimental data. The results indicate that the two-phase Reynolds number was between 500 and 1800, and the vapor quality varied in the range of 0.17–0.56. Also, the heat transfer surface contribution of the adjacent cold and hot fluids was between 0.18 and 0.5. The two-phase flow in the wavy channel has a wavy and stratified pattern. The examinations showed that raising the Reynolds number of hot and cold fluids, respectively, led to maximum 13.8 % and 9.5 % of reduction in the vapor quality, 8.8 % and 9 % of increase in the two-phase Nusselt number, and 18 % and 12 % of reduction in the average value of friction factor. The domain change in the two-phase vapor quality, the two-phase fluid heat transfer surface contribution, and the flow pattern determination parameters including the dimensionless mass parameter and the Lockhart-Martinelli parameter was 33.67 %, 80.81 %, 32.72 %, and 19.09 %, respectively. As the Reynolds number of the cold fluid was changed, the variation domain of these parameters was higher compared to when the Reynolds number of the hot fluid was altered. Increasing the dimensionless temperature of the hot and cold raised the vapor quality by 12–16 %. The experimental results revealed that by decreasing the temperature of adjacent fluids and increasing their Reynolds number, the thermal performance factor of the two-phase flow was increased.

Experimental study of induced airflow characteristics during liquid metal pouring process through PIV, thermography, and color schlieren imaging

Contaminated airflows are frequently generated during various liquid-metal pouring processes in industrial plants. An in-depth understanding of the induced airflow characteristics is necessary to develop an energy-saving ventilation system. In this study, the airflow characteristics induced by liquid metal pouring were investigated experimentally. The results indicate that the time-averaged velocity distribution of induced airflow at different pouring heights Z/r’ essentially follow Gaussian curves and that the influence range of the dimensionless horizontal velocity of the induced airflow is 0–2.5 at a Z/r’ of 0 to −3 with the maximum pouring flow rate. The angle Ф between the mainstream movement direction and the horizontal plane is approximately 85° based on the streamline variations. In addition, the temperature attenuation of the induced airflow approximately follows an exponential decay, and the dimensionless horizontal influence range of the temperature is almost four times that of the velocity. Moreover, the air mass formation and contaminated airflow generation process are illustrated, and the temperature peak of the induced airflow at the pouring cup outlet is explained in terms of the air mass generation. By combining the air mass position S* and dimensionless air mass diameter D* variations, it is demonstrated that the polluted airflow generation function is similar to a trigonometric function during the pouring period. In summary, the obtained conclusions can assist in the design of high-efficiency ventilation systems and in reducing energy consumption in industrial plants.

An upper observable black hole mass scale for tidal destruction events with thermal X-ray spectra

ABSTRACT We comprehensively model the X-ray luminosity emergent from time-dependent relativistic accretion discs, developing analytical models of the X-ray luminosity of thermal disc systems as a function of black hole mass M, disc mass Md, and disc α-parameter. The X-ray properties of these solutions will be directly relevant for understanding tidal disruption event (TDE) observations. We demonstrate an extremely strong suppression of thermal X-ray luminosity from large mass black holes, LX ∼ exp (− m7/6), where m is a dimensionless mass, roughly the black hole mass in unity of 106M⊙. This strong suppression results in upper observable black hole mass limits, which we demonstrate to be of order Mlim ≃ 3 × 107M⊙, above which thermal X-ray emission will not be observable. This upper observable black hole mass limit is a function of the remaining disc parameters, and the full dependence can be described analytically (equation 82). We demonstrate that the current population of observed X-ray TDEs is indeed consistent with an upper black hole mass limit of order M ∼ 107M⊙, consistent with our analysis.