Number Mass Transfer Research Articles

Numerical analysis of Nano-encapsulated PCM magnetohydrodynamics double-diffusive convection and entropy generation in vertical enclosures with porous layer

This study investigates the effects of Nano-Encapsulated Phase Change Materials (NEPCMs) on double diffusive free convection in a partially porous cavity, considering Soret-Dufour effects and magnetohydrodynamics. The problem is modeled using non-dimensional governing equations, solved numerically through a Galerkin finite element method. The research examines the influence of key parameters including Rayleigh number (Ra: 103–105), Darcy number (Da: 10–4 -10–1), Hartmann number (Ha:0−80), NEPCM volume fraction (ϕ:0−0.04), Lewis number (Le:0.1−10), fusion temperature (θf:0.1−0.9), and Stefan number (Ste:0.1−0.9) on heat and mass transfer characteristics and entropy generation. Results show that increasing Ra significantly enhances heat and mass transfer, with Nusselt and Sherwood numbers rising by 424.8 % and 547.3 % respectively as Ra increases from 103 to 105. Higher Da and ϕ improve heat transfer, while stronger magnetic fields suppress both heat and mass transfer. An optimal fusion temperature (θf=0.5) is identified for maximum heat transfer enhancement. Total entropy generation, considering thermal diffusion, nanofluid friction, magnetic effects, porous medium, and mass diffusion contributions, increases by 15,957 % with Ra and decreases by 42.5 % with increasing Ha. The Bejan number analysis reveals that non-thermal irreversibilities become increasingly dominant at higher Ra and Ha values. The study concludes that NEPCMs can effectively enhance heat transfer in partially porous cavities, with their performance strongly influenced by Ra, Da, and Ha. The findings provide valuable insights for optimizing thermal management systems incorporating NEPCMs, particularly in applications involving porous media and magnetic fields.

Significance of heat transfer in a reversible esterification of Arrhenius activation energy with partial slip

The significance of heat transfer during a reversible esterification process in a magnetohydrodynamic boundary layer Casson fluid flow along a vertical stretching plate is examined. The multi-slip conditions are considered in a porous medium. The presence of chemical process requiring an activation energy is considered in the analysis. The study also investigates the hydromagnetic boundary layer Casson fluid flow alongwith partial slip conditions across a vertical stretching plate. The incorporation of multi-slip constraints in a porous medium, alongside magnetic fields and other parameters, highlights its relevance in diverse engineering fields such as thermal engineering, polymerization, and biodiesel industries. Understanding the characteristics of such fluids under complex conditions is vital for optimizing heat and mass transfer in industrial applications, making this investigation timely and valuable. The nonlinear differential set of equations are solved numerically involving Runge-Kutta based shooting approach of fourth order and the results are verified with the bvp4c tool and the findings are explored using graphical plots. The predominance of significant factors on flow configurations are analyzed and presented in graphs and tables. A comprehensive analysis is provided on the effects on velocity, concentration, and temperature of diverse parameters such as reaction rate constant, magnetic parameter, suction parameter, mass Grashof number, Prandtl number, Casson parameter, thermal radiation parameter and slip parameters. The tabular representation of the adverse effects of drag coefficient, rate of mass transfer and Nusselt number on flow configurations for various significant parameters is presented. It is inferred that for the case of reversible and irreversible flows, the shear stress rate escalates by 29% when the magnetic parameter elevates from 0.5 to 1.5 and about 35% when the Casson parameter elevates from 0.5 to 1.5. For the suction parameter, the coefficient of drag increased by 27% and 26% for irreversible and reversible flows respectively. When the reaction rate increases from 0.5 to 1.5, the rate of shear stress elevates by 0.5% and 0.02% for irreversible and reversible flows in order. The Nusselt number decreased about 7% and 8% when the magnetic parameter and Casson parameter rises from 0.5 to 1.5 respectively, for irreversible and reversible flows. It is noteworthy that the previous studies are in precise agreement with the present investigation.

Local Burning Behavior of Wind-Driven Flames under the Influence of Mixed-Convective Turbulent Flow Conditions

ABSTRACT Experiments were conducted to investigate the burning behavior of wind-driven turbulent flames stabilized over a condensed fuel surface. A controlled turbulent crossflow environment was established to examine the impact of external flow velocity and turbulence intensity on the flame profile parameters and mass burning rates. To address the complexities of practical fire scenarios, a mixed-convection parameter ξ x in the form of G r x 1 / ψ x 2 n was defined, encapsulating the combined effects of momentum, buoyancy, and freestream turbulence. Furthermore, the property of fuel (in terms of mass transfer number B) was integrated into the mixed-convection parameter ( ξ x ) to establish a fuel-dependency factor within the formulation . The interdependence of flame characteristics and the mass burning process was observed using ξ x , that yielded several meaningful correlations. In this regard, a power-law trend was obtained between flame standoff distance and the dimensionless parameter ξ x . Finally, the local mass burning rates were estimated and plotted against mixed-convective parameter ( ξ x ), resulting in a unified local mass burning rate correlation. This correlation incorporates the fuel-dependency aspect in its formulation and is applicable in both laminar and turbulent crossflow environments.

Numerical study of Marangoni convective hybrid-nanofluids flow over a permeable stretching surface

This paper is discussing nanofluid flow with effect of radiation along a stretching sheet in a porous means. Also, magnetic field is applied uniformly. The hybrid nanofluid is blend of base fluid kerosine oil and suspending particles of Copper Aluminum Oxide (Cu − Al2O3). The Marangoni boundary condition is considered. The flow considered is mathematically modeled with suitable boundary conditions in partial differential equations. Similarity transformations applied and followed numerical computations with Runge–Kutta method of order 4th aided by shooting approach. The graphs for different flow control parameters plotted and analytical study carried with illustration of temperature and velocity fields. Heat transfer rate for hybrid-nanofluid falls with increasing Mass transfer, Wall parameter (fw)and Prandtl Number (Pr), and the reversed effect for same is seen for higher Radiation parameter values (R). The current study's relevance has numerous applications in the key fields of materials processing, industrial thermal control, and heat transfer optimization in energy-efficient systems.

Quality of Mixedness Using Information Entropy in a Counter-Current Three-Phase Bubble Column

Knowledge of mixing phenomena is of great value in the mineral and other chemical and biochemical industries. This work aims to analyze the quality of mixedness (QM), the intrinsic mass transfer (MT) number, and the MT efficiency based on information entropy theory in the counter-current microstructured slurry bubble column. A thorough analysis is conducted to assess the effects of particle loading, gas and slurry velocity, and axial variation on the QM. The range of gas velocity, slurry velocity, particle size, and particle loading was 0.011–0.075 m/s, 0.018–0.058 m/s, 242.72–408.31 μm, and 15.54–88.94 kg/m3, respectively. QM is a time-dependent parameter, and the concept of contact time has been used for scale-up purposes. The maximum QM was achieved at dimensionless times of 0.40 × 10−3, 0.15 × 10−3, and 0.85 × 10−3 for the maximum superficial gas velocity, particle loading, and axial height, respectively. The gas velocity positively influenced both the intrinsic MT number and its efficiency. In contrast, the slurry velocity and particle loading had a negative effect. The present theoretical analysis will pave the path for industrial process intensification in counter-current flow systems.

Heat transfer in wind-driven fires stabilized under a mixed-convective turbulent flow environment

This study experimentally investigates the heat flux distribution over a horizontally placed condensed fuel surface under mixed-convective turbulent flow conditions. The study explores different freestream conditions, including variations in crossflow velocity (ranging from 1 m/s to 1.8 m/s) and turbulent intensity (ranging from 3% to 9%) on local heat fluxes at the condensed fuel surface. Further, to decipher the collective influence of momentum, buoyancy, and turbulence on local heat fluxes, a mixed-convection variable ξx was defined in the form of ξx=Grx1/ψx2n. The defined variable also encapsulates the property of fuel as a function of mass transfer number B, thereby establishing a fuel-dependency factor in the formulation of the mixed-convective parameter (ξx). A methodology was adopted to quantify heat flux components (convective and radiative) with the knowledge of local mass burning rates and local temperature gradients at the condensed fuel surface in the pyrolysis zone. An inverse relationship was observed for incident heat flux with flame standoff distance and ξx. The present study considered the experimental data for two fuels, n-heptane, and ethanol, which showed almost similar trends. However, the radiative heat flux was dominant for the n-heptane case due to the higher sooting propensity of heptane.

Radiation Absorption and Diffusion Thermo Effects on Unsteady MHD Kuvshinski Fluid Flow Past an Inclined Porous Plate in the Presence of Thermal Radiation and Chemical Reaction

The aim of the present paper is to investigate investigated the Radiation absorption and diffusion thermo on unsteady magneto hydrodynamic Kuvshinski fluid flow past an infinite vertical permeable moving plate in Presence of thermal radiation, heat absorption and homogenous chemical reaction, subjected to variable suction. The plate is assumed to be embedded in a uniform porous medium and Moves with a constant velocity in the flow direction in the presence of a transverse magnetic Field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using perturbation technique. Graphical results for the velocity distribution, temperature distribution and concentration distribution based on the numerical solutions are presented and discussed. Also discuss the effects of various parameters on the skin-friction coefficient and the rate of heat transfer in the form of Nusselt number and rate of mass transfer in the form of Sherwood number at the surface. Velocity and temperature distribution is observed to increase with an increase in Radiation absorption and Dufour parameter, whereas diminishes with enhances of Magnetic field, heat absorption coefficient, radiation parameter and chemical reaction parameter in respective velocity, temperature and concentration distributions.

Radiation Absorption and Diffusion Thermo Effects on Unsteady MHD Casson Fluid Flow Past a Moving Inclined Plate Embedded in Porous Medium in the Presence of Chemical Reaction and Thermal Radiation

The aim of the present paper is to investigate the effects of Radiation absorption and diffusion thermo on unsteady magnetohydrodynamic Casson fluid flow past an inclined permeable moving plate in Presence of thermal radiation, heat absorption and homogenous chemical reaction. The plate is assumed to be embedded in a uniform porous medium and Moves with a constant velocity in the flow direction in the presence of a transverse magnetic Field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using perturbation technique. Graphical results for the velocity distribution, temperature distribution and concentration distribution based on the numerical solutions are presented and discussed. Also discuss the effects of various parameters on the skin-friction coefficient and the rate of heat transfer in the form of Nusselt number and rate of mass transfer in the form of Sherwood number at the surface. Velocity and temperature distribution is observed to increase with an increase in radiation absorption and Dufour parameter, whereas diminishes with enhances of Magnetic field, heat absorption coefficient, radiation parameter and chemical reaction parameter in respective velocity, temperature and concentration distributions.

Radiation absorption on MHD free conduction flow through porous medium over an unbounded vertical plate with heat source

The aim of the present paper is to investigate the radiation absorption and diffusion thermo on unsteady magneto hydrodynamic flow past an infinite vertical permeable moving plate in the presence of thermal radiation, heat absorption and homogenous chemical reaction, subjected to variable suction. The plate is assumed to be embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using perturbation technique. Graphical results for the velocity distribution, temperature distribution and concentration distribution based on the numerical solutions are presented and discussed. Also we discuss the effects of various parameters on the skin-friction coefficient and the rate of heat transfer in the form of Nusselt number and rate of mass transfer in the form of Sherwood number at the surface. Velocity and temperature distribution is observed to increase with an increase in radiation absorption and Dufour parameter, whereas it diminishes with the enhancement in magnetic field, heat absorption coefficient, radiation parameter and chemical reaction parameter with respect to velocity, temperature and concentration distributions.

On the orientation effect on the flame spread over discrete fuel using a mass-transfer number

The concept of discrete fuels provides a good representation of the real fire scenario. Many efforts on this issue have been conducted with the aid of heat transfer analyses, while little work has focused on the mass transfer analyses, nor considering the orientation effect. In this work, four PMMA (Polymethyl methacrylate) panels (8 cm × 10 cm × 1 cm) as a discrete fuel array are burned on the fireproof board at various angles θ (60°, 75°, 90°, 105°, and 120° based on the horizontal plane). The mass-transfer number, serving as a flammability index, is estimated and discussed based on the analyses of the flame morphology, pyrolysis length and mass loss rate. It is found that the mass-transfer number for discrete fuel presents a wave pattern including surges at the gaps. The increase in inclination angle can raise the average level of the mass-transfer number. The present work suggests that the exposed surface of flame bulk to the ambient may cause this defamation, since its increase can induce an enhanced radiation loss fraction χ. This conclusion is supported by the observed changes in the flame morphology, such as the monotonous decrease in flame width with inclination angle. Furthermore, the higher mass transfer numbers at the large inclination angles are observed, accompanied by a low flame height and a low pyrolysis spread rate, which indicate that the building façade with a proper large inclination angle may be a potential solution to tackle façade fires from the perspective of architectural design. The limitations of this paper are also identified for further considerations on the application of mass-transfer number.

Voltage-induced concentration enhancement of analyte solutes in microfluidic chips

Microfluidic-based enrichment techniques have had a profound impact on chemistry, owing to their ability to improve the sensitivity of detection by increasing the concentration of analytes in minute fluid volumes. Herein, concentration enrichment of analyte solutes is achieved by using voltage assist in a microchip with two reservoirs. A numerical model is developed to describe the complex analyte focusing process, which to date has not been investigated before. Numerical computations are systematically conducted to study the influences of applied voltage, mass transfer coefficient, electrode location, reservoir diameter and number of mass transfer channels on the concentration enrichment in a designed Polydimethylsiloxane (PDMS)/Glass microfluidic electrophoresis chip. The electric fields, concentration distributions, and electrophoretic fluxes are obtained, which can reveal insightful enrichment mechanisms. It is found that the factors that can increase the electrophoretic flux in the mass transfer channel and enhance the electric field strength in the enrichment reservoir, such as moving the electrode back or increasing the number of mass transfer channels, are particularly important to improve the enrichment performance. The final microchip after considering the Joule heating effect has a 335-fold and 2.8-fold maximum and average concentration enrichments, respectively. Furthermore, this method is applied to the experimental enrichment of Rhodamine B and heavy metal cadmium (II) ions to test it performance.

Characterizing burning behavior of biomass fuels with discrete distribution

Discrete distribution of biomass fuels is an important configuration for the implication of wildland fire. In this study, flame spread and burning behaviors were examined by designing 90 groups of birch array geometries. Five inclination angles (denoted by θ, 15°−90°), three spacings (S, 3 mm, 6 mm, and 9 mm), and five column numbers (n, 3–11) were varied. Flame spread behavior is characterized by three regimes, a steady fire (regime Ⅰ), a growing fire (regime Ⅱ), and a fast-developed fire (regime III). Correlations of determining flame spread regime are proposed. Under these regimes, mass loss rate per unit area (ṁ″) has a power-law dependency on porosity (φ), where the power-law index increases from regime Ⅰ, Ⅱ to regime III. In the regime III, ṁ″ is independent of φ when φ > 1.6 mm. The three spread regimes are attributed to the transition of the controlling mechanism from radiation to convection dominance. Moreover, by introducing the total mass transfer number BT, the influence of the controlling mechanism is classified into two regions, radiation dominance (region I) and convective dominance (region II), in which the three flame spread regimes are evaluated.

Defect and interface engineering of templated synthesis of hollow porous Co3O4/CoMoO4 with highly enhanced electrocatalytic activity for oxygen evolution reaction

The development of oxygen evolution reaction (OER) electrocatalyst with high efficiency, low cost and robust stability is of great significance for practical water electrolysis. Herein, a series of hollow porous Co3O4/CoMoO4 hybrids were synthesized based on defect, interface and nano/microstructure engineering. The comprehensive engineering greatly improved number and activity of active sites, mass and charge transfer of the catalysts. The catalysts consequently exhibited excellent electrocatalytic activities for OER under alkaline conditions. Especially, the optimum Co3O4/CoMoO4-0.1-FO catalyst exhibited ultralow overpotential of 342 mV to afford a current density of 100 mA·cm−2 and a small Tafel slope of 72 mV·dec–1. The theoretical calculations revealed that the defect and interface engineering can effectively adjust the adsorption energy of the reactive sites to intermediates and greatly decrease energy barrier of the Co3O4/CoMoO4 in the process of OER, and consequently increase the OER activity. This work supplied a vivid example to fabricate highly effective composite catalysts by comprehensive employing multiple engineering.

Ultrafine Ru nanoparticles in shape control hollow octahedron MOF derived cobalt oxide@carbon as high-efficiency catalysts for hydrolysis of ammonia borane

BackgroundEvolving cost-effective and high-efficiency catalysts for efficient ammonia borane (AB) hydrolysis is highly desired but leftovers are a great challenge. Catalysis with high efficiency may be achieved by rationally modifying the intention and electronic state. MethodsThe development of carbonized zeolite imidazole framework (ZIF-67) based Ru nanoparticles (NPs) dispersed Ru@Co3O4/NC-350 NPs catalyst composition was prepared for the carrier catalysts. The ZIF-67 was introduced with different calcination temperatures for the carbonized porous materials. Only the calcination temperature at 350 °C with Ru@Co3O4/NC-350 NPs shows the good ability in its catalytic activity. The addition of 3.0 wt.% Ru NPs into the hollow ZIF-67 porous metal-organic framework (MOF) yielded highly stable with good morphology and porous. Significant findingsRu NPs dispersed on carbonized Co3O4/NC have a hollow porous structure with a convoluted nano restricted inner region between Co3O4 and NC, allowing for a large number of accessible active sites and easy mass transfer and controlling the carbonized temperature can change the composition of Co3O4/NC heterostructures. These hollow porous carbon materials show much higher turnover frequency during a very short time and also high stability after ten cycles for the AB hydrolysis. This carbonized sample of Ru@Co3O4/NC-350 NPs exhibited increased catalyst stability and materials reusability. There is particularly great potential for industrial application of this catalytic system in fuel cells, because of its simple preparation method, the use of relatively cheap metals, and its highly active catalysis.

Performance analysis on open thermochemical sorption heat storage from a real mass transfer perspective

Internal mass transfer coefficient is considered as a key parameter for open thermochemical sorption heat storage which usually has a large margin between theoretical and actual value. This paper aims to analyze the role of mass transfer on system performance prediction. Al2O3 and LiCl composite sorbents are prepared and adsorption behavior is tested through a thermal gravimetric analyzer and a small-scale air duct experiment. An equation of kinetic coefficient is fitted to describe adsorption process more accurate than empirical equation. For simulation, a one-dimensional model is established based on dimensionless number of heat and mass transfer, and similarity theory is built to predict output parameters. Results indicate that the sorbent with 16.44 % salt content reaches 0.39 g·g−1 maximum water uptake on the condition of 20 °C, 80 % relative humidity. It is indicated that the system using composite sorbents has a heat storage density of 345.58 kWh·m−3. Parameters that influence system output power and duration are also investigated. By adjusting air flow rate and sorption length of sorption reactor, the system can achieve temperature rise of 30 °C at the exit and a steady output of 6 h. One striking fact is that mass transfer coefficient can be used to well predict the performance of real open adsorption thermal energy storage system which is also conducive to system design and optimization.

Chemical reaction with aligned magnetic field effects on unsteady MHD Kuvshinski fluid flow past an inclined porous plate in the presence of radiation and Soret effects

AbstractThe present paper studies the effect of a chemical reaction and aligned magnetic field on an unsteady magnetohydrodynamic free convection Kuvshinski fluid flow past an inclined plate through a porous medium in the presence of Soret and radiation. The plate is assumed to be embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. The systems of nondimensional governing linear partial differential equations are solved analytically by using the perturbation technique. The influences of various nondimensional parameters on the velocity, the temperature, and the concentration are discussed, as also the effects of various parameters on the skin‐friction coefficient and the rate of heat transfer in the form of Nusselt number and rate of mass transfer in the form of Sherwood number at the surface. Velocity distribution is observed to increase with an increase in viscoelastic parameter and Soret parameter, whereas it shows reverse effects in the case of the aligned magnetic field, inclined parameter, magnetic parameter, the temperature diminishes with the increase of radiation parameter and heat absorption parameter.

Combustion characteristics of aromatic-enriched oil droplets produced by pyrolyzing unrecyclable waste tire rubber

The purpose of this work is to study the combustion characteristics of aromatic-enriched tire pyrolysis oil (TPO) produced from typical small vehicles and truck tires. Pyrolysis oils (NRTO: natural rubber tire oil and SRTO: synthetic rubber tire oil) from two raw radial tire materials were produced and condensed at 25 °C and 130 °C in a three-stage auger pyrolysis reactor under negative pressure. Combustion particularities were acquired using a single-droplet suspension combustion device and evaluated by five different indicators: kinetics, flame shape, burning rates, flame stand-off ratio (FSR) and mass transfer parameters. It was found that TPO was a potential fuel with higher calorific value (40–44 MJ/kg) and lower combustion apparent activation energy (10–40 MJ/mol) than that of bio-oil and solid fuels. Oil produced from synthetic rubber and condensed at 25 °C exhibited higher stable burning rate (1.93 ± 0.03 mm2/s) than that of nature rubber pyrolysis oil. Comparing with traditional fuels, tire oil droplets displayed higher surface local heat transfer coefficient, but the mass transfer number (B ≈ 2.5) and FSR (<3.1) under stable combustion conditions were much lower. The combustion behavior of TPO has partial similarity with unsaturated hydrocarbons and ester biofuels. The reported results support the well-characterized TPO condensates for subsequent atomized combustion in realistic industrial burners.

Experimental analysis and rate-based stage modeling of multicomponent distillation in a Rotating Packed Bed

Rotating Packed Beds (RPBs) offer increased flexibility and the potential of significant size-reductions for distillation processes through mass transfer intensification. This may be of interest for example for retrofits or off-shore applications. However, validated models for process design of multicomponent distillation in RPBs are not available up to now. To bridge this gap, distillation of binary and ternary mixtures at total reflux was experimentally investigated in an RPB test rig. Depending on the flowrate and rotational speed, up to 10 theoretical stages were achieved in the investigated RPB, corresponding to an HETP (height equivalent of a theoretical plate) of as low as 17mm at the best operating point. With increasing centrifugal acceleration, separation efficiency increased at first, but decreased again at high centrifugal accelerations. Using the rate-based stage approach, a correlation for gas-side volumetric mass transfer coefficient in the RPB is developed. It is capable of reproducing the observed maximum of separation efficiency. Coefficients are fitted for this correlation, based on results obtained from distillation of ethanol/n-propanol. The model is validated using data obtained from distillation of ethanol/water and ethanol/n-propanol/water. Overall volumetric mass transfer coefficients and numbers of theoretical stages are described for most of the data within ±30%.

Optimization of a Hierarchical Porous-Structured Reactor to Mitigate Mass Transport Limitations for Efficient Electrocatalytic Ammonia Oxidation through a Three-Electron-Transfer Pathway.

Regulation of fast three-electron-transfer processes for electrocatalytic oxidation of ammonia to nitrogen by achieving efficient generation and utilization of active sites is the optimal strategy in ammonia-containing wastewater treatment. However, the limited number of accessible active sites and sluggish interfacial mass transfer are two main bottlenecks restricting conventional ammonia oxidation configurations. Herein, we develop a macroporous Ni foam electrode integrated with vertically aligned two-dimensional mesoporous Ni2P nanosheets to create sufficient exposure of active centers. A novel ammonia oxidation reactor with the developed hierarchical porous-structured electrodes was assembled to construct an intensified microfluidic process with flow-through operation to mitigate macroscopic mass transport limitations. The confined microreaction space in the hierarchical porous reactor further promotes spontaneous nanoscale diffusion/convection of the target contaminant to high-valence Ni sites and enhances the microscopic mass transfer. The combined results of electrochemical measurements and in situ Raman spectra showed that the ammonia degradation mechanism results from direct oxidation by the high-valence Ni, significantly different from the conventional indirect active-chlorine-species-mediated oxidation. The optimized reactor achieves high-efficiency three-electron-transfer ammonia conversion with an ammonia removal efficiency of ∼70% from an initial concentration of ∼1400 mg/L and byproduct production of ∼4%, significantly superior to a conversion unit comprising a featureless Ni-based electrode in the immersed configuration, which had >50% byproduct yield. 20 days of continuous operation under variable conditions achieved >90% ammonia degradation performance and an energy consumption of 25.42 kW h kg-1 N (1 order of magnitude lower than the active-chlorine-mediated process), showing the potential of the reactor in medium-concentration ammonia-containing wastewater treatment.

Grid dependence of evaporation rates in Euler–Lagrange simulations of dilute sprays

The present study addresses the grid dependence of evaporation rates in the context of Euler-Lagrange simulations and presents error estimates as a function of characteristic parameters. The common approach of using local cell values as ambient conditions for the evaporation model and returning heat and mass to the gas phase via source terms, which is known as the particle-source-in-cell (PSI-cell) model, is not grid independent and leads to large deviations in the evaporation rates if the cell size is of the order of the droplet diameter. This problem has become increasingly important in recent years as increased computing power now allow direct numerical simulations of the carrier gas and large-eddy simulations with much smaller cell sizes to be used, making the point-source approximation increasingly inadequate. It is therefore necessary to estimate the error that is introduced by the PSI-cell model to be able to perform simulations with a given (and a priori known) error level. Focusing on a single droplet in an infinite environment, expressions are derived for the deviation of the evaporation rate and time compared to a reference solution for both quiescent and convective environments and including the effects of heat transfer. It is found that the error of the steady-state evaporation rate is a function of the ratio of cell size to droplet diameter and the cell Péclet number. The error of the evaporation time additionally depends on the initial ratio of liquid to gaseous mass in the computational cell and on the reference mass transfer number, whose influence can be combined in a modified mass ratio. The presented expressions are simple to use and valid across a wide range of gas and droplet properties that are typical for spray combustion applications and provide guidelines for the correct choice of the cell size in Euler-Lagrange simulations of dilute sprays.