Non-uniform Temperature Conditions Research Articles

Examination of the Behavior of Double Cold-Formed Steel Columns with Σ-Shaped Sections Subjected to Non-Uniform Temperature Conditions

Examination of the Behavior of Double Cold-Formed Steel Columns with Σ-Shaped Sections Subjected to Non-Uniform Temperature Conditions

Experimental and numerical studies of the fuel concentration distribution within the near-wall area in a compact space for a gas turbine combustor

Interstage combustion is known for its small axial distance, high combustion efficiency and low lean blowout boundary. However, in a compact space, the distance between the fuel injection location and the wall is confined, and the high-temperature wall may affect the fuel distribution and in turn affect the combustion efficiency. In this study, an experiment of kerosene single-droplet evaporation was conducted, and the fuel distribution in an interstage combustor was numerically simulated. The experimental results showed that the evaporation rate of fuel droplets decreased with increasing distance from the high-temperature wall, and the influence of the lower wall on fuel evaporation was greater than that of the sidewall. The fuel evaporation rate at the high-temperature position within the nonuniform wall temperature field was relatively high. The numerical simulation results indicated that with increasing temperature, the effect of the wall on fuel evaporation increased, as did the uniformity of the fuel distribution. The direction of the temperature gradient imposed the greatest effect on the fuel distribution under nonuniform temperature conditions. This will facilitate the selection of the optimal ignition location within the cavity to achieve efficient combustion. Moreover, it's possible to control the fuel distribution by adjusting the wall temperature.

Enhancement of the precooling system performance for aviation engines by volatile liquid injection

Water injection precooling in aviation engines is a promising technique that can enhance performance, improve efficiency, and reduce emissions, especially at high altitudes and Mach numbers. However, its implementation in aviation engines requires careful engineering and design considerations due to the restricted space available for installation and operation, as well as the challenges posed by high inlet air velocities. Therefore, the present study experimentally and numerically evaluates the effectiveness of spray precooling for jet engines and introduces novel insights into optimizing droplet dynamics and nozzle configurations in short, narrow spray ducts under high inlet air temperature and velocity. The impact of water spray cooling on the uniformity of inlet air is also investigated for nonuniform air temperature conditions, which has yet to be mentioned in previous research. An experimental configuration has been devised and implemented to investigate water injection precooling within a rectangular spray duct. The evaporative cooling process through the spray duct and the injected droplet trajectories were predicted using an Eulerian-Lagrangian computational fluid dynamics (CFD) model. The CFD model was verified using the present experiments, and there is a strong correlation between the experimental data and simulation findings, with an average discrepancy of less than 7%. The effectiveness of the water injection system is investigated at different operating parameters such as nozzle arrangements, coolant type, droplet size, and variable velocities. The results showed that sprays characterized by small mean diameters and high initial droplet velocity significantly enhance spray cooling performance. Changing the nozzle configurations impacts spray cooling performance considerably, with the cross-outside case providing the best results. Notwithstanding its advantageous evaporation rate, introducing methanol via injection does not yield significant enhancements. Water injection is crucial in achieving a more homogeneous temperature distribution by reducing temperature disparities and promoting mixing and evaporation.

Thermal error compensation in length inspection of large-scale aircraft spars in nonuniform temperature environments

As the primary load-bearing structures, large-scale aircraft spars are subject to the influence of nonuniform temperatures in field conditions, resulting in thermal errors during on-site length inspections. These errors require accurate compensation. Conventional linear scaling methods, based on the assumption of uniform temperatures and a retrieved coefficient of thermal expansion (CTE), suffer from low accuracy in nonuniform temperature environments. To address this issue, this paper proposed a thermal error compensation method that incorporates CTE recalibration. First, we established a predictive model for thermal errors in nonuniform temperature fields through differential thermoelastic analysis. Secondly, a recalibration technique for the sensitive parameter, CTE, was introduced to enhance the prediction accuracy. Finally, leveraging the equivalent form of the model, an uncertainty assessment approach tailored for nonuniform temperature conditions was formulated for the compensated lengths. Numerical and case studies of a nearly 1 m long simplified wing spar were implemented to validate the performance of the thermal error compensation method. The results indicate that the presented method improved accuracy by over 57.6% in terms of RMSE compared to the linear scaling method using average temperatures, which would provide a viable approach to achieve a more accurate on-site length inspection of aircraft components.

Real-time monitoring of ground-tire rubber microwave devulcanization with thermal and electrochemical sensors

Devulcanizing ground-tire rubber (GTR) properly requires the removal of the sulphur linkages that crosslink the polymer. The volatile sulphur compounds (VSCs) released during the process must be extracted from the reactor to avoid any chemical recombination, and the sulphur gas concentrations conveniently sensed during the extraction, along with a thermal sensoring of the payload, can be used to monitor the whole devulcanization process. In this contribution, a modified conventional microwave oven was used to devulcanize the GTR. The microwave-processed GTR was evaluated by determining the values of its mass loss (ML), soluble fraction (sol fraction), and the variation of its electric permittivity. Results show a direct relationship between the energy delivered, sol fraction, the VSCs concentrations, the ML, and the permittivity values. Thus, this paper demonstrates that monitoring the VSCs can provide a reliable indication of ML and, consequently, devulcanization evolution even at non-uniform temperature conditions.

Experimental studies of effects of temperature gradients on performance of pouch type large format NMC/C lithium-ion battery

Cell to pack design concept for energy storage in automotive applications leads to a substantially increased cell size that results in temperature gradients over the surface induced by non-uniform heat transfer linked to the cooling system design, which influences the cell performance. In this paper, temperature gradient effects on life performance of a large-format cell are experimentally investigated, using a developed device that can actively control appropriate gradients in the longitudinal direction and simultaneously measure the heat generation rate (HGR). Performances under uniform and non-uniform temperature conditions (MMM: uniform temperature, LMH: low-mean-high, HLH: high-low-high) are compared and quantified. At beginning of life (BOL), the low-temperature regions in the HLH and LMH conditions dominantly limit the cell capacity, and the HLH condition suppresses the HGR at high C-rates. During aging, the cell experiences a larger capacity fade and HGR increase under the HLH than MMM condition. The analyses of half coin cell, differential capacity (dQdV), dynamic resistance and impedance reveal that the attributing mechanisms are mainly the loss of Cathode active material, potentially the loss of lithium inventory, and the increase of impedances, indicating the electrochemically promoted side reactions and corrosions in the high-temperature regions of the HLH condition.

Enhanced magneto-convective heat transport in porous hybrid nanofluid systems with multi-frequency nonuniform heating

In high-performance thermal systems, convective heat transport is a critical phenomenon for sustainable operation from an energy efficiency standpoint. This study examines the convective heat transport dynamics of a hybrid nanofluid (aluminum oxide-copper–water nanofluid) under spatially varying nonuniform temperature conditions within a porous thermal system in the presence of a magnetizing field. The flow domain experiences nonuniform heating (following a half-sinusoidal profile) from both sidewalls and is cooled from the top, while the lower wall remains adiabatic. The flow domain is filled with a porous substance and a hybrid nanoliquid. The non-dimensional governing equations are derived and numerically solved using a finite volume method-based solver. To accurately capture thermal behavior, available experimental data on hybrid nanofluid thermophysical properties are utilized. The study analyzes significant control variables such as half-sinusoidal heating amplitude, frequency, and offset temperature, as well as flow control variables such as Darcy number (Da), modified-Rayleigh number (Ram), and Hartmann number (Ha). The analysis shows that non-uniform heating consistently enhances transfer by up to approximately 722% compared to uniform heating. The three temperature-controlling parameters (amplitude, frequency, and offset temperature) play a crucial role in enhanced heat transfer, and the higher their magnitudes, the higher the heat transfer. Heat flow dynamics between the heat source and the heat sink are well visualized through heat function and heatlines. Heat transfer is an increasing function of Ram and frequency, which is opposite to the rising Da or Ha. An optimum frequency at which thermal convection is maximum is about 70 for the considered range of Ram. Furthermore, mathematical correlations that combine control variables are developed for predicting heat transfer characteristics.

Effects of physical properties and operating parameters on numerically developed flat-tube solid oxide fuel cell performance

Fuel cells are promising as a clean energy conversion device in the era of global warming threat. Solid oxide fuel cells stand out among other fuel cell types because they are especially feasible for high-temperature applications. Besides the operating parameters, which are frequently encountered problems in SOFCs, physical parameters also directly affect cell performance. For this reason, careful examination of the effects of the parameters while designing the SOFC will contribute to the increase of the maximum power to be provided from the cell in applications. In this study, a solid oxide fuel cell (SOFC) created in flat-tube geometry is numerically modeled. The effect of the electrode and electrolyte layers on the performance is investigated parametrically on the created geometry. In addition, the effect of temperature on cell power is investigated comparatively by making analyzes at different temperatures for each case. In the analyzes, performance values are investigated for electrode layer thicknesses of 0.75 mm, 0.5 mm, and 0.25 mm, and electrolyte layer thicknesses of 1.25 mm, 1 mm, and 0.75 mm, respectively. As a result of the study, the highest cell power is obtained at 0.25 mm of the anode layer thickness. The maximum predicted average cell power of the flat tubular solid oxide fuel cell (FT-SOFC) is approximately 68.2 mW/cm2 for the operating temperature of 1273 K. In the study, the effect of electrolyte conductivity on the performance of the developed cell is also investigated. It is observed that the cell with a conductivity value of 100 S/m at 1073 K operating temperature has the best performance. In addition, in the last part of the study, the performance of SOFC under non-uniform operating temperature conditions is also examined and a comparison is made for this situation, which is frequently experienced in practice. The results show that small changes in fuel cell operating temperature affect the cell performance in positive and negative directions depending on the increasing and decreasing temperature values.

Numerical study on restrained thermal elongation of cold-formed steel Column subjected to non-uniform thermal loading under transient state

Cold-formed steel (CFS) is extensively used as non-load bearing and load-bearing structural members because of its less weight to strength ratio, transportation economy, and handling ease. Since CFS members are treated as slender sections, they are highly susceptible to buckling under the compression loads at ambient and elevated temperatures. The codes IS801, EN1993–1.3, AS/NZS4600, and BS5950 are used to design the cold-formed steel compression members at ambient temperature, and the code EN1993–1.2 is used to design the CFS member by treating it as a slender member with a limiting temperature of 350 °C. Many researchers have attempted to study the behaviour of CFS members at elevated temperatures, both numerically and experimentally, under uniform thermal loading conditions at steady-state. However, studies on non-uniform thermal loading under transient states are minimal. The present study focuses on the numerical modelling of buckling behaviour of CFS members with restrained thermal elongation under non-uniform temperature conditions. The numerical modelling of the CFS column subjected to non-uniform temperature under a transient state is validated with the past results. The parametric study is carried out by varying the initial load, the member's slenderness ratio, the stiffness of the supporting structure, the width-thickness ratio(w/t), and the temperature difference between flanges.

Investigating the Structural Dynamics and Crack Propagation Behavior under Uniform and Non-Uniform Temperature Conditions.

The robustness and stability of the system depend on structural integrity. This stability is, however, compromised by aging, wear and tear, overloads, and environmental factors. A study of vibration and fatigue cracking for structural health monitoring is one of the core research areas in recent times. In this paper, the structural dynamics and fatigue crack propagation behavior when subjected to thermal and mechanical loads were studied. It investigates the modal parameters of uncracked and various cracked specimens under uniform and non-uniform temperature conditions. The analytical model was validated by experimental and numerical approaches. The analysis was evaluated by considering different heating rates to attain the required temperatures. The heating rates were controlled by a proportional-integral-derivative (PID) temperature controller. It showed that a slow heating rate required an ample amount of time but more accurate results than quick heating. This suggested that the heating rate can cause variation in the structural response, especially at elevated temperatures. A small variation in modal parameters was also observed when the applied uniform temperatures were changed to non-uniform temperatures. This study substantiates the fatigue crack propagation behavior of pre-seeded cracks. The results show that propagated cracking depends on applied temperatures and associated mass. The appearance of double crack fronts and multiple cracks were observed. The appearance of multiple cracks seems to be due to the selection of the pre-seeded crack shape. Hence, the real cracks and pre-seeded cracks are distinct and need careful consideration in fatigue crack propagation analysis.

Delineating impacts of non-uniform wall temperature and concentration on time-dependent radiation-convection of Casson fluid under magnetic field and chemical reaction

Purpose In various kinds of materials processes, heat and mass transfer control in nuclear phenomena, constructing buildings, turbines and electronic circuits, etc., there are numerous problems that cannot be enlightened by uniform wall temperature. To explore such physical phenomena researchers incorporate non-uniform or ramped temperature conditions at the boundary, the purpose of this paper is to achieve the closed-form solution of a time-dependent magnetohydrodynamic (MHD) boundary layer flow with heat and mass transfer of an electrically conducting non-Newtonian Casson fluid toward an infinite vertical plate subject to the ramped temperature and concentration (RTC). The consequences of chemical reaction in the mass equation and thermal radiation in the energy equation are encompassed in this analysis. The flow regime manifests with pertinent physical impacts of the magnetic field, thermal radiation, chemical reaction and heat generation/absorption. A first-order chemical reaction that is proportional to the concentration itself directly is assumed. The Rosseland approximation is adopted to describe the radiative heat flux in the energy equation. Design/methodology/approach The problem is formulated in terms of partial differential equations with the appropriate physical initial and boundary conditions. To make the governing equations dimensionless, some suitable non-dimensional variables are introduced. The resulting non-dimensional equations are solved analytically by applying the Laplace transform method. The mathematical expressions for skin friction, Nusselt number and Sherwood number are calculated and expressed in closed form. Impacts of various associated physical parameters on the pertinent flow quantities, namely, velocity, temperature and concentration profiles, skin friction, Nusselt number and Sherwood number, are demonstrated and analyzed via graphs and tables. Findings Graphical analysis reveals that the boundary layer flow and heat and mass transfer attributes are significantly varied for the embedded physical parameters in the case of constant temperature and concentration (CTC) as compared to RTC. It is worthy to note that the fluid velocity is high with CTC and lower for RTC. Also, the fluid velocity declines with the augmentation of the magnetic parameter. Moreover, growth in thermal radiation leads to a declination in the temperature profile. Practical implications The proposed model has relevance in numerous engineering and technical procedures including industries related to polymers, area of chemical productions, nuclear energy, electronics and aerodynamics. Encouraged by such applications, the present work is undertaken. Originality/value Literature review unveils that sundry studies have been carried out in the presence of uniform wall temperature. Few studies have been conducted by considering non-uniform or ramped wall temperature and concentration. The authors are focused on an analytical investigation of an unsteady MHD boundary layer flow with heat and mass transfer of non-Newtonian Casson fluid past a moving plate subject to the RTC at the plate. Based on the authors’ knowledge, the present study has, so far, not appeared in scientific communications. Obtained analytical solutions are verified by considering particular cases of the published works.

Three-dimensional moisture diffusion simulation with time dependent saturated concentration in ANSYS through native thermal and spring elements

This study presents a new modeling approach for moisture concentration in the presence of time dependent saturated moisture concentration and diffusivity by considering only native ANSYS elements. It removes the shortcomings of the ANSYS “diffusion” and “coupled field” elements by employing thermal (LINK33, PLANE55 and SOLID70) and spring (COMBIN14) elements. The accuracy of this modeling approach is established by demonstrating desorption and absorption process in a bar made of two different materials with equal and unequal values of solubility activation energy in the presence of time dependent saturated moisture concentration under uniform and nonuniform temperature conditions. Also, it is applied to a representative three-dimensional electronic package configuration to demonstrate the effect of time dependent saturated moisture concentration on moisture diffusion and weight gain.

Nanoparticles shape effects on thermal performance of Brinkman-type ferrofluid under heat injection/consumption and thermal radiation: A fractional model with non-singular kernel and non-uniform temperature and velocity conditions

The prime aim of this article is the construction of a fractional model to enhance the heat transfer rate for magnetohydrodynamic (MHD) convectional transport of ferrofluid by applying the time-fractional concept of Caputo-Fabrizio derivative on Brinkman-type fluid model. Kerosene oil and water are considered to serve as carrier fluids for iron oxide (Fe3O4) nanoparticles of various non-spherical shapes (brick, cylinder, platelet, and blade). The non-uniform time-dependent motion of an unbounded upward plate causes to generate the flow of ferrofluid. The supplementary physical phenomena such as ramped heating, thermal radiation, and heat injection/consumption are also analyzed. In addition, the effectiveness of using differently shaped Fe3O4 nanoparticles for heat transfer and ferrofluid flow is evaluated. The exact solutions for non-integer order modeled differential equations are computed by employing the Laplace transform method. The comparative graphical illustrations for ramped and constant (isothermal) velocity and temperature conditions are prepared to scrutinize the impacts of several associated thermal and physical quantities. Besides, the outcomes of numerical simulations of Nusselt number and shear stress are communicated through multiple tables for an in-depth analysis. It is perceived that blade and platelet shaped Fe3O4 nanoparticles are more effective to enhance the thermal efficiency of Brinkman-type ferrofluid in contrast to cylinder and brick shaped nanoparticles. It is interesting to report that an improvement of 13.80% in Nusselt number is observed for water based ferrofluid that significantly advances its thermal properties. The fractional parameter γ produces inverse variations in momentum boundary layer thickness for isothermal and ramped plate cases. Additionally, velocity and temperature curves for ramped plate case are always lower than those of isothermal plate case. This fact highlights the importance of plate ramping in heat and flow control problems.

Investigation of a novel multi‐input‐single‐output DC–DC converter topology with GWO‐based MPPT controller for energy harvesting using Seebeck generators at different thermal gradients

This research work proposes an energy harvesting system using Seebeck generators (SGs) with a novel multi-input-single-output (MISO) DC–DC converter and grey-wolf optimisation (GWO)-based maximum power point tracking (MPPT) controller at different thermal gradients. The thermoelectric modules (TEMs) of the SGs convert the thermal energy dissipated by the stator windings of the wind generator (WG) to electrical energy. The proposed MISO power converter topologies have been analysed for two-inputs, four-inputs, n-inputs, and a single-output for producing higher output power to power a DC micro-grid. It has the benefit of higher voltage gain and lower voltage stresses on metal–oxide–semiconductor field-effect transistor switches. The GWO-based MPPT is employed in this work that overcomes the drawbacks of traditional MPPT methods such as steady-state oscillation, transients, global convergence capability, and lower MPPT tracking accuracy under non-uniform temperature conditions. The MPPT controller has effectively tracked a maximum power with a higher tracking accuracy of 98.19%, and the converter has an efficiency of 90.77% corresponding to the wind velocity of 12.9 m/s of the WG. Also, the TEMs are associated in a square series–parallel configuration, and the MISO power converter is analysed with a GWO-based MPPT controller.

A complete framework for the simulation of photovoltaic arrays under mismatch conditions

The mismatch is a phenomenon intrinsically related to photovoltaic (PV) arrays, either because they are eventually subject to non-uniform irradiance and temperature conditions, or because of inner variations on the components, ageing or occurrence of failures. Despite mismatch losses being so present in the life of a PV system, the available tools for the study of PV arrays response through simulation today present limitations for the handling of mismatch conditions. Most of them do not support non-uniform conditions, and the ones that do, solely explore irradiance and temperature variations, ignoring other causes for mismatches, such as defects on PV cells. This paper proposes a simulation framework that allows manipulation of each parameter in each cell individually to reproduce mismatch conditions, including failures. Each PV cell is represented by the one diode equivalent circuit model, for which two different parameterisation methods were tested: California Energy Commission (CEC) and PVSyst. The proposed simulation framework was validated with laboratory measurements of a PV module under 15 different mismatch conditions of partial shading and failure (short circuit). The results showed a consistent similarity between calculated and measured I–V curves, and errors at the curves’ maximum power points stayed within the instruments’ accuracy range, roughly 1.0 V and 0.2 A. The proposed simulation framework brings great flexibility to the studies of mismatch through simulation, allowing the calculation of the I–V curve of PV strings and small arrays subjected to mismatch conditions due to non-uniform irradiance and temperature profiles, but most significantly failures in the cells.

Anomalous Thermodiffusion of Electrons in Graphene

We reveal a dramatic departure of electron thermodiffusion in solids relative to the commonly accepted picture of the ideal free-electron gas model. In particular, we show that the interaction with the lattice and impurities, combined with a strong material dependence of the electron dispersion relation, leads to counterintuitive diffusion behavior, which we identify by comparing a two-dimensional electron gas (2DEG) and single-layer graphene. When subject to a temperature gradient ∇T, thermodiffusion of massless Dirac fermions in graphene exhibits an anomalous behavior with electrons moving along ∇T and accumulating in hot regions, in contrast to normal electron diffusion in a 2DEG with parabolic dispersion, where net motion against ∇T is observed, accompanied by electron depletion in hot regions. These findings bear fundamental importance for the understanding of the spatial electron dynamics in emerging materials, establishing close relations with other branches of physics dealing with electron systems under nonuniform temperature conditions.

Inelastic Lateral-Torsional Buckling Strength of Steel I-Beams under Non-Uniform Temperature Conditions

Inelastic Lateral-Torsional Buckling Strength of Steel I-Beams under Non-Uniform Temperature Conditions

A Novel Global Maximum Power Point Tracking Strategy Based on Modified Flower Pollination Algorithm for Photovoltaic Systems under Non-Uniform Irradiation and Temperature Conditions

Due to the influence of mutative environmental conditions, the photovoltaic (PV) array of a PV system receives with non-uniform irradiation and temperature, which leads to the power-voltage (P-V) output characteristic appearing multi-peak and the current-voltage (I-V) output characteristic emerging multi-steps. With the assistance of various optimization algorithms, maximum power point tracking (MPPT) technologies have become an effective method to improve the conversion efficiency of the PV system under different weather conditions. However, the recognition ability of these algorithms for global peak are still not guaranteed under uneven irradiation and temperature, which have attributed to absence randomness for these algorithms after reaching the maximum power point (MPP) region. Therefore, a modified flower pollination algorithm (MFPA) is proposed in this paper for MPPT. In MFPA, switching between dual-mode optimization is affected by both switch probability and population fitness values, and therefore overcomes the defects that the flower pollination algorithm (FPA) falls easily into the local maximum and slowly convergences in the later period. The performance of MFPA for MPPT is verified by comparing with the perturb & observe method and FPA. Simulation experiment results show that the proposed algorithm can rapidly and accurately track the MPP under various environmental conditions, especially the performance being superior under the condition of strong irradiation and partial shading.

Current Distribution Measurements in Parallel-Connected Lithium-Ion Cylindrical Cells under Non-Uniform Temperature Conditions

Understanding internal state non-uniformity that occurs across the electrodes in large-format Lithium-ion batteries, and among parallel-connected cells, is a critical part of the cell and battery module design process. Two separate groups of parallel-connected 18650 cells were tested using LiFePO4/C6 (LFP), and LiNiMnCoO2/C6 (NMC) chemistries. Pulse and full-capacity discharges were performed at various States of Charge (SOC), C-rates, average temperatures, and levels of temperature non-uniformity. Current non-uniformity for the pulse testing was always lower for the LFP group compared to the NMC group. The hottest cell in the LFP group produced up to 40% more current than average, while this was up to 80% for NMC. Conversely, under charge depleting conditions the NMC group experienced less current non-uniformity, and in certain cases provided a nearly uniform current distribution in the presence of non-uniform temperature. The results indicate that higher temperature sensitivity in the impedance of a cell will cause larger current non-uniformity under pulse conditions. However, due to the presence of non-uniform SOC for charge depleting, the Open Circuit Voltage (OCV) versus SOC gradient plays a significant role in dictating the current distribution behavior, where steeper OCVs provide a corrective action that minimizes the effect of the non-uniform impedance.

Improving spinach quality and reducing energy costs by retrofitting retail open refrigerated cases with doors

The prevalence of open-refrigerated display cases is ubiquitous in retail supermarkets, even in the face of the non-uniform temperature conditions present in these cases. In this paper, the temperature variations (ΔT) of packaged ready-to-eat baby spinach were evaluated for an open display case and a display case with glass doors, in order to assess the advantages of this physical barrier in minimizing ΔT and decay rate, and improving the visual quality of the samples after four days of storage. The two 3.66m display cases were installed in the same room and conditions were constant at 21°C and 60–70% of relative humidity, with a thermostat setting for both cases set at 0.6°C. Results showed that the display case with doors significantly improved temperature uniformity and compliance with the U.S. Food and Drug Administration (FDA) Food Code recommendation of 5°C or less to prevent microbial pathogen growth in packaged leafy greens. Only 1% of the temperature readings over four days in the case with doors were non-compliant with the FDA Food Code, while 24% of the readings in the open case were non-compliant; mostly recorded by the front positions of the case. The lower temperatures and ΔT of the case with doors were consistent with the higher visual quality scores (P<0.001) for the baby spinach samples recorded by trained panelists, based on a 9-point hedonic scale, at 7.2 and 6.6 for the case with doors and the open case, respectively. Differences in decay rate were significant (P<0.001) by the front of the case, with mean values of 8.8% for the open case and 5.5% for the case with doors. Furthermore, operational energy costs were 69% less than the open display case and the cost of door retrofits can be recouped in less than two years by energy savings alone.