Temperature Dependence Of Time Research Articles

Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach.

Thermal loading, especially in fire scenarios, challenges the safety and long-term durability of concrete structures. The resulting heat propagation within the structure is governed by the heat conduction equation, which can be difficult to solve analytically because of the nonlinearity related to the thermophysical properties of concrete. A semi-analytical approach for the transient nonlinear heat conduction problem in concrete structures was established in the present work. The nonlinearity related to the temperature-dependent thermal conductivity, mass density, and specific heat capacity of heated concrete was taken into consideration. A Taylor series approximate solution was first established within a small neighborhood, employing the Boltzmann transformation in combination with the mean value theorem. Thereafter, it was extended to the whole domain by utilizing the Bernstein polynomial. The semi-analytical approach was validated by comparing it with the numerical results of two independent Finite Element simulations of nonlinear heat conduction along concrete plates, subjected to either moderate or fierce thermal loading. Absolute values of the relative errors are smaller than 5%. The validated semi-analytical approach was further applied to prediction of the temporal evolution of the temperature field of a scaled model of a subway station, subjected to fire disaster. The nonlinearities, related to the time-dependent surface temperature and the temperature-dependent thermophysical properties of concrete, were taken into consideration. The predictions agree well with the experimental measurements. The established semi-analytical approach exhibits good accuracy and stability, providing insight into the interaction between the thermophysical properties of concrete in the heat conduction process.

Effect of fin width ratio on thermal performance of fin based-heat sink with phase change materials

The rapid development of electronics, coupled with need of miniaturization in the design and manufacture, makes heat dissipation, which is critical for the performance, lifetime, and reliability of the components extremely challenging. To achieve higher heat dissipation rates, novel fin geometry with variable cross-section considering melting behaviour in medium is presented for PCM-based heat sink beyond previous efforts in literature. In this experimental study, effect of different variable cross-section, which refer different fin width ratio (s = 1, 0.5, 0.2 and 0) values are performed on the thermal performance of plate fin-based heat sink with PCM to enhance melting heat transfer. Decreasing fin width ratios point out increasing heat transfer surface area downwardly. N-eicosane is used. The constant input power is provided at the heat sink base. Thermal performance of novel fin design is evaluated by time-dependent temperature distributions, solid–liquid interface tracking photographs, reliable operating time, enhancement ratio, and thermal conductance. The results reveal that the proposed plate-fin geometry has a significant effect on the cooling performance of PCM-based heat sink. With the decrease of fin width ratio, higher temperature profile with more uniformity of 52% in the PCM medium, and so lower temperature distribution of 4.5% on the heat sink base are provided. Reliable operating time and thermal conductance values go up 15 % and 38%, respectively, for proposed fin geometry. The improvement on the thermal performance is achieved by the form of the plate-fin, which has increased surface area downward. This provides a great contribution to the conduction and convection heat transfer mechanisms at the lower half of the enclosure. Further, in this study, nearly the same reliable operating time is figured out with proposed fin geometry and fin number of s = 0 compared to higher fin number installation of s = 1 previously reported.

Synthesis, structure and slow magnetic relaxation of Ce(III) phenylacetate complex

[Ce(PAA)3(H2O)]n complex (1) (HPAA is phenylacetic acid) was synthesised and studied. The crystal structure of 1 was elucidated by the Rietveld method. Its crystal structure is polymeric and is built up of Ce(III) ions interconnected by bridging PAA− ligands. The Ce(III) ions in 1 are nona-coordinated by eight carboxylate oxygen atoms from six PAA− ligands, and one aqua ligand completes the coordination sphere yielding O8O donor set. The studied material displays field-induced slow magnetic relaxation. Temperature dependence of the relaxation time suggests the existence of direct and Raman relaxation processes. Similarly, as for the other Ce(III) complexes, the existence of Orbach process may be questioned due to the large discrepancy between the value of the energy gap obtained from static and dynamic measurements.

Decrypting the mechanisms of wicking and evaporation heat transfer on micro-pillars during the pool boiling of water using high-resolution infrared thermometry

Surfaces with micrometer-scale pillars have shown great potential in delaying the boiling crisis and enhancing the critical heat flux (CHF). However, physical mechanisms enabling this enhancement remain unclear. This knowledge gap is due to a lack of diagnostics that allow elucidating how micro-pillars affect thermal transport phenomena on the engineered surface. In this study, for the first time, we are able to measure time-dependent temperature and heat flux distributions on a boiling surface with engineered micro-pillars using infrared thermometry. Using these data, we reveal the presence of an intra-pillar liquid layer, created by the nucleation of bubbles and partially refilled by capillary effects. However, contrarily to conventional wisdom, the energy removed by the evaporation of this liquid cannot explain the observed CHF enhancement. Yet, predicting its dry out is the key to delaying the boiling crisis. We achieve this goal using simple analytic models and demonstrate that this process is driven by conduction effects in the boiling substrates and, importantly, in the intra-pillar liquid layer itself. Importantly, these effects also control the wicking flow rate and its penetration length. The boiling crisis occurs when, by coalescing, the size of the intra-pillar liquid layer becomes too large for the wicking flow to reach its innermost region. Our study reveals and quantifies unidentified physical aspects, key to the performance optimization of boiling surfaces for cooling applications.

Experimental and Numerical Predictions of Cryogenic Leakages in Welded Steel Plates

This study presented experimental and numerical research to investigate the effect of cryogenic leakage on a plate structure of AH36-grade steel containing welded joints. To simulate the cryogenic leakage conditions, the welded plate was exposed to a temperature of −196 °C by supplying liquid nitrogen (LN2) to the center of the steel plate. The time-dependent temperature history and strain variation were measured by using thermocouples and strain gauges attached to the plate surface. Additionally, the residual stress of the middle surface section before and after the cryogenic leakage process was measured by X-ray diffraction analysis (XRD). A three-dimensional finite element model was created with the use of a commercial finite element analysis (FEA) program to simulate the flux-cored arc welding process and cryogenic leakage process. The steel surface temperature dropped sharply and reached approximately −196 °C at 160 s after LN2 supplement. After the first 650 s of the LN2 leakage experiment, the outside of the trough reached approximately −75 °C and −25 °C, depending on the location of the thermal couples. Although there was a relative difference in the results, the experiment and numerical simulation results for temperature and stress distribution showed good agreement. The results could be utilized in the ship design stage adopting welded structures as a basic database.

Theoretical analysis for thermal consolidation of marine sediments with depth variability subjected to time-dependent loading and heating

Because the spatial distribution of energy is restricted, many energies geotechnics would build on marine sediments and the resulting thermal consolidation would pose an inevitable threat to the safety and stability of the project. In this study, a new governing equation for thermal consolidation of saturated marine sediments is proposed, by considering the depth variability of the marine sediment layer and the time-dependent external loading and temperature. The corresponding one-dimensional (1D) analytical solution for thermal consolidation of saturated marine sediments is derived. The average degree of consolidation (Ua) and the normalized excess pore water pressure (u/u0) in the saturated marine sediment layer at different depths and time durations are calculated and compared with the typical loading case. The results show that the loading rate of the external force only affects the amplitude of the excess pore water pressure u and does not affect the proportion of u with depth; the depth variability of bulk modulus has a greater effect on the distribution of Ua relative to the depth variability of permeability; the depth variability of permeability has a greater effect on the distribution of u/u0 with depth relative to the depth variability of bulk modulus when Ua = 50%; the assumption of instant thermal loading will lead to an over-assessment of Ua and u/u0. This study provides useful insights for energy geotechnical engineering design and practice.

Analytical solution of two-dimensional unsteady heat conduction in multi-layered cylindrical sectors applied to thermal plug and abandonment of oil wells

In this work, a hybrid analytical and numerical solution for transient heat conduction across a composite cylindrical sector is presented. A two-dimensional domain consisting of a multi-layer circular sector of angle φ was investigated (φ<2π). The Separation of Variables Method (SVM) was applied to solve the partial differential equation with non-homogeneous boundary conditions of the first, second and third kinds prescribed in the radial direction. Homogeneous boundary conditions of first and second kinds were arbitrated in the angular direction. A spatial time-independent source term gi(r,θ) was considered. The radial eigenvalues problem for the (r,θ) domain returns only real quantities and depends implicitly on the angular eigenvalues. Results for time dependent temperatures using the Separation of Variables Method were compared with numerical results, showing good accuracy. A second set of results was developed to investigate boundary conditions, material properties and the thermal source power required to rise temperature levels (mainly around the mid-angle φ/2) high enough to promote melting of certain layers of materials. These results might be useful for investigating a novel technology for the decommissioning of oil wells using thermal sources, often referred to in the literature as Thermal Plug and Abandonment (TP&A).

Implications of Drug-Polymer Interactions on Time-Temperature-Transformation: A Tool to Assess the Crystallization Propensity in Amorphous Solid Dispersions.

The critical cooling rate (CRcrit) to prevent drug crystallization during the preparation of nifedipine amorphous solid dispersions (ASDs) was determined through the time-temperature-transformation (TTT) diagram. ASDs were prepared with polyvinylpyrrolidone, hydroxypropylmethyl cellulose acetate succinate, and poly(acrylic acid). ASDs were subjected to isothermal crystallization over a wide temperature range, and the time and temperature dependence of nifedipine crystallization onset time (tC) was determined by differential scanning calorimetry (DSC) and synchrotron X-ray diffractometry. TTT diagrams were generated for ASDs, which provided the CRcrit for the dispersions prepared with each polymer. The observed differences in CRcrit could be explained in terms of differences in the strength of interactions. Stronger drug-polymer interactions led to longer tC and decreased CRcrit. The effect of polymer concentrations (4-20% w/w) was also influenced by the strength of the interaction. The CRcrit of amorphous NIF was ∼17.5 °C/min. Addition of 20% w/w polymer resulted in a CRcrit of ∼0.05, 0.2, and 11 °C/min for the dispersions prepared with PVP, HPMCAS, and PAA, respectively.

Αn integrated life cycle assessment and life cycle costing approach towards sustainable building renovation via a dynamic online tool

Building stock retrofitting is essential to achieve the ambitious sustainability goals of the building sector due to its high energy consumption rates. The evaluation of the various building interventions shall be holistically assessed in terms of environmental and costing impact. The aim of this paper is twofold: First, it presents the innovative characteristics of a developed online tool (Virtual intEgrated platfoRm on LIfe cycle AnalYsis - VERIFY) able to perform dynamic life cycle analysis and global warming impact assessments by capitalizing on the well-known LCA and LCC methodologies, applicable in the case of building renovation. VERIFY is able to analyse dynamic life cycle inventories that consider the temporal profiles of energy consumption, and the time-dependent temperature changes, while being also interoperable in terms of exchanging data with other available energy simulation engines, or even using real-time monitoring data from sensors, processing any data time granulation. Second, the paper evaluates, from a life cycle perspective, the impact of specific energy retrofitting measures, meeting the Passive House Standard, for the case of a multi-family residential building in Athens, Greece. The proposed energy-retrofitting scenario examines actions related to the deep retrofitting of the building envelope and the upgrade of the thermal components as well as to the incorporation of clean electricity generation based on renewable energy systems; all aiming to drastically reduce the environmental impact of the building, rendering it almost near zero energy. Through the planned infrastructure installations, the primary energy needs and CO2eq emissions were reduced by 91 % and by 95 % respectively, while for a building operational lifespan of 25 years, savings up to 515 k€ compared to the baseline scenario, can be achieved.

Reconstruction of the Thermal Load of a Functionally Graded Hollow Sphere by Surface Displacements

We formulate and solve a problem of reconstruction of the unknown time-dependent temperature distribution on one boundary surface of a functionally graded hollow sphere according to the temperature and radial displacements on the other boundary surface. We suggest a procedure reducing the formulated problem to the inverse thermoelasticity problem. By applying the finite-difference method, we construct a numerical algorithm aimed at solving the obtained inverse problem. By using the solution of the direct thermoelasticity problem, we analyze the stability of the obtained solution of the inverse problem and the distributions of displacements and stresses obtained on the basis of this solution against the errors of the input data.

Structural, magnetic, and biocompatibility evaluations of chromium substituted barium hexaferrite (Co2–Y) for hyperthermia application

In the present work, chromium-substituted cobalt-based Y-type barium hexaferrite ceramics having a general formula of Ba2Co2Fe12-xCrxO22 (0.0 ≤ x ≤ 0.5) have been studied to evaluate its potential candidacy as an optional replacement for various soft ferrite materials in the field of magnetic hyperthermia. The as-obtained ferrite powders are characterized for structural, magnetic, and morphological properties after being calcined at 1200 °C for 2 h. The structural parameters confirm single-phase nanocrystalline Y-type barium hexaferrite formation within all the samples. The room temperature magnetic parameter, i.e., saturation magnetization (Ms), is found to decrease (from 39.07 to 33.50 emu/g), and the coercive field (Hc) is increased (86.87–281.84 Oe) consistently. Later, oleic acid-coated ferrite samples' heating capability is governed within the applied AC magnetic field (25 mT at a frequency of 114.1 kHz) in terms of specific absorption rate (SAR) using time-dependent temperature performance. The superiority of the sample having the greatest SAR value (84.39 w/g for Ba2Co2Fe11.7Cr0.3O22) is interrelated with the particles' geometry, size distribution, magnetic parameters, and surface chemistry obtained from the XPS analysis. This sample is further analyzed for its biocompatibility performance against the MG-63 cell line; the results indicate that it may be a potential candidate for magnetic hyperthermia due to its significant SAR & ILP value along with better biocompatibility.

Photo-activated time-dependent color-changeable ultralong organic room temperature phosphorescence by co-doping strategy

We for the first time report photo-activated time-dependent color-changeable ultralong organic room temperature phosphorescence (UORTP) by co-doping derivatives (CN2BdBr and CN2BCzBr) of two phosphorescence units, H-benzo[f]indole (Bd) and 7H-benzo[c]carbazole (BCz).

Low-temperature magnetoresistance of functionalized multiwall carbon nanotubes

Temperature and magnetic field dependencies of resistance for functionalized multiwall carbon nanotubes (MWCNTs) have been studied. The measurements were carried out in the temperature range T = 4.2–200 K. It is shown that in magnetic fields up to B = 9 T, the conductivity behavior for the functionalized MWCNTs sample can be described in terms of charge carriers weak localization and interaction phenomena. We show that the contribution to the functionalized MWCNTs conductivity due to the weak localization effect exceeds the quantum correction due to the effect of the charge carriers interaction for all the temperatures and in the entire range of the applied magnetic fields except for the magnetic fields above B = 6.5 T at T = 5 K. Within the terms of the specified models, we estimate the value of the Fermi energy and determine the explicit form of the temperature dependence of the phase relaxation time for the wave function. We show that for the functionalized MWCNTs sample, the phase relaxation time for the wave function has a less pronounced temperature dependence, and its Fermi energy is more shifted to the valence band compared to non-functionalized MWCNTs. The charge carriers’ interaction constant at different temperatures can also be estimated from our experiments.

Dielectric relaxation of ice in a partially crystallized poly(N-isopropylacrylamide)microgel suspension compared to other partially crystalized polymer-water mixtures.

A broadband dielectric spectroscopy study was conducted on a partially crystallized 10 wt% poly(N-isopropylacrylamide) [PNIPAM] microgel aqueous suspension to investigate the dielectric relaxation of ice in microgel suspensions. The measurements covered a frequency range of 10 mHz to 10 MHz and at temperatures ranging from 123 K to 273 K. Two distinct relaxation processes were observed at specific frequencies below the melting temperature. One is associated with the combination of the local chain motion of PNIPAM and interfacial polarization in the uncrystallized phase, while another is associated with ice. To understand the temperature-dependent behaviour of the ice relaxation process, the relaxation time of ice was compared with those observed in other frozen polymer water mixtures, including gelatin, poly-vinylpyrrolidone (PVP), and bovine serum albumin (BSA). For concentrations ≥ 10 wt%, the temperature dependence of the relaxation time of ice was found to be independent. Therefore, the study primarily focused on the 10 wt% data for easier comprehension of the ice relaxation process. It was found that the microgel and globular protein BSA had no significant effect on ice crystallization, while gelatin slowed down the crystallization process, and PVP accelerated it. To discuss the mechanism of the dielectric relaxation of ice, the trap-controlled proton transport model developed by Khamzin et al. [Chem. Phys., 2021, 541, 111040.] was employed. The model was used to discuss the dynamic heterogeneity of ice observed in this investigation, distinguishing it from the spatial heterogeneity of ice commonly discussed.

Synthesis, structures and magnetic studies of hexanuclear lanthanide complexes: SMM behavior of the DyIII analogue and MCE properties of the GdIII analogue.

The synthesis, structure and magnetic properties of homometallic hexanuclear lanthanide complexes [Ln6(HL)4(tfa)4(S)2]·2NO3·x H2O·yMeOH (1, Ln = Gd, S = MeOH, x = 0, y = 0; 2, Ln = Tb, S = H2O, x = 2, y = 2; 3, Ln = Dy, S = MeOH, x = 0, y = 2; 4, Ln = Er, S = MeOH, x = 0, y = 2). [(H4L) = 6-((bis(2-hydroxyethyl)amino)-N'-(2-hydroxybenzylidene)picolinohydrazide) (tfa = trifloroacetylacetone)] are reported. These hexanuclear assemblies are made up of two trinuclear triangular sub-units linked through the oxygen atoms of two phenoxide bridging groups in a corner sharing arrangement. Magnetic studies reveal that 1 displays a magnetocaloric effect with a maximum value of -ΔSm = 21.03 J kg-1 K-1 at T = 3 K and under an applied field change ΔB = 5 T. Complex 3 shows slow relaxation of magnetization even under zero applied field although a clear maximum in the ac susceptibility plots cannot be seen. However, under an optimal applied field of 0.2 T, clear maxima are observed in the out-of-phase (χ''M) component of the ac susceptibility in the temperature range 3.5 K (2 kHz) to 10.5 K (10 kHz). The temperature dependence of the relaxation times could be fitted to the sum of Orbach, Raman and QTM relaxation processes affording the following parameters: τo = 3.4(9) × 10-8 s, Ueff = 94(2) K, BRaman = 16.43(1) K-n s-1, n = 3.2(3) and τQTM = 0.0044(3) s. 4, under an applied magnetic field of 0.2 T, shows slow relaxation of magnetization through a thermally activated Orbach process with Ueff = 18.2(9) K and τo = 3.5(3) × 10-8 s.

Revisiting “Non-Thermal” Batch Microwave Oven Inactivation of Microorganisms

Over the last few decades there has been active discussion concerning the mechanisms involved in “non-thermal” microwave-assisted inactivation of microorganisms. This work presents a novel non-invasive acoustic measurement of a domestic microwave oven cavity-magnetron operating at fo = 2.45 ± 0.05 GHz (λo ~ 12.2 cm) that is modulated in the time-domain (0 to 2 minutes). The measurements reveal the cavity-magnetron cathode filament cold-start warm-up period and the pulse width modulation periods (time-on time-off and base-time period, where time-on minus base-time = duty cycle). The waveform information is used to reconstruct historical microwave “non-thermal” homogeneous microorganism inactivation experiments: where tap-water is used to mimic the microorganism suspension; and ice, crushed ice, and ice slurry mixture are used as the cooling media. The experiments are described using text, diagrams, and photographs. Four key experimental parameters are indentified that influence the suspension time-dependent temperature profile. First, where the selected process time > the time-base, the cavity-magnetron continuous wave rated power should be used for each second of microwave illumination. Second, external crushed ice and ice slurry baths induce different cooling profiles due to difference in their heat absorption rates. In addition external baths may shield the suspension resulting in a retarding of the time-dependent heating profile. Third, internal cooling systems dictate that the suspension is directly exposed to microwave illumination due to the absence of surrounding ice volume. Fourth, four separated water dummy-loads isolate and control thermal heat transfer (conduction) to and from the suspension, thereby diverting a portion of the microwave power away from the suspension. Energy phase-space projections were used to compare the “non-thermal” energy densities of 0.03 to 0.1 kJ·m-1 at 800 W with reported thermal microwave-assisted microorganism inactivation energy densities of 0.5 to 5 kJ·m-1 at 1050 ± 50 W. Estimations of the “non-thermal” microwave-assisted root mean square of the electric field strength are found to be in the range of 22 to 41.2 V·m-1 for 800 W.

Second order hydrodynamics based on effective kinetic theory and electromagnetic signals from QGP

We study the thermal dilepton and photon production from relativistic heavy ion collisions in presence of viscosities by employing the recently developed second order dissipative hydrodynamic formulation estimated within a quasiparticle description of thermal quantum chromo-dynamics (QCD) medium. The sensitivity of shear and bulk viscous pressures to the temperature dependence of relaxation time is analyzed within one- dimensional boost invariant expansion of quark gluon plasma (QGP). The dissipative corrections to the phase-space distribution functions up to first order in gradients are obtained from the Chapman–Enskog like iterative solution of effective Boltzmann equation in the relaxation time approximation. Thermal dilepton and photon production rates for QGP are calculated by employing this viscous modified distribution function. Yields of these particles are quantified for the longitudinal expansion of QGP with different temperature dependent relaxation times. Our analysis employing this second order hydrodynamic model indicates that the spectra of dileptons and photons get enhanced by both bulk and shear viscosities and are well behaved. Also, these particle yields are found to be sensitive to relaxation time. Further, we do a comparison of these particle spectra with a standard hydrodynamic formulation.

Experimental and kinetic modeling study of tetramethylethylenediamine: A promising green propellant fuel

Tetramethylethylenediamine (TMEDA) is a promising green propellant fuel and reactivity promoter. However, the reactions between TMEDA and O2 are usually overlooked under ignition conditions. In this study, significant low-temperature reactivity was observed for 2%TMEDA/O2 mixtures, and autoignition could occur even at 470 K. To probe the chemical kinetics of TMEDA/O2, ignition delay times were measured in a rapid compression machine and a high-pressure shock tube. TMEDA pyrolysis products were also obtained in a single pulse shock tube. The autoignition of TMEDA/O2 in rapid compression machine experiments showed multi-stage heat release, a characteristic which became more obvious at oxygen-lean conditions. During the oxidation experiments, a non-Arrhenius temperature dependence of ignition delay time was observed. A chemical kinetic model of TMEDA was developed hierarchically, based on current reaction kinetics knowledge about hydrocarbons, small amines and NOx. Ignition delay times and pyrolysis products measured in this study, along with experimental data on small amines from the literature, were used to validate the kinetic model, which generally produced good predictions across different temperature, pressure and equivalence ratio conditions.

Effect of casting temperature on the solidification process and (micro)structure of Zr-based metallic glasses

Bulk metallic glasses (BMGs) bear versatile advantages compared to traditional crystalline metallic materials. However, preparation of large size BMG components remains a great challenge due to the lack of understanding the casting dynamics of BMGs. The present work investigates the dynamics of the solidification process during casting of a Zr41.2Ti13.8Cu12.5Ni10Be22.5 BMG by measuring the time-dependent temperature evolution and constructing distance–time curves showing the progress of solidification. The experimentally probed temperature evolution proves that a higher casting temperature causes a lower cooling rate and induces more pronounced nanocrystal phase formation in the final BMG casting. Thus, optimization of the casting temperature is crucial for casting BMG components. The solidification coefficient K of the studied Zr-based BMG in copper mold was determined. The solidification time can be calculated with model: τ=M2K2. The solidification of the Zr-based BMG occurs in a narrow transition layer region following a “layer-by-layer” solidification mode. This feature is vital for designing the casting process appropriately to avoid the formation of casting defects in BMG components. The present work sheds new light on the solidification mechanism of bulk glass-forming liquids and underlines the importance of optimizing the technology and processing conditions for fabrication of BMG components with practical applications.

Stochastic thermodynamics of fractional Brownian motion

This paper is concerned with the stochastic thermodynamics of nonequilibrium Gaussian processes that can exhibit anomalous diffusion. In the systems considered, the noise correlation function is not necessarily related to friction. Thus there is no conventional fluctuation-dissipation relation (FDR) of the second kind and no unique way to define a temperature. We start from a Markovian process with time-dependent diffusivity (an example being scaled Brownian motion). It turns out that standard stochastic thermodynamic notions can be applied rather straightforwardly by introducing a time-dependent temperature, yielding the integral fluctuation relation. We then proceed to our focal system, that is, a particle undergoing fractional Brownian motion (FBM). In this case, the noise is still Gaussian, but the noise correlation function is nonlocal in time, defining a non-Markovian process. We analyze in detail the consequences when using the conventional notions of stochastic thermodynamics with a constant medium temperature. In particular, the heat calculated from dissipation into the medium differs from the log ratio of path probabilities of forward and backward motion, yielding a deviation from the standard integral fluctuation relation for the total entropy production if the latter is defined via system entropy and heat exchange. These apparent inconsistencies can be circumvented by formally defining a time-nonlocal temperature that fulfills a generalized FDR. To shed light on the rather abstract quantities resulting from the latter approach, we perform a perturbation expansion in terms of $\ensuremath{\epsilon}=H\ensuremath{-}1/2$, where $H$ is the Hurst parameter of FBM and $1/2$ corresponds to the Brownian case. This allows us to calculate analytically, up to linear order in $\ensuremath{\epsilon}$, the generalized temperature and the corresponding heat exchange. By this, we provide explicit expressions and a physical interpretation for the leading corrections induced by non-Markovianity.