Longitudinal Thermal Conductivity Research Articles

Spatiotemporal Variability of Hyporheic Flow in a Losing River Section

AbstractCharacterizing the spatiotemporal variability of water fluxes at the stream‐groundwater interface is extremely challenging due to the lack of methods for estimating hyporheic flows at different scales. To address this, we demonstrate the potential of Active‐Distributed Temperature Sensing (DTS) methods for measuring and mapping hyporheic flow in a lowland stream. Experiments were conducted by burying a few hundred meters of heatable Fiber‐Optic cables within streambed sediments in a large meander, where permanent stream‐losing conditions are observed along the stream reach. We propose a new methodology to filter ambient temperature variations along the heated section of the DTS cable and to extend the application of Active‐DTS to losing streams. After data processing, the results show that, along lateral and longitudinal stream profiles, both thermal conductivity and water flux values follow normal distributions with relatively small standard deviations. Hyporheic fluxes vary by one order of magnitude. The absence of correlation between water fluxes within the hyporheic zone and streambed topography variations suggests that the variability is mainly controlled by local streambed heterogeneities. This means that the spatiotemporal variability of fluxes may be used as a marker of the variability of streambed hydraulic conductivities. The relatively low spatial variability (one order of magnitude) in hyporheic flow suggests a small variability of streambed properties. This is an important result for calibrating models assessing hyporheic processes, in which the hydraulic conductivity distribution is generally assumed. Additionally, measurements made over three years yield similar estimates showing the remarkable stability of hyporheic flows through time.

Cryogenic thermal conductivity of carbon fiber reinforced polymer composite laminates

Carbon fiber reinforced polymer (CFRP) composites with excellent mechanical properties and low thermal conductivity are promising materials for cryogenic facility support structures. However, the temperature dependence and stacking sequence dependence of the laminates’ thermal conductivities challenge their thermo-mechanical design. Previous work dealing with the cryogenic thermal conductivity of laminates was relatively inadequate, and the effect of stacking sequence has not been sufficiently clarified. Herein, the cryogenic thermal conductivity of CFRP composite was investigated, and a theoretical model for the out-of-plane thermal conductivity of laminate was developed. To this end, the thermal conductivities of epoxy resin and laminates were measured at temperatures from 20 K to 293 K. The cryogenic thermal conductivity of carbon fiber was then extrapolated. Subsequently, a theoretical model was developed based on the thermal-electrical analogy method to evaluate the effect of stacking sequence. The obtained model was then validated by numerical analysis and experimental work. Lastly, the effects of lay-up angles and component properties on out-of-plane conductivity were examined. The test results suggested longitudinal thermal conductivity of composites exhibiting significant temperature dependence, with a decreasing trend recorded from 6.317 Wm−1K−1 to 0.355 Wm−1K−1 and transverse thermal conductivity decline from 0.626 Wm−1K−1 to 0.156 Wm−1K−1. The theoretical analysis indicated that the stacking sequence could reduce the out-of-face thermal conductivity by up to approximately 6.5 %, while the lay-up angle did not show any influence. In sum, novel insights into the cryogenic thermal conductivity of CFRP composites were provided, with guidance for the design and analysis of CFRP composites in cryogenic applications.

Progress of open systems at Budker Institute of Nuclear Physics

This paper is based on a report at the 2nd International Fusion Plasma Conference & 13th International Conference on Open Magnetic Systems for Plasma Confinement (iFPC & OS 2023), August 21–25, 2023, Busan, Korea and provides a brief overview of the status of work at the Budker Institute on the study of hot plasma confinement in open-type magnetic traps with a linear axisymmetric configuration. The main attention is paid to key problems: magnetohydrodynamics (MHD) stability in regimes with extremely high relative pressure, longitudinal electronic thermal conductivity, stability with respect to the development of kinetic modes and transverse transport. This paper provides an overview of the methods we are developing to address these problems, the experimental and theoretical results achieved and plans for future development. The last section of the article provides brief information about the preliminary design of the gas-dynamic multiple-mirror trap device, the development of which has been completed.

Mechanism of Beam-Plasma Discharge Development in the Gas Dynamic Trap

The work studies how a plasma discharge in the Gas Dynamic Trap (GDT) is ignited in a volume significantly exceeding the volume of the injected electron beam. This property of a beam-plasma discharge makes it attractive to use relatively low-power electron beams to create starting plasma in open traps with parameters sufficient for its further effective heating by the neutral injection. Despite the fact that effective ionization of plasma far beyond the electron beam in open traps has been observed experimentally for more than 60 years, the detailed mechanism of this phenomenon is still not clear. Particularly many questions arise in regimes that are implemented in such large fusion facilities as GDT, where the relaxation length of the beam turns out to be significantly less than the length of the trap, and the turbulence excited by the beam is localized near the entrance magnetic mirror. Based on recent experiments [E.I. Soldatkina et al. Nucl. Fusion 62, 066034 (2022)], we have proposed a scenario for the development of a discharge in GDT, according to which a compact region of intense plasma turbulence first rapidly expands radially, ionizing the gas outside the beam tube in the vicinity of a magnetic mirror, and then a slower ionization process begins in the rest trap volume both due to the tail of suprathermal particles that are formed in the turbulence zone, and due to thermal electrons that receive energy from the pumping region via the longitudinal electron thermal conductivity. To assess how well this scenario explains the experimentally observed dynamics of plasma density growth in different parts of the facility, we carry out particle-in-cell simulations of the radial expansion of the turbulence zone and propose a simplified model of impact ionization in the entire volume of the trap by both thermal and suprathermal electrons.

Horizontal flame spread behavior of densified wood: Effect of structural characteristics

Densified wood (DW) is a recently developed material with excellent mechanical properties, considered as an ideal construction material for high-rise timber buildings. However, its flame spread behavior has not been well understood limiting its applications. This work for the first time experimentally and analytically investigates the horizontal flame spread behavior of DW. The influences of material structural characteristics (e.g. density) on heat transfer characteristics are focused. Thermally thin DW with density ranges of 441–1025 kg/m3 and a constant thickness of 2 mm were tested. The flame spread rate, mass loss rate (MLR) and flame height decreased with the increased wood density. A power-law correlation between the dimensionless MLR and dimensionless density is proposed, which well predicts the experiments with an R2 of 0.922. The increased wood density decreases flame height and reduces flame radiation. The gas-phase heat transfer shifts from radiation-dominant to convection-dominant. The longitudinal and radial thermal conductivities of DW increased with wood density. Empirical equations are optimized to predict the thermal conductivities of DW with R2 of 0.870 (longitudinal) and 0.837 (radial). The preheating zone length and the temperature gradient per unit length don’t vary significantly with wood density. Their values are averaged to 25.62 mm and 9.312 K/mm respectively. The longitudinal heat conduction is increased with the wood density due to the increased conductivity. However, this conduction increase is lower than the radiation decrease as the wood density increases. Thus, the total heat flux is slightly decreased with the wood density. The gas phase heat transfer dominates the flame spread. However, the longitudinal heat conduction can account for more than half of the gaseous heat transfer, and thus cannot be negligible. Results of this work improve the understanding of DW flame spread, which helps to evaluate the fire behaviors of timber construction.

Advancing the precision of thermal Hall measurements for novel materials research

Precision thermal Hall measurements unlock potential for unraveling fundamental thermal transport principles in novel materials. This work addresses the challenge of resolving sub-mK temperature differences in magnetic fields by employing high-precision capacitance thermometry with thermalized electronics, achieving a background noise of approximately ▪ at ▪. The novelty lies in the improvement and combination of innovative approaches, including the application of attenuators for thermal anchoring, a modular multi-stage approach to reduce thermal gradients, direct thermometer-sample assembly, and the use of individual capacitance bridges for faster measurements. The setup performance is demonstrated for the pyrochlore oxide terbium titanate and the longitudinal and transverse thermal conductivities agree with the literature. We show that the transverse temperature difference is proportional to the product of magnetic field times heating power for fields up to ▪, enabling improved statistics compared to individual sweeps analysis. We conduct an analysis of uncertainties in the transverse thermal conductivity, considering various thermometer calibrations for extracting temperature differences. This analysis reveals a significant influence of the longitudinal conductivity on the transverse thermal conductivity. These advancements allow for unprecedented temperature resolution and stability, while identified resolution limitations pave the way for next-generation setups.

Determination of the longitudinal thermal conductivity of low‐ordered carbon fibers by using an optothermal Raman technique

AbstractThe usage of carbon fibers (CFs) for high‐temperature applications has been increasing in recent years. However, the determination of thermal properties at high temperatures is a challenging task. In this study, the thermal conductivity of two different types of CF having a diameter in the range from 5–7 m, as a function of temperature, was examined by using the optothermal Raman method. Raman spectroscopy was first used to obtain the structural organization and structural homogeneity of the fibers. Then, owing to the fact that Raman spectra are sensitive to laser excitation power and external temperature, Raman spectroscopy was used as a contactless thermometer to determine the local temperature rise of the fibers. A formula was derived by solving the heat diffusion equation for cylindrical fibers and a set of boundary conditions, similar to the experimental conditions, which allows accurate estimation of longitudinal thermal conductivity. The results are discussed in relation with the phonon scattering theory and can be attributed to the combined effect of scattering from defects. The radiative and convective heat losses were estimated, and their influence on thermal conductivity was also determined.

Improving permeability and fouling resistance of GO hydrophilic/hydrophobic Janus membrane by polyether amine crosslinking for membrane distillation of dye wastewater

Graphene oxide (GO) modification is promising to increase vapor flux and antifouling properties of hydrophobic membranes in membrane distillation for wastewater treatment. However, the acid bonding of GO with dyes impedes its wide application in dye wastewater treatment. In this study, polyether amine D400 was used to modify hydrophilic GO layer of Janus membrane. The GD3/PTFE composite membrane (GO and D400 mass ratio of 1:2) demonstrated the best water flux and antifouling performance for methyl orange (MO) containing 3.5 wt% NaCl. The flux was increased by 170.3%− 228.9% compared to PTFE pristine membrane and the flux decline due to fouling was decreased by 41.3%− 60.8% to GO/PTFE membrane. The observed increase in the longitudinal thermal conductivity of the cross-linked GO layer suggests that the enhanced permeability is attributed to improved heat transfer resulting from the higher density of GO nanosheets. Acid bonding of GO layer with dye molecular is weakened and electrostatic repulsion is also increased, leading to the excellent antifouling performance. This study indicate that polyether amine crosslinking is promising method for modification of GO composite membrane for dye wastewater treatment.

MXene/Graphene modified cellulose aerogel for photo-electro-assisted all-weather cleanup of high-viscous crude oil from spill

The frequent occurrence of oil spills has led to serious environmental pollution and ecological issues. Given the high-viscosity of crude oil, it is essential to develop sorbents with efficient viscosity reduction and sorption capacity in various environmental conditions. Herein, a superhydrophobic carboxymethyl cellulose (CMC) aerogel co-modified by MXene and graphene jointly (M-Mxene/Gr CA) with aligned channels structure was prepared. The aligned channels structure can effectively improve the longitudinal thermal conductivity and reduce the sorption resistance. Through the modification of MXene and graphene, the aerogel realized efficient photo/electro-thermal conversion, thus ensuring its adaption to various working environments. The rapid heat generation can significantly reduce the viscosity of crude oil, achieving rapid recovery. Under one sun illumination (1.0 kW/m2), the surface temperature of M-Mxene/Gr CA can reach 72.6 °C and its sorption capability for high-viscous crude oil reaches 18 g/g. Combining photo-thermal and electro-thermal (0.5 kW/m2 and 23 V), the average sorption rate of crude oil can reach 1.3 × 107 g m−3 s−1. Finally, we present a continuous sorption system to recover offshore oil spills under the assistance of a pump. This work provides a new option for tackling high-viscous offshore oil spills due to its environmental friendliness and fast sorption capacity.

Analysis of heat transfer in an aquifer thermal energy storage system: On the role of two-dimensional thermal conduction

Aquifer thermal energy storage (ATES) system plays an important role in application of renewable energy, efficient energy utilization, and reduction of CO2 emission. To realize the successful operation of ATES systems, it is essential to understand the thermal behaviors thoroughly during heat injection. Serving as a powerful tool, analytical model is widely adopted while the existing analytical models usually simplify ATES systems by ignoring aquifer transverse thermal conduction and rock longitudinal thermal conduction. This study develops a novel analytical model for an ATES system, which accounts for thermal convection, dispersion, longitudinal and transverse thermal conduction in the aquifer, and longitudinal and transverse thermal conduction in the surrounding rocks. The Green's function method is applied to derive the semi-analytical solutions of temperature. A global sensitivity analysis is conducted to analyze the relative importance of each parameter. The results indicate that ignoring the aquifer transverse thermal conductivity will overestimate the temperature in the aquifer and ignoring the caprock longitudinal thermal conductivity may underestimate the heat loss in ATES systems. Similar conclusion can be made about the bedrock longitudinal thermal conductivity. The global sensitivity analysis indicates that temperature is sensitive to the changes in the flow velocity, thermal dispersivity and aquifer thickness.

Facile fabrication of green and sustainable functionalized Bombax ceiba L. wood based aerogel for multifunctional applications

Design and development of biobased porous, strong, and anisotropic aerogels through easy and ecofriendly process for multifunctional applications has been research priority for the globe. Wood is considered as a preferable renewable precursor to prepare aerogels with inherent heirarchical structure and high porosity. In this work, Bombax ceiba L. wood has been delignified through a top to bottom process to develop wood aerogel (WA) which retain the heirarchical nature of wood. Wood aerogel (WA) was functionalized with 3-Aminopropyl triethoxy silane (APTES) to graft silane functionality for achieving multifunctional applications like oil/water separation, thermal insulation, acoustic panel making etc. Prepared delignified and silanised wood aerogels (DWS10 or DWS) showed good surface morphology, impressive super hydrophobicity (167.6° ± 5.4°) and high compression modulus of 82.6 ± 5.0 MPa which is 3.75 times greater than that for the wood aerogel (WA). The longitudinal (along the fibres) and transverse (across the fibres) thermal conductivity of DWS (0.122 ± 0.006 and 0.081 ± 0.002) showed 15.3 % and 27.7 % decrease respectively with respect to native wood. TGA analysis revealed the improvement in thermal stability after the silanisation of the aerogel. Acoustic properties showed ∼80 % sound absorption over a frequency range of 1500–3000 Hz for DWS with a maximum sound absorption coefficient of 0.8 at high frequency range. Thus, the current work paves the way to replace the petroleum-based aerogels currently used for such multifunctional applications being ecofriendly and biodegradable in nature.

Statistical upscaling workflow for warm solvent injection processes – Longitudinal and transverse dispersivity and thermal conductivity

Accurately simulating, upscaling, and optimizing the warm solvent injection process (WSI) is challenging due to its complex heat and mass transfer mechanisms. This manuscript presents a comprehensive two-step flow-based upscaling workflow designed explicitly for WSI simulation in heterogeneous reservoirs. The technique builds upon previous research on particle transport in single-phase flow and extends the upscaling method to incorporate multiple correlated properties relevant to the process physics. Specifically, the upscaling methodology considers the correlation between longitudinal and transverse dispersivities. The influence of scale variation on thermal conductivity is examined. The proposed statistical upscaling technique does not rely on explicit assumptions about the distribution of heterogeneity. The results highlight the directionality in dispersivity. Due to the limited temperature variation observed in the case study, upscaling thermal conductivity has little impact. The method's efficiency can be verified by coarser model simulations that capture similar fine-scale model responses with less computational run time.

Oriented High Thermal Conductivity Solid-Solid Phase Change Materials for Mid-Temperature Solar-Thermal Energy Storage.

As the global energy crisis intensifies, the development of solar energy has become a vital area of focus for many nations. The utilization of phase change materials (PCMs) for photothermal energy storage in the medium temperature range holds great potential for various applications, but their conventional forms face several challenges. For instance, the longitudinal thermal conductivity of photothermal PCMs is inadequate for effective heat storage on the photothermal conversion surface, and there is a risk of leakage due to repeated solid-liquid phase transitions. Here, we report a solid-solid phase change material, tris(hydroxymethyl)aminomethane (TRIS), which has a phase change temperature of 132 °C in the medium temperature range, enabling high-grade and stable solar energy storage. To overcome the low thermal conductivity problem, we propose a large-scale production of oriented high thermal conductivity composites by compressing a mixture of TRIS and expanded graphite (EG) using the pressure induction method to create in-plane highly thermally conductive channels. Remarkably, the resulting phase change composites (PCCs) exhibit a directional thermal conductivity of 21.3 W/(m·K). Furthermore, the high phase change temperature (132 °C) and large phase change entropy (213.47 J/g) enable a large-capacity high-grade thermal energy to be used. The developed PCCs, when combined with selected photo-absorbers, exhibit efficient integration of solar-thermal conversion and storage. Additionally, we also demonstrated a solar-thermoelectric generator device with an energy output of 93.1 W/m2, which is close to the power of photovoltaic systems. Overall, this work provides a technological route to the large-scale fabrication of mid-temperature solar energy storage materials with high thermal conductivity, high phase change enthalpy, and no risk of leakage, and also offers a potential alternative to photovoltaic technology.

Vibration Analysis of Laminated Composite Plate under Thermo- Mechanical Loading

The present study focused mainly on the vibration analysis of composite laminated plates subjected tothermal and mechanical loads or without any load (free vibration). Natural frequency and dynamicresponse are analyzed by analytical, numerical and experimental analysis (by using impact hammer) fordifferent cases. The experimental investigation is to manufacture the laminates and to find mechanicaland thermal properties of glass-polyester such as longitudinal, transverse young modulus, shear modulus,longitudinal and transverse thermal expansion and thermal conductivity. The vibration test carried tofind the three natural frequencies of plate. The design parameters of the laminates such as aspect ratio,thickness ratio, boundary conditions and lamination angle were investigated using classical laminatedplate theory (CLPT) and Finite element coded by ANSYS, in addition to the design parameters ofdynamic response such as load type with respect to time, x and y dimension and temperature value forsimply supported symmetric cross ply. The main conclusion was the natural frequency could increaseand decrease depending on the boundary conditions, thickness ratio, and lamination angle, the aspectratio of the plate. Present of temperature could increase dynamic response of plate also depending onlamination angle, type of mechanical load and the value of temperature.

Вплив конструктивних параметрів термоплати на гістерезис за тепловим навантаженням

The contact heat exchangers designed to remove heat from the cooled devices are used in mechanically pumped two-phase loops of thermal management systems for ground and space applications, a thermoplate (heat sink). After the device is turned on, it may overheat abnormally during the process of reaching a stationary operating mode. Overheating is associated with the phenomenon of thermal load hysteresis during the onset of boiling, the transition from single-phase convection to developed boiling in the evaporator of a heat sink material. This work studied the influence of the construction parameters of thermoplate on the hysteresis phenomenon at the integral level. For this purpose, a thermoplate testing methodology was implemented, which includes experiments with slow (quasi-stationary) and quick heating after turning on the device immediately at full power. Overheating of the device is possible during both "slow" and "quick" heating. The maximum overheating in the experiments performed was ~18 K. Such overheating can pose a danger to the reliability of the device. The study was performed with ammonia as a coolant on 5 models of thermoplate that differ in evaporator channel roughness, length, material, longitudinal thermal conductivity, the heat capacity of the structure, etc. The danger of overheating the device is also determined by the maximum thermal load at which the device is operated. The following conclusions were made: the greatest influence on the hysteresis parameters is the value of the evaporator channel surface roughness. Increasing the roughness reduces the risk of overheating the device, and changes the nature of the "boiling curves" in the thermoplate; an increase in the length and longitudinal thermal conductivity has a favorable effect on reducing the risk of overheating; the evaporator surface is made of aluminum alloy instead of stainless steel, which makes hysteresis impossible; in the case of rapid heating of the thermoplate, the maximum heat flux at steady-state has an ambiguous effect: with its increase, overheating due to hysteresis first increases, and in the case of further increase, it decreases and may disappear altogether. A significant increase in the maximum heat flux compared to the heat flux at the beginning of boiling reduces the danger of hysteresis affecting the overheating of the device. The results of this work provide recommendations on how to avoid the dangerous overheating of the device due to the hysteresis phenomenon.

Electric field-dependent phonon spectrum and heat conduction in ferroelectrics.

This article shows experimentally that an external electric field affects the velocity of the longitudinal acoustic phonons (vLA), thermal conductivity (κ), and diffusivity (D) in a bulk lead zirconium titanate-based ferroelectric. Phonon conduction dominates κ, and the observations are due to changes in the phonon dispersion, not in the phonon scattering. This gives insight into the nature of the thermal fluctuations in ferroelectrics, namely, phonons labeled ferrons that carry heat and polarization. It also opens the way for phonon-based electrically driven all-solid-state heat switches, an enabling technology for solid-state heat engines. A quantitative theoretical model combining piezoelectric strain and phonon anharmonicity explains the field dependence of vLA, κ, and D without any adjustable parameters, thus connecting thermodynamic equilibrium properties with transport properties. The effect is four times larger than previously reported effects, which were ascribed to field-dependent scattering of phonons.

Thermal and arc erosion behavior of CuCr contact material based on large plastic deformation treatment

CuCr alloys are the main contact materials used in medium-voltage and high-current vacuum interrupters. In this paper, the effect of large plastic deformation on microstructure and the transverse/longitudinal thermal conductivity of CuCr30 contact material were studied. The results show that the morphology of Cr particles in CuCr30 changes from dendritic to oriented fibrous after large plastic deformation, and the longitudinal thermal conductivity of CuCr30 contact material is about 1.5 times higher than its transverse thermal conductivity. During the electrical contacting process, the mass loss of the extruded CuCr30 contact material is lower than that of as-cast CuCr30 contact material, which is directly related to the significantly higher longitudinal thermal conductivity of the extruded CuCr30 contact material. The enhancement of longitudinal thermal conductivity is beneficial to reduce the mass loss of the contact material and improve the arc erosion resistance of the contact material. The mass loss of the cathode with higher longitudinal thermal conductivity is significantly lower than that of the anode contact in extruded CuCr30 contact material.

Вплив поздовжньої і поперечної теплопровідності міжфазних щілин на ефективні параметри біматеріалу

The effective parameters of the bi-material with a periodic system of interfacial cracks are studied, taking into account their longitudinal and transverse thermal conductivity. The bi-material is subjected to tensile forces and uniform heat flow. The transverse and longitudinal thermal conductivity of the cracks is taken into account by the thermal resistance of the filler and the thermal conductivity of the surface films, respectively. The thermal resistance of the filler is directly proportional to the opening of the cracks and inversely proportional to the thermal conductivity of the filler. Thermal conductivity of surface films does not change under the influence of load. The thermo-elastic problem is reduced to nonlinear systems of singular integro-differential equations for an opening cracks and a temperature jump between the cracks faces. An analytical-numerical iterative procedure for solving this system is proposed. Based on the obtained solution, the effective temperature jump and the effective thermal resistance of the bi-material are determined. The dependences of the effective parameters of the bi-material on the applied load and thermal conductivity coefficients of the filler and the surface films of the cracks are analyzed.

Study on damage evolution and radon exhalation of uranium-bearing granite under high temperature.

Deep geological disposal of high-level radioactive waste is a feasible method for solving the problem of spent fuel storage in China. High-level radioactive waste releases heat during the decay process, which increases the temperature of the surrounding rock in the repository, resulting in a significant increase in radon concentration. In this study, the surrounding rock (granite) of a high-level radioactive waste repository was taken as the research object and, based on the similarity principle, an orthogonal test designed. Similar materials of uranium-containing granite were prepared in the laboratory and the physical and mechanical properties and cumulative radon concentration of granite samples assessed under different temperatures (25, 50, 100, 150, and 200°C). The results showed that, with increased temperature, the compressive and tensile strengths of samples gradually increased and their pore volume gradually decreased. After heat treatment, the longitudinal wave velocity and thermal conductivity of samples decreased linearly with increased temperature. The radon exhalation rate first increased and then decreased, with the rate reaching a maximum at 100°C. The radon exhalation rate of single-sided and double-sided samples was 0.00914 and 0.00460Bq·m-2·s-1, respectively. When the temperature was 25-100°C, the dominant stage was pore water. The radon exhalation rates of samples were positively correlated with compressive and tensile strengths and negatively correlated with pore volume, longitudinal wave velocity, and thermal conductivity. The temperature of 100-200°C was range of the dominant stage of pore structure. The conclusions obtained in this study can provide theoretical support for radon reduction and radon control of granite in high temperature environments.

Diagonal and off-diagonal thermal conduction with resonant phonon scattering in Ni3TeO6

The coupling between phonon and magnon is ubiquitous in magnetic materials and plays a crucial role in many aspects of magnetic properties, most notably in spintronics. Yet, this academically and technologically interesting problem still poses a severe challenge to a general understanding of the issue in certain materials. We report that Ni3TeO6 exhibits clear evidence of significant magnon-phonon coupling in both longitudinal thermal conductivity ($\kappa_{xx}$) and thermal Hall coefficient ($\kappa_{xy}$). The Debye-Callaway model, a phenomenological description for phonon heat conduction, can explain the measured magnetic field dependence of $\kappa_{xx}(H)$: phonon scattering from spin fluctuation in the paramagnetic phase and additional scattering due to magnon-phonon coupling in the collinear antiferromagnetic phase. We further suggest that a similar approach could be applied to understand the finite $\kappa_{xy}$ values in $Ni_3TeO_6$.