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The onset of instability of thermal convection in an inclined layer of viscous, incompressible fluid having internal heat source is studied using linear stability analysis. The heat source consists of a uniform component as well as a temperature-dependent component. The boundaries of the layer are maintained at different constant temperatures. The thermal Rayleigh number R 1 and the dimensionless parameters R 2 and R 3 determining the strength of the internal heat source are used to establish the onset of instability. The collocation method utilising Chebyshev polynomials is adopted to obtain the critical values of various parameters. The Prandtl number of the fluid and the angle of inclination of the layer are also the key factors in determining the onset of instability. [ABSTRACT FROM AUTHOR]

The effect of an internal heat source linearly dependent on the solid fraction on the onset of convection in a composite air‐porous channel with vertical throughflow has been analyzed. We considered boundaries to be insulating to temperature perturbations. The governing equation that satisfies the air‐porous configuration is analyzed by the normal mode approach, solved by the regular perturbation technique for linear stability, and the critical internal Darcy–Rayleigh number for the onset of stationary convection has been derived. The paper aims to analyze the effects of parameters like heat source size, depth ratio, Darcy number, throughflow direction, solid fraction, and Prandtl number on stationary convection in a composite air‐porous configuration. Understanding these influences can illuminate thermal behaviors in intricate systems and inform applications in heat transfer and fluid dynamics. The observed stability configuration decreases monotonically due to increasing the effect of the depth ratio and solid fraction at any direction and velocity of the throughflow. The thermal and vertical velocity profiles and the results obtained during the analysis have been presented graphically. [ABSTRACT FROM AUTHOR]

The current work establishes research into the non-Newtonian Casson fluid's linear and weakly non-linear stability analysis under the influences of internal heating and gravitational modulation. The study is confined to stationary convection, where marginal stability is determined by the critical Rayleigh number, which is derived from linear stability analysis. The marginal stability curves are plotted to observe the onset of convection due to different parameters that exist in the problem. Heat and mass transfer are measured in terms of the Nusselt number (Nu) and Sherwood number (Sh), respectively, in the non-linear stability analysis. These measurements are based on the Ginzburg-Landau (GL) equation. One of the main outcomes of this stability analysis is that the internal Rayleigh number and Casson parameter behave similarly for mass transport in a fluid whereas it operates oppositely for heat transfer in a fluid. [ABSTRACT FROM AUTHOR]

The present work is focussed on analyzing the stability of fluid within the porous structure, accounting for constant internal heat generation by employing both linear (normal mode technique) and nonlinear stability (energy) techniques. The impact of diverse sets of boundary constraints, encompassing impermeable, conducting, porous, and insulating on the stability is also explored. The governing equations are transformed into an eigenvalue problem derived from stability analysis, which is transformed into a fourth-order problem on separating Fourier component and then numerically solved using the Chebyshev pseudospectral method for finding the critical Rayleigh numbers. It is found that the presence internal heat generation gives rise to the potential of subcritical instability. Five models are considered based on bounding surfaces and the impact of internal heating is analysed which suggest that the stability can be enhanced or convection can be accelerated by taking appropriate combination of these models and values of heat generation parameter. It is also noted that in the absence of internal heating the subcritical region of instability does not exist. [ABSTRACT FROM AUTHOR]

Over the last 10 years, heat transfer performance in immediate cooling and heating applications has grown into the foremost concern for heat transfer practitioners in Engineering and manufacturing practices. Henceforward, the study in new heat transfer fluids is extremely intense and challenging. This study examines flow and thermal management in axisymmetric hydrodynamic pure water-based hybrid solid nanoparticles in a flow induced by a swirling cylinder with Fourier Heat source. Flow and heat transfer are analyzed and compared for CNT+Graphene+Al 2 O 3 and Paraffin wax+Sand+AA7072 hybrid nanofluid flow. Shooting technique (R-K 4th order) is applied to work out the flow equations numerically. Simulated results are exhibited through graphs and tables. The computational results are statistically validated with the published research work and a modest concurrence is found. The main outcome of this study is found to be in Multi-regression analysis, where the Λ w.r.t Pr has higher domination compared to Φ w.r.t Pr. Also, it is interesting to know that Φ w.r.t Re has more rate of heat transfer compared to Φ w.r.t M. As the volume fraction rises, the size of the particle is less and Reynolds number dominated the flow, due to this, a decrement is seen in the friction values. Overall, it is observed that heat transfer rate is higher in CNT+Graphene+Al2O3 compared with Paraffin wax+Sand+AA7072. [ABSTRACT FROM AUTHOR]

The stability of natural convection in an internally heated vertical porous layer confined between two impermeable boundaries which are kept at different constant temperatures is investigated. The momentum transfer is modeled by adopting Darcy's law including time-dependent velocity term contribution. The conduction stream function and temperature fields are significantly altered due to internal heating, and the linear instability is analyzed through a study of normal mode perturbations on the base flow. The neutral stability curves and the critical Darcy–Rayleigh number for the onset of instability are evaluated by solving the stability eigenvalue problem numerically. It has been established that a uniform volumetric heat source and the Prandtl–Darcy number reinforce together in initiating the instability of the base flow under certain conditions despite their isolation presence evidences stability for all infinitesimal perturbations. Although the internal heat source strength is to hasten the onset of instability, and the Prandtl–Darcy number is found to induct both destabilizing and stabilizing impact on the base flow. [ABSTRACT FROM AUTHOR]

Using a Ca(OH)2/CaO thermochemical heat storage system is an effective way to promote the utilization of renewable energy. However, poor thermal conductivity restricts the application of a widely used fixed-bed reactor. To improve the heat storage rate, the internal heating mode, which heats the reactant via the internal heating tube instead of the external wall, was adopted, and the heat storage process in the fixed-bed reactor was investigated numerically. The results show that the number and location of tubes have a significant impact on heat storage performance. Compared with the external wall heating mode, the optimized scheme of six internal heating tubes can shorten the reaction time by 21.78%. The temperature and reaction extent distribution reveal that as the reaction proceeds, the optimized scheme has a higher temperature and reaction extent. Additionally, the effects of different conditions, such as solid particle porosity, wall temperature, outlet pressure, and solid particle size, were also analyzed. The study demonstrates that increases in solid particle porosity, wall temperature, and solid particle size as well as a decrease in outlet pressure can improve the heat storage rate. [ABSTRACT FROM AUTHOR]

The study is devoted to a new problem concerning the onset of penetrative convection via internal heating in a multilayered air-porous system under the gravitational field. The system consists of porous sublayers separated by thin air interlayers. The governing equations are supplemented by the effective boundary conditions which contain the interlayer parameter and parameter of thermal conductivity jump. The parameters are combinations of the relative air interlayer depth, Darcy number and thermal conductivity ratio. The numerical results show that the large-scale convection covering the entire unstably stratified upper region initiates in a multilayered system with porous sublayers of equal depth and permeability. The addition of air interlayers speeds up the convection onset and increases the wavelength of convective patterns. The effect becomes stronger as the number of porous sublayers increases because the number of air interlayers also increases. Local convection can be obtained when the permeability of any one porous sublayer exceeds that of the other porous sublayers by an order of magnitude or more. The local flow originates in the highly permeable porous sublayer that belongs to the upper half of the system. Convection becomes of a large scale at any other position of this sublayer. It is found that the permeability ratio can be both destabilizing and stabilizing. It is explained by a transition from the large-scale to local convective regimes. The destabilizing effect of air interlayers is observed for both local and large-scale regimes in the multilayered system with a highly permeable porous sublayer. [ABSTRACT FROM AUTHOR]

As the share of renewable energy increases, green electricity may help reduce the carbon footprint in the lime industry. Electrifying the calciner can produce relatively pure CO2 from the calcination process (CaCO3 → CaO + CO2), which may be utilized or stored. All the previous literature studied electrically heated rotary calciner with external heating. This work presents a novel design of an electrical rotary calciner through which internal heating is possible. The design can utilize existing kiln drums made from relatively inexpensive refractory and steel materials. The designed calciner operated smoothly for around four days, and the concept was technically feasible. The outer wall temperature and calcination degree was measured during the condition of a pseudo-steady state in the calciner. A model was developed and implemented in OpenModelica, which was validated by comparing it against measured variables. The modelling results revealed that the current setup had low thermal efficiency, as the heat loss amounted to around 60%, and the average heat transfer coefficient was around 101 W/(m2K). A step-by-step procedure with the help of the model was discussed to improve heat efficiency and reduce heat loss by up to 11% by improving thermal insulation and increasing the residence time of particles. With the improved thermal efficiency, energy intensity and electricity cost per unit CO2 were reduced from 35 to 7 MJ/kg-CO2 and 4.9 to 1 NOK/kg-CO2, respectively. So, improving thermal efficiency can improve both the environmental and economic aspect of the process.

Low temperatures seriously affect the performance of lithium-ion batteries. This study proposes a non-destructive low-temperature bidirectional pulse current (BPC) heating method. Different from existing heating approaches, this method not only optimizes heating frequency and amplitude but also considers the optimization of the charge/discharge pulse duration ratio. To optimize the BPC heating strategy, a precise electro-thermal coupled model is established, and a neural network is employed to delineate the relationship among model parameters, temperature, and state of charge (SOC). Additionally, the interplay between the impedance of the graphite anode and that of the full cell is analyzed by constructing a three-electrode battery. Then, a novel full-cell-oriented lithium plating criterion is introduced. Finally, based on the constructed electro-thermal coupled model, lithium plating criterion, and terminal voltage constraint, a novel non-destructive BPC heating method is proposed. The results show a significant improvement in heating efficiency compared to conventional BPC heating. Especially for high SOCs, the heating power is increased at least 8 times. When the battery SOC is below 40 %, the average heating rate from −10 °C to 10 °C is 11.28 °C/min. Even at 90 % SOC, the heating rate remains at 2.88 °C/min. Furthermore, the capacity and impedance of a battery at 50 % SOC exhibit no significant changes after 60 heating cycles using the optimal BPC heating strategy at 100 Hz. These findings show that the optimized method proposed in this study has high heating efficiency and no damage to the battery. [Display omitted] • The kinetic processes of the graphite and full cell are compared. • A novel full-cell-oriented lithium plating criterion is introduced. • The heating power is studied for different BPC parameters. • A novel non-destructive BPC heating method is developed. [ABSTRACT FROM AUTHOR]

Convection induced by internal heating and adverse temperature gradient in a porous medium has various real-world applications, such as solar energy collectors, solar-based drying and cooking. Thus, it is crucial to analyze such flows to understand the physics behind the flow and analyze heat transfer through the system. We assume that volumetric heating occurs within the fluid phase due to radiation exposure from an overhead source or a stratified arrangement of heat-generating materials. For modeling convenience, we further assume that internal heating diminishes exponentially with the depth of the porous layer and fluctuates sinusoidally over time, affecting the mean value. Solid and fluid phases of the porous layer are considered out of thermal equilibrium. Floquet theory is employed to determine the linear instability bound of the system. By analyzing the eigenvalue spectrum, we identify the critical Rayleigh number that marks the onset of instability. Subsequently, a weakly nonlinear analysis is carried out using a truncated Fourier series expansion of the physical quantities to analyze the heat transfer within the system. The effect of governing nondimensional parameters on the system's stability and heat transport is graphically illustrated and thoroughly discussed. The effect of modulation amplitude and volumetric heat is to enhance heat transfer, whereas depth coefficient and modulation frequency suppress heat transfer. • Effect of a non-uniform time-dependent volumetric heat source on the thermoconvective flow in a porous layer is studied. • Solid and fluid phases of a porous layer are considered out of thermal equilibrium. • Heat source diminishes exponentially with the depth of the porous layer and fluctuates sinusoidally over time. • Modulation amplitude affects the onset of convection significantly for different values of LTNE parameters in comparison to modulation frequency. • The effect of volumetric heating is to enhance heat transfer, whereas depth coefficient suppresses heat transfer. [ABSTRACT FROM AUTHOR]

In the present study we use two-dimensional direct numerical simulations (DNS) to understand the coupled heat transfer to fluid flow in a liquid target for the production of nuclear medicines. Fluid motion is driven by buoyancy created by heat generated by a proton beam. The internal heat source has a gaussian distribution in the vertical direction and a rapidly growing intensity in the horizontal direction until it reaches a range at the Bragg peak where the heating drops to zero. The structure of the heating imposes two convective cells, separated at the location of the range. We solve the governing fluid flow and energy equations in a square cavity subject to highly nonuniform internal heating generated by the energy deposition of a proton beam. While most studies of convection driven by an internal heat source in a fluid layer have been focused on a uniform heating of the fluid, our study shows that the nonuniformity in the heat source has important implications for the temperature and flow fields, the boundary heat fluxes, and the growth of convective instabilities in the flow. Interestingly, the scalings of the maximum and averaged temperatures with the Rayleigh number compare similarly to previously found power laws for uniformly heated fluid layers. At higher power levels, the layer of fluid near the top cold boundary becomes convectively unstable via Rayleigh–Taylor instabilities. By comparing the rate of growth of these instabilities to their rate of advection to the boundaries of the cavity, a model is developed that predicts the instability of the convective cells for different values of the range of the beam and the Rayleigh number. Crucially, we demonstrate that the disturbances in the production of isotopes due to convective instabilities and the design of the cooling system is dependent on the location of the Bragg peak and must be considered in design of future generation of this class of target. [Display omitted] • Thermal performance of liquid targets depends on the location of the Bragg peak. • For higher input heat Rayleigh–Taylor instabilities grow near the top boundary. • Advection of the of Rayleigh–Taylor instabilities to the boundaries inhibits their growth. • The scaling of the temperature with the Rayleigh number is similar to uniform heating. [ABSTRACT FROM AUTHOR]

• A novel internal heating method for LiBs, called AIM heating, is proposed. • Graphite anode electrodes with integrated nichrome wires as heating element. • Fast and uniform heating from 0 °C, −20 °C and −40 °C up to 20 °C. Lithium-ion batteries (LiBs) have been widely used in a variety of applications, such as consumer electronics, stationary storage systems and electric vehicles (EVs), thanks to their high energy and power density and long cycle life. However, when LiBs operate at low temperature environments, they suffer from low capacity retention, large capacity fade ratio or inability to charge efficiently. As a result, the performance of EVs is significantly affected, reducing the available driving range and prolonging the required charging times. In order to address these issues, EV manufacturers incorporate external heating technologies, which are, however, limited by high energy consumption, low temperature uniformity and prolonged heating duration. Herein, we propose an internal method for pre-heating the batteries, called AIM heating technology, by using AIM anode electrodes which incorporate ultra-thin resistance wires as a heating element integrated inside graphite films. Simulation studies, conducted to investigate different AIM electrode designs, demonstrated high temperature uniformities of less than ± 1 °C across the graphite film's surface. Experimental measurements conducted at low temperatures showed that the developed AIM electrodes can be heated up in exceptionally short times, from extremely low temperatures of -20 °C and -40 °C up to 20 °C in only 44 s and 82 s, respectively. Thus, simulation and experimental studies demonstrated that the proposed internal heating method is able to offer fast heating of the active materials of LiBs, improving their electrochemical performance at low temperatures. [Display omitted] [ABSTRACT FROM AUTHOR]

Background: Various irrigation techniques for cleansing the endodontic space have been proposed, and internal heating combined with ultrasonic activation (3D cleaning technique) is considered an effective technique. This prospective multicenter clinical study aims to evaluate healing rates for teeth after root canal treatment utilizing the 3D cleaning technique and to report predictive values for success. Material and Methods: Ninety patients referred for a root canal treatment were included. All enrolled patients were treated with the 3D cleaning protocol. Four endodontists performed the clinical procedures and follow-up evaluations. Preoperative, postoperative and follow-up data were gathered from the consented patients. Each patient was assessed for any clinical signs or symptoms. Afterwards, two trained, blinded, and independent evaluators scored the subject's periapical radiographs. This score was made by checking for the presence or absence of apical periodontitis using the periapical index (PAI). Then, the teeth were classified as healing or healed and were considered a success based on a cumulative success rate of healing. Statistical analysis was performed using the Fisher's exact test, Pearson correlation, and logistic regression analyses of the preoperative prognostic factors at a 0.05 significance level. Results: 90 patients were evaluated at two years with a follow-up rate of 97.7%. The cumulative success rate of healing was 95.4%. Eight predicting aspects were identified by employing bivariate analyses. Then, using logistic analyses, the two prognostic significant variables directly correlated to healing were the preoperative presence of periapical index (p value = 0.016). Conclusions: In this two-year clinical study, the cumulative success rate of healing was 95.4% when patients were treated with the 3D cleaning protocol. [ABSTRACT FROM AUTHOR]

The vertical throughflow effect on the onset of penetrative convection in a horizontal air sublayer overlying a porous sublayer is investigated in the gravitational field. The porous sublayer contains an internal heat source with the volumetric strength linearly dependent on the solid fraction. It has been found that the depth ratio and solid fraction are destabilizing at any direction and velocity of the throughflow. The upward and downward throughflows can be both stabilizing and destabilizing in the range of the Peclet number of - 6 < Pe < 6 considered. The study has revealed that the non-monotonic dependence of the onset internal Darcy-Rayleigh number versus the Peclet number may get a second minimum in addition to the first dominant one. It is due to an abrupt change in the critical wave number of convection patterns. A special attention is paid to the local and large-scale convective regimes which replace each other with the variation of the Peclet number, solid fraction and depth ratio. One has obtained a regime map which includes a demarcation line between the two regimes and a region of parameters for the bimodal marginal stability curves. [ABSTRACT FROM AUTHOR]

Fast charging of Lithium ion batteries (LIBs) is expected to boost the extensive electrification of transportation sector. However, fast charging a LIB comes at the cost of increased internal heat generation that results in higher reaction rates of both the necessary as well as unwanted reactions at the electrode–electrolyte interface. This can trigger a chain of events that can possibly lead to thermal runaway. Electrolyte has a critical effect on the internal heating of a LIB and thus plays an inherent role in its safety. We elucidate the role of electrolyte salt in reducing internal heating by evaluating two different salts—Lithium bis(fluorosulfonyl)imide (LiFSI) and Lithium hexafluorophosphate ( LiPF 6 ). Using a physics-based electrochemical–thermal model, we study these electrolyte salts individually in LiCoO 2 (Cathode)/Graphite (Anode) LIB system. Under fast charging conditions, internal heating and polarization were studied in each of the LIB system. The temperature rise seen in the two systems shows that LiFSI is a better electrolyte salt for fast charging application as compared to LiPF 6 . This is primarily due to better transport properties of LiFSI compared to LiPF 6 , as elaborated using polarization studies. This study can aid in choosing the appropriate electrolyte salt for mitigating the internal heating and thermal issues during fast charging. [ABSTRACT FROM AUTHOR]

Rapidly warming up batteries is an important challenge both for conventional lithium-ion batteries, which operate best over 15 °C, and for most solid-state batteries, which currently require operating temperatures over 60 °C. Internal heating using an alternating current (AC) has been proposed as a possible solution in automotive applications, with faster heating rates possible than conventional external heating methods. This paper investigates the performance of internal AC heating on cells of different sizes, for both cylindrical and pouch formats. A novel experimental arrangement is used in which two cells are tested in series while connected with opposing polarity to create a zero-voltage string, allowing the use of less expensive testing equipment. The results show that larger cells exhibit a considerably greater distribution of surface temperature than smaller format cells during internal heating. This is likely due to the more extreme spatial variation in current density in the current collectors, causing an uneven distribution of internal heat generation. This highlights a significant difference compared to external heating methods, which are not affected by this, and has important implications for temperature measurement and battery management if this type of internal heating is to be used, since temperature sensors must be placed in hot spots or supplemented by validated models to ensure all parts of the battery stay within safe temperature limits. [ABSTRACT FROM AUTHOR]

This comprehensive review investigates the role of maintaining temperature in anaerobic digestion (AD), a process that converts biowaste from agriculture, industry, and municipal sources into biogas. As most regions experience significant seasonal temperature variations, there is a need to maintain consistent temperature within the digester to ensure optimal plant performance. Various approaches for maintaining desired temperature in digesters are discussed, emphasizing the positive impact of a stable digestion temperature on biogas production and process stability. For both internal and external heating systems, the potential of biogas, solar, fossil fuels, and geothermal energy as heating energy sources is analysed along with insulation approach for achieving a desired temperature within the digester. The economic aspects associated with these heating methods are addressed, providing insights into their feasibility and cost-effectiveness. The integrated renewable energy sources for heating such as solar-biogas, geothermal-biogas, and solar-geothermal-biogas, along with thermal insulation is recommended, but the economic feasibility of these systems warrants further investigation at pilot and commercial scale in different parts of the world. This review provides valuable insights to the AD plant developers, operators, and owners for designing AD heating system and maintaining desired digestion temperature. [Display omitted] • Digestion temperature, ambient conditions, influent temperature, and heat loss affect energy demand. • Different heating approaches and heat sources for maintaining the digestion temperature are examined. • Selection of IHS or EHS depends on influent characteristics, cost, and digestate use regulations. • Integrated renewable energy sources for heating along with thermal insulation is recommended. [ABSTRACT FROM AUTHOR]

In this analysis, the collective impact of external electric field and internal heat generation on the onset of thermal convection of Jeffery fluid in a porous matrix is investigated analytically. Utilising linear stability hypothesis reliant on the normal mode process, a dispersion relation is derived and this dispersion relation is investigated for stationary and oscillatory styles of convective activities. The results reveal that the stability of the system diminishes by increasing the Jeffery parameter λ , the electric field parameter R E and the internal heating parameter S H . It is also shown that the oscillatory style of convective movement has not been feasible for the problem. [ABSTRACT FROM AUTHOR]

A theoretical and computational study of MHD natural convection in an isotropic non-Darcian porous medium saturated with electrically conducting helium gas in an enclosure in the presence of heat generation is presented. A Brinkman extended Darcy-Forchheimer model is employed and the working fluid is assumed to be incompressible. The model is non-dimensionalised and converted into pressure-velocity form. The Harlow-Welch marker and cell (MAC) finite difference technique is employed to solve the nonlinear boundary value problem via pressure-vorticity coupling. A parametric investigation of the influence of Grashof number (Gr), Hartmann magnetic number (Ha), Darcy number (Da), and the internal heat generation parameter (Γ) on streamline and isotherm distributions with Prandtl number (Pr) is 0.71 (Helium) is conducted. The variation in local Nusselt number along the left and right walls of the computational 2 D enclosure is also studied. Validation house-computational numerical MATLAB code is tests are included. Local Nusselt number is elevated at both left and right walls with greater Darcy number (higher medium permeability) and Grashof number. However, with greater internal heat generation, local Nusselt number magnitudes are enhanced at the left (cold) wall only but suppressed at the right (hot) wall. Increasing magnetic field reduces local Nusselt number at both left and right walls. With increasing magnetic field, the single vortex is strongly distorted and skewed towards the top left and lower right corners of the enclosure. Temperature contours at the left and right wall are however less intense with greater magnetic field effect. The simulations are of relevance to hybrid electromagnetic gaseous fuel cells, magnetic field control of filtration processes and porous media materials processing systems. [ABSTRACT FROM AUTHOR]

The investigation of thermal modulation on double-diffusive stationary convection in the presence of an applied magnetic field and internal heating is carried out. A weakly nonlinear stability analysis has been performed using the finite-amplitude Ginzburg-Landau model. This finite amplitude of convection is obtained at the third order of the system. The study considers three different forms of temperature modulations. OPM-out of phase modulation, LBMO-lower boundary modulation, IPM-in phase modulation. The finite-amplitude is a function of amplitude δ T , frequency ω and the phase difference θ. The effects of δ T and ω on heat/mass transports have been analyzed and depicted graphically. The study shows that heat/mass transports can be controlled effectively by thermal modulation. Further, it is found that the internal Rayleigh number Ri enhances heat transfer and reduces the mass transfer in the system.

This study assessed the pulp tissue dissolution from isthmus of a two‐rooted maxillary premolar using different final irrigation protocols. After root canal preparation, the surface of the tooth was reduced to an extent that the isthmus could be observed, and 1 mg of pulp tissue was introduced into the isthmus which was covered with a glass slide. Following six groups were tested: syringe and needle; subsonic activation; sonic activation; ultrasonic activation; heating followed by sonic activation; and heating followed by ultrasonic activation. Before and after each experiment a photograph of the isthmus was taken at 30× to register the area of the pulp tissue. Statistical analysis was performed with Kruskal–Wallis and Mann–Whitney tests (P < 0.05). Syringe and needle group showed the lower value of pulp tissue dissolution followed by subsonic irrigation procedures. Pulp tissue dissolution was significantly higher when heating was followed by sonic or ultrasonic activation. [ABSTRACT FROM AUTHOR]

The present paper deals with a weakly nonlinear stability problem under an imposed time-periodic thermal modulation. The temperature has two parts: a constant part and an externally imposed time-dependent part. We focus on stationary convection using the slow time scale and quantify convective amplitude through the real Ginzburg-Landau equation (GLE). We have used the classical fourth order Runge-Kutta method to solve the real Ginzburg-Landau equation. The effect of various parameters on heat transport is discussed through GLE. It is found that heat transport analysis is controlled by suitably adjusting the frequency and amplitude of modulation. The applied magnetic field (effect of Ha) is to diminish the heat transfer in the system. Three different types of modulations thermal, gravity, and magnetic field have been compared. It is concluded that thermal modulation is more effective than gravity and magnetic modulation. The magnetic modulation stabilizes more and gravity modulation stabilizes partially than thermal modulation.

In this study, we consider Newtonian fluid with gyrotactic microorganisms flowing through a porous medium. The effects of gravity field and internal heating are investigated on Darcy–Brinkman bio-thermal convection. The threshold Rayleigh number expression in the form of stationary mode is derived to study the onset of bioconvection. Further, heat transfer is investigated using Nusselt number, which is governed by Ginzburg–Landau equation. The influence of internal Rayleigh number, Vadasz number, modified bioconvective Rayleigh–Darcy number, cell eccentricity, modulation frequency and modulation amplitude on heat transfer is explored by the research and depicted graphically. Also the effect of the above parameters on the threshold Rayleigh number against the wave number is studied graphically. These graphical study is called as marginal stability analysis. Also, a comparative graph is plotted to study modulated and unmodulated effect of gravity on Nusselt number. This highlights the effectiveness of the gravity modulation and internal heating effect in controlling heat transport within the system. • Theory of weakly nonlinear stability analysis is presented numerically. • Bioconvection analysis is investigated in a porous media in the presence of gravity modulation. • Ginzburg–Landau equation is employed to determine amplitude of bioconvection. • The effects of internal heating and gravitational modulation are discussed on bio-thermal convection. • Both biothermal convection and gravity modulations are contributed to stabilize the system also Transport analysis is presented within the bio-porous layer. [ABSTRACT FROM AUTHOR]

A mathematical model is considered for Rayleigh–Bénard convection of mantle where the viscosity depends strongly on both temperature and pressure defined in an Arrhenius form. The model is solved numerically for extremely large viscosity variations across a unit aspect ratio cell using a modified cut-off viscosity law, and steady solutions are obtained. The aim is to investigate the convection pattern with internal heating at a very high viscosity variation in the presence of high Rayleigh number. The study also investigates the relation between temperature dependent parameter and pressure dependent parameter in a basally heated convection cell. The numerical simulation is performed using the finite element method based PDE solver and the results are presented through figures, tables and graphs. [ABSTRACT FROM AUTHOR]

The current study aims to evaluate in vitro the extrusion of NaOCl, using an artificial root canal with an open apex, using different canal irrigation protocols. For this study, a transparent artificial root canal was used. The apex was shaped to be oversized and irregular in form. After root canal mechanical shaping, the artificial cylindrical chamber, which was made below the large apical foramen, was filled with fuchsine-stained bovine pulp tissue. Afterward, irrigation protocols were carried out and compared regarding their safety with regards to irrigant extrusion. Subsequently, the examiner created two groups, Group A: internal heating associated with ultrasonic activation and Group B: internal heating associated with ultrasonic activation, using the CAB technique. In both the groups, 5.25% sodium hypochlorite solution was used as the irrigant. Regarding assessing the presence or absence of the extrusion, photographs at ×20 were taken and analyzed. For the statistical analysis, a t-test for paired samples was used. Extrusion of irrigant beyond the apex was present only in Group A. The main objective of endodontic treatment is the removal of damaged tissues and bacteria. For this reason, active cleaning is crucial in all endodontic treatment cases. Internal heating followed with ultrasonic activation while using the CAB technique was an effective and safe technique to ensure no irrigant extrusion beyond the open apex. [ABSTRACT FROM AUTHOR]

The penetrative ferrothermal convection (FTC) in a ferrofluid (FF) saturated high porosity anisotropic porous layer via uniform internal heating is investigated. The Brinkman-extended Darcy equation is applied to describe the flow in the porous medium. The permeability in the vertical direction is taken to be twice that of the permeability in the horizontal direction while the ratio of horizontal to vertical effective thermal diffusivity is allowed to vary. The Galerkin method is applied to solve numerically the stability eigenvalue problem for different boundary combinations namely, (i) rigid-paramagnetic (R–P) with large and low magnetic susceptibility, (ii) rigid-ferromagnetic (R–F), and (iii) free-ferromagnetic (F–F). The R–P boundaries with large magnetic susceptibility offer most, while F–F boundaries offer least stabilizing effect against FTC. Besides, the effect of increasing the magnetic number, non-linearity of fluid magnetization parameter, Darcy number and internal heat source strength is to speed up FTC, while the thermal anisotropy and magnetic susceptibility parameter indict a contradictory effect on FTC.

In this paper, the joint impact of the interior heating and chemical reaction on the double diffusive convective flow in porous membrane enclosures soaked by a non-Newtonian Maxwell fluid is investigated applying linear and nonlinear stability techniques. The porous enclosures are square, slender and rectangular. Using the linear stability analysis, the expression for the critical thermal Rayleigh–Darcy number, above which the convective movement occurs, is derived analytically in terms of associated physical parameters. A nonlinear stability examination reliant on the Fourier double series is executed to calculate the convective heat and mass transports of the arrangement. It is observed that the pattern of convective activity is oscillatory only in the occurrence of a relaxation parameter and the threshold value of the relaxation parameter for the occurrence of the oscillatory pattern depends on the other physical parameters. The onset of convective instability accelerates with the increasing chemical reacting parameter, the interior heating parameter, the solute Rayleigh–Darcy number, the Lewis number, the Vadasz number, and the relaxation parameter, while it delays with the heat capacity ratio. The convective heat and mass transfers increase with the solute Rayleigh–Darcy number, the Vadasz number, the relaxation parameter, and the aspect ratio (for rectangular enclosure), while it decreases with the heat capacity ratio and the aspect ratio (for slender enclosure). Additionally, the convective heat transfer enhances with the interior heating parameter, while the convective mass transfer enhances with the chemical reacting parameter and the Lewis number. The effects of Vadasz number, heat capacity ratio, and relaxation parameter are witnessed only on the oscillatory pattern of convection and unsteady convective heat and mass transfers. Further, some existing literature results are compared with the current findings.

We offer a unifying theory for turbulent, purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, https://doi.org/10.1017/S0022112099007545; 2001, https://doi.org/10.1103/PhysRevLett.86.3316) for Rayleigh‐Bénard turbulence and of Shishkina et al. (2016, https://doi.org/10.1002/2015GL067003) for turbulent horizontal convection, which are both based on the splitting of the kinetic and thermal dissipation rates in respective boundary and bulk contributions. We obtain the mean temperature of the system and the Reynolds number (which are the response parameters) as function of the control parameters, namely the internal thermal driving strength (called, when nondimensionalized, the Rayleigh‐Roberts number) and the Prandtl number. The results of the theory are consistent with our direct numerical simulations of the Boussinesq equations. Plain Language Summary: Internally heated convection (IHC), that is, convective fluid motions driven by the internal heat generation, is an omnipresent phenomenon in many geo‐ and astrophysical convective flows. An important question for IHC is how the mean temperature and the global flow strength depend on the internal heating rate and the operating fluid. In this work, we offer a unifying theory to address this question. The results of the theory agree well with our direct numerical simulations. Key Points: A unifying theory on heat and momentum transport is offered for turbulent purely internally heated convectionThe results of unifying theory are consistent with our direct numerical simulations [ABSTRACT FROM AUTHOR]

Earth's continental crust is characterized by a strong enrichment in long‐lived radioactive isotopes. Recent estimates suggest that the continental crust contributes to 33% of the heat released at the surface of the Earth, while occupying less than 1% of the mantle. This distinctive feature has profound implications for the underlying mantle by impacting its thermal structure and heat transfer. However, the effects of a continental crust enriched in heat‐producing elements on the underlying mantle have not yet been systematically investigated. Here, we conduct a preliminary investigation by considering a simplified convective system consisting in a mixed heated fluid where all the internal heating is concentrated in a top layer of thickness dHL (referred to as "heat‐blanketed convection"). We perform 24 numerical simulations in three dimensional Cartesian geometry for four specific set‐ups and various values of dHL. Our results suggest that the effects of the heated layer strongly depend on its thickness relative to the thickness of the thermal boundary layer (δTBL) in the homogeneous heating case (dHL = 1.0). More specifically, for dHL > δTBL, the effects induced by the heated layer are quite modest, while, for dHL < δTBL, the properties of the convective system are strongly altered as dHL decreases. In particular, the surface heat flux and convective vigor are significantly enhanced for very thin heated layers compared to the case dHL = 1.0. The vertical distribution of heat producing elements may therefore play a key role in mantle dynamics. For Earth, the presence of continents should however not affect significantly the surface heat flux, and thus the Earth's cooling rate. Key Points: We study a mixed heated system where the internal heating is generated only within a horizontal layer close to the surfaceThe convective system becomes insensitive to the presence of the heated layer when its thickness is extremely smallWhen applied to Earth, our results suggest that the presence of continents does not impact significantly Earth's cooling rate [ABSTRACT FROM AUTHOR]

Rapidly warming up batteries is an important challenge both for conventional lithium-ion batteries, which operate best over 15 °C, and for most solid-state batteries, which currently require operating temperatures over 60 °C. Internal heating using an alternating current (AC) has been proposed as a possible solution in automotive applications, with faster heating rates possible than conventional external heating methods. This paper investigates the performance of internal AC heating on cells of different sizes, for both cylindrical and pouch formats. A novel experimental arrangement is used in which two cells are tested in series while connected with opposing polarity to create a zero-voltage string, allowing the use of less expensive testing equipment. The results show that larger cells exhibit a considerably greater distribution of surface temperature than smaller format cells during internal heating. This is likely due to the more extreme spatial variation in current density in the current collectors, causing an uneven distribution of internal heat generation. This highlights a significant difference compared to external heating methods, which are not affected by this, and has important implications for temperature measurement and battery management if this type of internal heating is to be used, since temperature sensors must be placed in hot spots or supplemented by validated models to ensure all parts of the battery stay within safe temperature limits.

Background and Objectives: The endodontic space is a complex area on both micro and macro levels; therefore, traditional irrigation techniques may not guarantee a complete cleaning of such a complicated tridimensional system. The presented ex vivo study aimed to evaluate root canal cleanliness, obtained through an equal volume of traditionally applied sodium hypochlorite (NaOCl), compared to ultrasonically activated NaOCl and ultrasonically activated NaOCl that had undergone intracanal heating NaOCl. Materials and Methods: A total of 60 freshly extracted human mandibular premolars underwent root sample length standardization (18 mm), root canal preparation and, based on the irrigation method employed, were randomly and equally assigned to three study groups, composed of root samples treated with ultrasonically activated NaOCl, ultrasonically activated NaOCl that had undergone intracanal heating and traditionally applied NaOCl. The root specimens were subsequently fixated with 4% buffered formalin solution and decalcified in Morse liquid. A total often 6-micron-thick serial cross-sections were obtained, dyed using hematoxylin and eosin and examined through an optical microscope at 40×, 100×, and 200×. Results: Ultrasonically activated NaOCl that had undergone intracanal heating showed a significantly smaller amount of debris compared to ultrasonically activated and traditionally applied NaOCl groups (p value < 0.05). Conclusions: Root canal cleanliness saw significant enhancements by ultrasonically activated NaOCl that had undergone intracanal heating.

The combined influence of temperature dependent viscosity and internal heat source on the onset of convection in porous enclosures saturated by a viscoelastic fluid is studied using linear and weak nonlinear stability theories. The enclosures are taken to be rectangular, square, and slender. For the viscoelastic fluid, the Oldroyd‐B type model is used, whereas the Darcy's model is taken for porous medium. The linear theory based on normal mode technique is used to find the criteria for the onset of marginal and oscillatory convections, and weakly nonlinear analysis based on minimal representation of truncated Fourier series is considered to discuss the convective heat transport in the system. It is observed that the beginning of convection will be oscillatory only if the strain retardation parameter is not greater than the stress relaxation parameter. The influence of raising the viscosity variation parameter, the internal heating parameter, and the stress relaxation parameter is to fast the onset of convection and also boost the heat transmission through the porous enclosures, but an opposite tendency is identified by raising the strain retardation parameter and the heat capacity ratio. The heat transmission decreases with the aspect ratio for rectangular enclosure, whereas this outcome is revered for the slender enclosure. [ABSTRACT FROM AUTHOR]

This study investigated the effect of ultrasonic activation of intracanal‐heated sodium hypochlorite (NaOCl) on its dentinal tubular penetration and root canal cleanliness in vitro. In experiment 1, mandibular premolars were randomly allocated to three groups (n = 8): group A, ultrasonic activation; group B, ultrasonic activation of intracanal‐heated NaOCl and group C, syringe‐and‐needle irrigation. Penetration of the fluorescent‐labelled NaOCl was investigated using light microscopy. In experiment 2, mandibular premolars were randomly allocated to group B or C (n = 10), for histological analysis of the remaining pulp tissue and debris. Data were statistically analysed using Kruskal–Wallis and Mann–Whitney tests (P = 0.05). The highest penetration of NaOCl was observed in group B, followed by group A (P < 0.05). Group B showed significantly less amount of debris than group C (P < 0.05). Dentinal tubule penetration of NaOCl and root canal cleanliness were significantly improved by ultrasonic activation of intracanal‐heated NaOCl. [ABSTRACT FROM AUTHOR]

Several researchers have modeled the heat transfer in a packed bed, heated externally, and determined its effective thermal conductivity (keff). But till date, very few researchers have studied the heat transfer of the pebble bed, where the heat is generated inside the bed; and the effective thermal conductivity of the packed bed with internal heat generation has not yet been reported. In the present work, heat generation inside the bed has been imitated by inductively heating randomly placed steel balls with lithium titanate (Li2TiO3) pebbles. The system has been modeled and validated with experimental results. The keff of the Li2TiO3 pebble bed is determined for various process conditions. A correlation has been developed to calculate the keff based on various process parameters such as pebble diameter, air flow rate, and induction temperature. The result presented in this study will be used for the design and scale‐up studies of future fusion reactors. [ABSTRACT FROM AUTHOR]

Preheating is an effective solution to the severe degradation of lithium-ion battery (LIB) performance at low temperatures. In this study, a bidirectional pulse-current preheating strategy for LIBs at low temperatures without external power is proposed, which involves the incorporation of a direct current/direct current converter and a series of resistances, inductances, and switches. The effects of ambient temperature, initial state of charge, and preheating strategy on the voltage and current evolution, heating rate, and heating efficiency are experimentally analysed in a climatic chamber, in addition to the effects of various preheating strategies on battery degradation. A comparative analysis is conducted using the classical pulse self-heating strategy. The results indicate that the bidirectional pulse-current preheating strategy enables preheating under an ambient temperature of −15 °C at a rate of 6.38 °C/min and affords a thermal efficiency of 31.9%. By contrast, the pulse heating method affords a heating rate of 3.46 °C/min and a thermal efficiency of 24.2%. As the battery temperature decreases, both the charge/discharge switching period and heating rate decrease, whereas the thermal efficiency and energy consumption ratio improve. No significant degradation occurs after 30 heating cycles, and the bidirectional pulse-current preheating strategy is demonstrated through capacity testing, incremental capacity curves, and electrochemical impedance spectroscopy testing. This study proposes a new approach for preheating LIBs internally and provides experimental evidence for a bidirectional-pulse preheating strategy. • Heating performance of the proposed self-heating strategy is experimentally tested. • Degradation under bidirectional pulse current self-heating strategy is analysed. • LIBs can be heated from −15 °C to 0 °C at 6.38 °C/min with little degradation. • No obvious degradation was observed after 30 cycles with the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

Previous estimates of the annual mean surface temperature of Jupiter's moon, Europa, neglected the effect of the eccentricity of Jupiter's orbit around the Sun, the effect of the emissivity and heat capacity of Europa's ice, the effect of the eclipse of Europa (i.e., the relative time that Europa is within the shadow of Jupiter), the effect of Jupiter's radiation, and the effect of Europa's internal heating. Other studies concentrated on the diurnal cycle but neglected some of the above factors. In addition, to our knowledge, the seasonal cycle of the surface temperature of Europa was not estimated. Here we systematically estimate the diurnal, seasonal and annual mean surface temperature of Europa, when Europa's obliquity, emissivity, heat capacity, and eclipse, as well as Jupiter's radiation, internal heating, and eccentricity, are all taken into account. For a typical internal heating rate of 0.05Wm−2, the equator, pole, and the global and mean annual mean surface temperatures are 96 K, 46 K, and 90 K, respectively. We found that the temperature at the high latitudes is significantly affected by the internal heating, especially during the winter solstice, suggesting that measurements of high latitude surface temperatures can be used to constrain the internal heating. We also estimate the incoming solar radiation to Enceladus, the moon of Saturn.

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The study deals with nonlinear convection in a three-layered porous-air-porous enclosure with zero temperature difference at the external impermeable thermally conductive boundaries. The upper and lower porous matrices are internally heated with a uniform energy source. To describe redistribution of heat energy between the top and bottom surfaces of the enclosure, we introduce a relative heat transfer coefficient q r that has the conduction and convection parts. The former part tends to unity in the fully filled porous domain. The symmetry of heat transfer from the inner area towards the outer surfaces breaks down if one adds an intermediate air layer with low thermal conductivity. Two sandwiched systems which have equal depth ratio d but distinct air layer location are considered. In system 1, the air layer is located in the upper unstably stratified half of the enclosure. In system 2, this layer is in the lower stably stratified half. The total value of q r always increases due to penetrative convection. At d = 0.1, local convection in system 1 is easily initiated in contrast to the hard-to-generate large-scale convection in system 2 due to a strong destabilization. The latter most effectively enhances heat transport though the top surface with increasing the supercriticality. • Nonlinear convection in a porous-air-porous enclosure, induced by energy source. • Air layer effect on redistribution of heat energy between top and bottom surfaces. • Comparing a relative heat transfer rate at different air layer locations and depths. • Local convection is easily initiated due to strong destabilization by depth ratio. • Hard-to-generate large-scale convection is more effective in heat transferring. [ABSTRACT FROM AUTHOR]

This paper describes issues related to the process of cutting with a punch with internal heating. The theoretical part explains the effects related to thermal expansion, conduction and transfer of heat in the body of punches. The experimental part refers to the design of a tool with an internally heated punch. Experimental results are summarised and the process is analysed in the discussion.

The effect of vertical throughflow and internal heating effects on fluid saturated porous medium under gravity modulation is investigated. The amplitude of modulation is considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weakly nonlinear stability analysis is proposed to study stationary convection. The Nusselt number is obtained numerically to present the results of heat transfer while using Ginzburg–Landau equation. The vertical throughflow has dual effect either to destabilize or to stabilize the system for downward or upward directions. The effect of internal heat source (Ri>0) enhances or sink (Ri