Strength Of Heat Source Research Articles

Instability of penetrative convection in a vertical porous layer with non-Dirichlet temperature conditions

The linear stability of penetrative convection in a differentially heated vertical porous layer with non-Dirichlet boundary conditions on the perturbed temperature field is investigated. The penetrative convection is realized through a uniform internal heating in a porous medium. The instability-driving parameters are the Darcy-Rayleigh number, dimensionless internal heat source strength, the Prandtl-Darcy number, and the Biot number. Neutral stability curves and the critical values of the Darcy-Rayleigh number, the wave number, and the wave speed are computed numerically by employing the Chebyshev collocation method. A comprehensive analysis is conducted on the onset of thermal instability, focusing on the effects of transitioning temperature boundary conditions from Dirichlet to Neumann. A novel finding is the emergence of bi-modal or tri-modal neutral stability curves, which unveil distinct onset modes arising from the combined effects of a heat source and the transition of boundary conditions from isothermal to adiabatic. The threshold value of the Biot number, at which the transition to instability occurs, shows a significant dependence on the internal heat source strength and this threshold value diminishes as the Prandtl-Darcy number attains higher values. Moreover, increase in the Biot number advances the onset of convection, while the Prandtl-Darcy number is found to exert both stabilizing and destabilizing influences on the stability of the base flow.

Estimation of heat source, specific heat, and thermal conductivity of insulation materials using modified conjugate gradient method

The use of insulation materials is crucial for minimizing thermal losses in various industries like automotive, building, solar, and aerospace. Plexiglass and Expanded Polystyrene (EPS) foam are popular choices due to their effective temperature regulation, lightweight nature, and cost-effectiveness. Accurate measurement of their thermal properties is vital for achieving conservation goals. While the parallel hot wire technique provides valuable insights, accurately determining heat source strength (HW) poses a challenge, impacting measurement accuracy. To address this, the modified Conjugate Gradient Method (CGM) is employed for simultaneous estimation of thermal conductivity (λ), specific heat (c) and HW of Plexiglass and EPS foam. The direct problem result has been validated with published experimental work that shows deviations less than 2 %. The study investigates the impact of sensor positioning relative to the hot-wire (rm) and introduces artificial Gaussian error with standard deviations (θ) of 0.01 °C, 0.02 °C and 0.1 °C. At θ = 0.1 °C the percentage relative errors in the estimation of λ, c and HW with rm = 5 mm for Plexiglass are 5 %, 1.442 %, and 4.651 % respectively. For EPS foam the corresponding errors are 2.44 %, 1.26 %, and 1.74 %. The modified CGM emerges as a reliable algorithm for the measurement of thermal properties of insulation materials.

CFD of the diffusion movement and concentration distribution of culinary particles in the respiratory zone of restaurant diners

Released aerosol particles during restaurant culinary activity affect diners' health. The air conditioning system is crucial for regulating indoor air quality. However, its improper air distribution increases the individuals' exposure to particle pollution. This study investigates restaurants employing side-up airflow during summer with numerous heat sources and examines the culinary particle diffusion in the diners’ respiratory zone under the combined influence of air conditioning cold jet air supply and culinary heat source heat plume. It elucidates the change rule of the concentration distribution of culinary particles under the combined action of these two heterogeneous airflows.This study investigated the movement and concentration distribution of indoor particle by numerical simulation under various air supply velocities, culinary heat source strengths and positions and tuyere opening modes. In restaurants with culinary sources, the thermal buoyancy by the heat plume causes particles to rise. However, the drag force exerted by the cold air supply jet impedes the particles’ upward motion. The particle concentration distribution is significantly influenced by both the air supply velocity and the relative positioning of the heat source and the tuyere. Particle concentration increases by 27.13 % in the respiratory zone when the air supply jet trajectory is above the pollution emission source than below. Therefore, lowered air supply velocity is ideal with increased horizontal distance between the emission source and the tuyere under the condition of comfort satisfaction. This scenario mitigates the downward movement exerted by the jet on the particles. The drag force is increased with the air supply velocity increasing from 2.5 m/s to 4.0 m/s. Particle concentration is raised to 41.38 % in the respiratory zone. The drag force by the cold jet on the particles is also heightened with the bilateral tuyere than its single-side counterpart which increases particle concentration maximum by 40.30 % in the respiratory zone.

A Numerical Study of Smoke Concentration Distribution near Low-Intensity Fires: Sensitivity to Vertical Canopy Structure and Fire Heat Source Strength

Abstract Broadly speaking, prediction of the negative impacts of prescribed fire on air quality is limited by gaps in our understanding of the underlying fire, fuels, and atmospheric processes. These knowledge gaps hinder our ability to accurately predict smoke concentration distributions, leading to unintended smoke intrusions into nearby communities and subsequent threats to public health and safety. In this study, numerical simulations are performed using the Flexible Particle Weather Research and Forecasting (FLEXPART-WRF) Model, a Lagrangian particle dispersion model, with particle motion driven by output from a full-physics atmospheric model with a forest canopy submodel and 10-m horizontal grid spacing [Advanced Regional Prediction System (ARPS)-CANOPY], to address two research questions. First, what is the relationship between near-fire (within ∼50–150 m of fire) smoke concentration distribution and (i) vertical canopy structure and (ii) fire heat source strength? Second, what roles do mean transport (i.e., transport by the mean wind) and turbulent diffusion play in shaping the near-fire smoke concentration distribution? To address these questions, simulations are run with 25 combinations of plant area density profile and fire sensible heat flux magnitude, and smoke is represented by particles with diameters ≤ 2.5 μm (PM2.5). Results show that near-fire PM2.5 concentration distribution is primarily controlled by vertical canopy structure, with fire heat source strength primarily controlling the PM2.5 concentration magnitude. Analysis of the underlying ARPS-CANOPY variables driving the FLEXPART-WRF particle dispersion helps elucidate the roles of mean transport and turbulent diffusion. In total, the study findings suggest that the vertical distribution of canopy vegetation and fire heat source strength are important factors influencing PM2.5 dispersion and concentration distribution near low-intensity fires.

Geothermal heat source estimations through ice flow modelling at Mýrdalsjökull, Iceland

Abstract. Geothermal heat sources beneath glaciers and ice caps influence local ice-dynamics and mass balance but also control ice surface depression evolution as well as subglacial water reservoir dynamics. Resulting jökulhlaups (i.e., glacier lake outburst floods) impose danger to people and infrastructure, especially in Iceland, where they are closely monitored. Due to hundreds of meters of ice, direct measurements of heat source strength and extent are not possible. We present an indirect measurement method which utilizes ice flow simulations and glacier surface data, such as surface mass balance and surface depression evolution. Heat source locations can be inferred accurately to simulation grid scales; heat source strength and spatial distributions are also well quantified. Our methods are applied to the Mýrdalsjökull ice cap in Iceland, where we are able to refine previous heat source estimates.

Simultaneous estimation of heat source strength of hot wire and thermal conductivity of material

The hot-wire (HW) technique is a widely used method for measuring the thermal conductivity (k) of insulation materials. However, there are some limitations to the applicability. For instance, inaccuracies may arise when the wire is assumed to be infinitely thin and long, or when the sample material is assumed to be an infinite medium. Additionally, the accuracy of k measurements relies on accurately specifying the heat source strength (QW ) generated by the HW. The modified conjugate gradient method (CGM) provides a solution to these limitations of the HW technique. In the modified CGM technique, a scaling factor based on the Levenberg-Marquardt method is utilized to address the low derivative and divergence issues of the traditional CGM. The current work simultaneously estimates QW generated by the HW and k of the sample materials by using modified CGM. The investigation looked into the effect of sensor positioning relative to the HW and the introduction of artificial Gaussian error (noise) with a standard deviation of 0.01 °C, 0.02 °C and 0.1 °C into the simulated temperature measurements. The modified CGM estimates the unknown parameters accurately compared to the traditional CGM. The measurement location should be closer to the HW to obtain accurate estimation results. The noise level of 0.1 °C results in low accuracy of estimation of k and QW for Plexiglas with one sensor, which can be enhanced by employing two sensors. Overall, the modified CGM algorithm proved to be a robust inverse algorithm that could be employed to estimate unknown parameters.

An inverse problem to estimate simultaneously the heat source strength for multiple integrated circuit chips on a printed circuit board

<abstract> <p>In this three-dimensional steady-state inverse heat transfer problem, we determine the magnitude of the spatially dependent volumetric heat source originating from multiple encapsulated chips mounted on a printed circuit board (PCB). Prior to the estimations, the functional form of the multiple heat sources is treated as unknown, leading to its classification as a function estimation challenge within the realm of inverse problems. The utilization of the conjugate gradient method (CGM) as an optimization tool is rooted in its distinct advantage of not requiring any a priori knowledge regarding the functional form of the unidentified quantities. Furthermore, the CGM empowers the simultaneous correction and estimation of multiple unknowns during each iteration, thereby ensuring the consistent possibility of precise estimates.</p> <p>To affirm the precision of the estimated heat source attributed to multiple chips, a series of numerical experiments were conducted. These experiments encompassed varying inlet air velocities and introduced measurement errors. Notably, the results revealed that meticulous measurements consistently yielded accurate heat generation assessments for the chips, regardless of the prevailing air velocity conditions. The findings underscored that the accuracy of chip heat generation estimates diminished as measurement errors escalated, predominantly due to the ill-posed nature inherent in the inverse problem.</p> </abstract>

Modeling of heat transfer at local convection over a vertical throughflow in a two-layered air-heat generating porous system

Convective heat transfer in an air layer partially filled with a heat-generating granular porous medium is studied. There is a slow seepage of air through the layer in the vertical direction with a constant velocity. Equal temperatures are maintained at the outer solid permeable boundaries, and the heat source strength is constant within the porous sublayer and is proportional to the solid volume fraction. The permanent heat generation within the porous sublayer, combined with the vertical throughflow, causes a nonlinear thermal profile which is conducive for convection to occur. The Boussinesq approximation and Darcy's law are used to describe this convection. Numerical solution of the nonlinear convective problem is obtained on the basis of Newton's method. In the limiting case, the numerical data for the onset of convection are compared with the results of the earlier paper of the authors, where a linear stability theory and a method for constructing of the fundamental system of partial solution vectors have been applied, and with the data by other authors. The stationary regimes of local convection, which occurs in an “air – heat-generating porous medium-air” system over the basic vertical throughflow, and its effect on the heat transfer from the porous air sublayer with the growth of supercriticality are studied. It is shown that, depending on the velocity of the basic throughflow (the Peclet number), convection excitation can be both soft (due to supercritical pitchfork bifurcation) and hard (when the loss of stability of the basic throughflow is accompanied by subcritical pitchfork bifurcation that gives rise to an unstable secondary convective regime). This secondary regime is replaced by a stable tertiary convective regime with increasing supercriticality. It has been found that the total heat transfer rate for the upward basic throughflow exceeds that for the downward basic throughflow significantly, and that local convection at any direction of this throughflow increases the heat transfer rate in the system. An increase in the Nusselt number with the growth of supercriticality is recorded. However, a noticeable contribution of local convection to the total heat transfer is observed only when all values of the Pecklet number are negative and its positive values are lower than 2.

Buoyancy-driven natural ventilation performance of a multi-story building with vertical shaft designed by using dimensionless design approach

Components with a tall vertical space attached to multi-story buildings are used to assist natural ventilation, which however unavoidably results in different buoyant forces on different stories. To achieve equal flow rates on all stories, a dimensionless design approach was developed in literature. This study aims to examine the reliability of the dimensionless approach for designing the buoyancy-driven ventilation of multi-story buildings. Moreover, it validates the application of the approach to scenarios where the heat source strengths on stories vary. The experimental and numerical results confirm the reliability of the dimensionless approach for designing naturally ventilated buildings with uniform airflow rates and air temperatures on each story. In the case of a story with flexible heat flux, changing the heat flux affects the ventilation rates on all the stories. In particular, when the heat flux on this story is zero, buoyant ventilation continues and may even be observed on the third story. Furthermore, an increase in the heat flux on the first or second story enhances stack ventilation, whereas increasing the heat flux on the third story has a damping effect on ventilation in the other stories. Additionally, stories with identical heat fluxes had similar ventilation rates and indoor temperatures.

Thermogravitational Convection in a Controlled Rotating Darcy-Brinkman Nanofluids Layer Saturated in an Anisotropic Porous Medium Subjected to Internal Heat Source

Thermogravitational convection in a controlled rotating Darcy-Brinkman nanofluids layer saturated in an anisotropic porous medium heated from below is Thermogravitational convection in a controlled rotating Darcy-Brinkman nanofluids layer saturated in an anisotropic porous medium heated from below is investigated. The presence of a uniformly distributed internal heat source and considers the Brinkman model for different boundary conditions: rigid-rigid, free-free, and lower-rigid and upper-free are considered. The effect of a control strategy involving sensors located at the top plate and actuators positioned at the bottom plate of the nanofluids layer is analysed. Linear stability analysis based on normal mode technique is employed. The resulting eigenvalue problem is solved numerically using the Galerkin method implemented with Maple software. The model used for the nanofluids associates with the mechanisms of Brownian motion and thermophoresis. The influences of the internal heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection. Conversely, the Darcy number, thermal anisotropy parameter, porosity, rotation, and controller effects are observed to slow down the process of convective instability.investigated. The presence of a uniformly distributed internal heat source and considers the Brinkman model for different boundary conditions: rigid-rigid, free-free, and lower-rigid and upper-free are considered. The effect of a control strategy involving sensors located at the top plate and actuators positioned at the bottom plate of the nanofluids layer is analysed. Linear stability analysis based on normal mode technique is employed. The resulting eigenvalue problem is solved numerically using the Galerkin method implemented with Maple software. The model used for the nanofluids associates with the mechanisms of Brownian motion and thermophoresis. The influences of the internal heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection. Conversely, the Darcy number, thermal anisotropy parameter, porosity, rotation, and controller effects are observed to slow down the process of convective instability.

Internal heat source effects on thermosolutal convection of Casson nanofluids embedded by Darcy-Brinkman model

The current study investigates Darcy-Brinkman convective instability for a non-Newtonian binary nanofluid layer in the presence of internal heat source. Non-Newtonian fluid behavior is characterized by Casson model. Normal mode technique is employed to convert the relevant PDEs into ODEs and Boussinesq approximation is used. The phenomenon is explored for both stationary as well as oscillatory modes of convection. The novelty and significance of the work lie in the fact that oscillatory motions have come into existence due to the presence of internal heat source term in the thermal energy equation which were non-existent otherwise for top-heavy configuration of nanoparticles. The impact of various nanofluid and solute parameters except solute Rayleigh number is found to destabilize the nanofluid layer while solute Rayleigh number, Darcy number and porosity parameters are found to postpone the onset of convection. Non-Newtonian Casson parameter and internal heat source strength are found to hasten the convection for the present arrangement of nanoparticles.

Marangoni convection in a dielectric fluid layer with an AC electric field and nonuniform volumetric heat source due to incident radiation

AbstractThe role of a uniform AC electric field and a nonuniform volumetric heat source arising due to an external incident radiation on the onset of Marangoni convection in a horizontal layer of an incompressible dielectric fluid is investigated. The bottom rigid surface is fixed at a constant temperature while the top free surface at which the surface tension acts is considered to be nondeformable and a Robin boundary condition on the perturbation temperature is invoked. The nonuniform internal heating within the fluid layer alters the conduction temperature profile from linear to nonlinear in the vertical coordinate. The linear stability of the quiescent basic solution is studied with respect to normal mode disturbances. The resulting stability eigenvalue problem with variable coefficient is solved numerically using the Galerkin method. The impact of governing parameters on the instability of the system is discussed thoroughly. The forces causing instability reinforce together and are found to be tightly coupled. It is observed that the strength of nonuniform heat source and the electric Rayleigh number is to hasten, while an increase in the Biot number is to delay the onset of Marangoni electroconvection. Finally, the results obtained under the limiting cases are shown to be in good agreement with those published earlier.

A combined inverse prediction and experimental analysis for the frozen ground heat transfer in a structure foundation

This paper takes the representative buried structure in permafrost regions, a transmission line tower foundation, as the research object. An inverse prediction is conducted in a scaled-down experimental system mimicking actual heat conduction of the frozen ground in a tower foundation. In permafrost regions, global warming and the heat transfer through the buried structures bring significantly adverse thermal effects on the stability of the infrastructures. In modeling the thermal effects, it has been a challenge to determine the ground surface boundary condition and heat source strength from the buried structures due to the complex climate and environmental conditions. In this work, based on the improved model predictive inverse method with an adaptive strategy, an inverse scheme is successfully implemented to simultaneously identify the time-varying surface temperature and the time-space-dependent heat source representing the buried structures. In this scheme, an adaptive time-varying predictive model is established by the rolling update of the sensitivity response coefficients according to the predicted temperature field to overcome the influence of nonlinear characteristics in the heat transfer process. The inverse method is verified by simulation and experimental data. According to the experimental inversion results, the reconstructed temperature distribution efficiently predicts the thermal state evolution of the permafrost foundation under seasonal freezing and thawing. It is found that, under the experimental conditions, the intensified thawing and freezing are significantly severe, e.g., the increased area ratio of active layer thickness is as high as 28% after building a tower, and the depth of permafrost table ranges from about 14 mm to about 38 mm, which could be detrimental to the stability and safety of the tower foundation. This study will provide valuable guidance for risk assessments or optimizing the design and maintenance of the real tower foundation and similar buried structures.

Applications of three-dimensional uncertain heat equations.

Uncertain heat equation is a partial differential equation describing temperature changes with time, while the strength of heat source is affected by the interference of noise. This paper applies the three-dimensional uncertain heat equation in some practical problems, including average temperature, maximum temperature, minimum temperature and minimum time of reaching a given temperature by using mathematical tools of time integral, space integral, extreme value and first hitting time.

The laminar seabed thermal boundary layer forced by propagating and standing free-surface waves

A mathematical model is developed to investigate seabed heat transfer processes under long-crested ocean waves. The unsteady convection–diffusion equation for water temperature includes terms depending on the velocity field in the laminar boundary layer, analogous to mass transfer near the seabed. Here we consider regular progressive waves and standing waves reflected from a vertical structure, which complicate the convective term in the governing equation. Rectangular and Gaussian distributions of seabed temperature and heat flux are considered. Approximate analytical solutions are derived for uniform and trapezoidal currents, and compared against predictions from a numerical solver of the full equations. The effects of heat source profile, location and strength on heat transfer dynamics in the thermal boundary layer are explained, providing insights into seabed temperature forced convection mechanisms enhanced by free-surface waves.

MHD micropolar hybrid nanofluid flow over a flat surface subject to mixed convection and thermal radiation

Hybrid nanofluids play a significant role in the advancement of thermal characteristics of pure fluids both at experimental and industrial levels. This work explores the mixed convective MHD micropolar hybrid nanofluid flow past a flat surface. The hybrid nanofluid flow is composed of alumina and silver nanoparticles whereas water is used as a base fluid. The plate has placed vertical in a permeable medium with suction and injection effects. Furthermore, viscous dissipation, thermal radiation and Joule heating effects are taken into consideration. Specific similarity variables have been used to convert the set of modeled equations to dimension-free form and then has solved by homotopy analysis method (HAM). It has revealed in this investigation that, fluid motion upsurge with growth in magnetic field effects and mixed convection parameter and decline with higher values of micropolar factor. Micro-rotational velocity of fluid is upsurge with higher values of micropolar factor. Thermal flow behavior is augmenting for expended values of magnetic effects, radiation factor, Eckert number and strength of heat source. The intensification in magnetic strength and mixed convection factors has declined the skin friction and has upsurge with higher values of micropolar parameter. The Nusselt number has increased with the intensification in magnetic effects, radiation factor and Eckert number.

A numerical investigation for tangent hyperbolic hybrid nanofluid transportation across Riga wedge

This communication presents an enhancement of heat transportation of tangent hyperbolic nanofluid comprised of silver / Gasoline oil and silver /Gasoline oil. The flow of fluid is caused by the stretching Riga wedge. The leading nonlinear coupled differential formulation is transmuted into ordinary differential form with the utilization of similarity transform. Numerical findings are yielded by hiring the Runge–Kutta method and shooting procedure coded in a MATLAB script. The computational run is carried out to explore the influence of notable parameters on skin friction, velocity, local heat transfer rate, and temperature of the fluid. The range of the parameters are taken arbitrarily as , , , and , etc. It is noticed that flow accelerates with modified Hartman number and Weissenberg number. The temperature is incremented directly with heat source strength and Biot number. The velocity of mono nanofluid (Ag/Gasoline) is slow as than that of hybrid nanofluid but the temperature behaves reciprocally.

Thermal performance analysis of ground source heat pump system for low-temperature waste heat recovery storage

This study investigated the thermal performance of a ground source heat pump (GSHP) system for low-temperature waste heat storage. Considering the large amount of low-temperature heat from industrial effluents wasted to the environment, this study intends to store this low-temperature waste heat in the ground. A GSHP system for low-temperature waste heat storage was established, which could simultaneously achieve heat storage and extraction. In this system, the borehole cluster comprises two parts: inner and outer layers of ground heat exchangers (GHEs). The inner layer was used for space heating as a common GHE, which extracts heat from the ground, whereas the outer layer connected to the industry was designed for injecting low-temperature waste heat to the ground seasonally. The heat fluxes of the GHEs for heat injection and extraction were set differently and were taken as two different strengths of heat sources in this study. A heat and moisture transfer model was established and experimentally validated. Subsequently, the waste heat storage and heat extraction processes are modelled numerically. The results show that the average soil temperature increases by at least 2.63 and 6% when the heat flux of the outer layer GHEs are 40 and 50 Km−1, respectively. It reveals that the injection of low temperature waste heat into the soil is not only beneficial to waste heat recovery, but can also alleviate soil thermal imbalance, providing significant support in heating dominated area, especially in cold regions. This study complements the thermal analysis between two different strength of heat sources, providing a reference for practical engineering design.

Exploration of energy‐based volumetric heating on ferrothermal porous convection: Effects of MFD viscosity and boundary conditions

AbstractThe impact of energy‐based volumetric internal heating and magnetic field‐dependent (MFD) viscosity on the onset of ferrothermal porous convection for different types of boundary conditions is investigated. The lower and upper boundaries are considered to be either rigid or stress‐free. The lower boundary is insulating, while at the upper boundary a Robin type of thermal condition is applied. Besides this, a general type of boundary conditions is invoked on the magnetic potential. The stability eigenvalue problem is solved numerically using the Galerkin‐type of weighted residuals technique with the Rayleigh number, as the eigenvalue. The results obtained for different boundary combinations are found to be qualitatively similar though not quantitatively. The effect of Biot number, MFD viscosity, and porous parameters is to hinder, while the influence of internal heat source strength, magnetic number, and the nonlinearity of fluid magnetization is to advance the onset of convection. The rigid and conducting boundaries offer a more stabilizing influence on the onset when compared to stress‐free and insulating boundaries. The convection cells get contracted the most when the boundaries are rigid and also when the upper boundary is conducting. The results delineated under the limiting cases are found to be in good agreement with those available in the literature.

PENETRATIVE THERMO-GRAVITATIONAL AND SURFACE-TENSION DRIVEN CONVECTION IN A FERROFLUID LAYER THROUGH VOLUMETRIC INTERNAL HEATING WITH VARIABLE VISCOSITY

This work pertaining to analytical and numerical studies on FTC in a FF layer with impact of coupled buoyancy-gravitational and surface-tension forces through the strength of internal heat source on the system subjected to the magnetic field dependent (MFD) viscosity effect. The lower boundary is considered to be rigid at either conducting or insulating to temperature perturbations, while upper boundary free open to the atmosphere is flat and subject to a Robin-type of thermal boundary condition. The Rayleigh-Ritz method with Chebyshev polynomials of the second kind as trial functions is employed to extract the critical stability parameters numerically. The onset of FTC is delayed with an increase in MFD (  ) parameter and Biot number ( Bi ) but opposite is the case with an increase in Rayleigh number( M1 ), non-linearity of fluid magnetization ( M 3 ) and strength of internal heat source ( Ns ). Their effects are complementary in the sense that the critical Mac and Rmc decrease with an increase in Rt .