Uniform Heat Generation Research Articles

Entropy generation due flow passing over the porous block in the cavity

Flow over porous structures finds applications in heat transferring devices due to attainment of high heat transfer rates. Thermodynamic irreversibility can be used as a measure of quality of the porous body in the thermal system. In the present study, flow over a porous block situated in a square open–ends cavity and rate of entropy generation due to heat transfer and fluid friction are considered. The effects of the block aspect ratio and porosity on volumetric entropy generation rate are examined numerically. In the simulations, four aspect ratios and three porosities of the block are accommodated. The total area of the block is kept constant for all the aspect ratios considered in the simulations. A uniform heat generation (105 W/m²) is considered in the block resembling the heat generating device, such as encapsulated electronic device, and air is used as working fluid in the cavity. It is found that volumetric entropy generation rate in the cavity reduces with increasing aspect ratio and porosity of the block. Entropy generation rate due to heat transfer is considerably higher than its counter part due to fluid friction because of low Reynolds number flow at cavity inlet and small natural convection current generated in the cavity.

Investigations on the internal shape of Constructal cavities intruding a heat generating body

This paper deals with the influence that the internal shape of open ‘cavities’ exerts on the Constructal design of a heat generating body. Several shapes of cavity are studied; triangular, elliptical, trapezoidal and Y-shaped cavities intruding into a trapezoidal shaped solid with uniform heat generation. The trapezoidal solid is commonly used in round electronic devices. The geometric aspect ratios of the cavities and the solid are free to vary while the total volume occupied by the solid and the cavity are fixed. The objective is minimizing the peak (hot spot) temperature with respect to the geometrical parameters of the system. Finite element method is employed to calculate the peak temperature of the solid. With respect to the Constructal thermal design, the numerical results prove that, utilizing the triangular and Y-Shaped cavities can result more reliable and effective rather than other studied cavities.

Application of Different Conductive Substrate Materials for Heat Transfer Enhancement in Cooling of Electronic Components

In this research, a study of the heat transfer enhancement in electronic components mounted in channels was conducted by using different materials in the conductive substrate. In this context, a numerical analysis was performed to investigate the cooling of 3D protruding heaters mounted on the bottom wall (substrate) of a horizontal rectangular channel using the ANSYS/FluentTM 15.0 software. Three different materials of the conductive substrate were analyzed, polymethyl methacrylate (PMMA), fiberglass reinforced epoxy laminate (FR4), and pure aluminum (Al). Uniform heat generation rate was considered for the protruding heaters and the cooling process happened through a steady laminar airflow, with constant properties. The fluid flow velocity and temperature profiles were uniform at the channel entrance. For the adiabatic substrate, the cooling process occurred exclusively by forced convection. For the conductive substrate, the cooling process was characterized by conjugate forced convection-conduction heat transfer through two mechanisms; one directly between the heaters surfaces and the flow by forced convection, and the other through conduction at the interfaces heater-substrate in addition to forced convection from the substrate to the fluid flow at the substrate surface. The governing equations and boundary conditions were numerically solved through a coupled procedure using the Control Volumes Method in a single domain comprising the solid and fluid regions. Commonly used properties in cooling of electronics components mounted in a PCB and typical geometry dimensions were utilized in the results acquisition. Some examples were presented, indicating the dependence of the substrate thermal conductivity related to the Reynolds number on the heat transfer enhancement. Thus, resulting in a lower work temperature at the electronic components.

Effect of second-order temperature jump in Metal-Oxide-Semiconductor Field Effect Transistor with Dual-Phase-Lag model

The present numerical investigation is concerned with the role of second-order temperature jump in a horizontal planar micro-channel heat transfer. We solve numerically Dual-Phase-Lag model in a two dimensional configuration coupled with a new jump boundary condition. The nanodevice of model consists of Metal-Oxide-Semiconductor Field Effect Transistor with either uniform or non-uniform heat generation. A new temperature jump boundary condition of first and second order is used especially in the oxide–semiconductor interface. The finite element method is used to bring forth the results for a 10nm channel length of the transistor. Thermal properties of transistor device have been investigated for different orders of the temperature jump boundary condition. It has already been deduced that the increasing orders of temperature jump boundary condition lead to an increase of phonon-wall collisions. This new condition can lead to a significant increase in the heat flux and the calculated lattice temperature.

Determination of thermal diffusivity, conductivity, and energy release from the internal temperature profiles of energetic materials

Abstract A novel data processing technique has been developed to obtain thermal diffusivity, conductivity, and reaction heat release for energetic materials from Sandia Instrumented Thermal Ignition (SITI) experiments heated with a linear ramp temperature boundary condition. The method is based on the equivalence of the temperature responses of: (a) ramped temperature boundary condition with no internal heat generation and (b) uniform heat generation (that is, with a negative value) with constant temperature boundary conditions; which is true regardless of the spatial domain. For the specific case analyzed herein (the SITI apparatus), the midplane temperature profile is well represented by a quadratic expression in the radial coordinate for both ramped boundary temperature and uniform heat generation responses. Internal temperature data from temperature ramped SITI experiments with various pyrotechnics, propellants, and explosives were analyzed. Quadratic fits to the temperature profile data were made and the associated fitting coefficients were converted to yield thermal diffusivity directly. Thermal conductivity was then determined from thermal diffusivity, given knowledge of the material’s specific heat capacity and density. Finally, because of the equivalence of the cases (a) and (b) above, their individual contributions to a combined temperature profile can be easily separated, thereby yielding internal heat generation as well. This technique allows for measurements of properties for pressed and powdered materials over a range of densities and temperatures. The technique is demonstrated using pyrotechnic materials (KClO4 and Ti/KClO4), a composite solid propellant (herein referred to as “Propellant A”, a class 1.3 AP-HTPB-aluminum propellant) and an explosive (PBX 9502).

Development of a Coupled Electrical, Thermal and Degradation Supercapacitor Model for Automotive Applications

Despite the fact that supercapacitors are less complex than lithium ion batteries, they are less well understood. Although supercapacitors do not possess sufficient energy density to make them suitable as the only source of energy storage in the majority of applications, they are ideal as a buffer for the primary energy source. Applied to hybrid and electric cars, supercapacitors can be used to reduce the degradation and power requirements of the primary energy source, typically lithium ion batteries. To the best of the author’s knowledge, currently, no unified, high fidelity, electrical, thermal and degradation model exists of a supercapacitor that meets automotive requirements. This is because the electrical and thermal models must re-create both short term and long term cell behavior over a large range of temperatures, frequencies, and currents. They must also include degradation models that are valid under complex cycling conditions and not simply under constant current cycling.The state-of-the-art electrical models of a supercapacitor are equivalent circuit models, which utilize a de-Levie transmission line. The length of the transmission line is analogous to the path length of an ion from its initial location to forming part of the electrical double layer, or pore depth penetration. Thus, the transmission line can be utilised to either model the available electrode surface for ion adsorption, and hence capacitance variation with frequency, or model the charge distribution throughout the porous structure, and hence determine voltage hysteresis as a result of charge re-distribution. The standard de-Levie transmission line cannot be used to characterize both of these effects simultaneously, (which is necessary for automotive requirements) without being adapted.The majority of supercapacitor thermal models are either lumped models or axi-symmetric models utilizing an assumption of uniform heat generation. Although these models are suitable for determining thermal management strategies, and degradation under steady state conditions, they are unsuitable for determining degradation in highly dynamic systems. They are unable to predict localized hotspots at the electrode/electrolyte interface, which are caused by the entropy effects of the generation or breakdown of the electrical double layer. Furthermore, they are unable to predict the temperature difference between the positive and negative terminals. This talk will outline the development and validation of a new equivalent circuit model of a supercapacitor for automotive use. The electrical model is capable of reproducing cell behavior, including power limits, variation of capacitance and resistance with operating temperature and frequency, charge re-distribution and self-discharge. The coupled thermal model is capable of predicting reversible and irreversible heat generation and its spatial distribution throughout the cell, and the resultant degradation.

CONSTRUCTAL DESIGN OF A X-SHAPED CAVITY COOLED BY CONVECTION

This paper applies Constructal design to study the geometry of a X-shaped cavity that penetrates into a solid conductive wall. The objective is minimizing the dimensionless maximal excess of temperature between the solid body and the cavity. There is uniform heat generation on the solid body. The cavity surfaces are cooled by convection heat transfer while the solid body is subjected to adiabatic conditions on its outer surfaces. The total volume and the cavity volume are fixed, but the lengths and thickness of the X-shaped cavity can vary. The emerged optimal configurations and performance are reported. The effect of the area fraction φ which denotes the ratio between the cavity area and the total area of the geometry, and the ratio between the length and thickness of the branch cavity, H1/L1, on the dimensionless maximal excess of temperature is numerically investigated. The results show that the dimensionless maximal excess of temperature θmax,min decreases approximately 60% when the cavity fraction increases from φ = 0.05 to 0.25. The results also show that the X-shaped cavity performs approximately 45% better when compared to a C-shaped cavity under the same thermal conditions. The optimal X-shaped cavity is also in accordance with the optimal distribution of imperfections principle.

A remote-activated shape memory polymer network employing vinyl-capped Fe3O4 nanoparticles as netpoints for durable performance

A new type of shape memory polymer (SMP) employing vinyl-capped Fe3O4 nanoparticles as netpoints that determine the permanent shape for remote activation has been presented. The new design effectively prevents the nanoparticles from moving and re-aggregating in a polymer matrix and guarantees the stability of the SMP networks when a high temperature and external stress are applied. Therefore, durable shape memory performance is obtained during the programmed deformation-recovery processes. Meanwhile, a homogeneous distribution of vinyl-capped Fe3O4 nanoparticles achieves uniform heat generation and heat transfer in the alternating magnetic field. Consequently, the novel remote-activated SMP also exhibits a fast magnetic responsiveness compared to the SMPs physically dispersed with Fe3O4 nanoparticles.

Conjugate Cooling of 3D Protruding Heaters with Laminar Flow in a Rectangular Channel

The conjugate forced convection-convection heat transfer from 3D protruding heaters mounted on a conductive substrate of a horizontal rectangular channel was investigated numerically using the ANSYS/FluentTM 15.0 software. A uniform heat generation rate was assumed in the protruding heaters and the cooling was performed by means of a steady laminar airflow, with constant properties. At the channel entrance the flow velocity and temperature profiles were assumed uniform. The governing equations were solved numerically within a single domain through a coupled procedure by the Control Volumes Method with the SIMPLE algorithm. To obtain the numerical results, typical properties values and geometry dimensions found in forced convection cooling of electronics components mounted in a printed circuit board were used. The Reynolds number effects were investigated from 100 to 300. The airflow behavior around the 3D protruding heaters was shown with streamlines. The thermal parameters of interest, such as temperature distribution, local and average Nusselt numbers, local and average heat transfer coefficients, conjugate, convective, and overall thermal conductance, were found and compared, when possible, with the available results in the literature.

Geometric optimization of X-shaped cavities and pathways according to Bejan’s theory: Comparative analysis

This paper applies constructal design to study the geometry of a X-shaped isothermal cavity and a X-shaped high conductivity pathway that penetrate into a solid conducting wall. The objective is to minimize the maximal excess of temperature of the whole system, i.e. the hot spots, independent of where they are located. There is uniform heat generation on the solid body, which is insulated on the external perimeter. The total volume and the cavity volume, as well as the high conductivity material volume, are fixed, but the geometric lengths and thickness of both X-shaped configurations can vary. The emerged optimal configurations and performance are reported graphically and numerically. The results indicate that the increase of the complexity of the geometry can facilitate the access of heat currents and improve the thermal performance. The degree of freedom L1/L0 proved to be significant on the performance of the X-shaped isothermal cavity, e.g. the once optimized ratio (L1/L0)o increases approximately 10% as the area fraction ϕ increases from ϕ=0.05 to 0.3. As for the X-shaped pathway case, it has been demonstrated that the dimensionless thermal conductivity of the path k̃p and the area fraction ϕ have a strong effect on the performance and configuration of the X-shaped blades: the twice minimized θmax,mm decreases approximately 70% as k̃p increases from 30 to 300 and it decreases approximately 84% as ϕ augments from 0.01 to 0.2.Furthermore, the X-shaped conductive pathways configuration increases its performance monotonically with the augmentation of the pathways thermal conductivity: in correspondence to the highest possible value of k̃p, the X-shaped conductive pathways present approximately the same heat removal capacity of the X-shaped cavities optimized in the first part of the paper.

Heat Flux Analysis in Electrical Transformers through Integral Operators of Mechanics

Considering the continuous functioning of a power transformer under charge of high capacity of 50 MVA, predicted studies are proposed to be performed of their thermal behavior under perma nent and variable regimens of flow of charge, using noninvasive methods based in integral trans forms that measure and determine parameters of geometrical, analytical and physical type of the transformer. In before works, we have studied a basic geometry of a winding composed of high and low voltage sections with a uniform heat generation and heat convection boundary conditions. The heat conduction equation representing the phenomena of heat generation in a cylindrical structure was solved by using an integral transform. In this sense, this new study considers the basic geometry composed of a three cylindrical windings (high and low voltage turns) and a rec tangular core. Thus it is proposed to solve magnetic flow equations using integral transforms (Han kel transforms and Bessel integrals) in order to obtain the heat source distribution in the core due to the magnetization currents which are developed in function of the magnetic field flow equations. Based on this, it is proposed as a second step to use this heat source distribution to obtain the corresponding temperature distribution in the core by solving the cylindrical heat conduction equation for the core (cylindrical). Bearing this in mind, it is proposed finally to solve the 3D cylindrical heat conduction equation for the one winding using the calculated heat convection coefficients, the conductivity of the winding, behavior of the mineral oil and the non uniform winding heat generation predicted in recent researches. This equation will be solved by using integral methods (Radon, Hankel and Fourier transforms). This methodology will be useful to establish a new design of a power transformer based on the values of their integrals and the results that throw the inverse methods for this case. Finally if possible we will use the programs of Fluent and/or Phoenics for the validation of functional proposed models of prediction and prevention of heat flow and charge based on the obtained results.

Constructal design of isothermal X-shaped cavities

This paper applies Constructal design to study the geometry of a X-shaped cavity that penetrates into a solid conducting wall. The objective is to minimize the maximal dimensionless excess of temperature between the solid body and the cavity. There is uniform heat generation on the solid body. The total volume and the cavity volume are fixed, but the geometric lengths and thickness of the X-shaped cavity can vary. The cavity surfaces are isothermal while the solid body has adiabatic conditions on the outer surface. The emerged optimal configurations and performance are reported graphically. When compared to the Y- and C- and H-, the X-shaped cavity performs approximately 53% better than the Y-shaped cavity and 68% better than the C-shaped cavity for the area fraction ? = 0.05, while its performance is 22% inferior to the performance of the H-shaped cavity for the area fraction ? = 0.1. The results indicate that the increase of the complexity of the cavity geometry can facilitate the access of heat currents and improve the performance of the cavities.

Investigating flow and heat transfer characteristics in a fuel bundle with split-vane pair grids by CFD methodology

In this paper, a computational fluid dynamics (CFD) methodology is proposed to investigate the thermal–hydraulic characteristics in a rod bundle with split-vane pair grids. The SST k–ω turbulence model is primarily adopted in the present CFD model. Thickness of grids is considered in order to precisely simulate their effects in reduction of the effective flow area and increase of the flow velocity and the heat transfer capability. In addition, the uniform heat generation rate is also used to model the heat generation rate within the fuel rod, rid of constant heat flux assumption as the previous simulation works. Existing data of Nusselt (Nu) number distributions in the axial and azimuthal directions obtained by Holloway et al. (2008) have been employed to validate the CFD model. The Nu decreasing trend downstream of a split-vane pair grid and the Nu variation around the circumferential surface of rod can be explained by the predicted flow characteristics, including flow swirling, detachment, separation, etc.

Analysis of the Validity of a Constant Surface Heat Flux Model for the Case of Blocks Submitted to Uniform Volumetric Heat Generation and Periodically Mounted on the Lower Wall of a Horizontal Channel

The validity of the heat flux redistribution method is examined in the case of heating blocks submitted to a volumetric heat generation, and periodically mounted on the lower wall of a horizontal channel by considering two models. In the first model (model 1), the blocks generate uniform volumetric heat dissipation, while in the second (model 2), the blocks release a uniform heat flux at their peripheral surface. The latter model was adopted in many previous works, but its validity has never been discussed. Hence, the objective of this study is to examine the combined effects of the thermal conductivity ratio of the solid blocks and the fluid (), the Rayleigh number(104 ≤ Ra ≤ 107), and the relative height of the blocks (1/8 ≤ B ≤ 1/2) on the validity of the model with constant surface heat flux by using criteria based on local and mean heat transfer characteristics.

Thermal Stresses in a Hollow Cylinder with Convective Boundary Conditions on the Inside and Outside Surfaces

Analytical solutions for thermal stresses (radial, tangential, and axial) in a hollow cylinder with uniform internal heat generation for the thermal boundary condition of convective heating on the inside surface and convective cooling on the outside surface are derived. The analysis assumes the ends of the cylinder to be clamped, the axial strain to be negligible, and the radial stresses on the inside and the outside surfaces to be zero. Results are presented to illustrate the effects of internal heat generation parameter Q, convective environment temperatures ratio θ*, Biot number for convection on the inside surface Bi 1, Biot number for convection on the outside surface Bi 2, and the radii ratio ρ on thermal stresses distribution in the cylinder. The analytical solutions should serve as benchmarks for validating the numerical codes for dealing with more complicated cases.

Chemical Reaction and Uniform Heat Generation or Absorption Effects on MHD Stagnation-Point Flow of a Nanofluid over a Porous Sheet

The objective of this work is to analyze the chemical reaction and heat generation or absorption effects on MHD stagnation-point flow of a nanofluid over a porous stretching sheet. The uniform magnetic field strength B is applied in the direction normal to the flow. A highly nonlinear problem of nanofluid is modeled for the modified Bernoulli's equation of an electrically conducting nanofluid by incorporating the effects of embedded flow parameters such as Brownian motion parameter, thermophoresis parameter, velocity ratio parameter, heat generation/absorption parameter, suction or injection parameter, chemical reaction parameter, Hartmann number, Prandtl number and Lewis number. A system of nonlinear partial differential equations is reduced to nonlinear ordinary differential equations and then solved using finite difference scheme known as the Keller-box method. A parametric study of the involved physical parameters is conducted and a set of numerical results is illustrated in graphical and tabular forms. A comparison with published results is also provided.

Convective–radiative radial fins with convective base heating and convective–radiative tip cooling: Homogeneous and functionally graded materials

This paper studies a radial fin of uniform thickness with convective heating at the base and convective–radiative cooling at the tip. The fin is assumed to experience uniform internal heat generation. The exposed surfaces of the fin lose heat by simultaneous convection and radiation to the surroundings. Two types of fin materials are investigated: homogeneous material and functionally graded material (FGM). For the homogeneous material, the thermal conductivity is assumed to be a linear function of temperature, while for the FGM fin the thermal conductivity is modeled as a linear function of the dimensionless radial coordinate. The analysis is conducted using the differential transformation method (DTM). The accuracy of DTM is verified by comparing the results for the simplified versions of the present model with an exact analytical solution derived here. Once the accuracy of DTM is authenticated, the method is used to generate results for the general problem formulated here. These results illustrate the effects of various dimensionless parameters on the thermal performance of homogeneous material fins and FGM fins.

Optimal homotopy asymptotic method for heat transfer in hollow sphere with robin boundary conditions

In this article, we have investigated heat transfer from a hollow sphere using a powerful and relatively new semi‐analytic technique known as the optimal homotopy asymptotic method (OHAM). Robin boundary conditions are applied on both the inner and outer surfaces. The effects of Biot numbers, uniform heat generation, temperature‐ dependent thermal conductivity, and temperature parameters on the dimensionless temperature and heat transfer are investigated. The results of OHAM are compared with a numerical method and are found to be in good agreement. It is shown that the dimensionless temperature increases with an increase in Biot number at the inner surface and temperature and heat generation parameters, whereas it decreases with an increase in the Biot number at the outer surface and the dimensionless thermal conductivity and radial distance parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 124‐133, 2014; Published online 20 June 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21067

Optimal architecture of heat generating pieces in a fin

This paper documents the optimal architecture of heat generating pieces connected to and cooled in a circular-shaped fin. Relying on the constructal theory, the optimal distribution of multiple heat sources is obtained by minimizing the thermal resistance of the fin. Since the heat sources are contemplated as electronic devices with uniform heat generation, the minimization of the thermal resistance is indicated by minimization of the hot spot (peak) temperature. Temperature fields in the fin and in the heat sources are calculated using a finite elements approach of MATLAB PDE toolbox. Comparison among the considered configurations reveals that the regular configurations of the heat sources commonly used in cooling industry are not optimal and must be avoided. Optimal configurations such as triangular arrangement of heat sources are proposed to replace the unfavorable configurations.

MHD boundary-layer flow over a stretching surface with internal heat generation or absorption

This article is concerned with the steady laminar magnetohydrodynamic boundary-layer flow past a stretching surface with uniform free stream and internal heat generation or absorption in an electrically conducting fluid. A constant magnetic field is applied in the transverse direction. A uniform free stream of constant velocity and temperature is passed over the sheet. The effects of free convection and internal heat generation or absorption are also considered. The governing boundary layer and temperature equations for this problem are first transformed into a system of ordinary differential equations using similarity variables, and then solved by a new analytical method and numerical method, by using a fourth-order Runge–Kutta and shooting method. Velocity and temperature profiles are shown graphically. It is shown that the differential transform method solutions are only valid for small values of independent variables but the results obtained by the DTM-Padé are valid for the entire solution domain with high accuracy. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21054