Discrete Heat Sources Research Articles

Three-dimensional instabilities in a discretely heated annular flow: Onset of spatio-temporal complexity via defect dynamics

The transition to three-dimensional and unsteady flow in an annulus with a discrete heat source on the inner cylinder is studied numerically. For large applied heat flux through the heater (large Grashof number Gr), there is a strong wall plume originating at the heater that reaches the top and forms a large scale axisymmetric wavy structure along the top. For Gr ≈ 6 × 109, this wavy structure becomes unstable to three-dimensional instabilities with high azimuthal wavenumbers m ∼ 30, influenced by mode competition within an Eckhaus band of wavenumbers. Coexisting with some of these steady three-dimensional states, solution branches with localized defects break parity and result in spatio-temporal dynamics. We have identified two such time dependent states. One is a limit cycle that while breaking spatial parity, retains spatio-temporal parity. The other branch corresponds to quasi-periodic states that have globally broken parity.

Analytical Solution for Temperature Rise in Complex Multilayer Structures With Discrete Heat Sources

Temperature rise and thermal spreading resistance in multilayered structures are an important research topic in several branches of the thermal-fluid sciences, including thermal management of electronics and contact resistance. Previous work in developing analytical solutions for the temperature rise and thermal spreading resistance has been limited to relatively few layers and simple conditions at the interfaces. Recent development of multilayer epitaxial structures for high power electronics has led to the need for more general and flexible analytical solutions because numerical methods, such as the finite element method, are often computationally inefficient. This paper presents a closed-form, analytical solution for the temperature distribution in a rectangular structure with rectangular isoflux heat sources, any number of layers of arbitrary thermal conductivity, and perfect interfacial contact or finite interfacial conductance. Extensions are also presented for convective boundary conditions in the source and sink planes. The proposed analytical solution is demonstrated and validated to study gallium nitride (GaN)-based epitaxial structures in realistic device configurations. The capability to explore the parametric space in a computationally efficient manner provides the ability to understand the key dependencies of the temperature rise on the properties of the structure, such as the substrate thickness in GaN-on-diamond epitaxial structures. Our results show that reduction of the thickness of diamond substrates may actually increase the device temperature in a realistic device configuration due to the importance of thermal spreading within the first ~100 μm of the heat source.

Interaction of surface radiation with conjugate mixed convection from a vertical channel with multiple discrete heat sources

Important results of a numerical study performed on combined conduction–mixed convection–surface radiation from a vertical channel equipped with three identical flush-mounted discrete heat sources in its left wall are provided here. The channel has walls of identical height with the spacing varied by varying its aspect ratio (AR). The cooling medium is air that is considered to be radiatively transparent. The heat generated in the channel gets conducted along its walls before getting dissipated by mixed convection and radiation. The governing equations for fluid flow and heat transfer are considered without boundary layer approximations and are transformed into vorticity–stream function form and are later normalized. The resulting equations are solved, along with relevant boundary conditions, making use of the finite volume method. The computer code written for the purpose is validated both for fluid flow and heat transfer results with those available in the literature. Detailed parametric studies have been performed and the effects of modified Richardson number, surface emissivity, thermal conductivity and AR on various pertinent results have been looked into. The significance of radiation in various regimes of mixed convection has been elucidated. The relative contributions of mixed convection and radiation in carrying the mandated cooling load have been thoroughly explored.

Review on convection heat transfer in channel flow with discrete heater arrays for electronic cooling

A review on three convection modes, forced, natural or free and mixed, is made related to laminar and turbulent direct air and liquid cooling channel flow, for application to cooling of electronic systems, and with emphasis on useful correlations. The scope covers single-phase flow over plain heaters, protruded heaters and wall heating. For forced convection, the review continues from the previous review, and describes work from 1995 onward. It is observed that protruded heater distorts the flow in the channel, causing a substantial increase in heat transfer. In natural convection, the methods of cooling and channel aspect ratio strongly affect the heat transfer. In the mixed regime, the location of the heater is less important, and at low Reynolds number, heat transfer is mainly controlled by the Grashof number. However, there are still inconsistent findings among reported results. Keywords : Forced, Natural and Mixed Convection Heat Transfer, Discrete Heat Sources, Electronics Cooling, Channel Flow.

Heat transfer enhancement with discrete heat sources in a metal foam filled vertical channel

This paper reports the results of experimental investigations of convective heat transfer in a vertical channel lined up with three discrete heat sources on one vertical wall of a vertical channel and cooled by air. The channel is filled with a metallic foam. The objective of the study is to investigate the heat transfer enhancement with the presence of metal foam and to identify the ratio of heat sources so as to achieve near isothermality of the heat source surfaces. The results of the study show that with the presence of a metal foam over the discrete heat sources the temperature variation among the heat sources drastically reduces which can be further optimized using a coupled artificial neural network (ANN)–genetic algorithm (GA) hybrid technique for a given velocity and heat input condition. A sensitivity analysis of the optimum thus obtained was also carried out to study the effect of inlet velocity and heat input on the isothermality of the heater surfaces.

The discrete heat source approach to dust cloud combustion

In the present paper, combustion of dust clouds from the discrete point heat source method has been addressed. Time-place temperature profile generated by single particle burning has been obtained to study the dust combustion. The summation of the temperature profiles of burned and burning particles predict the temperature in the preheating zone so that the ignition time of layer in flame front can be determined. Consequently the flame propagating speed was obtained based on the dust concentration corresponding to particles spacing and particle diameter. This method has been validated with aluminum dust cloud combustion. Decrease in the dust concentration leads to the lean limit of dust combustion. Increase in particles diameter or reduction in the dust concentration causes higher lean limit and also reduction in the flame propagating speed. Adding the ignition energy as igniter to this system, provides the path to study the effects of ignition energy in the dust combustion.

A NUMERICAL STUDY OF NANOFLUID FORCED CONVECTION IN A POROUS CHANNEL WITH DISCRETE HEAT SOURCES

A numerical simulation is carried out to investigate the laminar forced convection flow of Al2O3−water nanofluid in a porous parallel plates channel with discrete heat sources using a single-phase approach. The heat sources are placed on the bottom wall of the channel, and the remaining surfaces of the channel are considered adiabatic. The effects of Darcy number (Da = 10−1, 10−2, 10−4, and 10−6), particle volume fraction (φ = 0% (distilled water), 3%, 5%, and 9%), heat flux of heat sources (q = 5000,10,000, 20,000, and 30,000 W/m2), porosity (0.4, 0.6, 0.8, and 0.95), and thermal conductivity ratio (ks/kf = 1, 5,10, and 30) on the average heat transfer coefficient (h), pressure drop (ΔP), thermal-hydraulic performance (η), and wall temperature (Tw) are investigated. A remarkable decrease in wall temperature is observed, especially on the heat sources. It is founded that heat transfer and pressure drop increase for all cases as volume fraction increases. Results also reveal that in a fixed volume fraction, the average heat transfer coefficient ratio, referring to the values calculated for base fluid, increases as heat flux and porosity increase or thermal conductivity ratio decreases. No change in the average heat transfer coefficient ratio is observed with Darcy number variation. Furthermore, it is found that the pressure ratio, referring to the values calculated for base fluid, is approximately independent of all considered parameters, except volume fraction.

Augmentation of the Heat Transfer Performance of a Sinusoidal Corrugated Enclosure by Employing Hybrid Nanofluid

This paper numerically examines laminar natural convection in a sinusoidal corrugated enclosure with a discrete heat source on the bottom wall, filled by pure water, Al2O3/water nanofluid, and Al2O3-Cu/water hybrid nanofluid which is a new advanced nanofluid with two kinds of nanoparticle materials. The effects of Rayleigh number (103≤Ra≤106) and water, nanofluid, and hybrid nanofluid (in volume concentration of 0% ≤ ϕ ≤ 2%) as the working fluid on temperature fields and heat transfer performance of the enclosure are investigated. The finite volume discretization method is employed to solve the set of governing equations. The results indicate that for all Rayleigh numbers been studied, employing hybrid nanofluid improves the heat transfer rate compared to nanofluid and water, which results in a better cooling performance of the enclosure and lower temperature of the heated surface. The rate of this enhancement is considerably more at higher values of Ra and volume concentrations. Furthermore, by applying the modeling results, two correlations are developed to estimate the average Nusselt number. The results reveal that the modeling data are in very good agreement with the predicted data. The maximum error for nanofluid and hybrid nanofluid was around 11% and 12%, respectively.

Heat transfer of Cu–water nanofluid in an enclosure with a heat sink and discrete heat source

Heat transfer inside horizontal and vertical enclosure filled with Cu–water nanofluid is studied. A heat sink with rectangular fins represents the base plate of the enclosure where it is heated by a discrete heat source at the bottom of the heat sink. The front face of the heat sink is kept at constant low temperature while the side walls are assumed adiabatic. The results are presented for the enclosure without and with a heat sink of one to seven fins. The ratio of enclosure height to enclosure width is 0.25 and the study is carried out at a fin length to enclosure height ratio of 0.25 and 0.5. The effect of the volume fraction and nanoparticle diameter of Cu nanoparticles is carried out for different spacings between the fins of the heat sink and different Rayleigh numbers. The numerical model is solved by a finite volume method. The results show that the average Nusselt number on the heat source increases with increase Rayleigh number and volume fraction of Cu nanoparticles and with decreasing diameter of Cu nanoparticles. At low Ra number (Ra=103), the average Nusselt number increases with increasing number of fins and increasing L/H. At high Raleigh number (Ra=106), an increase in the value of L/H has no great effect on the average Nusselt number. At high Rayleigh number (Ra=106) and low nanoparticle diameter and high volume fraction, the enclosure with a heat sink of one fin and L/H of 0.5 has the maximum average Nusselt number for horizontal and vertical enclosure.

Thermal Spreading Resistance and Heat Source Temperature in Compound Orthotropic Systems With Interfacial Resistance

In this paper, a new and more general solution for thermal spreading resistance in compound, orthotropic systems with interfacial resistance is considered. This new solution, which extends beyond previously published results, is obtained for a finite rectangular heat source of uniform strength arbitrarily located on a rectangular substrate. By means of superposition, one can obtain the temperature field in the source plane for multiple heat sources as well as the source mean and centroid temperatures. By means of orthotropic transformations, systems containing orthotropic materials can be easily modeled. Extension of the present solutions using a computationally efficient influence coefficient method is also given, such that the effects of large numbers of heat sources are superimposed. The application of these closed-form expressions for the temperature rise is demonstrated with calculations for Gallium nitride (GaN) high electron mobility transistors (HEMTs). These solutions are shown to be more flexible than previously reported analytical expressions and much more computationally efficient than 3-D finite element analysis, especially for a large number of discrete heat sources associated with multifinger GaN HEMTs.

Characteristics of Natural Convection Heat Transfer in an Array of Discrete Heat Sources

This study aims to investigate experimentally the natural convection flow over an array of discrete surfaces mounted on a flat vertical substrate. The investigation covers the case where the discrete surfaces/substrate unit forms a wall of a closed cavity. Experimental measurements of the flow and thermal fields were conducted. The experimental study is aimed at investigating the influence of the Rayleigh number on the velocity and thermal fields inside the cavity. Two cases of heat source distribution were considered: uniform heat source distribution and non-uniform heat source distribution. Measurements of vertical and horizontal velocity components were obtained for three heating values: 10, 15, and 20 W corresponding to Rayleigh number values of Ra = 9.06 × 109, Ra 1.19 × 1010, and Ra 1.41 × 1010. For each case, the velocity measurements were conducted at three different vertical locations, located at the middle of each of the three heaters. Velocity measurements were also obtained for non-uniform heater distribution at Ra 9.53 × 109. The energy loss was found to be about 10% of the power input in each case. Empirical correlations were obtained for the data for uniformly distributed heaters.

Experimental and Numerical Study of Mixed and Natural Convection in an Enclosure With a Discrete Heat Source and Ventilation Ports

An experimental and numerical study has been carried out in order to investigate mixed and natural convection heat transfer in a two-dimensional enclosure. A discrete isothermal heat source is located at one of the vertical walls. Also, two ventilation ports are at the bottom and on top of the opposite wall. A forced flow condition was imposed by providing an inlet of air at the bottom port. A Mach–Zehnder interferometer was used to visualize the temperature field within the enclosure and to determine the local and average heat transfer characteristics of the heat source. Five heater positions on the vertical wall and different Rayleigh numbers (4.5 × 105 to 1.15 × 106) and Reynolds numbers (120 to 1600) were considered in the experiments. A finite volume code has been developed based on the SIMPLE algorithm and hybrid discretization scheme for the numerical study. It is observed that the interaction of natural convection with the forced flow leads to various flow fields depending on the Richardson number, Reynolds number and the heater position. Also, results show different trends for variation of the average Nusselt number with the heater position at low and high Reynolds numbers. An optimum position for the heat source, at which the maximum heat transfer is achieved, exists for high Reynolds numbers and has been found to be at the middle of the vertical wall.

Mixed Convection with Conduction and Surface Radiation from a Vertical Channel with Discrete Heating

A numerical investigation into fluid flow and heat transfer for the geometry of a vertical parallel plate channel subjected to conjugate mixed convection with radiation is attempted here. The channel considered has three identical flush-mounted discrete heat sources in its left wall, while the right wall that does not contain any heat source acts as a sink. Air, assumed to be a radiatively non-participating and having constant thermophysical properties subject to the Boussinesq approximation, is the cooling agent. The heat generated in the left wall gets conducted along it and is later dissipated by mixed convection and radiation. The governing equations, considered in their full strength sans the boundary layer approximations, are converted into vorticity-stream function form and are then normalized. These equations along with pertinent boundary conditions are solved through finite volume method coupled with Gauss-Seidel iterative technique. The effects of modified Richardson number, surface emissivity, thermal conductivity and aspect ratio on local temperature distribution along the channel, maximum channel temperature and relative contributions of mixed convection and radiation have been thoroughly studied. The prominence of radiation in the present problem has been highlighted.

Numerical investigation of thermal radiation effects on open cavity with discrete heat sources

PurposeNatural convection heat transfer combined with radiation heat transfer is used in electronic cooling. The purpose of this paper is to investigate the thermal loading characteristics of an enclosure.Design/methodology/approachThe goal is to investigate the effect of thermal radiation on thermal and flow characteristics of the cavity. The enclosure lower wall is at constant temperature and the upper wall is adiabatic while there are several discrete heat sources inside the cavity. In addition the effect of parameters such as heating number (Nr), aspect ratio (A), the number of heaters (N), and thermal radiation on the maximum and mean temperature of system, thermal loading characteristics of the system, Nusselt number, and the maximum stream function rate is performed. To solve the governing nonlinear differential equations (mass, momentum, and energy), a finite‐volume code based on Patankar's SIMPLE method is utilized.FindingsHeat transfer by natural convection solely and it's conjugation with thermal radiation on the thermal and flow characteristics of the system is studied. Also a parametric study illustrating the influence of the heating number, aspect ratio, the number of heaters, and thermal radiation on the maximum and mean temperature of system, thermal loading characteristics of the system, Nusselt number, and the maximum stream function rate is investigated. The results have revealed that the thermal radiation have an important effect on the thermal characteristics of system at low heating numbers.Research limitations/implicationsThe relevant governing parameters were: the heating number, Nr from 0.05 to 500, the cavity aspect ratio, A=H/L from 0.1 to 1 and the number of heaters, N, is an odd number ranging from 1 to 19Practical implicationsThis work is numerical investigation only but can have engineering application such as electronic cooling, transformers, fusion reactors technology, hot structures, fuel cells, fibrous insulations and solar‐energy drying systems.Originality/valueThe effect of radiation in enclosure with discrete heaters within fluid has not been addressed in the literature.

Numerical Study of Natural Convection in a Vertical Porous Annulus with an Internal Heat Source: Effect of Discrete Heating

This article reports a numerical study of natural convection in a vertical annulus filled with a fluid-saturated porous medium, and with internal heat generation subject to a discrete heating from the inner wall. The relative importance of discrete heating on natural convection in the porous annulus is examined via the Brinkman-extended Darcy equation. The inner wall of the annulus has a discrete heat source and the outer wall is isothermally cooled at a lower temperature. The top and bottom walls and the unheated portions of the inner wall are kept adiabatic. The governing equations are numerically solved using an implicit finite difference method. A wide range of numerical simulations is conducted to understand the effects of various parameters like heat source length, heat source location, Darcy number, radius ratio, and Rayleigh numbers due to external and internal heating on the flow and heat transfer. The numerical results reveal that the placement of the heater near the middle portion of the inner wall yields the maximum heat transfer and minimum hot spots rather than placing the heater near the top and bottom portions of the inner wall. The heat transfer increases with an increase in the external Rayleigh number and Darcy number, while it decreases with an increase in the internal Rayleigh number, porosity of the porous medium, and the size of the heater. Further, we found that the size and location of the heater has a profound influence on the heat transfer rate and maximum temperature in the annular cavity.

Conjugate Convection with Surface Radiation from a Square-Shaped Electronic Device with Multiple Identical Discrete Heat Sources

Numerical simulation studies on combined conduction–convection–radiation from a square-shaped electronic device with multiple identical flush-mounted discrete heat sources have been performed and the prominent results are reported here. The problem geometry comprises a square shaped slab with four symmetrically located flush mounted identical discrete heat sources. The heat generated in the heat sources gets conducted through the slab and subsequently gets dissipated from its boundaries by the combined modes of convection and radiation. Air, a radiatively transparent medium is considered to be the cooling agent. The governing equations for temperature distribution in the entire computational domain are obtained by appropriate energy balance between the heat generated, conducted, convected and radiated. The resulting partial differential equations are solved using finite difference method in conjunction with Gauss–Seidel iterative technique. A computer code is prepared for the purpose. Exhaustive numerical studies are performed to elucidate the effects of parameters like volumetric heat generation, thermal conductivity, surface emissivity and convection heat transfer coefficient on local temperature distribution, peak device temperature and relative contributions of convection and radiation in heat dissipation.

Natural convection of nanofluids flow with “nanofluid‐oriented” models of thermal conductivity and dynamic viscosity in the presence of heat source

Purpose – The purpose of this paper is to make a numerical study of natural convection of water‐based nanofluids in a square cavity when a discrete heat source is embedded on the bottom wall, applying a “nanofluid‐oriented” model for the calculation of the effective thermal conductivity (Xu‐Yu‐Zou‐Xu's model) and the effective dynamic viscosity (Jang‐Lee‐Hwang‐Choi's model). Another motivation is the numerical solution of the equations of the flow with a meshless method.Design/methodology/approach – A meshless point collocation method with moving least squares (MLS) approximation is used. A test validation study of the numerical method takes place for pure water flow, as well for water/Al2O3 nanofluids. The influence of pertinent parameters such as Rayleigh number (Ra), the non‐uniform nanoparticle size keeping the mean nanoparticle diameter fixed, the volume fraction of nanoparticles and the location of heat source on the cooling performance are studied.Findings – The presence of a discrete heat source, ...

Radiation heat transfer in transient dust cloud flame propagation

This study investigates the impact of radiation heat transfer and heat conduction on dust cloud combustion. Radiation plays a very important role in the stability of dust cloud flame, and increasing the amount of radiation drastically raises the possibility of instability and explosion in a dust cloud mixture. Flame speed, which is a function of mixture characteristics, can exhibit a fluctuating behavior. By using the discrete heat source method, it would be possible to study the transient propagation of dust flames. Thus, the propagation speed of flame can be obtained, and as time goes by, the transient speed of dust flame will reach its steady state value. By considering the radiation effect, better agreement is observed between the obtained results and experimental data.

Experimental investigation of thermal loading of a horizontal thin plate using infrared camera

This study reports the results of experimental investigations of the characteristics of thermal loading of a thin plate by discrete radiative heat sources. The carbon–steel thin plate is horizontally located above the heat sources. Temperature distribution of the plate is measured using an infrared camera. The effects of various parameters, such as the Rayleigh number, from 107 to 1011, the aspect ratio, from 0.05 to 0.2, the distance ratio, from 0.05 to 0.2, the number of heaters, from 1 to 24, the thickness ratio, from 0.003 to 0.005, and the thermal radiative emissivity, from 0.567 to 0.889 on the maximum temperature and the length of uniform temperature region on a thin plate are explored. The results indicate that the most effective parameters on the order of impact on the maximum temperature is Rayleigh number, the number of heat sources, the distance ratio, the aspect ratio, the surface emissivity, and the plate thickness ratio. Finally, the results demonstrated that there is an optimal distance ratio to maximize the region of uniform temperature on the plate.

Use of Nanofluids for Enhanced Natural Cooling of Discretely Heated Enclosures

Natural convection heat transfer from discrete heat sources to nanofluids is of great importance because of its application in the cooling of electronic components. The presence of the nanoparticles in the fluids increases appreciably the effective thermal conductivity of the fluid and consequently enhances the heat transfer characteristics. The present study is aimed to investigate numerically the natural convection heat transfer from discrete heat sources to nanofluids. The behavior of nanofluids was investigated numerically inside a heated cavity to gain insight into convective recirculation and flow processes induced by a nanofluid. A computational model was developed to analyze heat transfer performance of nanofluids inside a cavity taking into account the solid particle dispersion. The model was validated through the comparison with available experimental data. The results showed good agreement. The influence of the solid volume fraction on the flow pattern and heat transfer inside the cavity was investigated. The results show that the intensity of the streamlines increases with the volume fraction. It is also indicated that higher velocities along the centerline of the enclosure are achieved as the volume of nanoparticles increases. The influence of the loading factor is more distinguished at the upper heaters and in particular at the highest heater. The heat transfer increases as the volume fraction of the nanoparticles increases from 2 to 10%.