Discrete Heat Sources Research Articles

Effect of a discrete heat source location on entropy generation in mixed convective cooling of a nanofluid inside the ventilated cavity

In this paper, the effect of localised heat sources on entropy generation owing to mixed convection flow in a vented square cavity has been studied numerically. Laminar steady forced convection flow of copper–water nanofluid through the cavity has been affected by density variations as a result of heat input from a wall–mounted heat source. To investigate the effect of the heat source location, three different placement configurations of the heat source have been considered. Furthermore, to further generalise the results, three different non–uniform heat flux conditions were also examined. The entropy generation rate has been analysed for Richardson numbers 0 ≤ Ri ≤ 10 and for solid volume fraction within 0 ≤ φ ≤ 0.05. With either uniform or non–uniform wall heating, the entropy generation rate is found to be minimal when the heat source and cavity exit are on the same wall. The maximum heat transfer rate, however, corresponds to the case when the main flow is parallel to the heated wall.

Use of Nanofluids for Improved Natural Cooling of Discretely Heated Cavities

The present study is aimed at investigating 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, and the results showed good agreement. The influence of the solid volume fraction and the aspect ratios 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. The influence of the loading factor is more distinguished in the vicinity of the upper heaters and, in particular, at the highest heater. The heat transfer increases with the increase in the volume fraction of the nanoparticles in the range of 2 to 10%. As the aspect ratio (AR) increases (channel width is reduced), the streamlines change and the intensity of the streamlines increases slightly, showing flow in the middle of the channel. The stagnation region disappears, and interaction between the two boundary layers at the hot and cold walls is evident.

Role of distributed heating on enhancement of thermal mixing for liquid food processing with heat flow visualization method

Abstract Thermal treatment is an important step in food processing. The conventional methods of heating of an enclosure may result in inadequate thermal mixing and poor temperature distribution leading to energy wastage. In this work, an alternative, energy-efficient method of distributed heating of the cavity is studied and compared with the isothermal bottom wall heating case in enhancing the thermal mixing and improving the temperature distribution in the cavity. Steady laminar natural convection of liquid food materials with a representative Prandtl number, Pr = 3.14 is studied in the range of Rayleigh number, Ra = 103–105 in differentially and discretely heated square cavities. Detailed analysis is carried out by visualizing the heat flow by heatlines. Further, the thermal mixing and the temperature uniformity are analyzed based on the cup-mixing temperature and root-mean square deviation. It is found that the thermal management policy of distributed heating significantly influences the thermal mixing and the temperature uniformity within liquid food. In a case with multiple discrete heat sources, a remarkable uniformity in temperature across the cavity is achieved with moderate thermal mixing. Based on heatlines, cup-mixing temperature and root-mean square deviation, optimal heating policy for food processing may be chosen. Industrial Relevance Three types of discrete heating situation are considered. Numerical simulations were carried out to predict the temperature and flow characteristics. Numerical simulation results were benchmarked or validated with literature data. Thus, current numerical simulation results are useful to select the suitable heating strategy for efficient thermal processing of liquid food. The proposed methodology with the numerical data would be useful to practicing industries for efficient juice heating.

HEAT TRANSFER FROM TWO DISCRETE FLUSH-MOUNTED HEATERS SUBJECTED TO LAMINAR PULSATING AIR FLOW IN A CHANNEL

In this article, a numerical study on heat transfer in laminar pulsating air flow in a channel around two discrete flush-mounted heat sources is reported. Simulations are conducted for five different frequencies and three different amplitudes while the Reynolds number (Re = 125) and Prandtl number (Pr = 0.71) remain constant for all cases. In addition, limited geometric parameters such as spacing between the two discrete heaters are investigated. Numerical simulations are performed by using the commercial CFD code Fluent. The optimum heat transfer parameters are analyzed. The time-mean Nusselt number is obtained for a cycle and given as dimensionless parameters. The heat transfer enhancements are found for low frequencies and high amplitudes.

Propagation and extinction of dust flames in narrow channels

This article has investigated the propagation and extinction of aluminum dust cloud flame in a narrow channel. The burned and burning dust particles act as heat sources and the channel walls act as heat sinks. In this method, discrete heat source has been used to analyze dust combustion in a narrow channel. Using the superposition of sources and sinks, the preheat zone temperature is predicted as an indicator of flame propagation or extinction. Dust concentration and channel width are two major parameters which affect the quenching distance and flame propagating speed. Wall temperature affects the heat loss; and by preheating the walls, quenching distance is reduced and flame propagation speed is increased.

Nu–Ra–Fo correlations for transient free convection in 2D convective diode cavities with discrete heat sources

This work allows to quantify the transient natural-convection heat transfer taking place in air-filled convective diode cavities. The results are presented in terms of Nusselt–Rayleigh–Fourier numbers correlations. They are valid for the specific configuration of the hot wall that consists of three horizontal, isothermal discrete bands separated by two adiabatic ones of the same dimensions. The channel that connects the hot and cold walls is adiabatic and is inclined between −60° and +60° with respect to the horizontal. The correlations proposed are obtained from numerical results based on the finite volume method and are validated by measurements. They complement those obtained in a previous work for steady state and Rayleigh number in the range 1.84×105⩽Ra⩽1.70×109, which make them suitable for applications in several industrial sectors.

Effect of surface radiation heat transfer on the optimal distribution of discrete heat sources under natural convection

Experiments have been conducted for natural convection heat transfer from protruding discrete heat sources, mounted at different positions on a substrate, to determine the optimal configuration, and to study the effect of surface radiation on them, which reduces their temperature upto 12 %. The optimal configuration has been determined by a non-dimensional geometric distance parameter (λ). An empirical correlation has been proposed between the non-dimensional steady state temperature (θ) and λ, by taking into account the effect of surface radiation heat transfer.

Constant-flux discrete heating in a unit aspect-ratio annulus

Natural convection in an annulus with a discrete heat source on the inner cylinder is studied numerically. The outer cylinder is isothermally cooled at a fixed low temperature, and the top wall, the bottom wall and unheated portions of the inner cylinder are thermally insulated. For low applied heat flux through the heater, as measured non-dimensionally by a Grashof number, Gr, the flow in the annular gap consists of a single-cell overturning meridional flow driven by the radial temperature gradient between the heater on the inner cylinder and the cold outer cylinder. In this regime, the flow is very weak and heat is transported primarily via conduction. The flow structure does not change until Gr ∼ 104, although the flow strength steadily increases with Gr. As the nonlinear convection terms become more important, the meridional circulation sweeps the isotherms from being almost vertical near the outer cylinder to almost horizontal near the bottom wall. By the end of the transition from the conduction-dominated regime (Gr < 104) to the convection-dominated regime (Gr ∼ 106), the flow becomes segregated into three distinct regions: (i) for vertical levels below that of the bottom of the heater, an essentially cold stagnant pool develops, with the heat flux through the outer cylinder dropping to zero. (ii) At vertical levels between the bottom and the top of the heater, most of the region in between the two cylinders is stably stratified with a relatively weak radial flow from the cold to the heated cylinder. The horizontal isotherms adjust to the temperatures on the cylinders in thin buoyancy boundary layers which drive fluid down the cold cylinder and up the heated cylinder segment. The boundary layer on the heater is about half as thick as that on the cold cylinder, but about twice as intense. (iii) The third region is above the heater top. The boundary layer flow from the heater continues upward where it meets the top endwall and bounces off of it. A wavy jet bounces on its way radially outward between the top insulated wall and the stably stratified region below. Flow separation on the top wall leads to the formation of a recirculation zone there. The vast majority of the heat flux through the outer cylinder occurs at this upper level, and is heavily concentrated near the very top. Geometric factors, such as the radius ratio of the cylinders and the heater placement, have quantitative effects, which are described, but the overall qualitative picture remains unchanged.

Numerical Simulation of Mixed Convection Flows in a Square Double Lid-Driven Cavity Partially Heated Using Nanofluid

A numerical study has been done through an Al2O3–water in a double lid-driven square cavity with various inclination angles and discrete heat sources. The top and right moving walls are at low temperature. Half of the left and bottom walls are insulated and the temperatures of the other half are kept at high. A large number of simulations for a wide range of Richardson number of 0.1 to 10, Reynolds number from 1 to 100, inclination angle of cavity from -90 o to 90 o and solid volume fraction between 0 and 0.06 are performed. The results are presented in the form of streamline, isotherm and Nusselt number plots. The influence of solid volume fraction of nanofluids and angle of inclination on hydrodynamic and thermal characteristics have been analyzed and discussed. As a result, it was found that the heat transfer increases with increase in solid volume fraction for a constant Reynolds number, heat transfer also increases with increase in Richardson and Reynolds for a particular volume fraction.

Thermosolutal convection from a discrete heat and solute source in a vertical porous annulus

Double-diffusive convection in a vertical annulus filled with a fluid-saturated porous medium is numerically investigated with the aim to understand the effects of a discrete source of heat and solute on the fluid flow and heat and mass transfer rates. The porous annulus is subject to heat and mass fluxes from a portion of the inner wall, while the outer wall is maintained at uniform temperature and concentration. In the formulation of the problem, the Darcy–Brinkman model is adopted to the fluid flow in the porous annulus. The influence of the main controlling parameters, such as thermal Rayleigh number, Darcy number, Lewis number, buoyancy ratio and radius ratio are investigated on the flow patterns, and heat and mass transfer rates for different locations of the heat and solute source. The numerical results show that the flow structure and the rates of heat and mass transfer strongly depend on the location of the heat and solute source. Further, the buoyancy ratio at which flow transition and flow reversal occur is significantly influenced by the thermal Rayleigh number, Darcy number, Lewis number and the segment location. The average Nusselt and Sherwood numbers increase with an increase in radius ratio, Darcy and thermal Rayleigh numbers. It is found that the location for stronger flow circulation is not associated with higher heat and mass transfer rates in the porous annular cavity.

Forced convection in a wavy channel with discrete heat sources

PurposeThis paper presents the heat transfer enhancement from discrete heat sources using a wavy channel.Design/methodology/approachThe finite element method is utilized to solve the hydrodynamic/thermal problem. The considered geometry consists of a channel formed by two wavy plates with six discrete heat sources placed on upper and lower walls. The global objective is to maximize the heat transfer from the heat sources. The wavy channel enhances heat transfer from the heat sources through the modification of the flow pattern in the channel. The effects of the Reynolds number, Prandtl number, waviness of the wavy wall, and the location of the heat sources on the thermal characteristics of the flow are investigated.FindingsResults indicate that the wavy channel significantly enhances the heat flow out of the heat sources, with heat sources located at the minimum channel cross sections having the best performance. The Nusselt number increases with an increase in Reynolds number and waviness of the wavy channel. The higher Prandtl number has a positive effect on the heat flow out of the heat sources. The heat transfer enhancement can reaches as high as 120 percent for high Reynolds numbers and waviness of the channel.Originality/valueThe combination of wavy plates and optimum placement of heat sources can lead to better, less expensive thermal management of heat sources in electronic devices.

Studying the effects of a longitudinal magnetic field and discrete isoflux heat source size on natural convection inside a tilted sinusoidal corrugated enclosure

In the present work, the effects of the longitudinal magnetic field and the heat source size on natural convection heat transfer through a tilted sinusoidal corrugated enclosure for different values of enclosure inclination angles are analyzed and solved numerically by using the finite volume technique based on body fitted control volumes with a collected variable arrangement. A constant heat flux source is discretely embedded at the central part of the bottom wall whereas the remaining parts of the bottom wall and the upper wall are assumed adiabatic, and two vertical sinusoidal corrugated walls are maintained at a constant low temperature. The range of the variable parameters considered in the present analysis is as follows: the enclosure inclination angle is varied from 0° to 135°, the ratio of the size of the heating element to enclosure width varied from 20 to 80% of enclosure reference length, Hartmann number is varied from 0 to 100, and Rayleigh number varied from 103 to 106. Liquid gallium with constant Prandtl number (0.02) is used as a working fluid with constant properties except the density. The obtained results indicated that streamlines are affected strongly by the magnetic field especially for small values of inclination angle (Φ=0°) and Rayleigh number (Ra=103–106). The magnetic field effect decreases with an increase in the enclosure inclination angle (Φ>0°) especially for large values of Rayleigh number. The increase in Hartmann number will cause the temperature lines to become symmetrical in shape for large values of Rayleigh number (Ra=105–106). The results also explain that the temperature lines are very little affected by the inclination angle especially for small values of (ε=0.4) and (Ra=104), but this effect will increase especially for (ε=0.8) and (Ra=106). The Nusselt number increases first with an increase in inclination angle (0°≤Φ≤45°), then is slightly affected for (45°<Φ≤90°), and finally decreases for (90°<Φ≤135°). An empirical correlation is developed by using Nusselt number versus Hartmann and Rayleigh numbers, and enclosure inclination angle. The increase in Hartmann number and the ratio of heating element to enclosure width will decrease the Nusselt number. Furthermore, four mathematical correlations are extracted from the results and presented, which can be used to accurately predict the average Nusselt number in terms of enclosure inclination angle, Hartmann, and Rayleigh numbers.

Numerical Investigation of Nanofluid Forced Convection in Channels with Discrete Heat Sources

Numerical simulation is performed to investigate the laminar force convection of Al2O3/water nanofluid in a flow channel with discrete heat sources. The heat sources are placed on the bottom wall of channel which produce much thermal energy that must be evacuated from the system. The remaining surfaces of channel are kept adiabatic to exchange energy between nanofluid and heat sources. In the present study the effects of Reynolds number (Re = 50, 100, 200, 400, and 1000), particle volume fraction (ϕ = 0 (distilled water), 1 and 4%) on the average heat transfer coefficient (h), pressure drop (ΔP), and wall temperature (Tw) are evaluated. The use of nanofluid can produce an asymmetric velocity along the height of the channel. The results show a maximum value 38% increase in average heat transfer coefficient and 68% increase in pressure drop for all the considered cases when compared to basefluid (i.e., water). It is also observed that the wall temperature decreases remarkably as Re and ϕ increase. Finally, thermal‐hydraulic performance (η) is evaluated and it is seen that best performance can be obtained for Re = 1000 and ϕ = 4%.

Conjugate Thermal Analysis of Air-Cooled Discrete Flush-Mounted Heat Sources in a Horizontal Channel

Thermal analysis with comprehensive treatment of conjugate heat transfer is performed in this study for discrete flush-mounted heat sources in a horizontal channel cooled by air. The numerical model accounts for mixed convection, radiative exchange and two-dimensional conduction in the substrate. The model is first used to simulate available experimental work to demonstrate its accuracy and practical utility. A parametric study is then undertaken to assess the effects of Reynolds number, surface emissivity of walls and heat sources, as well as thickness and thermal conductivity of substrate, on flow field and heat transfer characteristics. It is shown that due to radiative heat transfer, the wall temperatures are brought closer, and the trend of temperature variation along the top wall is significantly altered. Such effects are more pronounced for higher surface emissivity and/or lower Reynolds numbers. The influence of substrate conductivity and thickness is related in that a large value of either substrate conductivity or thickness facilitates redistribution of heat and tends to yield a uniform temperature field in the substrate. For highly conductive or thick substrate, the “hot spot” cools down and may occur in upstream sources. Radiation loss to the ambient increases with substrate conductivity and thickness due to the elevated temperature near the openings, yet the total heat transfer over the bottom surface by convection and radiation remains essentially unaltered.

Double-Diffusive Convection from a Discrete Heat and Solute Source in a Vertical Porous Annulus

This article reports a numerical study of double-diffusive convection in a fluid-saturated vertical porous annulus subjected to discrete heat and mass fluxes from a portion of the inner wall. The outer wall is maintained at uniform temperature and concentration, while the top and bottom walls are adiabatic and impermeable to mass transfer. The physical model for the momentum equation is formulated using the Darcy law, and the resulting governing equations are solved using an implicit finite difference technique. The influence of physical and geometrical parameters on the streamlines, isotherms, isoconcentrations, average Nusselt and Sherwood numbers has been numerically investigated in detail. The location of heat and solute source has a profound influence on the flow pattern, heat and mass transfer rates in the porous annulus. For the segment located at the bottom portion of inner wall, the flow rate is found to be higher, whereas the heat and mass transfer rates are higher when the source is placed near the middle of the inner wall. Further, the average Sherwood number increases with Lewis number, while for the average Nusselt number the effect is opposite. The average Nusselt number increases with radius ratio (λ); however, the average Sherwood number increases with radius ratio only up to λ = 5, and for λ > 5 , the average Sherwood number does not increase significantly.

Parametric studies and correlations for combined conduction-mixed convection–radiation from a non-identically and discretely heated vertical plate

The present paper reports the parametric studies and correlations for the problem of combined conduction-mixed convection–radiation from a non-identically and discretely heated vertical plate. Three discrete heat sources of non-identical heights but with identical volumetric rate of heat generation are assumed to be flush-mounted in a thin vertical plate. The longest and the shortest heaters are provided at the leading and trailing edges of the plate, while the remaining heater is located centrally. The governing fluid flow and heat transfer equations are considered in their full strength without the boundary layer approximations and are solved using the finite volume method. A computer code is written to solve the problem and various parametric studies have been performed. The relative roles of free convection, forced convection and radiation in various fluid flow and heat transfer results have been elucidated. In conclusion, based on a large set of data generated from the code, correlations for maximum non-dimensional plate temperature, average non-dimensional plate temperature and mean friction coefficient have been evolved.

Reducing temperature stratification using heated air recirculation for thermal energy saving

Using discrete heat sources such as a radiator or a gas heater, a large amount of heated air is accumulated under the ceiling surface where it is usually far enough from the occupancy zone. The idea of transferring this heated air into the occupancy zone has been the subject of the present study. A full length-scale model of a compartment was constructed and equipped with a radiator and an air circulating mechanism. Temperature distribution on the symmetry plane was specified for the two cases of usual heating and heating with air circulation. Heat loss from the surfaces of the enclosure was also determined using thermal maps of both the internal and the external surfaces of the enclosure. In order to examine the effect of circulating air on the thermal energy saving quantitatively, a numerical model was developed and validated using experimental results. The input heat rate of the enclosure was compared for the two cases of usual heating and heating with air circulation considering different heights for a typical heating space. Based on the results, having the same mean air temperature within the occupancy zone, the input heat rate of a compartment could be moderated using circulating air criterion.

Analysis of Liquid-Cooled Heat Sink Used for Power Electronics Cooling

Liquid-cooled heat sink (cold plate) used for power electronics cooling is numerically studied. Thermal performance and hydraulic resistance are analyzed, with emphasis on geometric construction of cooling channels. Two heat transfer enhancing channel shapes are investigated, such as alternating elliptical channel and alternating rectangular channel (AR-C). Their performances are compared with that of three traditional straight channel shapes, as straight circular channel, straight elliptical channel, and straight rectangular channel. A heat sink with uniform and discrete heat sources is studied. Thermal and hydraulic characteristics in the heat sink are simulated using computational fluid dynamics approach, with water as coolant. The results show that the AR-C has the highest thermal performance with a little penalty on pressure drop, considering fixed channel hydraulic diameter and coolant volumetric flow rate. Geometry optimization is investigated for the AR-C, as well as the effect of channel density. It is found that higher channel density can improve both thermal performance and hydraulic resistance. It is concluded that alternating channel can improve cold plate performance and should be taken into application to power electronics cooling.

Natural Convection in a Vertical Annuli with Discrete Heat Sources

In this article, we numerically study natural convection heat transfer in a cylindrical annular cavity with discrete heat sources on the inner wall, whereas the outer wall is isothermally cooled at a lower temperature, and the top wall, the bottom wall, and unheated portions of the inner wall are assumed to be thermally insulated. To investigate the effect of discrete heating on the natural convection heat transfer, at most two heating sources located near the top and bottom walls are considered, and the size and location of these discrete heaters are varied in the enclosure. The governing equations are solved numerically by an implicit finite difference method. The effect of heater placements, heater lengths, aspect ratio, radii ratio, and modified Rayleigh number on the flow and heat transfer in the annuli are analyzed. Our numerical results show that when the size of the heater is smaller, the heat transfer rates are higher. We also found that the heat transfer in the annular cavity increases with radii ratio and modified Rayleigh number, and can be enhanced by placing a heater with the smaller length near the bottom surface.

Heat Transfer in a Microtube or Microchannel with Protrusions

This paper presents the effects of protrusions on heat transfer in a microtube and in a two-dimensional microchannel of finite wall thickness. The effects of protrusion shape, size, and number were investigated. Calculations were done for incompressible flow of a Newtonian fluid with developing momentum and thermal boundary layers under uniform and discrete heating conditions. It was found that the local Nusselt number near a protrusion changes significantly with the variations of Reynolds number, height, width, and distance between protrusions, and the distribution of discrete heat sources. The results presented in the paper demonstrate that protrusions can be used advantageously for the enhancement of local heat transfer whereas the global performance may be enhanced or diminished based on the channel geometry.