Rectangular Heat Research Articles

Graph Theory-Based Mathematical Calculation Modeling for Temperature Distribution of LED Lights’ Convective Cooled Heat Sinks under Moisture Environment

In this paper, a mathematical model based on graph theory is proposed to calculate the heat distribution of LED lights’ convective cooled heat sink. First, the heat and mass transfer process of a single fin under moisture environment is analyzed. Then, the heat transfer process is characterized by a digraph, defining fins and joints of a heat sink as edges and vertices in graph theory. Finally, the whole heat transfer process is described by two criteria achieved based on graph theory. Therefore, the temperature-heat calculation equations of the whole heat sink are deduced. The accuracy of this model is verified by testing the junction temperature of different LED chips mounted on the same heat sink under moisture environment, and the relative errors between the calculated value and the experimental data are all within 5%, and it is also concluded from the model that heat sinks with an identical heat digraph but different types have close cooling performance and are verified by two typical heat sinks, cylindrical heat sink and rectangular plate-fin heat sink, under the same conditions. The mathematical model based on group theory developed in this paper combined with computer technology is convenient for the performance analysis among a large number of heat sink fin arrangement schemes.

Constructal design progress for eight types of heat sinks

This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives, respectively, by combining the methods of theoretical analysis and numerical calculation. The eight types of heat sinks are uniform height rectangular fin heat sink, non-uniform height rectangular fin heat sink, inline cylindrical pin-fin heat sink (ICPHS), plate single-row pin fin heat sink (PSRPHS), plate inline pin fin heat sink (PIPHS), plate staggered pin fin heat sink (PSPHS), single-layered microchannel heat sink (SLMCHS) with rectangular cross sections and double-layered microchannel heat sink (DLMCHS) with rectangular cross sections, respectively. And the ten performance indexes are heat transfer rate maximization, maximum thermal resistance minimization, minimization of equivalent thermal resistance which is defined based on the entransy dissipation rate (equivalent thermal resistance for short), field synergy number maximization, entropy generation rate minimization, operation cost minimization, thermo-economic function value minimization, pressure drop minimization, enhanced heat transfer factor maximization and efficiency evaluation criterion number maximization, respectively. The optimal constructs of the eight types of heat sinks with different constraints and based on the different optimization objectives are compared with each other. The results indicated that the optimal constructs mostly are different based on different optimization objectives under the same boundary condition. The optimization objective should be suitable chosen based on the focus when the constructal design for one heat sink is performed. The results obtained herein have some important theoretical significances and application values, and can provide scientific bases and theoretical guidelines for the thermal design of real heat sinks and their applications.

Numerical Investigation of Finned-tube Heat Exchanger with Circular, Elliptical & Rectangular Tubes

A three dimensional numerical study has been conducted on finned-tube heat exchanger with multiple rows of tubes using ANSYS (Fluent). The objective of this study is to numerically investigate finned tube heat exchanger with different type of tubes such as circular, elliptical and rectangular tubes. As circular tubes has much pressure drop so elliptical and rectangular tubes has been introduced in order to reduce pressure drop. As well as heat transfer has also been examined. The finite volume based CFD code ANSYS Fluent 16.2 is used to calculate the flow and temperature fields and by applying SIMPLEC algorithm. At low velocity of air and water, nothing significant occurred for the combination of tubes. At high velocity in maximum tube combination there was heat transfer (HT) enhancement and pressure drop reduction when compared with circular tubes only in case of air. When the combinations of circular, elliptical and rectangular tubes has been compared with circular tube heat exchanger (CTHX) heat transfer reduces as well as pressure drop (PD) also reduces for air. In case of water vapor HT and PD behaves the same. When those combinations has been compared with elliptical tube HX, for air in some cases heat transfer remains same and on other case it increases. For pressure drop in case of air, in some cases it reduces and on other cases it reduces. For elliptical tube HX for the fluid water vapor HT and PD both remains same or reduces. This work has not been with conducted any numerical simulation on rectangular Heat exchanger reason behind it there isn’t any existence of this kind of heat exchanger. However, it could be numerically conducted to examine the results between those combination and rectangular heat exchanger.

Transient Thermal Modeling of a Power Module: An N-Layer Fourier Approach

A transient model of a rectangular N-layer structure with an arbitrary number of rectangular heat sources on the top surface is obtained by Fourier series solution. As power modules can be closely approximated by this type of structure, the model may be used to accurately estimate the temperature field occurring in such modules. The Fourier-based method developed in this work is compared with a finite-element model and an excellent matching (under 2% error) in the transient region is found. An experimental validation is performed using a half-bridge silicon carbide power module monitored by a high frame-rate thermal camera. After the model outputs have been compensated to match the limited frequency response of the camera, a good matching is found between model and experiment (under 6% error).

Effect of Corrugated Baffles on the Flow and Thermal Fields in a Channel Heat Exchanger

The performance of corrugated baffles inserted in a rectangular channel heat exchanger is investigated. The fluid flows and thermal distribution are determined via numerical simulations. The working fluid has a shear thinning behavior. The influence of the baffle design is explored, we interest to the “wavy” shape. The corrugation angle of baffle (α) is changed from 0° (i.e. a straight baffle) to 45°. Also, the height (h) of the corrugated baffle is changed and three cases are considered, namely: h/H = 0.4, 0.5 and 0.6, where “H” is the channel height. In comparison with the unbaffled channel, the overall performance factor has increased from 1.27 up to 1.53 when the corrugation angle is increased from 0° to 45°. Concerning the corrugation height, the predicted results allowed us to select the case h/H = 0.5 as the best configuration from the cases studied.

Thermal–Hydraulic Performance in a Microchannel Heat Sink Equipped with Longitudinal Vortex Generators (LVGs) and Nanofluid

In this study, the numerical conjugate heat transfer and hydraulic performance of nanofluids flow in a rectangular microchannel heat sink (RMCHS) with longitudinal vortex generators (LVGs) was investigated at different Reynolds numbers (200–1200). Three-dimensional simulations are performed on a microchannel heated by a constant temperature with five different configurations with different angles of attack for the LVGs under laminar flow conditions. The study uses five different nanofluid combinations of Al2O3 or CuO, containing low volume fractions in the range of 0.5% to 3.0% with various nanoparticle sizes that are dispersed in pure water, PAO (Polyalphaolefin) or ethylene glycol. The results show that for Reynolds number ranging from 100 to 1100, Al2O3–water has the best performance compared with CuO nanofluid with Nusselt number values between 7.67 and 14.7, with an associated increase in Fanning friction factor by values of 0.0219–0.095. For the case of different base fluids, the results show that CuO–PAO has the best performance with Nusselt number values between 9.57 and 15.88, with an associated increase in Fanning friction factor by 0.022–0.096. The overall performance of all configurations of microchannels equipped with LVGs and nanofluid showed higher values than the ones without LVG and water as a working fluid.

How mushy zone evolves and affects the thermal behaviours in latent heat storage and recovery: A numerical study

Mushy zone is where the melting or solidification actually begins and proceeds, accompanying which the latent heat absorbs or releases. Thus, it is critical for the realization of latent heat storage. In this paper, attempts were made to examine the melting and solidification processes from a new perspective, that is, the mushy zone evolution, which tightly couples with the heat transfer, fluid flow, and phase change. A conjugate heat transfer model was developed including the lauric acid in a basic rectangular latent heat storage unit, the surrounded thermal insulations, and the ambient air. The enthalpy-porosity model was used and the mushy zone constant was reasonably evaluated to accurately predict the solid-liquid phase change processes. The model was validated against the experimental data from literature. In addition, a detailed description on the coupling of heat transfer, fluid flow, and phase change within the mushy zone was presented. It has been found that the mushy zone was highly suppressed during melting while widely extended during solidification. Moreover, the effects of the isothermal assumption for non-isothermal phase transition as well as mushy zone constant on the predicted heat storage performance were investigated. The results obtained can give some insights into the enthalpy-porosity method to accurately predict the mushy zone phase change processes. Meanwhile, more clues can be achieved to design more efficient heat storage devices and to develop better phase change materials.

Magnetohydrodynamic natural convection and entropy generation analyses inside a nanofluid-filled incinerator-shaped porous cavity with wavy heater block

The aim of the current study is natural convection analysis conjugated with entropy generation analysis in an incinerator shaped permeable enclosure loaded with Al2O3–H2O nanofluid subjected to the magnetic field with a rectangular wavy heater block positioned on the bottom of the cavity wall. The bottom and top horizontal walls are adiabatic; the inclined and vertical walls are thought to be cooled. Firstly, the governing expressions and standard k–e turbulence model are rewritten from dimensional form to non-dimensional form using dimensionless parameters such as vorticity and stream function. In the next step, the equation of entropy generation is written in dimensionless form. Then, the system of non-dimensional governing equations is solved by the finite volume method (FVM) conjugated with a non-dimensionalization scheme using ANSYS Fluent. Fine grids (wall y+ < 2) with inflated layers have been used for the higher Rayleigh number. The effects of the Rayleigh number in the laminar region (Ra = 103, 104, and 105) and turbulent region (Ra = 108, 0.5 × 109, and 109), Darcy number (Da = 0.01 and 100), Hartmann number (Ha = 0 and 40), and the nanoparticles ( $$ \phi = 2{{\% }} $$ ) on the entropy generation number and natural convection are investigated. The validation results were in good agreement with those of the literature. The results demonstrate that for the laminar region, the Nusselt number and entropy generation number increase as the Rayleigh number and the Darcy number grow, whereas both of them abate as Hartmann number increases. In the turbulent region, the average Nusselt number decreases by ascending the Darcy number. Also, for turbulent region (Ra = 109), convection flow strength decreases 6.28% when Hartmann number increases from 0 to 40, whereas the entropy generation number increases 31.5% at Da = 0.01.

Study of Mini Channel Heat Sink with Different Internal Configuration

In this paper a numerical analysis of three-dimensional laminar flow through rectangular channel heat sinks of different geometric configuration is presented and a comparison of thermal performance among the heat sinks is discussed. Liquid water was used as coolant in the aluminum made heat sink with a glass cover above it. The aspect ratio (section height to width) of rectangular channels of the mini-channel heat sink was 0.33. A heat flux of 20 W/cm2 was continuously applied at the bottom of the channel with different inlet velocity for Reynold’s number ranging from 150 to 1044. Interconnectors and obstacles at different positions and numbers inside the channel were introduced in order to enhance the thermal performance. These modifications cause secondary flow between the parallel channels and the obstacles disrupt the boundary layer formation of the flow inside the channel which leads to the increase in heat transfer rate. Finally, Nusselt number, overall thermal resistance and maximum temperature of the heat sink were calculated to compare the performances of the modified heat sinks with the conventional mini channel heat sink and it was observed that the heat sink with both interconnectors and obstacles enhanced the thermal performance more significantly than other configurations. A maximum of 36% increase in Nusselt number was observed (for Re =1044).

Effects of Nanofluid Flow in Micro channel Heat Sink for Forced Convection Cooling of Electronics Device: A Numerical Simulation

A computational study is carried out on a rectangular microchannels heat sink using nanofluids flow for cooling of electronics device under uniform heat flux condition. In the present investigation water, ethylene glycol and a mixture of ethylene glycol (20%wt) and water are considered as base fluids with varying concentration of five different nanoparticles includingAl2O3, TiO2, CuO, SiO2 and ZnO. Numerical computations are performed using ANSYS Fluent software by considering the single phase model and results are validated with available experimental and numerical data. Further parameters like thermal resistance, pumping power, local heat transfer coefficient and temperature variation of IC chip are presented and analysed. It was noted that with addition of nanoparticles there is sharp increment in local heat transfer coefficient and decrements in local thermal resistance compared to base fluid but at same time viscosity of fluid increases that provide more drag or pressure drop which ultimately increases the pumping power. -Water nanofluid of concentration 1% and 4% give large improvement in heat transfer parameters and at the same time there is little enhancement in pressure losses or pumping power also it has less cost and more stability in base fluid as compared to other nanofluids.

Electric field effect on the heat transfer enhancement in a vertical rectangular microgrooves heat sink

The EHD pumping is an attractive solution to insufficient liquid supply and dryout occurrence in open microgrooves heat sink and micro heat pipes. It offers the advantages of active control of capillary pumping capacity. In this study, effects of applied non-uniform electric field on evaporation heat transfer enhancement in a vertical rectangular microgrooves heat sink are investigated experimentally. The pin-plate electrodes pair is used to produce the non-uniform electric field. A series of experiments of parameters have been considered, including heat flux, interelectrode spacing and microgrooves dimension are conducted under various applied DC applied voltages. Results show that the application of pin electrode can promote the capillary wetting length, decrease the wall temperature of microgrooves and enhance the heat transfer performances effectively.

Generalized Solution for Rectangular Three-Dimensional Transient Heat Conduction Problems with Partial Heating

The development of a generalized solution is presented for a three-dimensional transient heat conduction problem in a rectangular parallelepiped. To make the method as general as possible, one face of the body is subjected to a nonhomogeneous boundary condition over part of the surface. The solution accommodates three kinds of boundary conditions: prescribed temperature, prescribed heat flux, and convective. The means of dealing with these conditions involves adjusting the convection coefficient. Large Biot numbers such as effectively produce a prescribed-temperature boundary condition, and small ones such as are used for generating an insulated boundary condition. This paper also presents three different methods to develop the computationally difficult steady-state component of the solution, as separation of variables can be inefficient at the heated surface. The generalized solution proposed here provides thousands of individual solutions with one analytical formulation. Boundary conditions of prescribed temperature, prescribed heat flux, and convection, as well as a semi-infinite boundary condition, can be simulated. Partial heating at the corner of a parallelepiped is featured as an example, which can be extended to any location on the heated surface using superposition, including subtractive superposition.

Research on flow and heat transfer characteristics of heat transfer surface of trapezoidal duct

A trapezoidal heat transfer surface was presented in this paper, which can overcome the defects of the rectangular heat transfer surface, and it has a uniform temperature distribution in the direction of air flow. A standard wind tunnel test bed was built, and the heat transfer coefficients of the trapezoidal and rectangular heat exchanger with the same total heat transfer area and flow conditions were compared. In the meanwhile, the feasibility of the numerical simulation method was also verified. The results showed that: when 0 ≤ β ≤ arctan(1/12), heat transfer intensity and pressure loss are increased with the increase of β, and the temperature field distribution tend to be uniform. When 1300 ≤ Re ≤ 4000, the heat transfer coefficient in trapezoidal duct is higher than that of rectangular; when the slope angle (β) is constant, the temperature field distribution becomes more uniform with the increase of air flow, and the turbulence intensity at the end of the flow field becomes stronger. Besides, the trapezoidal duct has a uniform temperature field distribution in the direction of air flow. By introducing evaluation index TPF (Thermal performance factor), we concluded that: the trapezoidal duct has better comprehensive heat transfer performance than that of the rectangular.

Parametric study of the particulate fouling characteristics of vortex generators in a heat exchanger

The geometric parameters and flow characteristics of vortex generators have attracted much attention in recent years. For this study, an improved Eulerian method was used to study the fouling characteristics of magnesium oxide nanoparticles in a heat exchanger channel with rectangular wing vortex generators. The fouling characteristics of the channel with and without vortex generators were studied using numerical simulations, with the inlet velocity, magnesium oxide concentration, inlet temperature, and water-bath temperature at 0.5 m/s, 400 mg/L, 298 K, and 318 K, respectively. The simulation results for the rectangular heat channel with and without vortex generators were verified experimentally. Finally, the effects of the vortex generators′ height, length, and spacing on particulate fouling characteristics were evaluated. In comparing the rectangular channel′s fouling characteristics with and without vortex generators, the fouling resistance decreases by 19% for the channel with rectangular vortex generators, and it has the significant advantage of fouling inhibition. Furthermore, the fouling resistance decreases with the increase in the height and length of vortex generators. Conversely, the fouling resistance increases with increased spacing between the vortex generators.

Nusselt Number Correlations for Forced Convection in a Microchannel Including Discrete Heat Sources

Using the finite volume scheme, a two-dimensional rectangular microchannel heat sink (MCHS) with discrete heat sources on top and bottom walls in the laminar flow regime was investigated numerically. Water and three homogenous nanofluids (–water, –water, and –water) were considered as the working fluids. To assess the effect of the location of discrete heat sources on thermal performance of the MCHS, a parameter called PFF (percentage of being face to face of the discrete heat sources), which determines to what extent the faces of discrete heat sources on top and bottom walls are in front of each other, was introduced. The findings showed that the effect of halving the Reynolds number on an increase of dimensionless temperature along the channel axis was greater than that of doubling the volume fraction of nanoparticles. Also, when the Reynolds number increases, the effect of PFF on the average Nusselt number reduces. Moreover, the nanofluid temperature along the centerline was maximum when the heat sources were located opposite to each other and minimum when arranged in a staggered pattern. Finally, correlations for calculating the average Nusselt number on the top and bottom walls as a function of PFFs and Reynolds numbers were proposed.

Effect of Protective Coating on Surface Properties and Candida albicans Adhesion to Denture Base Materials.

To evaluate the effect of protective coatings on the surface roughness, contact angle, and Candida albicans (C. albicans) adhesion to polymethyl methacrylate (PMMA) denture base materials. A total of 560 rectangular heat- and autopolymerized acrylic resin specimens were fabricated and divided into 5 groups (n = 14/group) according to coating agent. Uncoated specimens were used as control. Coating materials were: nano-coat, Optiglaze, nano-silica, or cyanoacrylate. Surface roughness (Ra ) was evaluated using a profilometer. Contact angle measurements were performed using the sessile drop method. C. albicans adhesion was evaluated using direct culture and slide count methods. ANOVA and Tukey's post hoc tests were used for data analysis (α = 0.05). Nano-coat and Optiglaze coating of heat-polymerized acrylic significantly decreased Ra (p < 0.001). No significant effect was seen with nano-silica coating while Ra significantly increased with cyanoacrylate (p < 0.001). For autopolymerized acrylic, nano-coat, Optiglaze, and nano-silica coatings significantly decreased Ra in comparison to control group (p < 0.001) while no significant difference was seen between control and cyanoacrylate coating (p = 0.45). In comparison to control group, nano-coat, Optiglaze, and nano-silica coating for both denture base materials significantly decreased contact angle, and C. albicans adhesion (p < 0.001) while cyanoacrylate significantly increased C. albicans adhesion (p = 0.002) with no effect on contact angle for heat- (p = 1.00) and autopolymerized resins (p = 0.83). Coating of removable prosthesis with nano-coat, Optiglaze, or nano-silica is an effective method to reduce C. albicans adhesion.

Pumping power and heat transfer rate of converging microchannel heat sinks: errors associated with the temperature dependency of nanofluids

To find the sensitivity and dependence degree of the numerical simulation predictions on the property variations arising from the temperature gradients, a 3D conjugate heat transfer of Al2O3–water nanofluid convecting through rectangular microchannel heat sinks (MCHS) is considered in the present study. The Koo–Kleinstreuer–Li model is adopted to capture the temperature-dependent nature of thermophysical properties of the working nanofluid compared to the pure fluid (i.e., water). Both straight and width-tapered flow passages are studied using finite volume method within the laminar flow regime to see how sensitive are the predictions to the temperature dependency of the thermophysical properties for both the pure base fluid and nanofluid. Results show that the constant property assumption obtains unrealistic results up to 140% for the Reynolds number, which may mislead in predicting the flow regime (laminar/turbulent). The constant property approach predicts the convection heat transfer coefficient and the pumping power, respectively, 31% lower and 33% higher than those of the temperature-dependent property approach. In addition, the present study concludes that the MCHS should be simulated based on the temperature-dependent thermophysical property approach to be more realistic, especially for converging flow passages due to high-temperature gradients and for nanofluids for their induced temperature-dependent properties. The last two issues induced each other and increase the deviation of the predictions based on the constant property assumption. Finally, because of underestimating the heat transfer rate and overestimating the pumping power, the MCHS would be over-designed if one adopts the constant property assumption for conceptual design and the MCHS would perform under inefficient and off-design conditions.

Constructal design of subcooled microchannel heat exchangers

This paper presents geometric optimization and flow parameters modelling for subcooled flow boiling (two-phase flow). The objective of the paper was to minimize the thermal resistance of the microchannel heat exchanger subject to fixed volume constraints of heat sink and microchannel. The geometric and flow parameters were allowed to morph, according to the constructal design principles to obtain their optimized values. The flow was highly subcooled at inlet temperature of 25 °C using deionized water as the cooling fluid and aluminium as the heat sink material. Velocities between 0.1 and 4.5 m/s and heat fluxes between 100 and 1200 W/cm2 (1 × 106 W/m2 and 1.2 × 107 W/m2) were used in the modelling and optimization. Computational fluid dynamics code, ANSYS was used for both the simulations and the optimization of the configurations. The numerical code used for the simulations was validated by available experimental data in the literature and the agreement showed the capability of CFD (ANSYS) to predict accurately, subcooled flow boiling (two-phase flow) in rectangular microchannel heat exchangers for cooling of microelectronic devices. Comparisons were made between two-phase flow and single-phase flow by using their optimized geometric and flow parameters, and the results clearly demonstrated the superiority of two-phase flow regime in rectangular microchannels for removal of high heat fluxes at low Reynolds numbers. As the optimized Reynolds number increases, the minimized thermal resistance (peak temperature) decreases which is consistent with previous results obtained in the open literature. Results further show the aspect ratio, the optimized diameter and axial length of the microchannel as a function of the dimensionless pressure drop number (Bejan number).

Composite metal foam/PCM energy store design for dwelling space air heating

The objective of this numerical study is to develop a latent heat storage (LHS) air heater in both charging and discharging processes to find the geometrical and operating conditions for dwelling space heating. The aim of the storage heater is to provide a uniform output temperature according to the required heating load of a typical room in the required heating hours. The phase change material (PCM) is embedded in a copper porous structure to enhance the rate of heat transfer and overcome the low thermal conductivity of PCMs. The geometrical parameters is first obtained from analysing the discharging process including the height, air channel and PCM shell widths and air mass flow rate according to the discharging time as well as the output temperature of the air. Then, the charging mechanism is assessed to find the required area for the employed rectangular heating element. The results show the significant advantages of composite metal foam/PCM-air heat exchanger in comparison with the PCM-only unit on both the discharging time (56.5% reduction) and the uniformity of output temperature. The system with the height of 30 cm, PCM and air channel thickness of 15 cm and 2 cm, respectively, and a depth of 1 m, is capable to provide the desired output temperature of 47 °C for almost 17.4 h with the air mass flow rate of 0.01 kg/s. The charging analyses shows that the dimensions of the required rectangular heating element with constant temperature of 100 °C is 15 × 60 cm located at both sides of the unit.

Heat Transfer Enhancement in a Microchannel Heat Sink: Nanofluids and/or Micro Pin Fins

Here, we show that overall thermal conductance in a rectangular microchannel heat sink can be maximized with the combination of nanofluids and micro pin fins. We uncover the effect of micro pin fins and nanofluids both separately and simultaneously in order to uncover their effect on the thermal conductance (i.e., thermal resistance). Both nanofluids and micro pin fins decrease the overall thermal resistance due to increase in the average thermal conductivity of the flow system. In addition, they increase the heat transfer surface area of the solid interacting with the fluid. However, the pumping power (pressure drop) increases in both methods due to the increase in the resistances to the fluid flow. The results document what should be the nanoparticle volume fraction mixed into the base fluid and the micro pin fin volume in order to minimize thermal resistance. If the thermal conductivity of the nanoparticles and micro pin fins are the same, the thermal conductance becomes the maximum with 4% and 0.14% volume fractions for the nanofluid and micro pin fins, respectively. This result shows that inserting micro pin fins and using nanofluids with a given volume fraction ratio maximize the overall thermal conductance.