Non-uniform Heat Source Research Articles

Numerical study on heat transfer characteristics of a pin–fin staggered manifold microchannel heat sink

• A pin-fin staggered manifold microchannel (PFSMMC) heat sink was designed. • The heat transfer characteristics of PFSMMC in single-phase flow were studied. • The staggered divider length-width ratio of PFSMMC was optimized. • The heat transfer characteristics of PFSMMC with different non-uniform heat sources were studied. Manifold microchannel(MMC) heat sink is an efficient thermal management solution for high heat flux electronic devices. A pin-fin staggered manifold microchannel(PFSMMC) heat sink is proposed to enhance the heat dissipation performance of the MMC heat sink in this paper. The heat transfer performance of the PFSMMC heat sink, the rectangular manifold microchannel(RMMC) and the pin-fin manifold microchannel(PFMMC) are compared by single-phase flow numerical simulation. The results show that the PFSMMC heat sink has better heat transfer capability and more uniform heating surface temperature. The effect of staggered divider length-width ratio on the heat transfer characteristics of PFSMMC heat sink is analyzed. The maximum heating surface temperature of PFSMMC heat sink has a valley with the increase of length-width ratio. The length-width ratio corresponding to the valley value of the maximum heating surface temperature is about 0.32. In addition, the heat characteristics of PFSMMC with different non-uniform heat sources are studied. The results show that the heating surface temperature uniformity deteriorates with the increase of length-width ratio, but the maximum heating surface temperature is lower at the length-width ratio of 0.32.

Optimized method for thermal through silicon via placement with non-uniform heat sources in 3-D-IC

In the past few years, thermal through silicon via (TTSV) has been experimentally investigated as an effective heat dissipation path. Although a lot of heat dissipation-related issues have been solved in 3-D integrated circuit (3-D-IC), there are neglections in TTSV placement with non-uniform heat sources so far. In this study, a unique optimization is proposed to locate TTSV while effectively alleviating hot spots in 3-D-IC. The thermal dissipation of non-uniform heat sources are studied using the finite element method. The simulation results show that the minimum temperature is reduced by 2.1% compared with peak temperature in the single-layer chip, and by 1.9% in the three-layer chip.

DARCY-FORCHHEIMER TANGENT HYPERBOLIC NANOFLUID FLOW THROUGH A VERTICAL CONE WITH NON-UNIFORM HEAT GENERATION

The convective flows through different geometries have numerous applications in high-speed aerodynamics, nuclear cooling systems, fiber technology, and polymer engineering. In the present paper, we investigate the non-linear, mixed convective, boundary-driven, tangent hyperbolic nanofluid flow through a cone. The flow takes place under nonuniform heat sink/source. Darcy-Forchheimer effects have also been taken into account in mathematical modeling and analysis. The Buongiorno model is implemented to examine the effects of thermophoresis and Brownian motion parameters. The governing equations are constructed through the laws of conservation. The modeled flow problem is converted into a set of ordinary differential equations with the help of proposed similarity transformations. To interpret the modified system of equations, the homotopy analysis method (HAM) is applied. The roles of versatile parameters of interest are analyzed and sketched for better understanding. The velocity profile increases by increasing the Darcy number, and converse behavior is found by giving rise to the Forchheimer inertial drag parameter. The rise in temperature profile occurs by increasing a non-uniform heat source variable. The concentration profile enhances when the value of the thermophoresis parameter increases, and shows inverse behavior for the Brownian motion parameter. In the Buongiorno model, nanoparticle concentration has an inverse relation with the Brownian motion parameter. So, the concentration profile declines for greater Brownian motion parameter. To understand the behavior of flow through a cone, the values of Nusselt number and Sherwood numbers are examined.

Effect of Uneven Heat Sink/Source and Nonlinear Radiation on Hydromagnetic Casson Fluid Flow Past an Inclined Elongating Sheet

Objectives: The present article investigates the steady flow of hydromagnetic Casson fluid flow past an inclined stretched sheet with the existence of nonlinear radiation and Joule heating effects. Methods: A numerical model is established and then solved using the BVP4c MATLAB technique. Findings: In this present work we described about the influence of the Grashof number, non-uniform heat source, Biot number, Casson fluid parameter, hydrodynamics, nonlinear radiation, chemical reaction, local Grashof number and Schmidt number parameters on the flow of mass and rate of heat transport was discussed through tabular result and graphs. It is clear that the rate of heat transport decreases with Joule heating and is higher with an increase in Biot numbers. Increases the amount of thermophoresis parameter and decreases with the rate of heat transport. Novelty: To the best extent of the authors’ belief so far, no attempt is made to inspect the flow, thermal and mass transfer of uneven heat sink/source and non-linear radiation on hydromagnetic and embedded with the viscous dissipation, thermophoresis, Brownian diffusion, Joule heating and Casson fluid. Keywords: NonUniform Heat Sink/Source; Casson Fluid; Joule Heating; NonLinear Radiation; Hydromagnetic

Power-Law Fluid Flow and Heat Transfer via Vertical, Parallel Porous Walls with Varying Thermal Conductivity and Viscosity, As Well As Nth Order Chemical Reaction

This analysis examines a non-uniform heat source or sink, the flow of a power-law fluid induced by vertical parallel plates, and heat transfer using variable viscosity and thermal conductivity. Temperature likely exponentially changes viscosity and thermal conductivity. The implicit finite difference approach solves governing partial differential equations. Power-law index, Prandtl number, variable viscosity, and thermal conductivity are analysed. Skin friction, Nusselt number, and Sherwood number are graphically depicted to analyse channel fluid behaviour.

Mathematical modeling and computational outcomes for the thermal oblique stagnation point investigation for non-uniform heat source and nonlinear chemical reactive flow of Maxwell nanofluid

Owing to fine thermal prospective of nanomaterials, different applications have been addressed in nanotechnology and thermal management systems. Multidisciplinary applications of such nanomaterials are commonly observed in nuclear reactors, thermal systems, transportation systems, industrial products cooling, power industry, renewable energy etc. The motivated work aims to predicts improved thermal consequences of Maxwell nanofluid with applications of non-uniform heat source and radiated phenomenon. The heat transfer analysis is assessed by using the Cattaneo-Christov theories. The thermal phenomenon is controlled with interference of slip effects. The flow pattern is based on the oblique stagnation point flow confined by stretched cylinder. The Keller Box numerical determination of problem is worked out with fine accuracy. The physical dynamic of flow parameters is visualized graphically. It is claimed that control of thermal transportation phenomenon is resulted when the slip effects are dominant. The exponential heat source with nonlinear radiated phenomenon is important when enhancement in thermal process needed.

Optimization of fin layout in liquid-cooled microchannels for multi-core chips

When the dense pin-fins array distributed uniformly is used to dissipate the non-uniform heat source, it is easy to generate excessive cooling at the non-hot spot, which leads to unnecessary heat dissipation loss. In this study, a three-dimensional model of a multi-core chip-microchannel heat sink is established. Fin layout in the chip-microchannel is optimized under the conditions of non-uniform power-partition chip based on constructal theory. The total volume of fins in a channel is selected as the constraint condition. A genetic algorithm is used to seek the optimal construct. Comparing the optimal fin layout with the dense pin-fins array, the results demonstrate that the maximum temperature can be reduced by 6.75 K when Re number is 750, and the total pressure loss can be reduced by 54.1% when Re number is 750. Namely, under the condition of non-uniform heat source, the fins with a certain total volume were distributed reasonably, which can maintain the optimal balance of heat dissipation capacity and heat dissipation cost, so that the accurate and efficient thermal design is realized, and the better comprehensive benefits are obtained.

Hybrid Nanofluid on Mixed Convection Flow Past a Stretching Sheet with Irregular Heat Source/Sink

This research studies the behaviour of hybrid nanofluid on mixed convection flow over a stretching sheet by considering the effect of non-uniform heat source/sink. The chosen base fluid is water with two different nanoparticles which are copper and aluminium oxide. The governing partial differential equations are reduced into ordinary differential equations using a similarity transformation technique. The resulting governing system then solved numerically using Keller-box method. The influence of space- and temperature-dependents of non-uniform heat source and sink parameters as well as the unsteadiness parameter is presented graphically. The current study shows that, the space- and temperature dependents of non-uniform heat source and sink significantly raises the fluid’s temperature. Comparative study also shows that hybrid nanofluid has higher temperature and heat transfer coefficient than single nanofluid and conventional fluid. It can also be concluded that, the enhancement of heat transfer rate can be achieved by reducing the parameter of space- and temperature dependents of non-uniform heat source and sink.

Entropy optimization analysis of Marangoni convective flow over a rotating disk moving vertically with an inclined magnetic field and nonuniform heat source

AbstractThe present study investigates the Marangoni convective fluid flow over a rotating disk with an inclined magnetic field and in the presence of a nonuniform heat source when the disk moves upward/downward with nonconstant velocity with the incorporation of the second law of thermodynamics. The Keller‐box method is applied to the reduced system of equations to draw graphical illustrations. The study of these illustrations to examine the effects of involved pertinent parameters, like, magnetic field, Marangoni number, angle of inclination, vertical disk movement parameter, heat source, and disk rotation, on velocity and temperature profiles, reveals some interesting findings. From the analysis, it can be concluded that the skin friction coefficient increases with more angle of inclination and the Marangoni number with the reverse trend in case of vertical disk movement. Also, the Marangoni number and vertical disk motion diminish the Nusselt number with a positive effect in the case of more angle of inclination. The rate of entropy generation is enhanced with the temperature ratio parameter while it diminishes with the inclined magnetic field of any strength. The current study in its reduced form is in excellent agreement with earlier published work to ensure the validity of the used numerical scheme.

Thermo-economic analysis of a hybrid system based on combined heat - isobaric compressed air energy storage and humidification dehumidification desalination unit

To solve the problem of electricity and fresh water supply in different low-efficiency independent systems in coastal areas or remote islands, a hybrid system based on energy cascade utilization principle is proposed for both small-scale electricity and fresh water supply purposes. Such hybrid system is made up by the combined heat - isobaric compressed air energy storage (CH-ICAES) and the water-heated humidification dehumidification (HDH) desalination unit. Meanwhile, the CH-ICAES is a synthesis of ICAES and power to heat (PtH) technologies. In operation, the low-grade heat from CH-ICAES charging and discharging is used to produce fresh water in HDH. The simulated results show that the gained-output-ratio (GOR) and total produced fresh water mass in a roundtrip cycle at design condition are 2.0678 and 851.77 kg, respectively. Meanwhile, the levelized cost of storage (LCOS) and levelized cost of water (LCOW) are 35.45 cents/kWh and 0.57$/ton, indicating a competitive economic performance. Moreover, the GORs in charge and discharge are different due to the non-uniform heat source conditions. In addition, the humidifier inlet seawater temperature, the effectiveness of humidifier and dehumidifier, the relative humidity of dehumidifier inlet air, the HDH operation pressure and some parameters of CH-ICAES have significant effect on hybrid system performance.

Radiative thermal analysis for four types of hybrid nanoparticles subject to non-uniform heat source: Keller box numerical approach

The advancement in the thermal engineering presented the idea of nanomaterials with stable thermal consequences and performances. The importance of hybrid nanomaterials attributes importance in solar energy production, electronics devices, heating systems, mechanical processes etc. The hybrid model is classified as a distinct thermal phenomenon with different tiny particles. The thermal evaluation of hybrid nanofluid containing four types of nanoparticles subject to the non-uniform heat source/sink and inclined magnetic field for two-dimensional unsteady flow due to permeable stretched surface has been numerically investigated. Four different types of nanoparticles, copper, titanium dioxide, silver and aluminum oxide have been considered with water base fluid. With the help of similarity transformation, we convert the governing partial differential equation into the ordinary differential equation. To solve these similarity equations a numerical technique known as Keller box method is used. The results are shown graphically and in tabular form. For special cases, comparison of numerical results to the previous results is presented with excellent agreement. The physical onset of parameters due to fluctuated heat transfer rate, wall shear force and Nusselt number is observed. It is observed that change in magnetic field inclination angle declines the velocity profile. The temperature profile can be effectively controlled with interaction of titanium oxide nanoparticles. The presence of heat source enhanced the nanoparticles temperature more effectively.

Comparative Study on Rosseland’s Heat Flux on Three-Dimensional MHD Stagnation-Point Multiple Slip Flow of Ternary Hybrid Nanofluid over a Stretchable Rotating Disk

This article investigates the three-dimensional magneto stagnation-point flow of ternary hybrid nanofluid caused by a radially extended infinite gyrating disk with multiple slip effects. The main concern is to analyze the characteristics of heat transport when linear thermal radiation (LTR), quadratic thermal radiation (QTR), and full nonlinear thermal radiation (FNTR) are significant. Ternary fluid is a composition of water, spherical-shaped silver, cylindrical-shaped aluminum oxide, and platelet-shaped aluminum nanoparticles. Non-uniform heat source effects are taken into account. The governing equations are constructed using a single-phase nanofluid model using boundary layer theory and von Karman variables. The consequent nonlinear problem is solved with an efficient finite element method and the results are verified with the available data. The Nusselt number and friction factors are computed for both clean fluid and ternary nanofluid subjected to three different forms of Rosseland’s thermal radiation. Our results demonstrate that the rate of heat transport (Nusselt number) is higher in the FNTR case than in QTR and LTR, and it is even higher for ternary nanofluid compared to clean fluid. Further, the heat transport rate gets reduced for a higher heat source parameter. The rotation of the disk escalates the shear stress along both the radial and axial directions. The multiple slip boundary conditions lead to condensed boundary layers over a disk surface.

Significance of variable thermal conductivity and nonuniform heating Source for Burgers nanofluid flow subject to modified thermal laws

The thermal conductivity attributes a major role to the thermal transportation and engineering processes where the fluid is used as an energy source. It has been commonly noted that much attention of research towards the heat and fluid flow is intended by keeping the fluctuation of thermal conductivity as a constant. However, experimental results shows that most of the times, thermal conductivity changes in variation of temperature, pressure or different configurations. The prime attention of current research is to explore the role of variable thermal conductivity for thermal transport of Burgers nanofluid due to inclined surface. The Buongiorno nanofluid model is used to illustrate the Brownian motion and thermophoresis properties. The heat transfer phenomenon is analyzed by incorporating the modified Cattaneo–Christov (CC) theories. Moreover, to maintain the improved heat transfer rate, the novel nonuniform heat source applications are also utilized. After altering the governing problem into dimensionless system, homotopy analysis scheme is used with excellent accuracy. The physical pattern of velocity, heat transfer rate and concentration phenomenon are observed in view of involved parameters. It is noted that the presence of variable thermal conductivity enhanced the thermal process more effectively as compared to constant thermal conductivity assumptions. Both heat and mass transfer phenomenon enhances for Deborah number. The declining concentration change is observed with variation of concentration relaxation number.

Numerical study of Reiner-Rivlin nanoliquid flow due to a rotating disk with Joule heating and non-uniform heat source using Bulirsch-Stoer algorithm

The flow of a Reiner-Rivlin hydromagnetic nanoliquid due to rotating disk in the presence of Joule heating and a non-uniform heat source is investigated. To control the volume fraction of nanoparticles on the surface of a disk, a realistic passive control strategy is used, taking the thermal jump condition into account. Nonlinear governing differential equations are solved numerically using the Bulirsch-Stoer technique and a parametric analysis is performed using graphical representations. Using the Response Surface Methodology (RSM), the interaction effects of the influential parameters on the rate of heat transfer are visualized via three-dimensional surface graphs and contours. Further, the optimum rate of the heat transfer is estimated through the RSM analysis. It is found that the surface drag demotes due to enhancement in the cross-viscosity coefficient. A rise in the space-dependent heat source augments the temperature profile. The heat transfer rate is negatively influenced by the Eckert number. Further, when thermal slip is augmented, the sensitivity of the heat transfer towards the Hartmann number decreases at the rate of 0.2267%, and the sensitivity towards the Reiner-Rivlin fluid parameter decrements at the rate of 0.0554%.

Couple stress Darcy–Forchheimer nanofluid flow by a stretchable surface with nonuniform heat source and suction/injection effects

The thermal enhancement of industrial and engineering processes with interaction of nanofluids is exclusively important and presents applications in extrusion systems, heat transfer devices, electronic chips, chemical reactions, nuclear processes, etc. Owing to such motivated significance of nanofluids, the aim of this investigation is to present the heat and mass transfer phenomenon in the Couple stress nanofluid flow containing the microorganism due to oscillatory stretched surface. Additionally, the Darcy–Forchheimer applications, nonuniform heat source and nonlinear thermal radiation effects are considered. The modification in the concentration equation is done by activation energy. The independent variables in the defined flow system are decreased via suitable variables. The computation is simulated using the homotopy analysis method. It is noticed that the magnitude of velocity periodically decreases for larger values of suction parameter and inertia coefficient. The presence of an external heat source parameter enhanced the temperature profile. Moreover, the increment in the suction parameter improves the heat and mass transfer rate.

Influence of heat source distribution optimization on gallium heat transfer characteristics in a annular tube based on MLA and CFD

ABSTRACT In this study, innovative combined Machine Learning Algorithm (MLA), Genetic Algorithm (GA) and Computational Fluid Dynamics (CFD) was used to investigate the influence of nonuniform heat source distribution on gallium heat transfer performance in the annular tube, and an optimization scheme of heat source distribution was proposed. First, the heat source distribution scheme was quantified using four intervals A, B, C, and D from the inlet to the outlet, and the effect of different schemes on the heat transfer performance was investigated by CFD. Second, the prediction model of the average surface heat transfer coefficient under different heat source distributions was established based on various MLAs, and the effect of heat source interval on heat transfer performance was obtained through the model analysis. The results show that the intervals A and B have more influence on heat transfer performance, the heat transfer coefficient increases with the increase in A and B intervals. Finally, the optimal heat source distribution scheme is solved by GA. Compared with the traditional distribution scheme, the optimal scheme makes the inner wall temperature more uniform, reduces the high-temperature areas, reduces the maximum temperature by 2.6%, and increases the average surface heat transfer coefficient of the inner wall by 6.42%.

Patterning of thermosetting resins via laser engraving towards efficient thermal management

Patterned composites with custom-tailored properties are essential for efficient thermal management required by the increasing integration and complexity of devices. In this work, a facile approach for the fabrication of functional, robust, and patterned composites was demonstrated using a simple and scalable laser engraving technique. Graphene patterns were incorporated into composites by the single- or multiple-lasing on poly(Ph-ddm) substrate. The resultant composites exhibited a high thermal conductivity (8.2 W/(m·K)) that was equivalent to an enhancement of 45 times compared to pure matrix. This increase was attributed to the formed high-quality graphene porous architecture, which established an effective heat conduction channel. With the merit of computer-aided design of the laser trajectory, the processing method offers the freedom to tailor the heat transfer pathway in composites. Besides, the composites presented the favorable Joule heating performance in terms of fast and stable response with the heating efficiency up to 276 °C‧cm2/W. More interestingly, the heaters with designable thermal patterns were also allowed, in which the electrical property of each heating unit could be tailored by adjusting laser parameters. This provides a unique opportunity to simulate the real case of non-uniform heat sources in many electronic devices, which will facilitate the design and development of heating dissipation systems. The material/process developed promises a wide range of possibilities for the efficient thermal management applications.

Unsteady magnetohydrodynamic nanofluid flow over a permeable exponentially surface manifested with non-uniform heat source/sink effects

Current research inspects the influences of two-dimensional unsteady nanofluid flow over a permeable exponential stretching sheet with the impact of magnetic field parameter, thermal radiation together with a non-uniform heat source or sink. The dimensional equations namely Partial differential equations (PDE’s) are transformed into dimensionless form as ordinary differential equations (ODE’s) by using the suitable transformations. The reframed ODE’s are solved numerically through the computer-based tool MATLAB with the bvp4c package. The derived results of velocity, temperature and species distributions are depicted graphically. Also, the numerical results of skin friction coefficients, heat transfer rate and mass transfer rate in terms of Nusselt number and Sherwood number are deployed via tables. The comparison of the present work with published work shows complete agreement for skin friction factor and Nusselt number. In absolute sense skin friction enhances as magnetic field parameter enhances. The Brownian motion and thermophoresis parameters play an essential role towards thermophysical flow field of nanofluids. Further, we noticed that both Brownian motion parameter and thermophoresis parameter cause an enhancement in the fluid temperature. Furthermore, the unsteady parameter causes increase in wall friction and heat transfer rate. However, the opposite trend is observed for the heat source/sink parameters.

A study on effectiveness of the variational theory in fluid dynamics applications

Owing to motivated applications of nanofluids in industrial and technological processes, many novel attempts have been reported by investigators in recent century. The interesting applications subject to the nanomaterials is noted in hybrid-powered engines, solar systems, thermal management, heat exchanger, energy generation, microelectronics etc. This framework presents a Cattaneo-Christov heat flux model for nonlinear convective transport of Walter-B nanofluid due to extending surface. The model is further supported with the non-uniform heat source and activation energy applications. The solutal thermal and mass flux constraints are utilized to inspect the thermal outcomes. The transformation of partial differential system to nonlinear ordinary differential system is carried out with proper conversions. The nonlinear system is analytically tackled with implementation of variational iteration method (VIM). The role of physical parameters appeared in the flow modelling are physical justified.

Magneto-hydrodynamics effects over a three-dimensional nanofluid flow through a stretching surface in a porous medium

This paper examines the approximate solution of the three-dimensional nanofluid flow. The viscous dissipation and non-uniform heat source are accounted for in the energy equation over the stretching sheet. The numerical solutions of the governing partial differential equation are solved using spectral quasi-linearization method (SQLM). The nonlinear differential equations are obtained from the ordinary differential equations using suitable similarity transformation. A comparison between the obtained results with solutions obtained early in the literature and the numerical solution has been made to test the validity, accuracy, and convergence of the SQLM. Physical parameters on the velocity, temperature, and concentration are determined and discussed. The thermophoresis parameter greatly influenced concentration level with nanofluid flow across the stretching surface with a high Schmidt number.