Non-uniform Heat Research Articles

Optimising integrated heat spreaders with distributed heat transfer coefficients: A case study for CPU cooling

Increasing power densities of modern CPUs has led to regions of high temperature on the semiconductor die which can lead to performance and reliability problems. In this case study, the effect of imposing a non-uniform heat transfer coefficient profile across the convective surface the CPU's integrated heat spreader was investigated as a potential enhanced cooling concept. A finite element model of a copper heat spreader of 40 × 40 mm2 area and 2.5 mm thickness with a centred 13 × 13 mm2 heat source at 100 W/cm2 heat flux was considered to approximate typical modern high-powered CPUs. Both uniform and Gaussian distributions of the heat transfer coefficient were then considered. For the latter, both single and multi-objective Genetic Algorithm optimisation were carried out for three source temperature objectives; average temperature, maximum temperature and maximum temperature difference. The analysis showed that the multi-objective optimisation strategy produced the best overall heat transfer coefficient distribution, with almost 5 K reduction in both the maximum temperature and temperature gradient across the heat source compared with a uniform heat transfer coefficient distribution.

Coupling effect between heat flux distribution and buoyancy of supercritical CO2 heat transfer with nonuniform heat flux in parabolic-trough collector

To promote the development of concentrating solar power generation technology using supercritical CO2 (sCO2), the heat transfer under non-uniform heat flux in the parabolic-trough collector was numerically simulated with emphasis on the coupling effect of the heat flux distribution, the property variations and the buoyancy effect. The non-uniform heat flux effect was first analyzed by comparing with two typical uniform heat flux conditions, which showed that the non-uniform heat flux reduced the overall heat transfer rate below that of the average uniform heat flux. Neither the average nor the maximum heat flux predictions could accurately reflect the heat transfer uniformity characteristics with the non-uniform heat flux. The circumferential non-uniformity was underestimated even with the maximum heat flux. Then, the analysis of the interaction between property variations and buoyancy effect showed that the use of sCO2 improves the heat transfer rate. The buoyancy effect dominates in modifying the flow field, which always enlarges the difference between top and bottom. The specific heat and viscosity variation effects are canceled out by the thermal conductivity variation. The buoyancy presents a negative effect on heat transfer when acting alone, but improves the heat transfer ability and their uniformity when coupled with the other property variations. Finally, the heat flux distribution effect coupled with the buoyancy effect was analyzed through changing the solar elevation angles. The maximum heat transfer coefficient is always located near the tube bottom due to the secondary flow effect. The circumferential non-uniformity increases with increasing Δθ as the relationship between heat flux distribution and the buoyancy effects change from competing to synergistic.

Thermal aspects of multiple slip and Joule heating in a Casson fluid with viscous dissipation and thermo-solutal convective conditions

Recently, in various biological processes such as endoscopic medication, blood pumping from the heart to different parts of the body, food supply, and in maintaining heat transfer phenomenon, slip plays a significant part in all aspects. Therefore, a study is aimed to enlighten the significance of multiple slips with Joule heating in a mixed convective Casson fluid. The flow regime is induced by the thermal radiation, chemical reaction and nonuniform heat source/sink in order to accomplish the heat and mass transportation. The modeled equations generated from the physical problem are transmuted into ordinary differential frameworks. The transformed system of equations was solved by means of numerical technique named Runge–Kutta Fehlberg method. The numerical results for involved engineering parameters like Joule heating, Eckert number, thermal, mass and velocity slip parameters for temperature, velocity and fluid concentration are analyzed by graphs using MATLAB. The numerical values for the drag force and Nusselt number are keenly observed and concluded that slip controls the flow closer to the boundary layer. Furthermore, magnetic factor decreases the velocity field and Eckert number enhances the temperature filed.

Mathematical modeling of magnetic dipole effect on convective heat transfer in Maxwell nanofluid flow: single and multi-walled carbon nanotubes

Improving the cooling process in an electrical power system is now the most critical topic. Nanoliquids are considered as dependable coolants because of their unique properties, which contain good thermal conductivity, larger critical heat flux and a quicker heat transfer rate. In light of these nanofluid characteristics, the current analysis deals with the flow and heat transference in Maxwell liquid suspended with single and Multi-walled carbon nanotubes (SWCNT/MWCNT) as nanoparticles in base fluid engine oil (EO) with non-uniform heat sink/source over a stretching sheet. For velocity and thermal profiles, a comparison is made between MWCNT-EO and SWCNT-EO Maxwell liquid. The modeled equations are reduced by using appropriate similarity variables and later, these reduced equations are numerically tackled by using fourth fifth order Runge–Kutta-Fehlberg's (RKF-45) procedure along with the shooting scheme. The influence of the dimensionless parameters on the flow, thermal field, Nusselt number and skin friction are broadly deliberated by using suitable graphs. Results reveal that, SWCNT-EO Maxwell fluid is highly affected by ferromagnetic interaction parameter and shows better heat transfer than MWCNT-EO Maxwell fluid. The MWCNT-EO maxwell nanoliquid shows less rate of heat transference Than SWCNT-EO Maxwell fluid for rise in temperature and space dependent heat sink/source parameters.

Hybrid nanofluid flow comprising spherical shaped particles with Hall current and irreversibility analysis: an application of solar radiation

This exploration intends to appraise the traits of hybrid nanofluid flow in a rotating channel influenced by the Hall current. The hybrid nanofluid is comprised of spherical nanoparticles of Silicon dioxide (SiO2 ) and Titanium dioxide (TiO 2) submerged in water. The hybrid nanofluid is performed as a solar energy collector. The heat analysis is conducted considering the non-uniform heat sink, Joule heating, and non-linear thermal radiation. To analyze the performance of spherical particles, the Maxwell model of thermal and electrical conductivity is used. Tiwari-Das hybrid nanofluid flow model is adopted here. The irreversibility analysis of the whole system is also an added feature of this study. The conversion of PDEs is by employing appropriate transformations into ODEs. A MATLAB software tool bvp4c is used to solve the translated mathematical formulations. Significant parameters’ physical behavior and graphical representations are thoroughly investigated. It is comprehended that the velocity profiles are influenced by the rotation parameter. The findings also revealed that the flow of hybrid nanofluid outperforms the nanofluid in solar thermal systems. Further, for escalating values of the rotational parameter, the surface friction increases, and the Nusselt number drops. For validation, a tabular comparison is also attempted. An excellent correlation is achieved.

Experience of non-uniform heat source/sink on the flow of micropolar nanofluid fluid with heterogeneous and homogenous chemical reaction

Due to the varied applications in industries, chemical reaction has a significant role in the perfect shape and size of the product that is dependent upon the proper cooling of the system. Therefore, the existing analysis reveals the impression of non-uniform heat source/sink on the micropolar nanofluid through a nonlinear vertical stretching surface for the interaction of heterogeneous and homogeneous chemical reactions. Oxide nanoparticle embedding with the traditional water is considered by introducing operational properties such as thermal conductivity and viscosity. The free convective water-based nanofluid past through a permeable medium interacts with the transverse magnetic field and the thermal buoyancy enriches the present discussion. Further, the convective heat transfer condition is useful to enhance the thermal properties as well. Imposing suitable transformations the present problem turned into ordinary and solved by employing the bvp5c built-in MATLAB code. Further, the important results are; inclusion of particle concentration favors for the enhancement in the shear stress as well as the heat transfer rate in conjunction with the resistive forces such as magnetic and porosity but the impact is reversed in case of couple stress coefficient however, retardation in the fluid temperature occurs for the increasing space and temperature dependent heat source.

Influence of the Directions of Vibrations and Gravity on the Formation of Vortex Structures of a Nonuniformly Heated Fluid in a Square Cavity

Influence of the Directions of Vibrations and Gravity on the Formation of Vortex Structures of a Nonuniformly Heated Fluid in a Square Cavity

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.

DNS analysis of flow and heat transfer of SCO2 in a square subchannel–Effect of gap width

The heat transfer and flow characteristics of supercritical carbon dioxide (SCO2) in a tight lattice are problematic in the thermal-hydraulic design of reactor fuel assemblies. Herein, direct numerical simulation (DNS) was performed to investigate the heat transfer and flow behavior of SCO2 in a vertically upward square subchannel. Emphasis was placed on clarifying the effect of the pitch-to-diameter (p/d) ratio, defined as the subchannel pitch over the rod diameter, on the time-averaged heat transfer and instantaneous velocity/temperature fluctuation. It was found that the wall temperature exhibits a “V-shaped” profile along the rod circumference, which is caused by the combined effects of buoyancy and an uneven flow area. The wall temperature is lower for subchannels with smaller p/d ratios; meanwhile, the circumferential non-uniform heat transfer becomes stronger, which also requires to be considered. The time-averaged streamwise velocity and fluid temperature have similar distributions on the subchannel cross-section, that is, high velocity and temperature occur near the rod gap, while regions with low velocity and temperature are identified in the subchannel interior. With an increase in the p/d ratio, both the temperature and velocity gradients are enlarged. Large-scale flow pulsations were identified in the subchannels. The instantaneous velocity fluctuation is weakened with increasing gap width; however, the fluctuation in the wall temperature exhibits an opposite trend. The effects of the p/d ratio on the dominant frequency of velocity/temperature fluctuation are not universal. Among the three selected cases, a subchannel with a small p/d ratio had a higher dominant frequency of instantaneous fluctuations. The turbulence structure was studied using a quadrant and anisotropy analysis. It was found that the outward and inward interactions included the main turbulence structures in the subchannel interior. In addition, with an increase in the p/d ratio, the transformation from disk-like turbulence to rod-like turbulence can be identified.

Mixed convective thermal transport in a lid-driven square enclosure with square obstacle

The prime motive of this disquisition is to scrutinize simultaneous aspects of external forcing mechanism and internal volumetric forces on non-Newtonian liquid filled in square enclosure. Inertially driven upper lid is assumed by providing constant magnitude of slip velocity whereas thermal equilibrium is disturbed by assuming uniform temperature at lower boundary and by keeping rest of walls as cold. To enhance thermal diffusion transport with in the flow domain cold as well as adiabatic temperature situation is provided. In view of velocity constraints all the extremities at no-slip except the upper wall which is moving with ULid. Formulation is attained in dimensional form initially and afterwards variables are used to convert constructed differential system into dimensionless representation. A numerical solution of leading formulation is sought through Galerkin finite element discretization. Momentum and temperature equations are interpolated by quadratic polynomials whereas pressure distribution is approximated by linear interpolating function. Domain discretized version is evaluated in view of triangular and rectangular elements. Newton’s scheme is employed to resolve the non-linearly discretized system and a matrix factorization based non-linear solver renowned as PARADISO is used. Validation of results is ascertained by forming agreement with existing studies. In addition, grid independence test is also performed to show credibility of performed computations. Stream lines and isothermal contours patterns are portrayed to evaluate variation in flow distributions. Kinetic energy and local heat flux for uniform and non-uniform heating situations are also divulged in graphical and tabular formats. Increase in Reynold number produces decrease in kinetic energy of fluid. Enhancement in Grashof number causes enrichment of thermal buoyancy forces due to which Nusselt number uplifts. Clock wise rotations increase against upsurge in magnitude of Reynold number which is evidenced form stream lines. Squeezing of secondary vortex against Prandtl number arises due to dominance of viscous forces.

Thermal performance enhancement in parabolic trough solar collectors by using an absorber tube with spherical pins

ABSTRACT Improving the overall performance of parabolic trough collectors (PTCs) represents the best method to reduce the cost of energy produced. The goal is to increase their potential to generate more useful heat, particularly at high ranges of temperatures. Therefore, various techniques have been thoroughly examined in the literature. Indeed, the non-uniform heat flux on the PTC receivers induces overheating of the absorber tube and significant thermal stress, which requires the use of expensive materials. It also reduces the overall thermal performance of the system. To overcome these issues, practical solutions must be introduced. In this paper, integrated spherical pins are used and different configurations have been proposed and investigated. To do so, a numerical model that combines optical and thermal aspects has been developed. For this, the Monte Carlo ray tracing technique (MCRT) is coupled with the finite volume method (FVM). Also, experimental tests on the MicroSol-R platform have been used to validate the numerical models. A number of energetic and exergetic performance indices are used to analyze the potential improvements due to the use of spherical pins. The analysis showed that the use of pins increases the heat transfer coefficient by up to 27.2% and reduces the heat loss by up to 9.32% compared with conventional smooth tubes. Moreover, it is found that the performance evaluation criterion (PEC) can be enhanced by up to 24.92%. Consequently, when using a solar receiver with five pins (which was selected as the best configuration among the examined configurations), the overall efficiency and the exergetic efficiency are increased by up to 4.1% and 2.2%, respectively. Indeed, the use of pins inside the solar receiver is a practical solution to improve the efficiency of the PTC system and has the potential to reduce the thermal stress on the receiver thanks to the high heat transfer coefficient. It also helps prevent overheating and reduce thermal losses by keeping the maximum temperature within a suitable operational range.

Experimental and numerical investigation on heat transfer of supercritical CO2 in a horizontal U-tube under thermal boundary of immersed tube

The heat transfer behaviors of supercritical CO2 (sCO2) under uniform heat flux have been widely investigated due to the excellent thermophysical properties. However, the heat transfer behaviors of sCO2 in an immersed tube as the heat exchanger of the pressurized fluidized bed have not been reported so far. In this work, we studied them by means of a pressurized fluidized bed-sCO2 closed-cycle heat transfer platform and a heat transfer model under circumferential and axial non-uniform heat flux with thermal boundary characteristics of immersed tube. The effects of operating parameters, circumferential and axial heat flux and wall thickness were analyzed. The experimental results revealed that the heat transfer coefficient (HTC) of sCO2 decreased sharply with the increase of the bed temperature. Mass flow rate can enhance heat transfer more significantly than inlet pressure. The simulation results showed that the unique circumferential heat flux of the immersed tube was beneficial to restrain buoyancy. And the increase of wall thickness can improve the circumferential uniformity of wall temperature. Axial non-uniform heat flux increased the risk of tube bursting. By comparing with experimental and simulated data, it is found that the supercritical-boiling-number and Liao-Zhao correlation can predict the heat transfer deterioration and the HTC in the immersed tube, respectively. This work can provide an understanding of the heat transfer behavior of sCO2 in an immersed tube.

Entropy generation minimization in the Blasius–Rayleigh–Stokes nanofluid flow through a transitive magnetic field with bioconvective microorganisms

The goal of this study is to underscore the attributes of nanofluid by discussing the Blasius-Rayleigh-Stokes (BRS) nanofluid flow with effects of modified Fourier law with gyrotactic microorganisms influenced by the transitive magnetic field past a moving semi-infinite plate. The proposed flow is supported by the non-uniform heat sink/source and radiation with zero mass flux at the surface. Analysis of entropy generation is also a part of this study. The most notable aspect of the presented model is that it discusses the entire problem using the Blasius-Rayleigh-Stokes flow. The envisioned model is reflected in the form of a system of PDEs that is transformed into a highly nonlinear system of ODEs engaging the boundary layer approximations and handled numerically. Graphical illustrations are designed for the arising parameters versus the associated profiles. It is comprehended that the thermal profile lowers for the thermal relaxation parameter. The results also disclosed that the motile density profile declines for Peclet number, and microorganism concentration difference parameter. Furthermore, the mass transfer rate is reduced by rising the chemical reaction parameter. Entropy generation upsurges versus heat generation absorption coefficients. A check for the validation of the presented model is also added to the problem.

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.

Heat transfer and flow structures of supercritical n-decane in a regenerative cooling channel loaded with non-uniform heat flux

A harsh and complex thermal environment in the combustor threatens safe working of scramjets. In this study, heat transfer and flow structures of supercritical n-decane under 3 MPa in a regenerative cooling channel loaded with non-uniform heat flux distributions are investigated, including uniform, sinusoidal, increased, and decreased heat flux distributions. A verified k–ω SST turbulence model was employed, and a corresponding mesh independence study was performed. From this work, the fluid temperature at the outlet of the heated channel is only determined by the averaged heat flux, and all the regenerative cooling channels achieve the same temperature although loaded with different heat flux distributions. Compared with the fluid temperature, the wall temperature distribution is more sensitive to the variations of heat flux distribution. The regenerative cooling channels loaded with the sinusoidal heat flux distributions exist in several high-temperature regions, and the channel loaded with linear distributions changes the trend of temperature distribution. A larger temperature gradient is found in the regenerative cooling channel wall with a lower thermal conductivity. This work provides a good insight into the characteristics of the flow and temperature field of regenerative cooling channels loaded with non-uniform heat flux considering the effect of conjugate heat transfer.

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.

Wall‐resolved large eddy simulation of turbulent flows in helically ribbed steam cracker reactors

AbstractHelically ribbed coils are commonly applied in steam cracking furnaces. To fully understand the impact of these ribbed wall modifications on the local heat transfer and associated pressure drop throughout the reactor, detailed experimental, and numerical studies have been performed. Experimental data based on stereo‐particle image velocimetry (S‐PIV) and liquid crystal thermography have been used to validate the numerical results from wall‐resolved large eddy simulations using OpenFOAM. The validation shows an excellent agreement in terms of mean and fluctuating velocities, pressure drop, and heat transfer behavior in a discontinuously ribbed tube. Compared with the pressure drop in a continuously ribbed tube, an approximately 40% lower pressure drop is obtained with a discontinuously ribbed tube, at the cost of a slightly decreased heat transfer enhancement. This makes the discontinuously ribbed tube design particularly interesting for steam cracking applications. The results also show that the nonuniform heat transfer at the wall is inherently linked to the flow reattachment and recirculation zones caused by the rib. Finally, the validated numerical model was used to study comparable designs and propose novel helical rib designs. Based on the results of the study, enlarging the trailing edge of the conventional ribbed geometry will improve the thermal enhancement performance, and is therefore found most promising for steam cracking reactor design.

Comparisons of Supercritical Loop Flow and Heat Transfer Behavior Under Uniform and Nonuniform High-Flux Heat Inputs

The heat transfer characteristic of supercritical water is one of the crucial issues in SuperCritical Water-Cooled Reactors (SCWRs). The efficiency and safety of the SCWR system are largely dependent on the local heat transfer performance. This paper establishes the numerical model for supercritical water in a long vertical circular loop (inside diameter = 10 mm) and analyzes the flow and heat transfer mechanism during the transition process from subcritical to supercritical states under various heat fluxes (uniform and nonuniform). The results reveal that the difference in thermophysical properties between the boundary layer and the core region is the main reason for the heat transfer behavior, especially during the transition from subcritical to supercritical and liquidlike to gaslike. The flow structure on the buffer layer is a dominating factor for heat transfer deterioration. The cases under variable nonuniform heat fluxes have a higher heat transfer coefficient compared with uniform heat fluxes. But, this will cause large changes of the parameter locally. The dominating factors of heat transfer deterioration under these conditions are also identified.

Analysis of phase change material thermal effects in large-scale proton-exchange membrane fuel cell based on open-source computational fluid dynamics

In recent years, solid–liquid phase change materials (PCM) have been used in various applications for thermal management. However, PCM thermal effects on proton-exchange membrane fuel cells (PEMFC) have not been investigated. In this study, the effects of PCMs on the thermal management of a PEMFC are evaluated using a novel 3D model based on an open-source computational fluid dynamics (CFD) software. In addition, metallic bipolar plates have been considered for this study. The results indicate that when the cooling system is turned off, PCMs can have a good cooling effect for more than 120 s. It is also observed that the temperature of the PCM-equipped model is uniform, contrary to the non-PCM model. Two types of boundary conditions, uniform and non-uniform heat flux, have been considered for this study. The results suggest that if PCM is embedded in anode section, non-uniform heat flux distribution leads to better thermal performance, whereas if PCM embedded in cathode section or in non-PCM design, it is the opposite. Moreover, it is figured out if PCM is located in cathode section, co-direction flows of coolant and reactants lead to lower thermal performance, while it is contrary for other designs. It is also demonstrated that the PCM can store a significant amount of waste heat.