Dimensionless Temperature Difference Research Articles

Application of machine learning in the investigation of entropy generation incurred during electroosmotic flows of Casson nanofluid

The present research article delves into the application of machine learning techniques in the study of entropy generation arising from the electro‐MHD Casson nanofluid flow in a symmetric microchannel. The inertial effect on fluid flow through a non‐Darcy porous medium is considered where we have taken into account the velocity, thermal, and concentration slips at boundaries. The resulting system of PDEs is converted to system of ODEs using appropriate wave frame transformations. The metamorphosed system is solved using bvp4c routine of MATLAB. The impact of several factors represented by respective parameters on velocity, nanofluid temperature, fraction of nanoparticles, entropy generation, and Bejan number are shown through graphs. This study also employs a machine learning technique in which Particle Swarm Optimization (PSO) algorithm has been used in conjunction with an Artificial Neural Network (ANN) to develop a predictive model capable of optimizing entropy generation within this specific fluidic context. Such an analysis could be useful in determining the optimum entropy generation in pulsatile transport of physiological fluid through intestine. With the use of above mentioned machine learning technique, the considered model offers the minimum entropy generation for specific values of the electroosmotic parameter, dimensionless temperature difference, and velocity slip parameter. It is observed that the flow with minimum electroosmosis effect and maintained at a specific velocity slip gives the optimal entropy generation.

Thermo-hydrodynamical optimization of direct absorption solar collector from Stokes to low Reynolds numbers regimes of nanofluid flow

It has been proven that optical properties of base working fluids are significantly enhanced, where very small amount of nanoparticles are exploited. In the current study, numerical investigation of microchannel-based direct absorption flat solar collector (DAFSC) filled with graphite water based nanofluids at various volume fractions in an independent-scattering regime map of nanofluids were taken into account to evaluate thermo-hydrodynamical performance of DAFSC. Furthermore, multi-response optimization of DAFSC including thermodynamics second law efficiency (ηII), thermal efficiency (η(th)), heat loss rate (Q̇(out)), dimensionless temperature difference (θ), pressure drop (Δp), and also cost function (Cost) was carried out by response surface methodology. Fifty four numerical designs proposed by face-centred central composite designs (FCCD) have been used to provide sufficient data to obtain mathematical regression models of response functions in which the significant model's terms were evaluated by analysis of variance. Furthermore, composite desirability function approach was taken into account for multi-response optimization of direct absorption solar collector to maximize ηII, η(th), θ, and to minimize Q̇(out),Δp and Cost functions. Strikingly, the CFD results unveiled that maximum thermal efficiency of DAFSC with black back absorber surface, which was enhanced up to 18% compare to base case, is mainly shape-dependent rather than to that of nanoparticles volume fractions, which can be justified by presence of different dominant heat absorption mechanisms transforming from volumetric absorption for nanofluids to surface one for pure water.

Constructal optimization of a rectangular non-uniform heat generation area with irregular high thermal conductivity material

Heat conduction models with three non-uniform heat generation conditions in a rectangular heat generation area (RHGA) are set up in this paper. Under given areas of the irregular high thermal conductivity material (HTCM) and RHGA, constructal optimization of the RHGA is conducted by changing the distribution of the HTCM and aspect ratio of the RHGA. The minimum dimensionless average temperature difference (DATD) of the RHGA is gained. It is found that the DATDs of the RHGA with linear heat generation distribution are abated by 82.43% and 82.65% after twice optimizations for boundary and central heat sinks, respectively. For the heat generation in one local area of the RHGA, the two decrements are 36.30% and 52.20%, respectively. For the heat generation in multiple local areas of the RHGA, the two decrements are 35.60% and 71.60%, respectively. The optimal structure of the RHGA with heat generation in multiple local areas and heat sink in the center exhibits the best cooling performance compared with the other models discussed in this paper. Moreover, the best cooling performance of the RHGA is at least augmented by 29.49% than those of the previous studies discussed in this paper.

Correlations for forced convective heat transfer coefficients at the windward building façade with vertical louvers

Vertical louvers are a widely used external shading system to control natural lighting and solar heat gain for buildings. However, when installed on a building façade, they can disrupt the flow field around the façade and affect the external convective heat transfer process of building's exterior surfaces. To this end, this paper conducted CFD simulations to clarify the forced convective heat transfer patterns in a vertical louver-facade system based on the k-ω SST model with a detailed verification. The extended Newton's cooling equation is used to describe the heat exchange process between louvers, building façade, and air, which generates four heat transfer coefficients: hwa, hwb, hba, and hbw. Then the impacts of dimensionless temperature difference (θ), louver angle (φ), louver slat width (B), and installation distance (W) on the heat transfer coefficients are investigated. The results show that θ does not affect the average heat transfer coefficients. hwa reaches a minimum value and hba reaches a maximum value when φ = 75o. In addition, hwa increases by 55.3% and hba decreases by 21.9% as B increases from 0.3 m to 1 m. When W increases from 0.25 m to 1 m, hwa decreases by 5.6% and hba increases by 39.6%. The variation in the heat transfer coefficients (hwb and hbw) between the louvers and building façade is also explained. Finally, new correlations of paired heat transfer coefficients are established as a function of φ, B, W, and wind velocity (U10). The accuracy of these correlations is evaluated by comparing calculated values with simulated results.

Thermodynamics analysis for Darcy model induced by beating waves of cilia under Hall impact

This study conducts the thermodynamics analysis of creeping viscous nanofluid influenced by metachronical waves in an inclined ciliated tube and investigates the effects of magnetic field, porous medium and Hall current. Moreover, heat transport analysis is performed to consider the viscous dissipation phenomena. Thermal conductivity of the fluid is made more effective by adopting water-based titanium dioxide nanoparticles. [Formula: see text] is chosen as it has many remarkable implications in nanobio-sensing, medical implants, drug delivery and antibacterial fields. The governing equations are formulated which are converted into ordinary differential system by taking into account the similarity variables. The analytical solution are obtained for momentum, pressure gradient and energy profiles. It is found that the entropy generation is an increasing function of the Eckert number, Prandtl number and dimensionless temperature difference. Both Darcy and Eckert numbers enhance the energy of flow system. The fluid velocity drops quickly with increasing magnetic parameter.

Optimal design of wavy microchannel heat sinks based on prediction and multi-objective optimization algorithm

In this paper, the multi-objective optimization of wavy microchannel heat sinks is performed by combining numerical calculation, prediction algorithm and genetic algorithm. In numerical calculation, the fluid-solid conjugate heat transfer of heat sinks with different parameters are simulated in Fluent. On this basis, the variable parameters and objective parameters are used to complete the training of neural network model, which aims to achieve accurate prediction of objective parameters. Finally, the multi-objective genetic algorithm is applied to find the Pareto front according to different requirements on the foundation of the prediction model. Results show that the coefficient of determination of the neural network models are all greater than 0.85, which proves that the prediction model has a high accuracy. The Pareto fronts are obtained by non-dominated sorting genetic algorithm (NSGA-II) with different objective parameters and they reveal that the channel with the optimal performance corresponds to a larger channel width or Reynolds number. In addition, it is also found the dimensionless temperature difference is correlated with Nusselt number.

Reverse flow analysis of hybrid nanofluid’ MHD mixed convection flow in a Vertical Cylindrical Annulus: An Exact Solution

In recent decades, reverse flow analysis in mixed convection flow has attracted the attention of many researchers owing to its applications in the design of medical and engineering systems. The presence of reverse flow is unfavorable in many respects; therefore, it is crucial to find values of critical parameters affecting the reverse flow to eliminate it. In this paper, the thermal and hydrodynamic behavior of MWCNT-Fe3O4 hybrid nanofluid is explored in a vertical cylindrical annulus and in the adjacency of radial magnetic field by achieving the results of the exact solution. Furthermore, the effective factors on the reverse flow are investigated, considering the effects of wall movement and suction/injection on it. The range of changes of the governing parameters includes constant velocity of cylinders’ walls A=0−10, B=0−10, Mixed convection parameter η=-1500−1500, dimensionless temperature difference ratio ξ=0−1, Hartman number Ha=0−50, Suction/injection S=-6−6, nanocomposite particles concentration φ=0−0.3% and radios ratio λ=2−10. The results reveal that hybrid nanofluid enhances the heat transfer rate. Moreover, by changing the above-mentioned parameters and selecting the appropriate values for them, the flow, heat transfer and occurrence of reverse flow can be optimally controlled. Meanwhile, such parameters as Ha, S and ξ perform better in eliminating reverse flow.

Constructal design of a fan-shaped high thermal conductivity path in a square heat generation body

A fan-shaped high thermal conductivity path (FSHTCP) model in a square heat generation body (SHGB) is built in this paper. For the given areas of the FSHTCP and SHGB, the structure of the FSHTCP is optimized by successively varying its width, central angle and radius, and the dimensionless maximum temperature difference (DMTD) and dimensionless entropy generation rate (DEGR) of the SHGB are minimized, respectively. It is found that the optimal dimensionless width, optimal central angle and optimal dimensionless radius can lead to the triple minimum DMTD and DEGR, respectively. When the area fraction is 0.15, the DMTD and DEGR after triple minimizations are abated by 33.37% and 32.46%, respectively. This illustrates that the optimization effect is remarkable after constructal design of the FSHTCP. The optimal structures of the FSHTCP with the minimizations of DMTD and DEGR are different, and the designers should choose the optimal construct of the FSHTCP according to different design requirements.

Heat transfer analysis of a borehole heat exchanger array in a layered subsurface

In the engineering design of borehole heat exchanger arrays, the subsurface is generally regarded as homogeneous, which leads to a large deviation in the prediction of actual performance. An analytical model with good flexibility describing the heat transfer behavior of BHE array in a layered subsurface is introduced using the Green’s function. The Green’s function which is the exact solutions to the temperature response of a ring coil heat source imbedded in a layered ground domain is obtained directly from the governing equations of the problem by the separation of variables techniques. Meanwhile, the nonuniformity of the heat flow rate along the borehole wall depth is addressed in the analytical layered model. Then, a numerical model of BHE array heat transfer in a layered subsurface is proposed based on the modified pipeline flow model. The numerical model is systematically verified with three experiment tests from the literatures and one test performed by the authors. The maximum RSM error and mean absolute percentage error for four test cases are 0.66 °C and 3.25%, showing a good agreement between the proposed numerical model and the measurements. Then, the accuracy of the analytical solution is validated with the existing simple homogeneous model and the proposed numerical model for multiple BHEs and multiple layers scenarios. The effects of the BHEs array and ground stratification on the temperature response are examined in details employing the analytical and numerical models, with the analytical model focusing on the thermal responses of the layered ground and the numerical model on the circulating fluid in the U-tubes. Results show that the presence of the BHE array increases the magnitude of the discrepancy in the temperature prediction between the layered and homogeneous model, particularly in the layers with low thermal diffusivities at large timescales. For the simulated case, the dimensionless temperature difference between the layered and homogeneous scenarios at the borehole wall in the BHE array is 0.35, while it is only 0.11 in a single BHE, resulting in an increase by 218%. Moreover, the ground stratification could affect the prediction of fluid temperature profile along the BHE depth, thus influencing the thermal circuiting between the two pipes of the U-tube. Compared with the homogeneous model, the coefficient of the thermal circuiting increases by up to 11.6% when the ground stratification is considered. Using the homogeneous model with equivalent thermal properties to design the ground source heat pump system in a layered subsurface would underestimate the short circuiting of the U-pipes and undersize the BHE system. The results of this study provide analytical formalism and numerical method to understand better how the design and operation of actual ground source heat pump is engineered.

Modeling filtered heat transfer model by considering dimensionless temperature difference between gas and solid phases

AbstractComputational fluid dynamics–discrete element method is used to simulate gas–solid flows with heat transfer. The strategy of repetitively resetting the gas phase temperature is adopted to maintain the temperature difference between the gas and solid phases. The difference between the heat transfer characteristics produced by this strategy and the traditional heat source method is analyzed. It is found that heat transfer in dense regions is artificially enhanced by the heat source method. Therefore, the results obtained by the temperature reset method are filtered to develop a three‐marker model for the filtered interphase heat transfer coefficient (IHTC). In the developed model, the filtered gas–solid temperature difference is nondimensionalized by the average gas–solid temperature difference in surrounding grids, which is shown to have an impact on the filtered IHTC. The developed model is demonstrated to be effective and accurate in both a prior and a posterior tests.

Experimental Investigation of a Prototype Thermal Refuge for Trout

Recent years have seen an increase in surface water temperatures in several streams and fisheries, which has a detrimental effect on cold-water species such as trout. One possibility to resolve this issue is to create localized refugia of colder water generated through active cooling. The current work focuses on a prototype thermal refugia design and field testing. Various configurations of the prototype thermal refugia were tested in a stream, which could benefit from additional refugia regions. The prototypes featured a staggered, tube-bundle heat exchanger placed inside an enclosure with an aperture. The results demonstrate that in remote locations, man-made refugia can be provided. While the base enclosure (91.5 cm × 91.5 cm × 45.8 cm) allowed for excess mixing with the warmer free stream and resulted in low performance (dimensionless temperature difference of θ¯avg= 0.07), additional modifications improved performance. By utilizing a panel or an extension, the dimensionless temperature difference quadrupled (θ¯avg= 0.26) while the average heat transfer per dimensionless temperature difference was reduced to approximately one-fifth (1.92 kWth/θ¯avg) of the base enclosure. But these configurations increased the standard deviation of the temperature differences inside the refugia due to localized cooling. The combination of the panel and the extension did not further increase the standard deviation but resulted in an even higher dimensionless temperature difference (θ¯avg= 0.55) and a lower heat transfer per dimensionless temperature difference (0.81 kW/θ¯avg). This suggests that the enclosure design can be used to achieve a desirable temperature differential while maintaining a reasonable spatial fluctuation in that temperature difference and power requirement.

Non-Boussinesq effects on natural convection airflows simulated in a tall rectangular cavity

Natural convection of air in a tall rectangular cavity is explored by solutions of the fully compressible transient Navier–Stokes equations in two-dimensional form, without the Boussinesq approximation. A temperature difference is imposed on the two vertical side walls, each isothermal, with the two horizontal boundaries adiabatic. Thermo-physical properties of air, including density, viscosity, thermal conductivity and specific heat, are all variable with temperature. Contrary to the conclusions in most previous numerical studies invoking the Boussinesq approximation, this study finds the instability of the conduction regime to be a traveling wave drifting downward in the cavity. The wave-drift speed is a strong function of the dimensionless wall temperature difference, ε, defined as the temperature difference between the vertical walls divided by twice the mean wall temperature. Wave-drift speeds and wave numbers are calculated over a range of ε less than 0.5 and Rayleigh numbers less than 9000. The dimensionless temperature difference ε is also found to have significant effects on local heat transfer and transient flow structure inside the cavity.

Natural convection of Boussinesq and non-Boussinesq airflows simulated in a tall annular cavity

Natural convection of air in a tall annular cavity is explored by numerical solutions of the fully compressible Navier­Stokes equations in transient, axisymmetric (two-dimensional) form. A temperature difference is imposed on the two vertical walls, each isothermal, with the two horizontal boundaries adiabatic; the outer cylindrical surface is heated and the inner cylindrical surface cooled. Thermophysical properties of air, including density, viscosity, thermal conductivity, and specific heat are all variable with temperature. Laminar flow inside a tall annular cavity is prone to an instability which takes the form of a multicellular cat’s eye pattern drifting downward in the cavity. In this study, non-Boussinesq effects on the cat’s eye instability are explored by simulating flows in an annular cavity of aspect ratio A = 40 and diameter ratio η = 0.8, for Rayleigh numbers less than 14,000. A range of dimensionless wall temperature differences are investigated, 0 < ε ≤ 0.2, where ε is the temperature difference between the two vertical walls, Th – Tc , divided by the sum of the absolute temperatures, Th + Tc . The dimensionless wall temperature difference is shown to have pronounced effects on: the onset of the cat’s eye instability, subsequent flow bifurcations, wave speeds, oscillation time-periods as well as local heat transfer rates. The critical Rayleigh number, Rac , signifies a transition from steady unicellular flow to transient multicellular flow; Rac is found to increase with ε. At higher values of dimensionless wall temperature difference ε, mono-periodic oscillatory flows are predicted to occur over a smaller range of Rayleigh numbers, prior to the onset of quasiperiodic flow.

Study on the Stability of Functionally Graded Simply Supported Fluid-Conveying Microtube under Multi-Physical Fields.

The stability of functionally graded simply supported fluid-conveying microtubes under multiple physical fields was studied in this article. The strain energy of the fluid-conveying microtubes was determined based on strain gradient theory, and the governing equation of the functionally graded, simply supported, fluid-conveying microtube was established using Hamilton’s principle. The Galerkin method was used to solve the governing equation, and the effects of the dimensionless microscale parameters, temperature difference, and magnetic field intensity on the stability of the microtube were investigated. The results showed that the dimensionless microscale parameters have a significant impact on the stability of the microtube. The smaller the dimensionless microscale parameters were, the stronger the microscale effect of the material and the better the microtube stability became. The increase in the temperature difference decreased the eigenfrequency and critical velocity of the microtube and reduced the microtube stability. However, the magnetic field had the opposite effect. The greater the magnetic field intensity was, the greater the eigenfrequency and critical velocity were, and the more stable the microtube became.

Natural convection of hybrid nanofluid heat transport and entropy generation in cavity by using Lattice Boltzmann Method

A mesoscopic study of natural convection due to MWCNT-Fe3O4/Water hybrid nanofluid is conducted utilizing the Lattice Boltzmann Method. The test fluid is filled in a differentially heated rectangular enclosure. Effects of aspect ratio in the range of 0.5–2.0, Rayleigh number varying from 103 to 105 and nanocomposite volume fraction on heat and fluid flow characteristics and entropy generation have been illustrated. It is observed that the mean Nusselt number rises with the increase in Rayleigh number, while it falls as the aspect ratio increases. However, the mean Nusselt number enhances with the increase in MWCNT-Fe3O4 volume fraction up to 0.001. On further increasing the volume fraction, the mean Nusselt number shows either no significant rise or deterioration for the case of MWCNT-Fe3O4 nanocomposite. The dimensionless entropy generation number rises with the increase in the Rayleigh number. However, it falls with an increase in aspect ratio and dimensionless temperature difference. Interestingly in the case of increasing nanoparticle loading fraction, entropy generation number augments first, attains a maximum at 0.001 ​vol fraction of nanocomposite, and then it decreases. Nevertheless, at the low Rayleigh number, it keeps on rising with an increase in nanocomposite volume fraction. The best thermal performance is obtained for the cavity of 0.5 aspect ratio. A correlation for the mean Nusselt number is proposed.

Performance validation of the heat extraction performance by the natural ventilation with a board-coupled shaft in a deep buried tunnel

Experiments were conducted in a 1/20 scale model tunnel, a higher shaft (5 times the tunnel height) was applied to model the shaft in a deep buried tunnel. Researches have validated that the board-coupled shaft can efficiently eliminate the plug-holing phenomenon and improve the smoke and heat extraction performance when the board-coupled shaft is suitably applied in a shallow buried tunnel. The purpose of this paper is to explore whether the board-coupled shaft (BCS) is effective and has stable heat extraction performance in deep buried tunnels. The influence of heat release rate (HRR) and board location on the heat extraction performance was investigated. The experimental results show that the BCS is effective and has stable heat extraction performance for the deep buried tunnels applied in this study. Also, an analytical solution for predicting the dimensionless smoke layer thickness in the one-dimensional flow region was developed, and it can be found that the dimensionless smoke layer thickness in the one-dimensional flow region depends only on the longitudinal position and doesn’t rely on the HRR. Furthermore, based on the general condition that the first shaft cannot extract the entirety of the smoke, two empirical correlations were derived for predicting the dimensionless temperature difference (ΔTs∗) and the dimensionless heat extraction rate (qs∗) in the BCS under different HRRs and board locations. These studies may contribute positive significance for promoting the application of natural ventilation with vertical shafts in deep buried tunnels.

Development of unsteady natural convection in a square cavity under large temperature difference

To investigate how the nonuniform fluid density distribution caused by large temperature variations affects the development of unsteady natural convection, we perform a series of direct numerical simulations of two-dimensional compressible natural convection in an air-filled square cavity. The cavity has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The simulations are done using a kinetic approach based on a modeled Boltzmann equation, from which the fully compressible Navier–Stokes–Fourier equations are recovered. No Boussinesq approximation or low Mach number approximation is made. An extra source term is introduced to adjust the fluid Prandtl number. Simulations are performed for a range of Rayleigh numbers (107−109) with a fixed dimensionless temperature difference of ε=0.6 to determine the critical Rayleigh number and study the development of unsteady flow. To illustrate the instability mechanism, instantaneous fluctuation field, time trace of temperature, and velocity at selected monitoring points, the spectrum and other statistics are presented and discussed. As expected, significant differences are observed between the instability of compressible natural convection and the Boussinesq-type natural convection. With a large temperature difference, the transition to unsteady flow is asymmetric for the flows near the hot wall and cold wall. For the Rayleigh number range we studied, the cold wall region is dominated by low-frequency impact instability of the boundary thermal jet at the bottom corner. For the hot wall region, besides the upper corner impact instability, a boundary layer instability featuring high-frequency oscillations is observed.

Impacts of Uniform Magnetic Field and Internal Heated Vertical Plate on Ferrofluid Free Convection and Entropy Generation in a Square Chamber.

The heat transfer enhancement and fluid flow control in engineering systems can be achieved by addition of ferric oxide nanoparticles of small concentration under magnetic impact. To increase the technical system life cycle, the entropy generation minimization technique can be employed. The present research deals with numerical simulation of magnetohydrodynamic thermal convection and entropy production in a ferrofluid chamber under the impact of an internal vertical hot sheet. The formulated governing equations have been worked out by the in-house program based on the finite volume technique. Influence of the Hartmann number, Lorentz force tilted angle, nanoadditives concentration, dimensionless temperature difference, and non-uniform heating parameter on circulation structures, temperature patterns, and entropy production has been scrutinized. It has been revealed that a transition from the isothermal plate to the non-uniformly warmed sheet illustrates a rise of the average entropy generation rate, while the average Nusselt number can be decreased weakly. A diminution of the mean entropy production strength can be achieved by an optimal selection of the Lorentz force tilted angle.

Steam condensation heat transfer on lubricant-infused surfaces

SummarySteam condensation is fundamental to several industrial processes, including power generation, desalination, and water harvesting. Lubricant-infused surfaces (LISs) promote sustained dropwise condensation, leading to significantly higher heat transfer performance that trades off with durability. Here, we present a systematic study on lubricant-infused copper tubes in a partial vacuum environment typical of power plant condensers to elucidate the influence of the design parameters—texturing, functionalizing agent, and lubricant viscosity—on condensation heat transfer performance and durability. Heat transfer effectiveness is introduced as a relevant parameter to quantify the effects of condensation heat transfer coefficient enhancement on the overall system heat transfer performance. Analytical expressions are developed for lubricant retention fraction and heat transfer effectiveness in terms of Bond number, viscosity ratio, and a dimensionless logarithmic mean temperature difference that can be used for predicting the performance of a LIS or for designing surfaces for a desired performance.

Theoretical study of partially return air flows in vertical mine shafts

This paper is concerned with a theoretical study of the conditions for occurrence of partially return air flows in vertical mine shafts. Such problem arises when the temperature of the air rising in the vertical mine shaft is much higher than the temperature of the shaft walls. This situation can occur during the construction of mine shafts using artificial freezing of surrounding rocks. The uncontrolled return air flows in the shaft under construction may cause an accumulation of harmful impurities released during drilling and blasting operations and a deterioration of microclimate parameters in the atmosphere of mine shafts. We investigate here a two-dimensional, fully turbulent, unsteady air flow in a vertical domain. In accordance with the Boussinesq approximation, the air density is specified as a function of temperature. The results of simulations show that a significant change in the transverse air velocity profile and the occurrence of return air flows are observed at Rayleigh numbers (dimensionless temperature difference) of order of 109. We propose two criteria for quantitative analysis of the flow structure: the critical Rayleigh number which denotes the occurrence of return flows in the cross section of the shaft and the transforming Rayleigh number which serves as indicator of significant changes in the velocity profile. Numerical dependences of the critical and transforming Rayleigh numbers on the Reynolds number of the airflow in the shaft are determined.