Search Results (97)

This study numerically investigates unsteady natural convection (NC) heat transfer (HT) and entropy generation (E_gen) in trapezoidal cavities filled with two thermally stratified fluids. Both air-filled and water-filled configurations are analyzed to evaluate and compare their thermal performance under varying conditions. The cavities are characterized by a heated base, thermally stratified sloped walls, and a cooled top wall. The governing equations are numerically solved using the finite volume (FV) approach. The study considers a Prandtl number (Pr) of 0.71 for air and 7.01 for water, Rayleigh numbers (Ra) ranging from 10³ to 5 × 10⁷, and an aspect ratio (AR) of 0.5. Flow behavior is examined through various parameters, including temperature time series (TTS), average Nusselt number (Nu), average entropy generation (E_avg), average Bejan number (Be_avg), and ecological coefficient of performance (ECOP). Three bifurcations are identified during the transition from steady to chaotic flow for both fluids. The first is a pitchfork bifurcation, occurring between Ra = 10⁵ and 2 × 10⁵ for air, and between Ra = 9 × 10⁴ and 10⁵ for water. The second, a Hopf bifurcation, is observed between Ra = 4.7 × 10⁵ and 4.8 × 10⁵ for air, and between Ra = 10⁵ and 2 × 10⁵ for water. The third bifurcation marks the onset of chaotic flow, occurring between Ra = 3 × 10⁷ and 4 × 10⁷ for air, and between Ra = 4 × 10⁵ and 5 × 10⁵ for water. At Ra = 10⁶, the average HT in the air-filled cavity is 85.35% higher than in the water-filled cavity, while E_avg is 94.54% greater in the air-filled cavity compared to water-filled cavity. At Ra = 10⁶, the thermal performance of the cavity filled with water is 4.96% better than that of the air-filled cavity. These findings provide valuable insights for optimizing thermal systems using trapezoidal cavities and varying working fluids. Full article

In this study, a numerical investigation of unsteady natural convection heat transfer (HT) and entropy generation (EG) is performed within a trapezoid-shaped cavity containing thermally stratified water. The cavity’s bottom wall is heated, the sloped walls are thermally stratified, and the top wall is cooled. The finite volume (FV) method is employed to solve the governing equations. This study uses a Prandtl number (Pr) of 7.01 for water, an aspect ratio (AR) of 0.5, and Rayleigh numbers (Ra) varying between 10 and 10⁶. To examine the flow behavior within the cavity, various relevant parameters are determined for different Ra values. These parameters include streamline and isotherm contours, temperature time series, limit point and limit cycle analysis, average Nusselt number (Nu) at the heated walls, average entropy generation (E_avg), and average Bejan number (Be_avg). It is found that the flow transitions from a steady symmetrical state to a chaotic state as the Ra value increases. During this transition, three bifurcations occur. The first is a pitchfork bifurcation between Rayleigh numbers of 9 × 10⁴ and 10⁵, followed by a Hopf bifurcation between Rayleigh numbers of 10⁵ and 2 × 10⁵. Finally, another bifurcation occurs, shifting the flow from periodic to chaotic between Rayleigh numbers of 4 × 10⁵ and 5 × 10⁵. The present study shows an increase in E_avg of 94.97% between Rayleigh numbers of 10³ and 10⁶, while the rate of increase in Nu is 81.13%. The findings from this study will enhance understanding of the fluid flow phenomena in a trapezoid-shaped cavity filled with stratified water. The current numerical results are compared and validated against previously published numerical and experimental data. Full article

This paper addresses the mixed convective flow and heat transfer in combustible third-grade fluids through a slant porous channel filled with permeable materials. The fluid layer in contact with the channel wall is exposed to asymmetrical slippage and isothermal conditions. We employ the spectral Chebyshev collocation method (SCCM) to the coupled nonlinear flow governing equations and validate using the Shooting–Runge–Kutta method (RK4). Fluid velocity and temperature profiles, local entropy generation, and irreversibility ratio are computed and analyzed quantitatively and qualitatively. The convergence of the numerical method was demonstrated. The flow and thermal effects results, entropy generation rate, and Bejan number revealed fascinating manifestations that have profound implications in the design of thermo-mechanical systems. In particular, the thermal analysis results are pertinent to optimal system designs that achieve efficient energy utilization. Full article

This paper concerns an economic and exergetic efficiency analysis of a plate heat exchanger placed in a solar installation with TiO₂:SiO₂/DI:EG nanofluid. This device separates the primary circuit—with the solar fluid—and the secondary circuit—in which domestic hot water flows (DHW). The solar fluid is TiO₂:SiO₂ nanofluid with a concentration in the range of 0.5–1.5%vol. and T = 60 °C. Its flow is maintained at a constant level of 3 dm³/min. The heat-receiving medium is domestic water with an initial temperature of 30 °C. This work records a DHW flow of ${\dot{V}}_{DHW,in}$ = 3–6(12) dm³/min. In order to calculate the exergy efficiency of the system, first, the total exergy destruction, the entropy generation number N_s, and the Bejan number Be are determined. Only for a comparable solar fluid flow, DHW ${\dot{V}}_{nf}={\dot{V}}_{DHW}$ 3 dm³/min, and concentrations of 0 and 0.5%vol. is there no significant improvement in the exergy efficiency. In other cases, the presence of nanoparticles significantly improves the heat transfer. The TiO₂:SiO₂/DI:EG nanofluid is even a 13 to 26% more effective working fluid than the traditional solar fluid; at Re = 329, the exergy efficiency is ${\eta }_{exergy}$ = 37.29%, with a nanoparticle concentration of 0% and ${\eta }_{exergy}$(1.5%vol.) = 50.56%; with Re = 430, ${\eta }_{exergy}$(0%) = 57.03% and ${\eta }_{exergy}$(1.5%) = 65.9%. Full article

The physiological system loses thermal energy to nearby cells via the bloodstream. Such energy loss can result in sudden death, severe hypothermia, anemia, high or low blood pressure, and heart surgery. Gold and iron oxide nanoparticles are significant in cancer treatment. Thus, there is a growing interest among biomedical engineers and clinicians in the study of entropy production as a means of quantifying energy dissipation in biological systems. The present study provides a novel implementation of an intelligent numerical computing solver based on an MLP feed-forward backpropagation ANN with the Levenberg–Marquard algorithm to interpret the Cattaneo–Christov heat flux model and demonstrate the effect of entropy production and melting heat transfer on the ferrohydrodynamic flow of the Fe₃O₄-Au/blood Powell–Eyring hybrid nanofluid. Similarity transformation studies symmetry and simplifies PDEs to ODEs. The MATLAB program bvp4c is used to solve the nonlinear coupled ordinary differential equations. Graphs illustrate the impact of a wide range of physical factors on variables, including velocity, temperature, entropy generation, local skin friction coefficient, and heat transfer rate. The artificial neural network model engages in a process of data selection, network construction, training, and evaluation through the use of mean square error. The ferromagnetic parameter, porosity parameter, distance from origin to magnetic dipole, inertia coefficient, dimensionless Curie temperature ratio, fluid parameters, Eckert number, thermal radiation, heat source, thermal relaxation parameter, and latent heat of the fluid parameter are taken as input data, and the skin friction coefficient and heat transfer rate are taken as output data. A total of sixty data collections were used for the purpose of testing, certifying, and training the ANN model. From the results, it is found that the fluid temperature declines when the thermal relaxation parameter is improved. The latent heat of the fluid parameter impacts the entropy generation and Bejan number. There is a less significant impact on the heat transfer rate of the hybrid nanofluid over the sheet on the melting heat transfer parameter. Full article

Understanding fluid dynamics and heat transfer is crucial for designing and improving various engineering systems. This study examines the heat transfer characteristics of a buoyancy-driven natural convection flow that is laminar and incompressible. The investigation also considers entropy generation (E_gen) within an octagonal cavity subject to a cold cylinder inside the cavity. The dimensionless version of the governing equations and their corresponding boundary conditions have been solved numerically using the finite element method, employing triangular mesh elements for discretization. The findings indicated that incorporating a cold cylinder inside the octagonal cavity resulted in a higher heat transfer (HT) rate than in the absence of a cold cylinder. Furthermore, using the heat flux condition led to a higher average Nusselt number (Nu_avg) and a lower Bejan number (Be) than the isothermal boundary condition. The results also showed that HT and E_gen were more significant in the Al₂O₃-H₂O nanofluid than the basic fluids such as air and water, and HT increased as χ increased. The current research demonstrates that employing the heat flux condition and incorporating nanoparticles can enhance the rate of HT and Egen. Furthermore, the thermo-fluid system should be operated at low $Ra$ to achieve greater HT effectiveness for nanofluid concerns. Full article

The numerical investigation of magneto-hydrodynamic (MHD) mixed convection flow and entropy formation of non-Newtonian Bingham fluid in a lid-driven wavy square cavity filled with nanofluid was investigated by the finite volume method (FVM). The numerical data-based temperature and nanoparticle size-dependent correlations for the Al${}_2$O${}_3$-water nanofluids are used here. The physical model is a two-dimensional wavy square cavity with thermally adiabatic horizontal boundaries, while the right and left vertical walls maintain a temperature of $T_C$ and $T_H$, respectively. The top wall has a steady speed of $u=u_0$. Pertinent non-dimensional parameters such as Reynolds number ($Re=10,100,200,400$), Hartmann number ($Ha=0,10,20$), Bingham number ($Bn=0,2,5,10,50,100,200$), nanoparticle volume fraction ($\varphi =0,0.02,0.04$), and Prandtl number ($Pr=6.2$) have been simulated numerically. The Richardson number $Ri$ is calculated by combining the values of $Re$ with a fixed value of $Gr$, which is the governing factor for the mixed convective flow. Using the Response Surface Methodology (RSM) method, the correlation equations are obtained using the input parameters for the average Nusselt number ($\overline{Nu}$), total entropy generation ($E_s{)}_t$, and Bejan number ($B{e}_{avg}$). The interactive effects of the pertinent parameters on the heat transfer rate are presented by plotting the response surfaces and the contours obtained from the RSM. The sensitivity of the output response to the input parameters is also tested. According to the findings, the mean Nusselt numbers ($\overline{Nu}$) drop when $Ha$ and $Bn$ are increased and grow when $Re$ and $\varphi$ are augmented. It is found that ${\left(E_s\right)}_t$ is reduced by raising $Ha$, but ${\left(E_s\right)}_t$ rises with the augmentation of $\varphi$ and $Re$. It is also found that the $\varphi$ and $Re$ numbers have a positive sensitivity to the $\overline{Nu}$, while the sensitivity of the $Ha$ and $Bn$ numbers is negative. Full article

The container shape and arrangement of the thermal storage systems (TES) play a vital role in enhancing thermal performance. In the current investigation, the impact of inner tube dimensions and arrangements of TES on the thermal performance of a PCM-based triplex-tube latent heat storage exchanger (TTHX) is numerically analyzed. COMSOL Multiphysics commercial software was employed to obtain the numerical solution of the governing equations. Eight different cases with the same volume of PCM and various configurations of the inner tubes were investigated. The results of the current study were presented in terms of temperature contours, liquid fraction, Bejan number, average temperature, and average Nusslet number. The shortest melting time was 48 min, which was achieved by a single inner tube configuration with a quicker melting time of >62% compared to other cases. While for multi-tubes, the shortest time was 78 min, which was achieved by the configuration of three tubes (two horizontal and the third placed at the lower section) with an enhancement of melting time reduction of >12% compared to other cases, except for a single inner tube configuration. Regarding the entropy generation, the single tube configuration achieved the lower Bejan number. Therefore, single tube configuration was found to be the best option for maximizing the thermal performance of the studied TTHX. Full article

In this study, we investigate what happens to entropy in the presence of electrokinetic phenomena. It is speculated that the microchannel has an asymmetrical and slanted configuration. The presence of fluid friction, mixed convection, Joule heating, presence and absence of homogeneity, and a magnetic field are modelled mathematically. It is also emphasized that the diffusion factors of the autocatalyst and the reactants are equal. The governing flow equations are linearized using the Debye–Huckel and lubrication assumptions. The resulting nonlinear couple differential equations are solved using the program’s integrated numerical solver, Mathematica. We take a graphical look at the results of homogeneous and heterogeneous reactions and talk about what we see. It has been demonstrated that homogeneous and heterogeneous reaction parameters affect concentration distribution $f$ in different ways. The Eyring–Powell fluid parameters $B_1$ and $B_2$ display an opposite relation with the velocity, temperature, entropy generation number, and Bejan number. The mass Grashof number, the Joule heating parameter, and the viscous dissipation parameter all contribute to the overall increase in fluid temperature and entropy. Full article

This study explores the influence of an inclined magnetic field and variable viscosity on the entropy generation in steady flow of a couple stress fluid in an inclined channel. The walls of the channel are stationary and non-isothermal. The fluid flow is driven due to pressure gradient and gravitational force. Reynold’s model for temperature-dependent viscosity was used. The dimensionless, non-linear coupled equations of momentum and energy was solved, and we obtained an analytical solution for the velocity and temperature fields. The entropy generation and Bejan number were evaluated. The variation of pertinent parameters on flow quantities was discussed graphically. The rate of volume flow, skin friction coefficient, and Nusselt number at the surfaces of the channel were calculated and their variations were discussed through surface graphs. From the results, it is noticed that the entropy generation rate can be minimized by increasing the magnetic field and the temperature difference parameters. The findings of the current study in some special cases are in precise agreement with the previous investigation. Full article

This article examines the effects of entropy generation, heat transmission, and mass transfer on the flow of Jeffrey fluid under the influence of solar radiation in the presence of copper nanoparticles and gyrotactic microorganisms, with polyvinyl alcohol–water serving as the base fluid. The impact of source terms such as Joule heating, viscous dissipation, and the exponential heat source is analyzed via a nonlinear elongating surface of nonuniform thickness. The development of an efficient numerical model describing the flow and thermal characteristics of a parabolic trough solar collector (PTSC) installed on a solar plate is underway as the use of solar plates in various devices continues to increase. Governing PDEs are first converted into ODEs using a suitable similarity transformation. The resulting higher-order coupled ODEs are converted into a system of first-order ODEs and then solved using the RK 4th-order method with shooting technique. The remarkable impacts of pertinent parameters such as Deborah number, magnetic field parameter, electric field parameter, Grashof number, solutal Grashof number, Prandtl number, Eckert number, exponential heat source parameter, Lewis number, chemical reaction parameter, bioconvection Lewis number, and Peclet number associated with the flow properties are discussed graphically. The increase in the radiation parameter and volume fraction of the nanoparticles enhances the temperature profile. The Bejan number and entropy generation rate increase with the rise in diffusion parameter and bioconvection diffusion parameter. The novelty of the present work is analyzing the entropy generation and solar radiation effects in the presence of motile gyrotactic microorganisms and copper nanoparticles with polyvinyl alcohol–water as the base fluid under the influence of the source terms, such as viscous dissipation, Ohmic heating, exponential heat source, and chemical reaction of the electromagnetohydrodynamic (EMHD) Jeffrey fluid flow. The non-Newtonian nanofluids have proven their great potential for heat transfer processes, which have various applications in cooling microchips, solar energy systems, and thermal energy technologies. Full article

In this manuscript, off-set strip fin structures are presented which are adapted to the possibilities of additive manufacturing. For this purpose, the geometric parameters, including fin height, fin spacing, fin length, and fin longitudinal displacement, are varied, and the Colburn j-factor and the Fanning friction factor are numerically calculated in the Reynolds number range of 80–920. The structures are classified with respect to their entropy production number according to Bejan. This method is compared with the results from partial differential equations for the calculation of the irreversible entropy production rate due to shear stresses and heat conduction. This study reveals that the chosen temperature difference leads to deviation in terms of entropy production due to heat conduction, whereas the dissipation by shear stresses shows only small deviations of less than 2%. It is further shown that the variation in fin height and fin spacing has only a small influence on heat transfer and pressure drop, while a variation in fin length and fin longitudinal displacement shows a larger influence. With respect to the entropy production number, short and long fins, as well as large fin spacing and fin longitudinal displacement, are shown to be beneficial. A detailed examination of a single structure shows that the entropy production rate due to heat conduction is dominated by the entropy production rate in the wall, while the fluid has only a minor influence. Full article

This communication deliberates the time-reliant and Darcy–Forchheimer flow of water-based CNTs/gold nanoparticles past a Riga plate. In addition, nonlinear radiation, heat consumption and multiple slip conditions are considered. Entropy generation is computed through various flow parameters. A suitable transformation with symmetry variables is invoked to remodel the governing mathematical flow models into the ODE equations. The homotopy analysis scheme and MATLAB bvp4c method are imposed to solve the reduced ODE equations analytically and numerically. The impact of sundry flow variables on nanofluid velocity, nanofluid temperature, skin friction coefficient, local Nusselt number, entropy profile and Bejan number are computed and analyzed through graphs and tables. It is found that the nanofluid velocity is reduced by greater porosity and slip factors. The thickness of the thermal boundary layer increases with increasing radiation, temperature ratio, and heat consumption/generation parameters. The surface drag force is reduced when there is a higher Forchheimer number, unsteadiness parameter and porosity parameter. The amount of entropy created is proportional to the radiation parameter, porosity parameter and Reynolds number. The Bejan number profile increases with radiation parameter, heat consumption/generation parameter and the Forchheimer number. Full article

The generation of entropy and mixed convection in a nanofluid-filled 3D wavy tank containing a rotating cylinder is investigated. The top wavy surface of the tank is heated and all vertical surfaces are assumed to be adiabatic, while the bottom horizontal surface remains isothermally cold. The tank contains a solid cylinder and is saturated with an Al₂O₃–water nanofluid. The numerical simulations using the FEM are performed for the Richardson number ($0.01\le Ri\le 100$), nanoparticle volume fraction ($0\le \varphi \le 0.04$) and number of oscillations ($0\le N\le 4$). The numerical results of the present work are given in terms of 3D streamlines, isotherms and local entropy generation, as well as average heat transfer and Bejan number. The results show that for low values of the Richardson number and oscillation, heat transfer enhancement can be achieved by increasing the nanoparticle volume fraction. Full article

The two-dimensional, time-independent conjugate natural convection flow and entropy generation are numerically investigated in three different cases of a wavy conducting solid block attached to the left wall of a square cavity. A hybrid nanofluid with titania (TiO₂) and copper (Cu) nanoparticles and base fluid water in the fluid part is considered in the presence of a uniform inclined magnetic field. The leftmost wall of the cavity is the hot one and the rightmost one is the cold one. Radial-basis-function-based finite difference (RBF-FD) is performed on an appropriate designed grid distribution. Numerical results in view of streamlines and isotherms, as well as average Nusselt number in an interface and total entropy generation are presented. The related parameters such as Hartmann number, Rayleigh number, conductivity ratio, amplitude in wavy wall, number of waviness, and inclination angle of magnetic field are observed. Convective heat transfer in the fluid part is an increasing function of $kr,Ra,\gamma$, while it deflates with the rise in $Ha$ in each case. Total entropy generation increases with the increase in $Ra$ and $kr$ but it decreases with $Ha$ values. Average Bejan number ascends with the rise in $Ha$ and descends with the rise in $Ra$. Full article