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The roles of nanoparticles and geometric effects are incredible in nanotechnology. The significant prospective of nanoparticles can be found in the manufacturing of machineries, heating/cooling of nuclear reactors, chemical and thermal engineering, mechanical and aerodynamics, etc. Thus, the current model study is performed for the heat transport mechanism in a newly engineered ternary nanofluid model for sinusoidal surface. The conventional model was updated via influences of ternary nanoparticles, transient phenomena, radiation and heat generation effects, convective and thermal slip impacts. The primary governing laws are reduced into the desired model form via transient similarity expressions and ternary nanoliquid models. Afterward, the shooting scheme supportive by RK technique is endorsed for physical configuration of the model dynamics under multiple ranges of the parameters. The outcomes revealed that both the components of velocity showed different behaviors for nodal and saddle points against the nodal-saddle parameter s1 that is, in the saddle case the velocity is decreased while in the nodal case its value is boosted when the value of s1 is slightly increased. Further, the temperature of the fluid is increased when Q1 and Rd varied from 0.1 to 0.7. Further, the skin friction augments from 119.5% to 121.55%, 121.54% to 129.15% when s1 and st vary from 0.1 to 0.5, respectively. The Nusselt number improved from 12.2124% to 12.218% (for nanoparticles concentration), 11.9109% to 11.7996% (for heating source Q1 from 0.2 to 0.5) and increased from 22.3815% to 47.5804% (for Biot number variations from 0.2 to 0.5). Hence, the Biot number highly contributes to the heat transfer rate than other parameters. [ABSTRACT FROM AUTHOR]

We consider the optimal control of unsteady natural convective flow of reactive viscous fluid with heat transfer. It is assumed that Newton's law governs the heat transfer within an exothermic reaction under Arrhenius kinetics and Navier slip condition on the lower surface of the channel. The flow is examined in a vertical channel formed by two infinite vertical parallel plates, with a distance (H) between them. Time-dependent natural convective slip flow of reactive viscous fluid and heat transfer equations are solved in a unit interval using the Galerkin-Finite Element Method (FEM) with quadratic finite elements in space and the implicit Euler method in time. The direct solutions are obtained for testing various values of the problem parameters: the Biot number, the Frank Kamenetskii parameter, the Navier slip parameter, and the computation of the skin friction and the Nusselt number (Nu). The optimal control problem is designed for the momentum and energy equations to derive the fluid-prescribed velocity and temperature profiles by defining controls on the boundary of the domain in two ways: (a) controls are formulated as parameters in the boundary conditions, such as slip length and Biot number; (b) controls are assigned as time-dependent functions in the boundary conditions, representing the slip velocity and the heat transfer rate. Following a discretize-then-optimize approach to the control problem, optimization is performed by the SLSQP (Sequential Least Squares Programming) algorithm, a subroutine of SciPy. Numerically simulated results show that the proposed approach successfully drives the flow to prescribed velocity and temperature profiles. [ABSTRACT FROM AUTHOR]

Prunes is one of the favorite fruits in the genus Prunus of the family Rosaceae, mainly planted in the Xinjiang Province of China. Fresh prunes are prone to water loss, softening, rotting, mold, and a series of quality degradations, due to the high moisture content. Drying prunes can extend the storage period for a long shelf life, particularly for the added value of the product. In this study, a series of experiments were carried out to investigate the moisture migration during drying. The drying characteristics of prunes were obtained at different temperatures (50, 65, and 80 ℃) and wind speeds (1, 2, and 3 m/s). Five kinetic models were then selected to fit the drying curve using the Biot number. Among them, the Bi-G model accurately represented the drying, according to the processing parameters and the fitted curves. Overall, the drying rate decreased gradually, while the moisture diffusion was first controlled externally, and then controlled by internal diffusion; The moisture diffusion efficiency increased with the increase of drying temperature and wind speed. The more significant effect of drying temperature was observed at the same time. The low-field nuclear magnetic resonance (LF-NMR) imaging technique was used to collect the relaxation spectrum and proton density images of prunes. Magnetic resonance imaging (MRI) images showed an uneven distribution of water in the fresh prune fruits. Particularly, the epidermal region shared a significantly higher water density than the pulp one. There was a variation in the water transfer potential inside the prune, as the drying process progressed. Water flowed to form a new equilibrium following the difference in transfer potential. The internal moisture reached the equilibrium point at 60% dry mass. The internal water existed in three forms: free, semi-bound, and combined water, which were dominated at different drying points: free water was the highest in fresh prunes, accounting for 93% of the total moisture; semi-bound water was the highest in prunes at the middle stage of the drying, accounting for 86% of the total; and combined water was the highest in prunes at the end of the drying, accounting for 93% of the total. There was an interconversion relationship among the three forms of water during the whole drying. However, the overall trend of conversion was attributed that the water with a weaker binding force was converted to the water with a stronger binding force. There were two main directions of water migration: water diffused from the skin of the prunes to the outside air by evaporation; and water diffused to the inside of the prunes following the difference of water gradient. The surface of the prunes was crusted to block the moisture migration pathway during drying. As such, the drying rate was reduced to obtain the high drying quality of prune. The step-down temperature drying was allowed for the prune skin moisture to maintain a moderate drying rate, in order to prevent the surface from drying too fast and crust formation. The drying quality of prunes was enhanced significantly, compared with the constant temperature drying. The finding can provide the theoretical basis to optimize the prunes drying. [ABSTRACT FROM AUTHOR]

In modern years, the conversion on solar radiation toward thermal energy had taken the important consideration by the appeal about sustainable power and heat raises. Nanofluid could show the significant role on developing the behavior on solar-thermal systems when that our capabilities about heat transfer improvement. That article analyzed numerically the flow on the hybrid nanofluid over the microchannel in existence of nonlinear solar radiation about different solar-thermal appliance. Effect of exponential heat source or sink and convective boundary condition are the focal concern of this study. The flow form was transferred with non-dimensionless model by convenient transformation, this numerical outcomes on nonlinear complex equations was formed to applying bvp4c technique. Subsequently, to influences on applicable parameters by the heat transfer of fluid had being revealed through the favor into tabular and graphical access. Outcomes communicate this solar radiation faster heat transport into division. The hybrid solution show massive increasing on heat transport 44.59% about division. Temperature decreased in the microchannel due to Biot number. The imitation outcomes are approved from the past issued work. [ABSTRACT FROM AUTHOR]

Zinc nanoparticles, for their potential in drug delivery due to their antibacterial properties and biocompatibility when combined with Sutterby fluid suspended in the sodium alginate acts as a natural biopolymer, and this colloid delivers the drugs more effectively to target sites.The major focus of this study is on the convective and Stefan blowing boundary conditions on the two-dimensional unsteady laminar flow of magnetohydrodynamic nanofluid across a stretched sheet when there is chemical reaction, viscous dissipation, and thermal radiation.The partial differential equation system modelled for the current situation is transformed as a series of nonlinear coupled ordinary differential equations by utilizing appropriately defined transformations. The bvp4c technique is an implicit shooting scheme that solves the highly nonlinear coupled system of partial differential equations. The processing of nanomaterials at high temperatures is pertinent to the current investigation. Using diagrams and tables, the numerical findings of the steady and unsteady solutions for the wall shear stress, heat and solute transfer rates, temperature, velocity, and concentration are explained.The study showed great agreement when compared to previously available research work. It was determined that velocity and magnetic fields had an exact opposite relationship. With an increase in stretching surface temperature, the convective parameter rises. In terms of physical characteristics, the fluid's thermal conductivity rises and rises the temperature. The slow momentum gain in the stretching scenario leads to increased fluid temperature due to the interplay between friction and energy transfer. Increasing boundary layer thickness is found in the fluid velocity curves with increasing power law index values. [ABSTRACT FROM AUTHOR]

Entropy analysis can help to identify the sources of entropy generation in a heat transfer process more accurately than other methods, such as energy efficiency analysis. This is because entropy analysis takes into account the quality of energy as well as its quantity. Nanofluids have already been shown to have superior heat transfer characteristics compared to conventional fluids. Stefan blowing can further enhance the heat transfer capabilities of nanofluids by increasing the mass flux and turbulence at the surface. This can be beneficial in a wide range of applications, such as heat exchangers, electronic cooling, and solar energy devices. The convective boundary condition accounts for heat transfer effects, influencing temperature distribution and the thermal boundary layer. Depending on the direction of heat transfer, the convective boundary condition can induce cooling or heating effects on the inclined plate. This has practical implications for various engineering applications, such as the cooling of electronic devices or heating in industrial processes. Carreau nanofluids have a wide range of potential applications in heat transfer, energy storage, drug delivery, and food processing. This research investigates how the presence of Stefan blowing affects the properties of Carreau nanofluid flow across a convectively heated tilted plate. Heat and mass transport phenomena are studied using quadratic thermal radiation and chemical reaction parameters. The mathematical model for this work is based on the Buongiorno model. The governing equations are converted into a system of ordinary differential equations and then solved using the bvp4c solver. Physical parameters such as the mass transfer rate can be visualized using bar graphs. The study's primary findings are that when the Weissenberg number increases, the velocity rises and the concentration profile declines due to Brownian motion. It is discovered that, when 0.5≤ϒ≤3 (the inverse porosity parameter), the friction factor declines by 0.34001 (in the presence of Stefan blowing), and 0.3284 (otherwise). It has been observed that as the Brinkman number and magnetic field parameters increase, there is an increase in entropy formation. Additionally, it has been noted that these same factors have an inverse effect on the Bejan number. At 0.1≤Nb≤0.6 (Brownian motion), the Sherwood number is seen to rise at a rate of 0.113353 (in the presence of Stefan blowing), and 0.479739 (otherwise). When the Stefan blowing parameter is absent, the rate of heat transfer is observed to be noticeably faster than when it is present. Furthermore, when the heat source parameter is set to 0.1≤Hs≤0.6, the decrement rates in heat transfer rate are 0.12208 (in the presence of Stefan blowing) and 0.02102 (otherwise).

Based on the discrete element method (DEM), four packed beds composed of soybean kernels with diameters of 6.4, 6.8, 7.4 mm, and the mixture of three kinds of particles were established. Then, a double-diffusion heat and mass transfer model between the grain pile and the interstitial air was established based on the local mass and thermal non-equilibrium (LMTNE) mechanism. Finally, employing particle-resolved computational fluid dynamics (PRCFD), the heat and mass transfer between the grain kernels and air during the drying process in the four packed beds were numerically resolved. It was found that the packed bed formed by stacking particles of different diameters had a minimum porosity of 0.4547. The radial porosity of the packed bed oscillates and decreases toward the central axis, while the tortuosity of the airflow path oscillates and decays toward the periphery. The mass transfer Biot number for soybean kernels with diameters of 6.4, 6.8, and 7.4 mm were 2.38 × 106, 2.44 × 106, and 2.53 × 106, respectively. This indicates that the mass transfer rate in the grain pile primarily depends on the magnitude of the moisture diffusion coefficient within the grain kernels. Compared with mass diffusion, thermal diffusion occurs much faster, which results in temperature gradients in packed beds only existing in the first 5 min of drying, and the drying rate in the early stage is higher than that in the later stage. Most importantly, the airflow characteristics, heat and moisture content are not in local equilibrium in the packed bed, and should be considered when designing drying systems. [ABSTRACT FROM AUTHOR]

Osmotic dehydration (OD) is an efficient preservation technology in that water is removed by immersing the food in a solution with a higher concentration of solutes. The application of OD in food processing offers more benefits than conventional drying technologies. Notably, OD can effectively remove a significant amount of water without a phase change, which reduces the energy demand associated with latent heat and high temperatures. A specific feature of OD is its ability to introduce solutes from the hypertonic solution into the food matrix, thereby influencing the attributes of the final product. This review comprehensively discusses the fundamental principles governing OD, emphasizing the role of chemical potential differences as the driving force behind the molecular diffusion occurring between the food and the osmotic solution. The kinetics of OD are described using mathematical models and the Biot number. The critical factors essential for optimizing OD efficiency are discussed, including product characteristics, osmotic solution properties, and process conditions. In addition, several promising technologies are introduced to enhance OD performance, such as coating, skin treatments, freeze-thawing, ultrasound, high hydrostatic pressure, centrifugation, and pulsed electric field. Reusing osmotic solutions to produce innovative products offers an opportunity to reduce food wastes. This review explores the prospects of valorizing food wastes from various food industries when formulating osmotic solutions for enhancing the quality and nutritional value of osmotically dehydrated foods while mitigating environmental impacts. [ABSTRACT FROM AUTHOR]

Prediction of kinetic, thermodynamic, and mass transfer parameters enable the comprehension of the structure of the solid–liquid extraction system. In this study, fig (Ficus carica) leaves were extracted by ethanol solution (10%, v/v) through microwave-assisted extraction (MAE) under 100, 200, 300, 400, and 500 W. Diffusion coefficient was calculated as 1.958 × 10−7, 1.543 × 10−7, and 1.089 × 10−7 m2 s−1, while mass transfer coefficient changed as 0.0364, 0.0573, and 0.0541 m s−1 under 345, 351, and 352 K, respectively. Biot number (1487.23, 2970.83, and 3974.28) was elevated with temperature. Pseudo-second-order kinetic equation characterized the kinetic findings of the MAE more satisfactorily comparing to pseudo-first-order kinetic equation. An endothermic, and spontaneous nature was observed based on the enthalpy (281.98 kJ mol−1), entropy (0.834 kJ mol−1 K−1) and Gibbs free energy changes (− 5.748, − 10.752, and − 11.586 kJ mol−1). [ABSTRACT FROM AUTHOR]

Ensuring sustained thermal propagation is a crucial role in many industrial and thermal systems since it facilitates the improvement of the efficiency of thermal engineering engines and machinery. Therefore, the usage of magnetized nanoparticles in a heat-carrying non-Newtonian fluid is a promising development for the enhancement of thermal power energy. This paper uniquely contributes by comprehensively analyzing heat and mass transfer characteristics in a Casson nanofluid subjected to bioconvection over a disk. The study also explores in detail the interaction of gyrotactic microorganisms, and activation energy in the system. Similarity transformations have been used to make the governing partial differential equations (PDEs) dimensionless, which has then transformed them into ordinary differential equations. The solution method has utilized the Shooting technique combined with the Bvp4c solver in MATLAB. Graphs have been drawn to explain the different parameters of the flow; also, other engineering quantities, like motile microbes density and Sherwood numbers, have been calculated and are represented graphically. Furthermore, the interplay of mixed convection, buoyancy ratio, bioconvection Rayleigh constant, and resistivity due to magnetization significantly influences the distribution of velocity in the Casson nanofluid. Remarkably, parameters that characterize the motile microorganism profile significantly attenuate said profile; therefore, they play a very important role in shaping the system dynamics. The application of bioconvection phenomena spans diverse fields, ranging from healthcare and environmental monitoring to agriculture and renewable energy, offering innovative solutions to address complex challenges.

This paper discusses the impact of unstable bioconvection microbial nanofluid drift with a revolving vertical funnel / cone in the spinning microbial nanofluid with a time-critical angular speed and chemical reaction, thermal radiation with the thermal, solute and microbial Biot numbers as the boundary conditions. The governing unsteady and the coupled partial differential equations equipped with non-linear terms are resolved mathematically using suitable similarity transformations. Further, these equations are analytically solved by the spectral quasilinearisation method (SQLM). The consequences of different physical constraints and other parameters are explained and analysed with the help of graphs. The surge of solute and microbial profiles was reflected in the rise of solutal Biot number and microbial Biot numbers, respectively, while the temperature profile of the fluid was enhanced for the increasing values of thermal, solutal and microbial Biot number parameters. The higher values of bioconvection Brownian motion increases the velocity and decreases the microbial profiles. The bioconvection Schmidt number and Peclet numbers enhance and discriminate the microbial profile correspondingly. [ABSTRACT FROM AUTHOR]

A numerical study was carried out on dual solutions of rotating stretching/shrinking surfaces to explore the influence of convective boundary conditions, viscous dissipation, thermal radiation, and heat sources/sinks on 3-D hybrid nanofluid flow. Hybrid nanofluids have great potential for a variety of applications due to their unique properties and versatility. It is improved the effectiveness of heat transfer rates. The main objective of this study is to investigate the influence that certain parameters on the temperature and velocities profiles against the parameters, including the volume fraction of copper, suction effect, viscous dissipation, thermal radiation, Biot number and rotating parameter. Further, the impact of the suction effect and shrinking sheet on reduced heat transfer and skin friction is also considered against the volume fraction of copper. The nonlinear partial differential equations are transformed into a collection of ordinary differential equations by including linear similarity variables. The generated combination of higher order nonlinear ODEs is solved via a boundary value algorithm called bvp4c, which executes on the MATLAB computing tool. The findings confirmed the existence of two branches (dual solution) with varied quantities of copper volume fraction according to the shrinking surface and suction effect. Additionally, as the Biot number, Eckert number, thermal radiation, and copper volume fraction all increase in strength, the rate at which heat flows in both solutions also increases. However, the heat transfer rate declined as increased the suction effect. Besides, when a positive and negative increment is applied to the rotational parameter, both solutions suffer an increase in both velocities. In summary, unique solutions are obtained S

The thermo convective instability of the Darcy-Benard problem (DB) using Robin (third-kind) thermal conditions is investigated here. We consider a viscous Newtonian fluid saturating a porous layer in which the layer is sandwiched between two impermeable boundaries. The upper and the lower walls are modelled in the form of the Neumann (second-kind) and the Robin (third-kind) thermal conditions, respectively. The difference in the temperature distribution between both phases allows the lack of a local thermal equilibrium model to be present. As a consequence, the third kind of thermal condition brings about one extra dimensionless parameter of the Biot number to the usual one of the inter-heat transfer coefficient and the thermal conductivity ratio. The normal modes method adopted in a linear stability analysis gives rise to perturbed governing equations. The eigenvalue problem is handled numerically as a result of the perturbed governing equations leading to the marginal stability condition. [ABSTRACT FROM AUTHOR]

Cryopreservation strives to maximize the viability and biofunctionality of cells and tissues by cooling them to a subzero temperature to facilitate storage and delivery. This technology has enabled clinics and labs to preserve rare and crucial samples and is poised to become more important with rising interest in cell therapy. Here, the biological impact of cooling rates on different cellular components is first described, paying special emphasis on the differences between slow cooling and vitrification with a heat transfer perspective based on the Biot number. This is followed by an overview of various classes of chemical‐based cryoprotective agents including small molecules, antifreeze proteins, hydrogels, and cryoprotective nanomaterials. Most importantly, fundamental concepts of cryopreservation including Mazur's "two‐factor hypothesis" are revisited, gaps in them are highlighted, and experiments to validate reported claims to deepen mechanistic understanding of cryoprotection are proposed. A matric is also introduced to assess the suitability of biomaterials for use in cell therapy to support manufacturers in making strategic choices for storing clinical samples. It is believed that this review would inspire readers to scrutinize fundamental concepts in cryopreservation to facilitate the development of new cryoprotective materials and technologies to support the emerging cell manufacturing and therapy industry. [ABSTRACT FROM AUTHOR]

The effect of heat conduction through the wall along the flow of heat carriers on the effectiveness of heat exchangers (HEs) when the wall ends are not thermally insulated from the environment has been investigated. An analytical solution of the problem for cocurrent flow of heat carriers was obtained for the same ratios of thermal equivalents of the heat carriers β and heat-transfer coefficients α on both sides of the wall separating hot and cold heat carriers and for a counter flow at β = α = 1. The solution to the problem depends on the number of heat-transfer units Ntu, parameter describing the axial wall heat conduction, the Biot number Bi, which determines relative heat transfer from the wall ends to the environment, and temperatures of the fluid in contact with the wall ends. The effect of axial wall heat conduction becomes more pronounced with decreasing parameter . Two cases are examined: case I with surrounding fluid temperatures assumed as equal to the inlet and outlet temperatures of the hot heat carrier and case II with surrounding fluid temperatures assumed as equal to the inlet and outlet temperatures of the cold heat carrier. The results obtained demonstrate that, at low Biot numbers (Bi < 10–3), the effectiveness of a heat exchanger ε for any values of in a cocurrent HE hardly differs at all from the effectiveness of the HE in the absence of the axial wall heat conduction effect, ε0, and for a counter flow at low the HE effectiveness is noticeably less than ε0 and decreases by two times at 1. At high Biot numbers (Bi > 1), the effect of axial wall conduction can increase the effectiveness of either heat carrier, while the temperature of the other heat carrier will change slightly during its flow through the heat exchanger. The predictions indicate that the best way for increasing the HE effectiveness is to employ the same thermal equivalents of two heat carriers and heat-transfer coefficients on both sides of the wall separating the hot and the heat carriers (β = α = 1). [ABSTRACT FROM AUTHOR]

Heat transfer models for condensation on hydrophobic and superhydrophobic interfaces are broadly available based on thermal resistance correlations. In the previous studies, very few models are presented based on the scaling factor or Nusselt number, and no model is available that directly correlates Biot number. This study develops a heat transfer model for dropwise condensation underneath a horizontal surface. The present model correlates with the Biot number to predict the heat transfer, temperature variation at the interfaces, solid-liquid, and liquid-vapor, and the growth rate of droplet condensate on the hydrophobic and superhydrophobic interfaces by using Archimedes' hat-box theorem. The present model is validated with analytical and experimental results against hydrophobic and superhydrophobic contact angles of similar working parameters made excellent agreements. The analytical model for dropwise condensation produces inaccurate results due to discrepancies and discontinuities due to multiple correlations in the modeling. The present model is modified to obtain a continuous result using experimental data. The modified model is used for analyzing heat transfer by varying Biot numbers from 0.0001 to 1000 using Python 3.6.1 with an accuracy of 10-4. Simulation of the present model results in constant heat transfer at Bi = 4, irrespective of the contact angle. A negligible amount of coating resistance and interface resistance when Bi > 0.1, curvature effect when Bi > 0.04, droplet resistance when Bi < 0.02, the maximum liquid-vapor interface temperature at Bi - 10, and maximum solid-liquid interface temperature at Bi = 5, are presented. [ABSTRACT FROM AUTHOR]

The results of using numerical solutions of the equations of nonstationary heat conduction in calculating the temperature of heat-insulating materials in the processes of their heat treatment and drying are presented. An approximation of nonlinear transport coefficients by linear coefficients is considered using the method of linearization and iteration. A simplification of the equation of unsteady heat conduction is proposed using the method of piecewisestep approximation of transfer coefficients, taking into account the continuous change in the temperature of the material over minimal time intervals. [ABSTRACT FROM AUTHOR]

The Brinkman–Bénard convection problem is chosen for investigation, along with very general boundary conditions. Using the Maclaurin series, in this paper, we show that it is possible to perform a relatively exact linear stability analysis, as well as a weakly nonlinear stability analysis, as normally performed in the case of a classical free isothermal/free isothermal boundary combination. Starting from a classical linear stability analysis, we ultimately study the chaos in such systems, all conducted with great accuracy. The principle of exchange of stabilities is proven, and the critical Rayleigh number,  R a c , and the wave number,  a c , are obtained in closed form. An asymptotic analysis is performed, to obtain  R a c  for the case of adiabatic boundaries, for which  a c ≃ 0 . A seemingly minimal representation yields a generalized Lorenz model for the general boundary condition used. The symmetry in the three Lorenz equations, their dissipative nature, energy-conserving nature, and bounded solution are observed for the considered general boundary condition. Thus, one may infer that, to obtain the results of various related problems, they can be handled in an integrated manner, and results can be obtained with great accuracy. The effect of increasing the values of the Biot numbers and/or slip Darcy numbers is to increase, not only the value of the critical Rayleigh number, but also the critical wave number. Extreme values of zero and infinity, when assigned to the Biot number, yield the results of an adiabatic and an isothermal boundary, respectively. Likewise, these extreme values assigned to the slip Darcy number yield the effects of free and rigid boundary conditions, respectively. Intermediate values of the Biot and slip Darcy numbers bridge the gap between the extreme cases. The effects of the Biot and slip Darcy numbers on the Hopf–Rayleigh number are, however, opposite to each other. In view of the known analogy between Bénard convection and Taylor–Couette flow in the linear regime, it is imperative that the results of the latter problem, viz., Brinkman–Taylor–Couette flow, become as well known. [ABSTRACT FROM AUTHOR]

A numerical study was carried out on dual solutions of rotating stretching/shrinking surfaces to explore the influence of convective boundary conditions, viscous dissipation, thermal radiation, and heat sources/sinks on 3-D hybrid nanofluid flow. Hybrid nanofluids have great potential for a variety of applications due to their unique properties and versatility. It is improved the effectiveness of heat transfer rates. The main objective of this study is to investigate the influence that certain parameters on the temperature and velocities profiles against the parameters, including the volume fraction of copper, suction effect, viscous dissipation, thermal radiation, Biot number and rotating parameter. Further, the impact of the suction effect and shrinking sheet on reduced heat transfer and skin friction is also considered against the volume fraction of copper. The nonlinear partial differential equations are transformed into a collection of ordinary differential equations by including linear similarity variables. The generated combination of higher order nonlinear ODEs is solved via a boundary value algorithm called bvp4c, which executes on the MATLAB computing tool. The findings confirmed the existence of two branches (dual solution) with varied quantities of copper volume fraction according to the shrinking surface and suction effect. Additionally, as the Biot number, Eckert number, thermal radiation, and copper volume fraction all increase in strength, the rate at which heat flows in both solutions also increases. However, the heat transfer rate declined as increased the suction effect. Besides, when a positive and negative increment is applied to the rotational parameter, both solutions suffer an increase in both velocities. In summary, unique solutions are obtained S < S ci for suction effect and λ < λ ci for the shrinking region. The outcomes came to the conclusion that hybrid nanofluid has a faster rate of transferring heat than standard nanofluid offers. [ABSTRACT FROM AUTHOR]

In the present work, a novel non-water Infrared Refractance Window drying (IR-RWD) method was developed for Malabar spinach. Experiments were conducted using a hybrid experimental design. Fresh Malabar spinach was pretreated using the vacuum steam pulsed blanching (VSPB) method. Results showed that VSPB inactivated POD and PPO activities to 9.77% and 5.42% within four cycles, respectively. The optimum conditions were found at 1.2 mm sample thickness, 40% infrared power, and 3.67 cm distance between IR emitter and glass plate resulting in 67.38 % chlorophyll retention, 7.72 overall color changes, 16.57 mgGAE g−1 total phenolic content, and 11.20 kJ kg−1 specific energy consumption. The Page model showed the best fit to the drying kinetics. Furthermore, Biot number indicated the impact of both internal and external resistance on moisture diffusivity. XRD and FESEM characterization of dried powder showed a semi-crystalline phase and square plate, porous morphology. The non-water IR-RWD was a promising alternative to traditional water RWD. [ABSTRACT FROM AUTHOR]

Phenolic antioxidants were extracted from Moringa oleifera leaves by applying ultrasound-assisted extraction (UAE). The feasibility of UAE was studied by analyzing the kinetics, thermodynamics, mass transfer, and effective diffusivity mechanisms to improve the process under several temperature values (298, 300, 306 K). Extraction rate increased with temperature (0.0028, 0.0028, and 0.0029 L mg−1 min−1). Activation energy for the process of UAE was calculated to be 3.5225 kj mol−1. Based on the results of thermodynamics parameters, UAE process of phenolic extraction from Moringa oleifera leaves was endothermic, random, and spontaneous, where the change in enthalpy, entropy, and Gibbs free energy were 1.6156 kj mol−1, 0.02977 kj mol−1 K−1, and − 7.2356, − 7.3247, − 7.4732 kj.mol−1, respectively. Furthermore, the diffusion and mass transfer model were used in order to evaluate the diffusion coefficients, mass transfer coefficients, and Biot numbers of the process. Diffusion coefficients (1.9800 × 10−10, 2.3070 × 10−10, and 2.3905 × 10−10 m2 s−1) and mass transfer coefficients (0.1320, 0.1447, and 0.1460 m s−1) increased with increasing temperature, while Biot numbers (285.00 × 103, 268.05 × 103, and 261.22 × 103) decreased slightly with increasing temperature. In addition, Biot number indicated that the external resistance is negligible. [ABSTRACT FROM AUTHOR]

In this study, microwave-assisted extraction (MAE) was applied to extract bioactive materials from leaves of Moringa oleifera. The current study was performed in order to clarify and understand the effects of extraction time, temperature, and power on the kinetics and thermodynamics of extraction, diffusion, and mass transfer coefficients and Biot number for the present system. One gram of Moringa oleifera particles with 80 mL solvent (60% ethanol) was extracted under different extraction temperature values (304, 305, 308, and 309 K) and microwave power values (200, 300, 400, and 500 W) for several time periods (30–400 s). According to the kinetic study, activation energy for the present MAE was calculated as 243.367 kj mol−1, where the extraction rate increased with temperature (0.0077, 0.0121, 0.022, and 0.0448 mL mg−1 s−1). Thermodynamic study produced the changes of enthalpy (31.572 kj mol−1), entropy (0.12817 kj mol−1), and Gibbs free energy (− 7.3917, − 7.5199, − 7.90434, and − 8.0325 kj mol−1), respectively. An empirical diffusion model was used for the estimation of diffusion coefficients, mass transfer coefficients, and Biot numbers depending on temperature. The diffusion coefficient (3.058 × 10-10, 3.114 × 10-10, 5.912 × 10-10, and 10.38 × 10-10 m2 s−1), mass transfer coefficient (0.2683, 0.4217, 0.7667, and 1.5613 m s−1), and Biot number (375 × 103, 578.9 × 103, 554.4 × 103, and 624.48 × 103) increased with increase in temperature. [ABSTRACT FROM AUTHOR]

An asymptotic analysis to the Cartesian Graetz problem with third-kind boundary conditions is carried out, the temperature profile is calculated for small values of the Biot number. The analysis is performed using asymptotic matching and shows that there are two scales for the axial coordinate, which allows us to find an analytical expression for the temperature field along the channel. This expression can be easily applied in thermal engineering applications. [ABSTRACT FROM AUTHOR]

The results of the study of heat and mass transfer in the processes of heat treatment and drying processes of thermal insulating materials when the values of the Biot heat exchange criterion are less than one and the main factor is the interaction of the evaporation surface of the material with the environment (external problem) are presented. It was assumed that at low temperature gradients over the cross section of a wet body, thermal transfer of matter can be neglected, and phase transformations are absent (Posnov's criterion is equal to zero). By processing the experimental data on convective heat treatment of materials carried out by the least squares method, experimental equations for calculating the kinetics of drying have been obtained. Equations are given for determining the duration of drying, material temperature, heat flux density. On the basis of the theory of regular thermal regime, equations for the rate of heating of a solid and the rate of decrease in moisture content have been obtained. The verification of the reliability of the obtained equations and comparison of the calculated values of the parameters with the experimental ones are presented. An experimental dependence of the relative drying rate on the dimensionless moisture content has been established. The dependence of the generalized drying time on the relative moisture content is given. Also, based on the analysis of the experimental data on the thermal conductivity coefficients for wet thermal insulation materials, the dependences of the thermal conductivity coefficients on moisture content and temperature have been established. As a result of solving the criterion heat transfer equation, the values of the heat transfer coefficients for the period of the decreasing drying rate are obtained. The values of the Biot criterion in the processes of drying porous ceramics and asbestos are determined, too. It has been determined that the ratio of the moisture content loss rate to the drying rate in the first period does not depend on the drying mode and is a function of the initial moisture content.

Current paper focusses on the mathematical simulation of thermo-fluidic unsteady flow in a magnetohydrodynamic (MHD) Couette channel containing novel (ZnO–Al2O3)-water hybrid nanofluid (HNF). The nanoparticles of zinc oxide(ZnO) and aluminium oxide(Al2O3) are supplemented to basefluid water in 1:1 ratio. The bottom wall of channel kept stationary and stretchable, while the top is set in uniform motion with convective cooling. A uniform magnetic field appealed normally to lower plate. The governed nonlinear partial differential equations(PDE) are integrated employing finite difference method (FDM). A comparison of effect of hybrid nanofluid versus nanofluid (NF) is performed. The effects of non-dimensional quantities namely, nanoparticle volume fraction(NVF), magnetic field, stretching parameter, Biot number and Eckert number are reported graphically. The results demonstrate that (ZnO+ Al2O3)-water HNF shows significant impact over ZnO–water NF on velocity and temperature in the Couette channel.

The study of non‐Newtonian fluid has gained more significant attention recently than ever due to its various applications in the associated discipline, among which is polymer processing. On the account of its application, this present work analytically investigates a steady‐state boundary layer flow on Walters' B fluid over a vertical plate, embedded in a porous medium. The model equations for momentum, heat, and mass transfer are transformed to the associated ordinary differential equation by suitable similarity variables which are executed by means of the homotopy analysis method. The results of various parameters encountered are discussed accordingly. The novel results showcase among others that various values of radiation parameters amplify the radiative flux, which intensifies the polymeric flow and magnifies the rate of heat exchange to the liquid. This increases the thermal energy and accentuates the temperature distribution, while the interaction of Biot number pioneers strong convective heating which overshoots the temperature of which its vast application is rooted in industries as well as technology disciplines for the drying of substances/components. [ABSTRACT FROM AUTHOR]

The purpose of this study is to explore the viscous dissipation stimulus on the steady convective magnetohydrodynamic shear thickening liquid stream across a vertically stretched sheet. The impact of thermic heat, first‐order velocity slip, and variable heat generation/absorption are considered and also ignored the effect of magnetic Reynold's number. We converted flow controlling equations into the set of dimensionless nonlinear ordinary differential equations by employing similarity variables to solve these coupled equations by R–K and shooting technique. The effect of different dimensionless variables on velocity, heat, friction factor, and local Nusselt numbers are presented through graphs and tables. Depreciation in velocity and growth in temperature distribution is detected when the Casson fluid parameter is increased. Temperature is the increasing function of the Eckert number. [ABSTRACT FROM AUTHOR]

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A stochastic computing approach is implemented in the present work to solve the nonlinear nanofluidics system that occurs in the model of atomic physics. The process converts the partial differential nanofluidics system with suitable level of similarities transformation into nonlinear systems of differential equations. For the construction of datasets, finite difference scheme (Lobatto IIIA) is applied through different selection of collocation points for nonlinear nanofluidics system having accuracy of order four. Lobatto IIIA has a strong point to tackle extremely nonlinear systems of ordinary differential equations in smooth way. For different scenarios, datasets are well trained through computing scheme to investigate the heat transfer and thermal performance of nanofluidic transportation system of nanofluids and hybrid nanofluids toward stretching surfaces with variation of Biot number, Nusselt number and skin fraction. Furthermore, the reliability, accuracy and efficiency are endorsed through various statistical analysis and graphical illustrations of proposed computing scheme. [ABSTRACT FROM AUTHOR]

The performance of nanofluid in the heat transport phenomena showed satisfactory results, which have been considered by scientists and researchers. The dispersion of two nanoparticles to form a mixture which named as hybrid nanofluid. It has been proved experimentally that hybrid nanofluid has good thermal performance compared to unitary nanofluid. The present study inspected the convective flow of a Williamson hybrid nanofluid through a cone and wedge in a porous medium of different shapes of nanoparticles (cylindrical‐, spherical‐, blades‐, platelets‐, bricks‐) under the influence of a magnetic field. The partial differential equations were converted to an ordinary differential equation and the resulting equations were solved using the bvp4c MATLAB code. The effect of some important physical parameters on both the velocity and temperature profile was graphically plotted and the effect of the shape and size of nanoparticles was discussed, the numerical values of the friction coefficient and Nusselt number were obtained. As observed, the friction factor of Ag–TiO2–H2O hybrid nanofluid was more than that of TiO2–H2O nanofluid. A significant enhancement in bulk temperature is seen for the Ag–TiO2 hybrid and nanofluid formed by blade‐shaped nanoparticles followed by cylindrical, platelet, brick, and spherical nanoparticles. In addition, for a 5% volume fraction of using blade nanoparticles shape givean increase in skin friction factor about 4.8% compared tobrick hybrid nanoparticles. A comparative study of different forms for Ag‐TiO2was presented graphically. [ABSTRACT FROM AUTHOR]

The impact of energy‐based volumetric internal heating and magnetic field‐dependent (MFD) viscosity on the onset of ferrothermal porous convection for different types of boundary conditions is investigated. The lower and upper boundaries are considered to be either rigid or stress‐free. The lower boundary is insulating, while at the upper boundary a Robin type of thermal condition is applied. Besides this, a general type of boundary conditions is invoked on the magnetic potential. The stability eigenvalue problem is solved numerically using the Galerkin‐type of weighted residuals technique with the Rayleigh number, Rt ${R}_{t}$ as the eigenvalue. The results obtained for different boundary combinations are found to be qualitatively similar though not quantitatively. The effect of Biot number, MFD viscosity, and porous parameters is to hinder, while the influence of internal heat source strength, magnetic number, and the nonlinearity of fluid magnetization is to advance the onset of convection. The rigid and conducting boundaries offer a more stabilizing influence on the onset when compared to stress‐free and insulating boundaries. The convection cells get contracted the most when the boundaries are rigid and also when the upper boundary is conducting. The results delineated under the limiting cases are found to be in good agreement with those available in the literature. [ABSTRACT FROM AUTHOR]

The present article describes the unsteady flow of a couple stress via a ternary hybrid nanofluid on a stretching surface with porous media. The nanofluid exhibits important properties for increasing heat transmission, and it is widely used in manufacturing and industrial applications. The basic similarity equations have been discovered to accommodate both stretching/shrinking surfaces. Ternary hybrid nanofluid is a colloidal combination of three types of microspheres: Al2O3, single wall carbon nanotubes, and graphene. For investigating spherical, cylindrical, and platelet nanoparticles, the governing partial differential equations are converted into ordinary differential equations, expending appropriate transformations. The analytical solution can then be carried out using various forms of nanoparticles, such as spherical, cylindrical, and platelet, to obtain the solution domain. Heat transfer is used in an electrically conducting fluid and also including thermal radiation, as calculated with the Biot number. The focus of the present effort is the evaluation of the flow of ternary hybrid nanofluid over a porous media via thermal radiation, with couple stress, using an analytical process. For various physical parameters, the velocity and temperature conditions are shown graphically. [ABSTRACT FROM AUTHOR]

The current paper aims to explain the peristaltic mechanism of a Bingham fluid with varying viscosity. The fluid is considered to flow within a porous medium and subjected to a magnetic field with significant inclination. Heat transfer characteristics are studied with convective conditions and variable thermal conductivity. The solution is obtained by the perturbation technique, where small values of variable liquid properties are utilized. The graphs plotted indicate that variation in viscosity as well as thermal conductivity actively contribute to reduce the pressure gradient. Further, for a higher radius of the plug flow region, a higher pressure rise occurs. The magnetic parameter and Grashof number influence the trapping phenomenon by reducing the dimensions of the bolus.

Brownian motion and thermophoresis impacts are discussed in relation to a tangent hyperbolic fluid encircling a sphere subject to a convective boundary condition and a Biot number. Concentration boundary conditions involving a wall normal flow of zero nanoparticles are an unexplored area of research. The governing non-linear BVP is transformed into a higher-order non-linear ODE using similarity transformations. Following equations were numerically solved for various values of emerging parameters using the matlab function bvp5c. Calculated values for velocity, concentration, temperature, the skin friction coefficient, Sherwood and Nusselt numbers are all shown, tabulated for analysis. Laminar boundary layer flow and heat transfer from a sphere in two-dimensional nano fluid is the novelty of the current work. The Weissenberg number decreases the velocity boundary layer thickness. The Biot number parameter lowers the field's temperature and speed.

This study focuses on the phase change behavior of a material subjected to an external heat transfer fluid. The work is based on a dimensionless study of heat flux involved during phase change, and a time-dependent boundary Robin condition is proposed to model the external heat transfer fluid. The charge/discharge cycles model relies on a time dependance of the external reference temperature, to represent successively the periods of phase change material melting (charge) and solidification (discharge). We chose an abrupt change in the external temperature to represent the action of an operator that switches between load and discharging periods. As the final shape of the tank will have an influence on the performances of charge and discharge, the simulations results, in terms of temperature, solid fraction and released heat flux, are presented for various Biot (B i) and Stefan (S t e) numbers that give information on time and magnitude of charged and discharged energies. The study shows that an increase of B i implies melting in a deeper thickness of PCM, higher values of temperature on the convective boundary condition and higher charged and discharged energies. An increase of S t e leads to higher temperatures on the convective boundary condition during charging periods, lower values during discharge and exhibits deeper melting during charge. Moreover, this energy varies during the cycles, and tends toward a constant value, this trend being fitted by a time function. The dimensionless study shows advantages concerning the material selection, but also drawbacks concerning the difficulty to highlight the specific temperatures (melting, external) when plotting the dimensionless form. • Storage and Discharge are modeled by a Robin condition to model an exchanger. • A dimensionless flux analysis is proposed through Biot and Stefan numbers. • A high Biot number increases the variations of discharged or charged heat. • A high Stefan number leads to low and rapid storage or discharge. • The dimensionless representation may lead to drawbacks when plotting some specific temperatures. [ABSTRACT FROM AUTHOR]