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This work gives an insight into the viscous effects of a viscoelastic fluid on the flow and heat transfer when it is put to flow between two nonparallel plates via some source/sink. Modeling of the problem is presented in detail with focus on the viscous dissipation effect. Afterwards, the problem is solved numerically by Keller Box method and bvp4c routine using MATLAB. The comparative analysis of the two techniques has been drawn on the basis of numerical values of Nusselt number. Alongside this, a comprehensive detail of the impact of pertinent parameters on the flow and temperature profiles have been given. The numerical results give an insight about the fluid characteristics like velocity, temperature, heat transfer and skin friction with variations in pertinent physical parameters. [ABSTRACT FROM AUTHOR]

This investigation focuses on the nanoparticle shape effect on the flow of conducting non-Newtonian Maxwell nanoliquid through an absorptive expanding surface. Insertion of inertial drag due to the Darcy–Forchheimer model and the dissipative heat in the flow phenomena supplements the work. The thermal properties of the fluid show its important role because of the use of various thermophysical models such as the Gharesim model of viscosity and the Mintsa model of thermal conductivity. The proposed mathematical model is designed by the implementation of suitable similarity transformations and then a numerical scheme is adopted to solve the transformed phenomena. In particular, shooting-based traditional Runge–Kutta (RK) fourth order is implemented for the solution. The behavior of the parameters that are participating in the flow phenomena is deployed via graphs and the computation of the engineering coefficients is displayed in tables. The impression of innumerable governing flow constraints is interpreted with the validation of these investigations with the earlier investigation. However, the major outcomes are; the particle concentration contributes its significant characteristics in enhancing the fluid velocity as well as temperature for the increasing shape. The dissipative heat formulated by the Eckert number also augments the fluid temperature in association with the thermal radiation whereas the unsteadiness parameter retards it significantly. [ABSTRACT FROM AUTHOR]

This study examines different fluid flow through an elaborated plate. In the modeling of the physical phenomena under investigation, the impacts of viscous dissipation, activation energy and chemical reaction are considered. Also, the heat transport phenomena are explained by the variable thermal conductivity theory. By using the right transformations, the flow-generating PDEs are converted into nonlinear ordinary differential equations. The parameters' impacts on the velocity, temperature and mass fields are analyzed in detail. The modeled problem is graphically handled in MATLAB using the numerical technique (BVP4c). Graphical representations of the important factors affecting temperature and velocity fields are illustrated through graphs. The findings disclose that the effectiveness of the velocity field is determined by the changing values of the magnetic parameter. The Prandtl values are decreased, the temperature profile becomes more pronounced. [ABSTRACT FROM AUTHOR]

Because of accelerated demands of advanced technologies like power station, chemical production and microelectronics, it necessitates the need of novel type of fluids with more heat transfer capability. Due to synergistic effect, ternary composite nanofluids (TCNFs) ensure better thermophysical and Rheology properties thereby acting as better suitable heat transfer fluid in wire coating, metal spinning, aerodynamics, medicine and engineering industries, etc. In view of such relevance, flow and heat transfer aspects of TCNF MWCNT + Al2O3 + TiO2 + water induced by linear and nonlinear slips over arbitrarily inclined moving thin needle are investigated in this study. Thompson and Troian nonlinear slip model is modified by developing it in polar coordinates. Quadratic thermal radiation phenomenon is adopted. Fourth-order Runge–Kutta method is used to obtain requisite numerical solution. Major outcomes indicate that fluid velocity of TCNF whittles down with amplification of magnetic parameter due to the flow induced by either linear or nonlinear slips. Lower value of Reynolds number favoring linear slip leads to effective intensification of nondimensional temperature distributions. Surface viscous drag and heat transfer rate get ameliorated with growth in size of thin needle under the influence of both linear and nonlinear slips. [ABSTRACT FROM AUTHOR]

The motivation of this paper is to explore an oscillatory flow of a magnetohydrodynamics (MHD) couple stress fluid with heat and mass transfer analyses through a porous medium. The modified Darcy–Brinkman couple stress fluid model is employed. There could be many potential applications of this study, such as thermal system, solidification of liquid crystals, cooling of metallic plates in a bath, exotic lubricants and colloidal solutions. In the wake of these potential applications, the study of MHD couple stress fluid flow with additional diffusing components has been found to be innovative and very interesting in the analysis of the influence of combined magnetic effects, couple stress fluid and two solutes. A governing coupled nonlinear partial differential equation with boundary constraints represents the modeled flow problem. In addition, these equations are converted into nondimensional form by employing the suitable nondimensionalizing quantities. It is possible to attain analytic solutions to the dimensionless equations that control the liquid flow, and the consequences of the flow's confines on velocity, temperature, concentration and skin friction profile are examined and also the results are discussed through graphs. It is noteworthy that when the injection level on the heated plate is increased, the skin friction on each channel plate also increases. [ABSTRACT FROM AUTHOR]

Steady flow of incompressible Maxwell–Sutterby fluid at stretching sheet is discussed in the presence of stagnation point region. The magnetic Reynolds number is considered very high and induced magnetic and electric fields are applied to the fluid flow. Temperature-dependent properties with radiation influence are considered in this analysis. The heat source or sink and melting impact are also debated in this analysis. A differential model of mathematics is developed by employing a governing constitutive equation. The differential equations' model is condensed and becomes ordinary differential equations by implementing the appropriate transformations. Furthermore, these equations are elucidated by the numerical scheme. The physical influence of physical parameters is exhibited in the graphs and tabular form. The escalating values of M cause a shear thinning attitude in the fluid; as a result, devaluation in the velocity is detected in the case of a / c = 0. 5 , while it depicted the counter behavior for a / c = 1. 5. The skin friction is heightened with improving values of Re because R e boosted which improved the viscosity of liquid as well as heightened the friction at sheet. The enhancing values of M p cause a decrement in skin friction. The melting parameter is enriched which reduces the viscosity of fluid due to temperature boosting as well as friction reduction. The diminution in skin friction is found for enhancing the values of β. [ABSTRACT FROM AUTHOR]

This paper intends to discuss the hybrid nanofluid flow through a cone in a Darcy–Forchheimer porous media, containing base fluid Methanol (CH3OH), nanoparticles of titanium oxide (TiO2) and copper (Cu). We have examined the flow under the influences of mixed convection, viscous dissipation, chemical reaction, and nonlinear heat source. In hybrid nanofluid flow, viscous dissipation and mixed convection play a crucial role in heat exchangers. By accounting for both mixed convection and viscous dissipation, the addition of nanoparticles into a base fluid improves the transfer of heat and optimizes the performance of the cooling system. Using the laws of conservation, governing equations have been constructed. The flow model is converted using the appropriate similarity transformations from partial differential equations to ordinary differential equations. The homotopy analysis method is used to solve the updated system of equations. When Forchheimer inertial drag parameter is increased, the velocity profile decreases, but it rises when the Darcy number is increased. As the value of exponential heat source parameter rises, the temperature profile increases as well. The result exposes that with an increment in nanoparticle volume fraction, temperature profile also rises but velocity profile decreases. [ABSTRACT FROM AUTHOR]

Variable permeability plays a crucial role in various manufacturing and technical applications such as fixed-bed catalytic reactors, heat exchangers, and dying, among others. The primary focus of this paper is to investigate the impacts of variable permeability on hybrid nanofluid (HNF) flow due to nonlinear sheet stretching with thermal heat flux. The HNF is made up of a mixer of TiO 2 and Fe 3 O 4 nanoparticles and water serving as the base fluid. Using efficient similarity transformations, the flow-governing equations are converted into a set of ordinary differential equations, and the resulting system is computationally solved by using the MATLAB program (bvp4c). The impact of various physical variables on the fluid velocity and heat transfer characteristics is analyzed via graphs. It is found that as the permeability parameter rises, the velocity of the HNF diminishes while the temperature amplifies. The drag force coefficient declines with an intensification of the volume fraction of the Fe 3 O 4 nanoparticles. The HNF ( TiO 2 + Fe 3 O 4 ∕ H 2 O) exhibits 0.45–0.75% increase in heat transfer rate when compared to a nanofluid ( Fe 3 O 4 ∕ H 2 O) for different values of heat source parameter. The current investigation is compared to the existing literature, revealing a good level of agreement. [ABSTRACT FROM AUTHOR]

The heat transfer characteristics of nanofluid play an important role in several industries to optimize their performance with the interaction of dissipative heat. However, in energy harvesting its application is vital. Therefore, the current heat transfer analysis was carried out based on the consequence of viscous and Joule dissipation in favour of the hybrid nanofluid flow over an elongating permeable curved convective thermal surface. Additionally, the external heat source and linear thermal radiation influence the flow phenomena whenever the velocity slip and nanoparticle shape effects associated with Hamilton–Crosser thermal conductivity model are significant. The designed equations relating to the flow phenomena are solved numerically using shooting-based Runge–Kutta fourth techniques followed by the similarity transformations used for the nondimensional form of the system of equations. The role of characterizing factors is deployed via graphs and described briefly. The correlation with the earlier investigation for the numerical outcomes of the rate of energy transport is also reported. The major outcomes of the study reveal that the enhanced curvature parameter along with the particle concentrations within their limit overshoots the velocity profiles further, the external heat source combined with thermal radiation also favors in enhancing fluid temperature. [ABSTRACT FROM AUTHOR]

The analysis of heat transfer of a hybrid nanofluid ( Al 2 O 3 − Cu ∕ H 2 O) in the MHD stagnation point motion toward an exponentially expanding/shrinking sheet with a nonuniform heat source/sink, multiple slip conditions and nonlinear thermal radiation effects are carried out in this study. By applying the similarity transformation, the governing equations are transformed into Ordinary Differential Equations (ODEs). The Runge–Kutta method using bvp4c in MATLAB software is implemented to explain the ODEs. The results show that the local Nusselt number is decreased while the skin friction coefficient remains unaltered by the accumulation of thermal slip, space, and temperature-dependent parameters. [ABSTRACT FROM AUTHOR]

Nanofluids, characterized by the dispersion of nanoparticles in a base liquid, have attracted significant attention in recent years due to their exceptional thermal properties. Specifically, the specific heat capacity of nanofluids plays a crucial role in the design and optimization of heat transfer systems. Traditional experimental methods for determining the specific heat capacity of nanofluids are often limited in terms of cost, time, and operating condition ranges. To address these limitations, this research focuses on the development of a novel predictive model for estimating the specific heat capacity of nanofluids. This study aims to develop a machine learning regression model called Gradient Boost Regression (GBR) with Grid Search optimization (GSO) for accurately predicting the specific heat capacity of aluminum nitride (Al2N3) nanoparticles that are suspended in both water and an ethylene glycol (EG) solution. The GBR-GSO model capitalizes on the strengths of GBR, which can effectively capture complex relationships, and GSO, a metaheuristic optimization technique inspired by the law of gravity. By integrating these two approaches, we aim to create a robust and accurate predictive model for specific heat capacity in nanofluids. To develop and validate the GBR-GSO model, a diverse dataset based on experimental-specific heat capacity collected from the literature has been designed. The performance of the model has been evaluated by comparing its predictions with experimental data. The GBR-GSO model achieved 99.99% accuracy with the experimental data of specific heat capacity. This research contributes to the advancement of nanofluid-based heat transfer systems by providing an effective tool for predicting the specific heat capacity of nanofluids. The developed model can facilitate the design and optimization of various engineering applications, leading to the development of energy-efficient and sustainable technologies. [ABSTRACT FROM AUTHOR]

The study offers a thorough evaluation of the complex fluid dynamics and heat transfer phenomena in Williamson viscoelastic fluid flow, taking into account thermal radiations and variable thermal conductivity. The paper extends its analysis to include heat transfer effects, which are critical in several engineering and industrial applications, and digs into the complexity of non-Newtonian fluid behavior, with a special focus on thermal radiation, heat production, diffusion and viscous dissipation. The study makes use of mathematical models and numerical method RK4 to clarify the nonlinear interactions between convection and diffusion processes in this viscoelastic fluid. The energy and concentration equations are simulated in the presence of the modified Fourier and Fick laws. Moreover, the predicted heat flow is based on the Cattaneo–Christov theory. This research also sheds light on the interaction between rheological properties and thermal characteristics, providing important new knowledge to the broader field of fluid dynamics and heat transfer. [ABSTRACT FROM AUTHOR]

This research offers an analysis of the mixed convective transient boundary film Casson fluid stream and thermal distribution through a vertical sheet. Viscous dissipation and the Soret effect are introduced to support the flow in stimulating heat capacity. Unlike typical investigations, the present flow-formulated model is done to capture an induced magnetic field. The Boussinesq approximation is used to describe the nonlinear formulated partial derivatives governing the heat transfer fluid that is non-dimensionalized using suitable dimensionless quantities. The transformed partial derivative model is numerically solved via the spectral Chebyshev technique and the results of shear stress, current density, Nusselt number, and mass gradient are tabulated. The role of numerous terms on dimensionless flow rate, induced velocity, and heat transfer with species distribution is discussed in a very effective way. Velocity and temperature of liquid decline as boosting the material parameter. Enhancing values G r , G r m favor the flow momentum and oppose the temperature profile. [ABSTRACT FROM AUTHOR]

The Casson viscous gas fluid flow with mass transpiration and radiation is demonstrated in this paper. A similarity transformation is utilized to interpret the representing construction of nonlinear PDEs by nonlinear ODEs. Then, using an exact analysis of the momentum equation, we constructed the dual solutions to the flow problem. This solution domain aids in the solution of the energy equation under the incomplete gamma function condition. The effect of radiation can also be seen in the heat equation. Physical parameters of interest, such as Brinkman number, porous media, thermal radiation number, induced slip, suction/injection and shear stress, are examined and graphically depicted. The gas slip velocity is used to simulate the slip flow model of the overall mass transfer on the moving sheet. Models of first- and second-order slip are introduced to induce the total mass transfer on the moving sheet. Additionally, the suction that causes the slip velocity rather than surface movement is investigated. The neighboring gases are forced to flow in the opposite direction of sheet movement by the mass suction-induced slip. As a result, the slip-induced suction and sheet movement cause the solution space to increase. The closed-form exact solutions are achieved for both the stretching and shrinking sheet cases. For stretched sheet instances, there is never a uniform solution. However, depending on the values of the Casson and wall mass transfer parameters, the solution in the case of the shrinking sheet may or may not exist, and if it does, it may or may not be unique or may have a dual nature. The research also demonstrates that stronger mass suction is required for a consistent flow of Casson fluid. The impacts of inverse Darcy number, induced slip parameter, Casson fluid and suction/injection on the flow and heat transfer properties of the fluid are examined under the influence of radiation, and the solution of each profile is shown in the form of figures along with the outcomes of the interface velocity and heat transfer rate at the surface. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids have unique characteristics that make them more useful than common heat transfer fluids. The potential applications can be found in applied thermal engineering, chemical engineering, hybrid powered engines, biomedical and mechanical engineering. Therefore, the analysis of SWCNTs–MWCNTs/C2H6O2–H2O with integrated effects of thermal radiations and perpendicular magnetic field is organized in this research. Thermal conductivity of C2H6O2–H2O is improved via Xue, Ota and Yamada thermal conductivity correlations. The mathematical problem is designed for two sheets and both the hybrid nanoliquid and the plates rotate in counter clockwise pattern. Mathematical treatment of the model is performed and the results were analyzed through graphical way. Keen observations of the results reveal that the fluid motion controlled by intensifying the magnetic field and higher density of SWCNTs–MWCNTs leads to optimum decrement. Further, the fluid movement is investigated optimum and slow for outward and inward plate movement, respectively. The temperature results for the parameters, especially the thermal radiations, showed that hybrid nanoliquid has the ability to store high thermal energy than common mono-nanoliquid, hence it would be suitable for future industrial applications. The parametric ranges are selected as A 1 = 0. 1 –1.7, α 1 = 0. 1 –0.9, M = 1. 0 –9.0 and Ω = 0. 0 –20.0 for the study. [ABSTRACT FROM AUTHOR]

In this research paper, we numerically analyze the flow and heat transfer rate of non-Newtonian pseudo-plastic nanofluid with variable apparent viscosity and thermal conductivity effects, respectively, through annular sector duct. Concentric pipes annular sector duct of an apex angle, 2 β and ratio of radii, R ̂ , is filled with saturated porous media. For this purpose, we utilize the power law Darcy–Brinkman flow model along with Forchheimer term. Also, the contribution of nanoparticles is accounted in carboxy methyl cellulose (CMC)-water, which has been taken as base fluid. Finite volume method (FVM) is utilized to discretize the governing mathematical model, whereas algebraic equations are solved numerically by using strongly implicit procedure (SIP). With the help of graphs, the impacts of nanoparticles' contribution and porosity factor have been discussed by giving physical interpretation. Results are also found in the limiting sense and show the good agreement with already published data. At β = π / 3 , ϕ = 0. 1 0 , D a = 0. 0 1 and R ̂ = 0. 2 5 , we can observe down in f Re and Nu upto 5. 6 5 8 % and 1 0. 0 1 % , respectively, when n decreases from 1 to 0. 9 1 , whereas 1 3. 4 7 % and 2 3. 5 7 % , respectively, by decreasing the value of n from 1 to 0. 7 6. For both cases of nanoparticles' contribution, the downs in Nu have been observed same by decreasing the value of n. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the forced convective heat transfer of power-law fluid flow through porous annular sector duct by applying the Brinkman-extended Darcy flow model. A strongly implicit procedure (SIP) is utilized to solve the algebraic momentum and energy equations which was discretized by using the finite volume method (FVM). The effects of permeability factor and power-law index corresponding to the Brinkman-extended Darcy flow model and power-law fluid, respectively, on flow and heat transfer rate are carried out numerically and graphically against different values of parameters corresponding to geometrical configuration. In the pseudo-plastic fluids, a maximum decrease of more than 1 0 0 % has been observed in f Re , whereas maximum decrease in dilatant fluid is around 3 0 % , when we increase the values of k. A decrease of 16.02% in Nu has been carried out in pseudo-plastic fluid, whereas unforeseen decrease in Nu has been observed in both Newtonian and dilatant fluids comparably pseudo-plastic fluid for particular values of k. [ABSTRACT FROM AUTHOR]

The increasing number of ways in which carbon nanotubes (CNTs) may be used in business and technology has led to an explosion of interest in these tiny tubes. As a result, the Yamada–Ota model is used to investigate the unsteady, non-axisymmetric MHD Homann stagnation point of carbon nanotubes passing over a convective surface with nonlinear radiation. Consisting of single-walled and multi-walled carbon nanotubes that are suspended in water (H2O). The length of the nanomaterial is between 3 μ m ≤ L ≤ 7 0 μ m nanometers, while its radius is between 1 0 nm ≤ R ≤ 4 0 nm. The method of similarity transformation is altered so that it may be used to get the dimensionless system of differential equations from the mathematical model that is envisioned for PDEs. After that, approximate solutions are obtained using MATHEMATICA and the Shooting with RK-IV technique. In this paper, we provide a graphical discussion and a physical interpretation of the results of measures of practical significance as a function of key factors. The results indicated that an increase in the volume fraction led to a corresponding rise in the heat transfer rate. However, it is reduced by the magnetic energy that is supplied to it. Carbon nanoliquids with a single wall have a greater melting point than nanoliquids with multiple walls. Industrial and technological uses of the issue under examination span several fields, including aviation and health. The results of the interface velocity and heat transfer rate at the surface, as well as the solution of each profile, are shown graphically, along with an analysis of the effects of MHD on the flow and heat transfer characteristics of the fluid under the influence of radiation. [ABSTRACT FROM AUTHOR]

An analysis is carried out to investigate the influence of the magnetic field over Carreau fluid flow and heat transfer in a liquid film on an unsteady stretching surface. The governing equations are converted to a system of boundary value problem (BVP) by using the similarity transforms. The differential equations are solved numerically using the modified Laplace decomposition method (MLDM) and the obtained results are compared with the existing schemes. An excellent agreement between them illustrates the accuracy of MLDM to the suggested model. The influence of the dimensionless governing parameters like magnetic field number, Prandtl number, unsteadiness parameter, Weissenberg parameter, and radiative number on velocity and temperature profiles is discussed in tabular form and shown through illustrative graphs. [ABSTRACT FROM AUTHOR]

This paper examines the heat transfer characteristics of magnetohydrodynamics (MHD), suction, and Marangoni convection under the stretching/shrinking Ag–Cu hybrid nanofluid surface flow. First, the governing partial differential equations (PDEs) were transformed into ordinary differential equations (ODEs), and the numerical result was obtained using the boundary value problem solver (bvp4c) in MATLAB. The development of the Nusselt number, the velocity profile and the temperature profile was plotted, discussed and inspected. Next, this paper undergoes stability analysis and heat transfer rate comparison between water, nanofluid and hybrid nanofluid. The dual solutions were observed, and the upper branch solution is determined to be stable. Compared to water, the heat transfer rates of Ag–Cu hybrid nanofluid and Cu nanofluid were accelerated by 2.84% and 2.75%, respectively. [ABSTRACT FROM AUTHOR]

This work is based on a numerical simulation to study the flow pattern and heat transfer characteristics inside a cavity in the form of an Islamic knot. The effect of height and length of the obstacle are investigated. Nine different obstacles with different lengths (a) and heights (b) are considered. It can be found that the variation in length and height of the hot obstacle leads to the obvious change in the flow field and temperature field. In addition, the small gap inside the cavity has a limited effect on the flow motion. Besides, the small gap between the cold and hot surfaces leads to higher conduction heat transport. For high Ra, the flow and heat transfer characteristics can be described in two situations. The first is included in the cases of (a , b) = (1 0 , 1) , (10, 2) and (10, 3), where the primary vortices are located on the top and bottom of the cavity. The second one consists of cases (a , b) = (3 , 3) , (4, 3), (5, 3), (6, 3), (7, 3) and (8, 3), where the primary flow circulations are established on the left and right sides. For all the cases, the average Nu increases by rising the Ra. By increasing the Ra, the average Nu in the second situation increases more significantly than that in the first one. The cases in the second situation always have better heat transfer performance than those in the first one, especially at higher Ra. [ABSTRACT FROM AUTHOR]

Over the last 10 years, heat transfer performance in immediate cooling and heating applications has grown into the foremost concern for heat transfer practitioners in Engineering and manufacturing practices. Henceforward, the study in new heat transfer fluids is extremely intense and challenging. This study examines flow and thermal management in axisymmetric hydrodynamic pure water-based hybrid solid nanoparticles in a flow induced by a swirling cylinder with Fourier Heat source. Flow and heat transfer are analyzed and compared for CNT+Graphene+Al 2 O 3 and Paraffin wax+Sand+AA7072 hybrid nanofluid flow. Shooting technique (R-K 4th order) is applied to work out the flow equations numerically. Simulated results are exhibited through graphs and tables. The computational results are statistically validated with the published research work and a modest concurrence is found. The main outcome of this study is found to be in Multi-regression analysis, where the Λ w.r.t Pr has higher domination compared to Φ w.r.t Pr. Also, it is interesting to know that Φ w.r.t Re has more rate of heat transfer compared to Φ w.r.t M. As the volume fraction rises, the size of the particle is less and Reynolds number dominated the flow, due to this, a decrement is seen in the friction values. Overall, it is observed that heat transfer rate is higher in CNT+Graphene+Al2O3 compared with Paraffin wax+Sand+AA7072. [ABSTRACT FROM AUTHOR]

In recent years, a novel technique for producing robust cementitious materials, called nanocomposites, has emerged. These materials are comprised of clay minerals and polymers. As a result, a vertical flat plate has been used to evaluate a clay-based cementitious nanofluid in this research. The impacts of first-order chemical reactions, heat generation/heat absorption, and the Jeffrey fluid model are taken into account for the study of flow. Newtonian heating and the conditions for slippage velocity have also been considered. The mathematical problem for the flow analysis has been established in relations of partially coupled partial differential equations and the model has been generalized using constant proportional Caputo (CPC) fractional derivative. The problem is solved using the Laplace transform technique to provide precise analytical solutions. On the concentration, temperature, and velocity fields, the physics of a number of crucial flow parameters have been examined graphically. The acquired results have been condensed to a very well-known published work to verify the validity of the current work. It is important to note here that the rate of heat transfer in the fluid decreases by 10.17% by adding clay nanoparticles, while the rate of mass transfer decrease by 1.31% when the value of ϕ reaches 0.04. [ABSTRACT FROM AUTHOR]

This paper discusses the impacts of velocity, temperature, and solutal slip on the mass and heat transfer characterization of MHD mixed convection Casson fluid flow along an exponential permeable stretching surface with chemical reaction, Dufour and Soret effects. The Casson fluid is supposed to flow across an exponentially stretched sheet, together with the exponential temperature and concentration fluctuations of the fluid. As governing equations, the momentum, energy and species concentration equations are constructed and represented as PDEs. Following that, these equations were converted via the similarity transformation into ODEs. Finally, the ODEs are numerically solved using the Keller-box method with MATLAB software's algorithm. Expressions are produced for the fluid flow, temperature and concentration gradients. We also determined the physical variables from which the friction factor, rate of mass and heat transfer are attained for engineering purposes. Using graphs and tables, the impacts of altered physical characteristics on flow amounts are explored. The consistency and validity of our outcomes revealed a significant degree of agreement when comparing them to previously published studies. The findings reveal that raising the Soret and Dufour parameter enhances the velocity profile at the wall, but the converse is true for increasing the velocity slip factor. [ABSTRACT FROM AUTHOR]

Nowadays, the heat thrust liquid electric heater is generally used in profitable applications since it protects upto 2–3 times the energy of ordinary liquid electric heater. The heat pump makes use of a refrigerant for its process. The small-temperature refrigerant engrosses permitted heat from full of atmosphere midair in the evaporator which is crushed by an extremely well-organized electrical compressor to an extraordinary-temperature and high-pressure vapor refrigerant. For entire heat transfer connoisseurs, heat transfer performance in cooling and heating applications has become a top priority. Hence, research towards new heat transfer fluids is extremely intense and challenging. This investigation examines flow and heat transfer analysis in axisymmetric magnetohydrodynamic flow polyethylene glycol (PEG)-based nanofluid, hybrid nanofluid and ternary hybrid nanofluid flow induced by a swirling cylinder. Flow and heat transfer are analyzed and compared for three cases PEG-based copper oxide, magnesium oxide and zirconium oxide ternary nanofluid (PEG + ZrO2 + CuO + MgO), PEG-based copper oxide (PEG + CuO) nanoparticles and PEG-based zirconium and magnesium oxide hybrid nanofluid (PEG + ZrO2 + MgO). Shooting technique (R–K fourth-order) is employed to work out the flow equations numerically. Simulated results are displayed through graphs. The computational results are validated with the published research work and a modest concurrence is found. The main outcome of this study is found to be as follows: It is interesting to note that C f x Re (x R) is lesser in nanofluid case compared with ternary and hybrid nanofluid cases. It is found that C f ϕ Re (G H R) is more in ternary hybrid nanofluid compared with hybrid and nanofluid cases. Overall, it is observed that heat transfer rate is higher in nanofluid compared with ternary and hybrid nanofluid cases whereas lesser rate of heat transfers in ternary nanofluid case. [ABSTRACT FROM AUTHOR]

In the research of porous media and the interior of microelectronic devices, fluids frequently shuttle among pores and wall cracks, therefore it is of great significance to explore the influence of media wall on fluid flow and heat transfer. In this paper, CFD-DSMC coupled iterative algorithm is first used in the research of the flow and heat transfer of gas near the wall in the porous media, which simplified into the flow and heat transfer in micron-scale tube with smooth and rough wall conditions. It is found that compared with the pure CFD method, the velocity field obtained by the coupled method is quite different in the region close to the wall, and this will affect the flow field in the mainstream region, that is, with the higher roughness of the wall, the velocity in the central region will be smaller. There is no significant difference in the temperature distribution in the microtube before and after coupling, but the temperature in the mainstream decreases with the increase of the roughness of the wall. In addition, the temperature jump was found from some of the coupling results close to the wall. The results will contribute to a deeper understanding of the influence of rough surfaces on gas flow and heat transfer near the wall, and provide guidance for the regulation of flow and heat transfer in porous media. [ABSTRACT FROM AUTHOR]

In recent years, physics-informed neural networks (PINNs) have come to the foreground in many disciplines as a new way to solve partial differential equations. Compared with traditional discrete methods and data-driven surrogate models, PINNs can learn the solutions of partial differential equations without relying on tedious mesh generation and simulation data. In this paper, an original neural network structure PINN-FFHT based on PINNs is devised to solve the fluid flow and heat transfer problems. PINN-FFHT can simultaneously predict the flow field and take into consideration the influence of flow on the temperature field to solve the energy equation. A flexible and friendly boundary condition (BC) enforcement method and a dynamic strategy that can adaptively balance the loss term of velocity and that of temperature are proposed for training PINN-FFHT, serving to accelerate the convergence and improve the accuracy of predicted results. Three cases are predicted to validate the capabilities of the network, including the laminar flow with the Dirichlet BCs in heat transfer, respectively, under the Cartesian and the cylindrical coordinate systems, and the thermally fully developed flow with the Neumann BCs in heat transfer. Results show that PINN-FFHT is faster in convergence speed and higher in accuracy than traditional PINN methods. [ABSTRACT FROM AUTHOR]

With the help of commercial software, we have discussed the novel numerical simulations for a two-dimensional rectangular cavity with two square rotating obstacles, Fig. 1, that has fixed dimensions from the reference point (0, 0) placed in it, and we have interpreted a detailed convection analysis for fluid flow that highlights the physical, mathematical and numerical aspects of this system. The square obstacles having an anti-clockwise rotation are heated to a certain temperature, respectively, where the behavior of the fluid distribution depends upon the values of Reynolds number. We have conducted this research by fixing Reynolds number at four different positions like Reynolds 10, 30, 50 and 80. The prime effects of Reynolds number and Prandtl number are highlighted for convection analysis. Finally, we have analyzed the results of velocity, pressure, vorticity and temperature from the viewpoint of numerical simulations. Heat transfer has a huge dependence on the Reynolds number and Prandtl number. [ABSTRACT FROM AUTHOR]

The progress in new inventions in the modern technological world demands outstanding heat transport. Unfortunately, common solvents are unable to produce such desired amount of heat which compelled the scientists and researchers towards the development of new heat transfer fluids (Nanofluids). Therefore, the study of C8H 1 8 with hybridization of [(MnZnFe2O4–NiZnFe2O 4) ] hnps under novel effects of thermal radiations and convective heat conditions over a slippery permeable surface is organized. The modified thermophysical correlations for hybrid nanofluids were used and successfully achieved the modified heat transfer model. After numerical investigation, the results were plotted under varying parameters and provided for comprehensive discussion. The results revealed faster fluid motion and G ′ (η) is dominant. The velocities drop significantly due to the permeability of the surface. Further, thermal radiations potentially boost heat transfer by providing extra energy to fluid particles. The temperature coefficient β w due to nonlinear thermal radiations also indicated faster heat transport. [ABSTRACT FROM AUTHOR]

The enhancement of the heat transfer of fluids is a very important task in engineering and technology which can be accomplished through the hybrid nanoparticles. In this theoretical investigation, the natural convection flow of nanoliquid through a square container is examined under the impacts of thermal boundary conditions. The considered nanoliquid is a combination of titanium alloy Ti6Al4V (class of titanium) and aluminum alloy AA7075 (class of aluminum) nanoparticles and water as a base fluid. Aluminum alloys are commonly used in household wiring and manufacturing of wheels, etc. The titanium alloy Ti6Al4V is commonly acknowledged as the "workhorse" of titanium which is extensively used in aerospace and biomedical engineering. The mathematical model is developed in the form of nonlinear partial differential equations and later transformed into dimensionless form. The resultant dimensionless set of equations is simulated numerically by using the eminent finite element method (FEM). The iterative Newton's Raphson method is used to get the optimal solutions. The stream function and temperature contours are displayed against the Rayleigh number and nanoparticle volume friction. The variation of local and average Nusselt numbers is also plotted. The outcomes revealed that water-based titanium alloy is the best choice to enhance the heat transfer rate in the cavity. The results obtained in this investigation are very important in engineering research, academic, and discussion about the heat transfer analysis with these two types of alloy nanoparticles inside the cavity flows. [ABSTRACT FROM AUTHOR]

The dissimilar multi-scale structures of shale to conventional reservoirs make it a challenge to understand the fluid flow and heat transfer through unsaturated shale formations. In this paper, the pore structure and moisture content of shale samples are measured by low-field nuclear magnetic resonance technique and thermogravimetric differential scanning calorimetry test, respectively. A pore-scale model is accordingly developed for the immiscible two-phase fluid flow and heat conduction through unsaturated shale based on the statistically self-similar fractal scaling law of pore size distribution. The analytical expressions of effective and relative permeability, as well as effective thermal conductivity (ETC), are proposed, which indicate good agreement with experimental results. It has been shown that the capillary pressure and gas slippage play important role in multiphase flow through unsaturated shale. Both pore and tortuosity fractal dimensions show significant influence on the relative permeability for nonwetting phase (RPNW), while they indicate the marginal effect on the relative permeability for the wetting phase (RPW). The ETC decreases with the increase of pore and tortuosity fractal dimensions, and it is positively and negatively correlated with RPW and RPNW, respectively. The correlation between ETC and relative permeability is found to follow a logistic function. The present fractal model can characterize the multiscale structures of shale reservoirs and may help understand transport mechanisms of immiscible multiphase flow and heat transfer through unsaturated shale. [ABSTRACT FROM AUTHOR]

In this paper, we focused on time-dependent flow of micropolar fluid between parallel permeable plates. Fluid is electrically conducting. Magnetic field is applied in the transverse direction to flow. Energy equation is modeled in the presence of viscous dissipation, thermal radiation and Joule heating. Suction is considered at lower plate while injection is considered at upper plate. Appropriate dimensionless variables are employed to reduce the governing PDE's system into dimensionless one. Nondimensional PDE system is tackled numerically by finite difference technique. Effects of flow parameters on velocity, micro-rotation, temperature, couple and shear stresses at plates and Nusselt number are discussed. The obtained outputs show that for nonzero electric field parameter the velocity increases with Hartmann number. For zero electric field parameter the velocity decreases with Hartmann number. Temperature increases with both electric and magnetic field parameters. Micro-rotation decreases with micro-rotation material parameter and it increases with time. [ABSTRACT FROM AUTHOR]

This paper contains natural convection of Ag–MgO/water micropolar hybrid nanofluid in a hollow hot square enclosure equipped by four cold obstacles on the walls. The simulations were performed by the lattice Boltzmann method (LBM). The influences of Rayleigh number and volume fraction of nanoparticle on the fluid flow and heat transfer performance were studied. Moreover, the effects of some geometric parameters, such as cold obstacle height and aspect ratio, were also considered in this study. The results showed that when the aspect ratio is not large (AR = 0. 2 or 0.4), at low Rayleigh number (103), the two secondary vortices are established in each main vortex and this kind of secondary vortex does not form at high Rayleigh number (106). However, at Ra = 1 0 6 , these secondary vortices occur again in the middle two vortices at AR = 0. 6 , which is similar to that at Ra = 1 0 3 . At AR = 0. 2 , the critical Rayleigh number, when the dominated mechanism of heat transfer changes from conduction to convection, is 104. However, the critical Rayleigh number becomes 105 at AR = 0. 4 or 0.6. When the cold obstacle height increases, the shape of the vortices inside the enclosure changes due to the different spaces. Besides, at Ra = 1 0 6 , for different cold obstacle heights, the location of the thermal plume is different, owing to the different shapes of vortices. Accordingly, the average Nusselt number increases by increment of the Rayleigh number, nanoparticle volume fraction, cold obstacle height and aspect ratio. [ABSTRACT FROM AUTHOR]

The heat transfer through the thermal radiation is very significant in many industrial processes, biomedical engineering, technological devices and thermal therapeutic process. These comprise nuclear power plants, propulsion of rockets, missiles, satellites and space vehicles, photochemical reactors, solar collector performance, heat exchangers. The boundary layer flow and the heat transport of dusty liquid over a stretching cylinder are discussed. The impact of nonlinear thermal radiation is explored. Cattaneo–Christov heat flux model is considered to formulate the energy equation. The resulting equations of the physical system are converted into a system of nonlinear ordinary coupled differential equations with the help of suitable similarity transformations and numerically solved by using Runge–Kutta–Fehlberg's method along with shooting technique. The influence of nondimensional parameters is analyzed and interpreted graphically. The heat transfer rate and local coefficient of skin friction are also calculated for diverse nondimensional constraints and plotted. [ABSTRACT FROM AUTHOR]

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement. [ABSTRACT FROM AUTHOR]

Machining with minimum quantity lubrication (MQL) or minimum quantity cooling (MQC) as a subset of green machining is a process in which small volume fluid of high lubrication and cooling properties alongside high pressure air is used in the material removal process. The heat generated in the grinding process has a great impact upon the workpiece quality. Serving lubrication and heat transfer functions, cutting fluids have an essential role in reducing the temperature and thus improving the process of grinding. In this research, nanofluid made of graphene nanoparticles in water-based fluid as a cutting fluid of high heat transfer is utilized to investigate the effects of nozzle number and nozzle geometry of the MQC system on the cutting temperature and surface roughness of the workpiece. The effect of geometry and number of nozzles on grinding with MQC has not been studied so far. The study findings show that the nozzle outlet cross-section of rectangular, compared to circular, decreases the surface roughness and temperature by 30% and 36%, respectively. Moreover, compared to the single nozzle, the use of three nozzles results in a decrease of 19% and 31.7% in the surface roughness and temperature. Under the same machining conditions, the MQC method by 0.15 wt.% nanofluid of graphene in water using a rectangular nozzle outlet of 1.2 mm width makes surface roughness and temperature reduced by 67.2% and 48.3% compared to the dry condition, whereas decreased by 13.4% and 8.8% compared to the wet method, respectively. [ABSTRACT FROM AUTHOR]

By establishing a three-dimensional (3D) numerical simulation of the Ti-6Al-4V Gas Metal Argon Welding (GMAW) molten pool, the molten pool's heat transfer and fluid flow behavior under a longitudinal magnetic field were investigated. The simulation results show that when the droplet enters the molten pool, the liquid metals on the molten pool's surface symmetrically flow towards both sides of the molten pool from different angles. With the increase of the magnetic field strengthens, the temperature gradually decreases, and the fluid flow velocity increases continuously. Besides, the magnetic field strength is correlated positively with the molten pool's size with a certain range of 0–0.03 T. However, when the magnetic field strengthens reach 0.04 T, the magnetic field is correlated negatively with the molten pool's size. Because the Marangoni and buoyancy begin to weaken, the molten pool's length change occurs before the width change. Simultaneously, a sizeable velocity region appears on the left side of the molten pool. Thus, the liquid metal gathers on the left side, resulting in the weld cross-section's asymmetry. It can conclude that only when the magnetic strengthen keeps in the range of 0–0.03 T, the longitudinal magnetic field can make the molten pool's surface profile smooth. [ABSTRACT FROM AUTHOR]

To evaluate the heat transfer performance (HTP) of hybrid nanofluids, numerical simulations are carried out in an industrial length single pass shell and tube heat exchanger. In shell, ISO VG 68 oil enters with 7 5 ∘ C and with 3 0 ∘ C, the coolant passes into the tube. CNT- TiO 2 /water and CNT- TiO 2 /sodium alginate (SA) are used as Newtonian and non-Newtonian hybrid nanofluid, respectively. The influence of base fluid and nanoparticles on thermal performance of heat exchanger is studied. The chosen nanoparticles are reliable to the industrial deployment. The current numerical procedure is validated with the earlier experimental results. Volume fraction of nanoparticles is optimized for an effective HTP of the heat exchanger. About 60% increment in heat transfer coefficient is observed when hybrid nanofluid is employed. By using Newtonian hybrid nanofluid, 50% improvement in Nusselt number is marked out. Effectiveness and heat transfer rate of heat exchanger are higher with the employment of Newtonian hybrid nanofluid. Results indicated that, even though Newtonian hybrid nanofluid shows higher thermal performance, non-Newtonian hybrid nanofluid is preferable for energy consumption point of view. [ABSTRACT FROM AUTHOR]

A numerical solution for steady-state, incompressible, laminar Casson fluid flow and heat transfer in the combined region of a boundary layer is presented for the case of mixed convection and slip velocity. Before introducing the present technique of non-Newtonian Casson model, reviewing the literature has been carefully performed, an improved technique for this model is studied, which has not been previously reported. The presented analysis involves the harness of a magnetic field, viscous dissipation, internal heat generation/absorption and the slip velocity. Finite difference method (FDM) has been used to get an accurate and complete numerical solution. In this novel study, it is proved by means of a finite difference technique, that the velocity and the thermal field may be influenced with the presence of mixed convection phenomenon. The results show that both the fluid velocity and temperature may be predicted from the values of the controlling parameters. Finally, the graphical output reveals that the fluid velocity is diminished by strengthening both the Hartman number and the Casson parameter while the reverse characteristics are observed for the Grashof number. [ABSTRACT FROM AUTHOR]

The thermal efficiency of the heat exchanger is substantial in chemical and mechanical systems. The presence of the non-homogeny magnetic field considerably enhances the heat rate of nanofluid stream. In this exploration, the presence of the non-uniform magnetic intensity on the heat rate of nanofluid stream is noted inside the 1 8 0 ∘ elbow pipe. FVM is used to model the flow characteristics and temperature distribution through the 1 8 0 ∘ elbow pipe. Our major focus is to demonstrate the main influences of the non-uniform FHD on flow stream and heat transfer of nanofluid in various inlet velocities and magnetic intensities. Achieved outcomes display that growing the magnetic intensity from 1e + 6 to 4e + 6 enhances the average Nusselt number about 30%. Our findings show that increasing the inlet velocity to Re = 100 decreases the magnetic effects about 17% on the heat transfer growth. [ABSTRACT FROM AUTHOR]

The hydrodynamics and thermal characteristics due to mixed convection in a vertical two-sided lid-driven differentially square cavity containing four hot cylinders in a diamond array are investigated by the lattice Boltzmann equation model. The moving walls of the cavity are cold while the others are adiabatic. The flow in the cavity is driven by both the temperature difference and the moving vertical walls. The influence of different flow governing parameters, including the direction of the moving walls (the left wall moves up and the right wall moves down (Case I), both the left and right walls are moving upward (Case II), both the left and right walls are moving downwards (Case III)), the distance between neighboring cylinders δ (0. 3 L ≤ δ ≤ 0. 5 L), and the Richardson number Ri (0. 1 ≤ Ri ≤ 1 0) on the fluid flow and heat transfer are investigated with the Reynolds number in the range of 3 7 5 ≤ Re ≤ 3 7 5 2 , the Grashof number of 1. 4 × 1 0 6 and the Prandtl number of Pr = 0. 7 1. Flow and thermal performances in the cavity are analyzed in detail by considering the streamlines and isotherms profiles, the average Nusselt number, as well as the total Nusselt number. It is found that the heat transfer efficiency is highest when Ri = 1. 0 for the cases of the walls moving in the opposite direction. When the walls move in the same directions, the heat transfer efficiency obtained by Ri = 0. 1 is maximum among the considered values of Ri. On the other hand, compared with the cases of Ri = 1. 0 and Ri = 1 0 , the cylinder positions corresponding to the largest and the smallest Nusselt numbers are very sensitive to the moving direction of the walls for Ri = 0. 1. Moreover, the results also show that in terms of the value of Nusselt number and the stability the case of both walls moving downwards works well. Besides, the effect of the distance between neighboring cylinders is also discussed, it is found that increasing or decreasing the spacing between cylinders could enhance heat transfer to different degrees for the range of Ri number considered. Finally, the empirical relationships among Nu ave , Ri , and the spacing between the cylinders (δ) are given, and predictive results match with the computed values very well. [ABSTRACT FROM AUTHOR]

In this paper, a steady solution is presented for the equations that represent the MHD rarefied gas fluid flow and heat transfer due to a permeable stretching sheet with second-order velocity slip and thermal slip phenomenon. By using nondimensional transformations, the system of partial differential equations governing the problem is transformed into another system of nonlinear ordinary differential another equations. Novel solutions are investigated for the resulting ordinary differential equation which describe the momentum equation. The numerical results obtained agreed very well with previously reported cases available in the literature. Additionally, the effects of the magnetic parameter, first- and second-order velocity slip parameter, conductivity parameter, thermal slip parameter and the suction (injection) parameter on both the velocity and temperature profiles and on the local skin-friction coefficient are discussed and presented through tables and graphs. [ABSTRACT FROM AUTHOR]

This study numerically investigates the magnetohydrodynamic (MHD) free convection of a fluid in a porous triangle cavity containing a circular obstacle subjected to various thermal configurations. The investigation is conducted using a penalty finite element technique. The inclined side walls are non-uniformly heated while the bottom is maintained cold isothermal. Three types of thermal configurations are considered at the obstacle boundary. The effects of various physical parameters on the MHD free convection have been studied. The temperature field, fluid flow and heat transfer are strongly dependent on the type of thermal boundary condition of the circular obstacle, Prandtl number and magnetic induction. The obtained results are verified with a grid sensitivity study and validated using existing results in literature. A comparison between the present results and ones existing in literature illustrates the reliability and dependability of this study. [ABSTRACT FROM AUTHOR]

The flow of viscous fluid between two parallel plates is investigated. The applications of the magnetic field effect have been considered in the vertical direction to the plates. Velocity has been presented in the presence of suction and injection. The temperature equation is assisted with the Joule heating effect. One of the numerical techniques, that is, finite difference approach has been used to tackle the given partial differential system. This method results in a system of simple algebraic equations. The unknown function is analyzed inside the domain. In this technique of solution, a system is subdivided into many smaller parts called finite elements. The obtained simpler algebraic equations are then assembled to form a system of equation which governs the original problem. The variational method is used to get an approximate solution by reducing the error function. The effects of pertinent variables on temperature and velocity are shown graphically in the discussion section. The obtained results show that the velocity decreases with magnetic and porosity parameters. Temperature increases for larger values of Hartmann and Eckert numbers. [ABSTRACT FROM AUTHOR]

The current study investigates theoretically and numerically the entropy generation in time-dependent free-convective third-grade viscoelastic fluid convection flow from a vertical plate. The nondimensional conservation equations for mass, momentum and energy are solved using a Crank–Nicolson finite difference method with suitable boundary conditions. Expressions for known values of flow-variables coefficients are also derived for the wall heat transfer and skin friction and numerically evaluated. The effect of Grashof number, Prandtl number, group parameter (product of dimensionless temperature difference and Brinkman number) and third-grade parameter on entropy heat generation is analyzed and shown graphically. Bejan line distributions are also presented for the influence of several control parameters. The computations reveal that with increasing third-grade parameter, the entropy generation decreases and Bejan number increases. Also, the comparison graph shows that contour lines for third-grade fluid vary considerably from the Newtonian fluid. The study is relevant to non-Newtonian thermal materials processing systems. [ABSTRACT FROM AUTHOR]

In this experimental study, exergy efficiencies of water and SiCwater nanofluid, prepared from 50nm particle size and 1% of volume fraction were compared based on the effect of thermal conductivities by a dish reflector receiver system. The average temperature difference between the receiver walls and heat transfer fluids have been studied to understand the thermal performance of the system with respect to the important properties of thermal conductivities and specific heat capacities. The enhanced thermal conductivity of 0.800115W/mK with the / ratio of 1.1759 was determined by the Koo and Kleinstreuer correlation which is considering both the Maxwell correlation and Brownian motion. The attained higher average exergy efficiencies for water and SiCwater nanofluid are 21.08% and 37.06.%, respectively with the enhanced nanofluid exergy efficiency of 75.80% than that of water at the flow rate of 0.5lpm. The result also shows that the system with SiCwater nanofluid produced higher exergy efficiency, because the rates of energy and exergy carried by the nanofluid are 0.2378kW and 0.7593kW higher than that of water for all the flow rates except at 0.2lpm, due to the enhanced thermal conductivity of the nanofluid. [ABSTRACT FROM AUTHOR]