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The time-dependent nonlinear convective Williamson nanofluid flow over a rough conical surface in the presence of numerous diffusions and Arrhenius activation energy effects are the main focus of the investigation in this paper. The unsteady flow is essentially due to the impulsive mainstream flow. Two diffusive species, namely, liquid Hydrogen and liquid Nitrogen, occur in the flow under investigation. A sinusoidal waveform mathematically models the rough conical surface with small amplitude and high frequency. Thus, the surface gradients, namely skin friction, exhibit wavy effects in the boundary layer regime. In the current flow problem, the governing equations for the fluid flow are highly coupled nonlinear PDEs that depend on the proper initial and boundary conditions. Mangler's transformations are used to convert them into non-dimensional forms, and implicit finite difference approximation and quasilinearization are employed to produce numerical semi-similar solutions. The numerical results representing the boundary layer effects are displayed graphically and analyzed for parametric values. The friction experienced by the rough surface is strongly fluctuating for higher values of Williamson parameter W. The heat transfer rate Re x - 1 / 2 N u increases approximately by 61% and 63% at ξ = 0.8 when Nt decreases from Nt = 0.5 to Nt = 0.1 , for the cases of W = 0 (Newtonian fluid) and W = 1(Williamson fluid), respectively. Additionally, there is a strong correlation between the current findings and the related results previously published in the literature. [ABSTRACT FROM AUTHOR]

In this work, the flow of ternary hybrid nanomaterials filling porous spaces is investigated in the presence of magnetohydrodynamics (MHD) and nonlinear convection. Three dissimilar nanoparticles copper (C u) , alumina (Al 2 O 3) , and magnesium oxide (M g O) are employed. Various features including Ohmic heating, heat generation, and variable thermal conductivity are studied, along with nonlinear radiation and entropy analysis. Solutions are developed using the ND Solve (shooting) method in Mathematica software. Analysis of parameters of interest is conducted, with conclusions highlighting key outcomes. Results show an increase in the thermal field for Eckert number and radiation, while a decrease in liquid flow is observed with increasing the magnetic parameter. The heat transport rate exhibits an opposite trend between heat generation and radiation. Temperature ratio parameter and Prandtl number show opposite trends in the thermal field, while the temperature gradient decreases against variable thermal conductivity. The drag force follows a similar trend against nonlinear convective and porosity variables. The entropy rate increases with the Brinkman number, and both porosity and radiation have an increasing impact on entropy rate. An increase in liquid flow is noted with the nonlinear convection variable. A comparative study of heat transport rate through the Prandtl number shows good agreement. [ABSTRACT FROM AUTHOR]

In this study, a Keller box calculation of magnetic nanopolymer coating flow over a circular cylinder in the presence of nonlinear convection is performed. A two-phase nanofluid model (Buongiorno model) is used to model the equations for nanofluid flow and heat and mass transfer. The problem at hand is first formulated in the dimensional form of nonlinear partial differential equations (PDEs) and then transformed into the dimensionless PDEs form by manipulating non-similar variables. The Keller box approach (implicit finite differences) is used for the calculations of the transformed PDEs. The characteristics of critical thermophysical physical parameters on the flow field, viz thermal convection, Brownian motion, Weissenberg number, thermophoresis, magnetic field, heat source/sink, Biot number, buoyancy ration parameter, Eckert number, and mixed convection, are graphically manifested. In addition, the flow control parameters estimate the sheath friction, heat transfer rate, and mass transfer rate in the flow coordinate. A significant increase in the velocity of the Williamson nanofluid is accompanied by an increase in the Biot number, magnetic field, and mixed convection. The isotherms show a higher fluid temperature near the wall in the absence of convection. The Weissenberg number, Biot number, and thermophoresis significantly increase the temperature of the Williamson nanofluid. The density of the streamlines is lowered with a larger buoyancy ratio parameter. The total entropy generation of the Williamson nanofluid is improved by increasing the Brinkman number and the Weissenberg number. [ABSTRACT FROM AUTHOR]

This study aims to investigate heat transfer and entropy production in the non-similar flow of an incompressible fluid, with nonlinear convection and viscous dissipation. To obtain precise solutions, the Sparrow-Quack-Boerner local non-similarity method is implemented. The non-similarity arises from the nonlinear convection term present in the momentum equation. The non-similarity arises from the nonlinear convection term present in the momentum equation. Consequently, the inclusion of non-similarity terms into the energy equation is achieved through the interconnection of momentum and energy equations. Entropy generation is explored by employing the second law of thermodynamics. Numerical results from several truncation levels are presented in tabular form, and equations for both first and second-level truncations are generated. The one- and two-equation models are solved by implementing the Generalized Differential Quadrature Method (GDQM). Comparison with a second level of truncation reveals significantly greater inaccuracies in numerical results obtained from the first level. This discrepancy arose due to the omission of non-similar terms in the primary governing equations at the first truncation stage. The validity and accuracy of the derived numerical solutions are further demonstrated by the application of the GDQM and the midpoint method with Richardson extrapolation. Additionally, a plot of the numerical data produced from the second level of truncations is presented together with a discussion of the various physical factors. Increasing the mixed convection parameter accelerates fluid velocity, also when the viscous dissipation parameter increases, temperature and the Bejan number increase. The Prandtl number and the thickness of the thermal boundary layer are observed to be inversely related. Moreover, the quantity of entropy generated at the stretching surface and inside the boundary layer rises in proportion to the increases in the Prandtl and Eckert numbers. [ABSTRACT FROM AUTHOR]

The study deals with nonlinear convection in a three-layered porous-air-porous enclosure with zero temperature difference at the external impermeable thermally conductive boundaries. The upper and lower porous matrices are internally heated with a uniform energy source. To describe redistribution of heat energy between the top and bottom surfaces of the enclosure, we introduce a relative heat transfer coefficient q r that has the conduction and convection parts. The former part tends to unity in the fully filled porous domain. The symmetry of heat transfer from the inner area towards the outer surfaces breaks down if one adds an intermediate air layer with low thermal conductivity. Two sandwiched systems which have equal depth ratio d but distinct air layer location are considered. In system 1, the air layer is located in the upper unstably stratified half of the enclosure. In system 2, this layer is in the lower stably stratified half. The total value of q r always increases due to penetrative convection. At d = 0.1, local convection in system 1 is easily initiated in contrast to the hard-to-generate large-scale convection in system 2 due to a strong destabilization. The latter most effectively enhances heat transport though the top surface with increasing the supercriticality. • Nonlinear convection in a porous-air-porous enclosure, induced by energy source. • Air layer effect on redistribution of heat energy between top and bottom surfaces. • Comparing a relative heat transfer rate at different air layer locations and depths. • Local convection is easily initiated due to strong destabilization by depth ratio. • Hard-to-generate large-scale convection is more effective in heat transferring. [ABSTRACT FROM AUTHOR]

Flows configured by moving surface holds considerable importance in fluid mechanics. The moving surface finds widespread usages in distinct real-world scenarios, for illustration rubber sheets, hot rolling, plastic drawing, paper manufacturing, glass blowing and wire fabrication. The rate of stretching/cooling during these processes play a vital role in ensuring the production of high-excellence end-products. This attempt features entropy optimized slip flow featuring rate type (Jeffrey) liquid subjected to Cattaneo–Christov (CC) dual diffusion and nonlinear convection aspects. Variable fluid aspects (i.e., thermal conductivity and mass diffusivity) along with thermal source and first order chemical reaction are scrutinized. The problem is formulated by employing fundamental laws of fluid dynamics. The non-linear partial differential equations are transformed into the ordinary ones using suitable transformations. Subsequently, optimal homotopic methodology (OHAM) is employed to achieve computational results. Developed nonlinear problems are determined for velocity, temperature and concentration fields. Bejan number, skin friction and the graphs of entropy generation parameters have been plotted and argued. To validate the problem, the comparison for different parameters has been addressed through Shooting and OHAM techniques. Total residual error is calculated. Main outcomes are presented in conclusions. [ABSTRACT FROM AUTHOR]

The time-dependent enhanced heat transport and nonlinear thermal buoyancy-driven flow of the MWCNT-MgO/EG hybrid nanofluid at the stagnation-point of the rotating sphere subjected to the thermal jump boundary condition are studied theoretically. The quadratic density-temperature variation is also examined together with the quadratic Rosseland thermal radiation. For realistic modelling, experimental data of MWCNT-MgO/EG viscosity and thermal conductivity are used. The monophasic model and the concept of the boundary layer are used to derive the governing partial differential equations, and then they are handled for self-similar solutions using the Finite Element Method (FEM). The effects of driving parameters are examined using 3D contour and surface plots. The further goal of the study is to optimize the heat transport and shear stress of the flow system by applying the central composite-response surface method (RSM) based on the desirability approach. The hybrid nanoparticles volume fraction (NVF) improves friction factors and heat transport. Thermal buoyancy and Coriolis forces condense the thickness of the thermal layer. Heat transport is greater for quadratic thermal convection/radiation than for linear thermal radiation/convection. By RSM, the maximum heat transport (19.0894), the minimum friction factor in the x-direction (2.2564), and the minimum friction factor in the z direction (0.7333) are simultaneously conquered at the low level of NVF, and mixed convection factor and at a high level of QTR factor. [ABSTRACT FROM AUTHOR]

The studies conducted in the recent past reveals that the non-Newtonian are extensively applied in several engineering applications. The atypical Oldroyd-B fluid, a specific sub-category of non-Newtonian fluids, with fractional derivative constitutive equations, is very expedient to determine the approximation of many dilute polymer liquids. Since very few studies regarding the numerical solution of the aforesaid model are conducted, so the literature that can be referred to in this regard is scarce. The current article investigates the unsteady magneto-hydrodynamic flow of irregular Oldroyd-B fluid with a modified thermal flux restricted between two infinite parallel plates. Here, it is assumed that the thermal conductivity of the fluid is variable, and the impact of body forces like gravity is accordingly analyzed in terms of non-linear convection. The linear acceleration of the lower permeable plate in its plane prompts the flow. Further, we have investigated the heat transfer in the flow field through a modified fractional thermal gradient and internal heat source. The temperature gradient accelerates with time and exists among the flow boundaries. In order to determine the approximate solution unified with finite difference approximation for Caputo fractional time derivatives, we have utilized the standard Galerkin finite element method. Moreover, we have conducted a convergence analysis of the suggested numerical scheme and offered some valid error approximations. In the non-integer viscoelastic model, the local number and coefficient of skin friction are also deliberated. We have also performed some upright numerical simulations to highlight the ascendency of characteristic flow parameters of velocity and temperature fields in the proposed scheme. Here, we have analyzed that the resistive force increases by 40 % , corresponding to an increment in α ranging from 0 to 0.4. Further, the heat transfer rate is diminish by 10.94 % against an increase in variable thermal conductivity while it is enhanced by 37.78 % corresponding to increased in Pr. [ABSTRACT FROM AUTHOR]

This paper seeks to analyze the core effects of entropy generation on the peristaltic flow of an incompressible fluid with nonlinear convective heat transfer. The analysis is carried out inside an asymmetric channel with flow subjected to the second order velocity slip conditions. The flow is firstly modeled by the system of partial differential equations (PDEs) and then is simplified using the assumptions of long wavelength and low Reynolds number, in wave frame of reference. Entropy production, its contributing factors and performance of heat and fluid against various parameters is described, discussed, and displayed graphically by assigning an increasing list of numerical values to them. Trapping of the fluid is also portrayed by streamline graphs. Entropy generation is witnessed to be minimized when first order velocity slip and thermal slip parameters are held in check account. [ABSTRACT FROM AUTHOR]