Statistical modeling for bioconvective tangent hyperbolic nanofluid towards stretching surface with zero mass flux condition

Heat transfer analysis of Maxwell tri-hybridized nanofluid through Riga wedge with fuzzy volume fraction

This contribution aims to optimize nonlinear thermal flow for Darcy-Forchheimer Maxwell fuzzy [Formula: see text] tri-hybrid nanofluid flow across a Riga wedge in the context of boundary slip. Three types of nanomaterials, [Formula: see text] Cu and [Formula: see text] have been mixed into the basic fluid known as engine oil. Thermal properties with the effects of porous surface and nonlinear convection have been established for the particular combination [Formula: see text] Applying a set of appropriate variables, the set of equations that evaluated the energy and flow equations was transferred to the dimensionless form. For numerical computing, the MATLAB software's bvp4c function is used. The graphical display is used to demonstrate the influence of several influential parameters. It has been observed that flow rate decay with expansion in porosity parameter and nanoparticles volumetric fractions. In contrast, it rises with wedge angle, Grashof numbers, Darcy-Forchheimer, nonlinear Grashof numbers, and Maxwell fluid parameter. Thermal profiles increase with progress in the heat source, nanoparticles volumetric fractions, viscous dissipation, and nonlinear thermal radiation. The percentage increases in drag force for ternary hybrid nanofluid are 13.2 and 8.44 when the Modified Hartmann number takes input in the range [Formula: see text] and wedge angle parameters [Formula: see text]. For fuzzy analysis, dimensionless ODEs transformed into fuzzy differential equations and employed symmetrical triangular fuzzy numbers (TFNs). The TFN makes a triangular membership function (M.F.) that describes the fuzziness and comparison. This study compared nanofluids, hybrid nanofluids, and ternary nanofluids through triangular M.F. The boundary layer flow caused by a wedge surface plays a crucial role in heat exchanger systems and geothermal.

Rheology of electromagnetohydrodynamic tangent hyperbolic nanofluid over a stretching riga surface featuring dufour effect and activation energy

The present model deals with the consequence of Dufour, activation energy, and generation of heat on electromagnetohydrodynamic flow of hyperbolic tangent nanofluid via a stretching sheet. This offers a broad significance in several engineering fields. With adequate similarity variables, the regulating governing equations of PDEs are renovated into nonlinear ODEs. The numerical output of the produced ordinary differential equations is conducted with MATLAB bvp4c. The influence of increasing features on temperature, velocity, concentration patterns, drag force coefficient, Sherwood number and Nusselt number is depicted graphically and numerically. Hence, the resultant conclusions are confirmed utilising contrast with earlier output. Interestingly, the activation energy retards the nanofluid's tangential hyperbolic concentration distribution and the rise in temperature of the hyperbolic tangential nanofluid flow is traceable to an increase in the Dufour effect, However, the electromagnetohydrodynamic variable increases the velocity distribution, which influences the Power law index. Conclusively, the rate of heat transfer is inhibited when the thermophoresis parameter, heat source and the Weissenberg number are enhanced.

Significance of concentration-dependent viscosity on the dynamics of tangent hyperbolic nanofluid subject to motile microorganisms over a non-linear stretching surface

The communication describes a theoretical framework for tangent hyperbolic fluid of nano-biofilm due to an extending or shrinking sheet that comprises a stagnation point flow, chemical reaction with activation energy, and bioconvection of gyrotactic microorganisms. The varying transport features due to dynamic viscosity, thermal conductivity, nano-particle mass permeability and microbe organisms diffusivity are taken into account for the novelty of this work. The inspiration is developed to enhance heat transfer. A set of leading partial differential equations is formed along with appropriate boundary constraints. Using similarity transformations, the basic formulation is transitioned into non-linear differential equations. To produce observational data, the shooting technique and Runge-Kutta fourth order method are employed. The coding of numerical scheme is developed in Matlab script. The visual representation of the effects of diverse fluid transport properties and distinctive parameters on speed, temperature, concentration and motile density are evaluated. The velocity become faster when the parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}ω, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}λ, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}ϵ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_0$$\end{document}V0 are enhanced. Brownian motion, thermal conductivity, heat generation as well as thermophoresis factors all strengthen the temperature distribution, however the nano-particle concentration profile is enhanced as the nano-particle mass conductivity variable, activation energy as well as the thermophoresis variable are boosted. The microorganism density improves significantly when the microorganism diffusivity factor increases. The skin friction, Sherwood number, Nusselt number and motile density number decline against the incremented transport parameters.

Computer Simulation of the Seismic Wave Propagation in Poroelastic Medium

This article presents an algorithm for the numerical solution of an initial-boundary value problem for a symmetric t-hyperbolic system of partial differential equations. This problem is based on continual filtration model, which describes the propagation of seismic waves in a poroelastic medium saturated with a fluid characterized by such physical parameters as the propagation velocities of longitudinal P- (fast and slow) and transverse S-waves, the density of the medium materials, and porosity. The system of linearized equations of saturated porous media is formulated in terms of physical variables of the velocity–stress tensor of the porous matrix and the velocity–pressure of the saturating fluid in the absence of energy dissipation. The solution is implemented numerically using an explicit finite difference upwind scheme built on a staggered grid to avoid the appearance of oscillations in the solution functions. The program code implementing parallel computing is developed in the high-performance Julia programming language. The possibility of using the approach is demonstrated by the example of solving the problem of propagation of seismic waves from a source located in the formation. Computational experiments based on real data from oil reservoirs have been implemented, and dynamic visualization of solutions consistent with the first waves arrival times has been obtained.

Significance of Rosseland’s Radiative Process on Reactive Maxwell Nanofluid Flows over an Isothermally Heated Stretching Sheet in the Presence of Darcy–Forchheimer and Lorentz Forces: Towards a New Perspective on Buongiorno’s Model

This study aimed to investigate the consequences of the Darcy–Forchheimer medium and thermal radiation in the magnetohydrodynamic (MHD) Maxwell nanofluid flow subject to a stretching surface. The involvement of the Maxwell model provided more relaxation time to the momentum boundary layer formulation. The thermal radiation appearing from the famous Rosseland approximation was involved in the energy equation. The significant features arising from Buongiorno’s model, i.e., thermophoresis and Brownian diffusion, were retained. Governing equations, the two-dimensional partial differential equations based on symmetric components of non-Newtonian fluids in the Navier–Stokes model, were converted into one-dimensional ordinary differential equations using transformations. For fixed values of physical parameters, the solutions of the governing ODEs were obtained using the homotopy analysis method. The appearance of non-dimensional coefficients in velocity, temperature, and concentration were physical parameters. The critical parameters included thermal radiation, chemical reaction, the porosity factor, the Forchheimer number, the Deborah number, the Prandtl number, thermophoresis, and Brownian diffusion. Results were plotted in graphical form. The variation in boundary layers and corresponding profiles was discussed, followed by the concluding remarks. A comparison of the Nusselt number (heat flux rate) was also framed in graphical form for convective and non-convective/simple boundary conditions at the surface. The outcomes indicated that the thermal radiation increased the temperature profile, whereas the chemical reaction showed a reduction in the concentration profile. The drag force (skin friction) showed sufficient enhancement for the augmented values of the porosity factor. The rates of heat and mass flux also fluctuated for various values of the physical parameters. The results can help model oil reservoirs, geothermal engineering, groundwater management systems, and many others.

Analytical investigation of magnetized 2D hybrid nanofluid (GO + ZnO + blood) flow through a perforated capillary

The hydrothermal features of unsteady, incompressible, and laminar hybrid nanofluid motion through a porous capillary are analytically studied in the magnetic field presence. The hybrid nanofluid (GO + ZnO + Blood) is synthesized by blending nanomaterials of graphene oxide and zinc oxide with blood acting as the host fluid. The mathematical model of the flow comprises of a coupled nonlinear set of partial differential equations (PDEs) satisfying appropriate boundary conditions. These equations are reduced to ordinary differential equations (ODEs) by using similarity transformations and then solved with homotopy analysis method (HAM). The impacts of various pertinent physical parameters over the hybrid nanofluid state functions are examined by displaying 2 D graphs. It has been observed that the fluid velocity mitigates with the varying strength of M, A₀, N₀, and N₁. The enhancing buoyancy parameter ϵ augments the fluid velocity. The increasing Prandtl number causes to reduce, while the enhancing A₀, B, and N₂ augment the hybrid nanofluid temperature. The fluid concentration mitigates with the higher Schmidt number values and A₀, and augments with the increasing Soret number strength. The augmenting magnetic field strength causes to enhance the fluid friction, whereas the convective heat transfer increases with the Prandtl number rising values. The rising Sherwood number drops the mass transfer rate of the fluid. The achieved results are validated due to the agreement with the published results. The results of this computation will find applications in biomedicine, nanotechnology, and fluid dynamics.

An inclination in Thermal Energy Using Nanoparticles with Casson Liquid Past an Expanding Porous Surface

The physical aspects of inclined MHD nanofluid toward a stretching sheet embedded in a porous medium were visualized, which has numerous applications in industry. Two types of nanoparticles, namely copper and aluminum oxide, were used, with water (limiting case of Casson liquid) as the base fluid. Similarity transformations were used to convert the partial differential equations into a set of ordinary differential equations. Closed solutions were found to examine the velocity and temperature profiles. It was observed that an increment in the magnitude of the Hartmann number, solid volume fraction, and velocity slip parameter brought a reduction in the velocity profile, and the opposite behavior was shown for the permeability parameter in Cu–water and Al2O3–water nanofluids. The temperature field, local skin friction, and local Nusselt number were further examined. Moreover, the study of Cu and Al2O3 is useful to boost the efficiency of thermal conductivity and thermal energy in particles. Reduction was captured in the velocity gradient and temperature gradient against changes in the thermal radiation number. The opposite trend was tabulated into motion with respect to the volume fraction number for both cases (Cu–water and Al2O3–water).

Significant Production of Thermal Energy in Partially Ionized Hyperbolic Tangent Material Based on Ternary Hybrid Nanomaterials

Nanoparticles are frequently used to enhance the thermal performance of numerous materials. This study has many practical applications for activities that have to minimize losses of energy due to several impacts. This study investigates the inclusion of ternary hybrid nanoparticles in a partially ionized hyperbolic tangent liquid passed over a stretched melting surface. The fluid motion equation is presented by considering the rotation effect. The thermal energy expression is derived by the contribution of Joule heat and viscous dissipation. Flow equations were modeled by using the concept of boundary layer theory, which occurs in the form of a coupled system of partial differential equations (PDEs). To reduce the complexity, the derived PDEs (partial differential equations) were transformed into a set of ordinary differential equations (ODEs) by engaging in similarity transformations. Afterwards, the converted ODEs were handled via a finite element procedure. The utilization and effectiveness of the methodology are demonstrated by listing the mesh-free survey and comparative analysis. Several important graphs were prepared to show the contribution of emerging parameters on fluid velocity and temperature profile. The findings show that the finite element method is a powerful tool for handling the complex coupled ordinary differential equation system, arising in fluid mechanics and other related dissipation applications in applied science. Furthermore, enhancements in the Forchheimer parameter and the Weissenberg number are necessary to control the fluid velocity.