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A curved heat transfer surface is proposed to improve the condensation process. The flow performance and condensation law in the cosine-shaped flow channel, a special curved surface, are numerically and theoretically studied. A theoretical model of surface filmwise condensation on a curved flow channel is established and the mathematical model is validated. The liquid film thickness equation in different zones of the curved surface is deduced and calculated. The results show that the main condensation heat transfer zone is in the middle zone (25 mm < s < 45 mm) and the wave crest zone (0 mm ≤ s ≤ 25 mm), the temperature gradient of the liquid film surface decreases along the liquid flow direction, and the liquid film thickness becomes thinner with the increase of steam velocity. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids are advanced heat transfer fluids that combine the benefits of traditional nanofluids with additional features to enhance their performance. These fluids have the potential to reduce energy consumption, improve heat transfer proficiency, and enhance the performance of thermal systems in diverse applications. Current work analyzes bioconvective Darcy–Forchheimer hybrid nanofluid flow by porous curved stretched surface. The thermal field is modeled accounting the effects of dissipation and thermal radiation. Chemical reaction and Arrhenius kinetics are accounted in the mass concentration field. Influence of the magnetic field is considered. Bioconvection phenomenon is taken into account to control the random motion of solid tiny particles of copper (Cu) and aluminum oxide (Al2O3) in hybrid base fluid water (H2O)–Ethylene glycol (C2H6O2). Cylindrical nanoparticles with shape factor m = 4.9 are considered. Boundary layer norms are utilized to acquire the flow governing dimensional equations. Appropriate transformations are utilized to alter the dimensional system into non-dimensional one. Runge–Kutta–Fehlberg (RKF-45) method in Mathematica is implemented to explore the effective consequences of involved variables on hybrid nanofluid velocity, motile density, thermal, and concentration fields. Surface drag force, mass, density, and heat transfer rates are tabulated and analyzed. The acquired results depict that the velocity field of hybrid fluid decays through porosity variable and Hartmann number. Motile density of microorganisms diminished versus bioconvection Lewis and Peclet numbers. Intensity of heat transfer boosts via Eckert number and thermal radiation parameter. [ABSTRACT FROM AUTHOR]

Ternary hybrid nanofluids (Thnf) are used in several fields, including enhancements of heat transfer, solar power systems, medical devices, electronics cooling, aviation industry, and automotive sector. Furthermore, Thnf provide a versatile solution to boost energy transport for the industrial applications. In the current analysis, an incompressible magnetized Thnf flow with the natural convection through a curved surface using Darcy–Forchheimer medium is addressed. The heat transfer is simulated by using the Cattaneo–Christov (C–C) heat flux model. Aluminum alloys (Ti6Al4V, AA7072 and AA7075) are dispersed in water (H2O) and ethylene glycol (C2H6O2) to synthesize the modified hybrid nanofluid. The model equations are reform into ODEs (ordinary differential equations) by using the similarity substitution. The non-dimensional set of ODEs is further numerically estimated through PCM (Parametric continuation method). The physical behavior of velocity, energy outline, Nusselt number and skin friction for distinct values of emerging variables are computed and analyzed in detail. The finding reveals that an improvement in entropy generation has been observed versus the rising values of unsteadiness and variable porosity parameters. The rising effect of permeability parameter enhances the velocity curve; whereas, fluid velocity drops with the influence of inertia coefficient. [ABSTRACT FROM AUTHOR]

The objective of the current study is to develop an investigation on the magnetohydrodynamic flow of viscous liquid through a nonlinear curved enlarging sheet due to the occurrence of heat source. The observation of heterogeneous and homogeneous reactions with the properties of heat source and transverse magnetic field is reflected in this discussion. Further, in a novel approach, the convective heating mechanism enriches the flow phenomena significantly. The governing partial differential equations are successfully transformed into the dimensionless form by using appropriate similarity transformations. The resultant non-dimensional form of equations is computed via the numerical scheme. The properties of the proposed physical constraints are observed and explored their significant behavior graphically. Additionally, the physical properties like surface drag force and local Nusselt numbers are calculated and presented in tabular form. Further, the major outcomes of the study reveal that the fluid velocity retards significantly for higher values of curvature constraint and stretching index and temperature of fluid enhances for the increasing power law stretching index along with the additional Biot number and heat source. [ABSTRACT FROM AUTHOR]

Numerical analysis of the time-dependent magnetized micropolar fluid flow over a curved surface is deliberated in this investigation. The thermal jumped and velocity slip effects are deliberated on the curved surface. Developed mathematical model has been developed under the flow assumptions. This model reduced into the dimensionless form by means of similarity transformations. Dimensionless system has been solved through the numerical technique. The involving physical parameters are analyzed through graphs and table. Surprisingly, fraction between surface and fluid increases and reduced heat transfer rate for augmenting of magnetic field. Heat transfer improved for increasing the values of Biot number. [ABSTRACT FROM AUTHOR]

Significant applications of chemical reaction in flow using a curve sheet include metabolic, plastic extrusion and biochemical engineering. A few instances include the management of moisture and temperature supplies during an agricultural fair and the transmission of energy in a drizzly cooling tower. The current study aims to examine the heat and mass transmission for Darcy–Forchheimer flow induced by the curved stretch surface looped in a circle of radius R\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R$$\end{document}. The flow is influenced by heat generation and thermal radiation with the effects of chemical reactions. Kerosene oil (KO) is used as the base fluid while three different types of nanoparticles, GO,ZrO2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{GO}}, \,{\text{ZrO}}_{2}$$\end{document} and SiO2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{SiO}}_{2}$$\end{document} are mixed with it. Convective heat conditions are incorporated in this model. A curvilinear coordinates system is studied to build the mathematical model of the flow condition under certain assumptions and then solved using the bvp4c approach in MATLAB. The effects of physical and geometrical characteristics relevant to this analysis on dimensionless physical quantities of interest are discussed using the necessary graphs and tables. According to the results, the Darcy–Forchheimer and porosity parameters caused a fall in the velocity profile, whereas the curvature parameter was found to cause an enhancement in the velocity profile. Our finding exhibits that GO\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{GO}}$$\end{document} has a greater influence on ZrO2andSiO2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text{ZrO}}_{2} \;{\text{and}}\;{\text{SiO}}_{2}$$\end{document}. Thermal distribution augments with growth in radiative flow and Biot number while has declined with the upsurge in curvature factor. Growth in curvature factor has supported the behavior of concentration distribution and has been opposed by an upsurge in chemically reactive factor and Schmidt number. A comparison of the results obtained here with those that have already been published in the relevant literature has been made with outstanding achievement. [ABSTRACT FROM AUTHOR]

Here, we addressed comparative investigation of hybrid nanofluid (MWCNTs + Cu + Water), nanofluid (MWCNTs + Water) and base fluid (Water). Flow is due to curved sheet. Flow via slip boundary condition is examined. Heat transport analysis is carried out in the presence of viscous dissipation, mixed convection and convective boundary condition. Transformation procedure is adopted for converting PDEs (continuity eq., momentum eq., energy eq. and boundary conditions) into ODEs. These nonlinear coupled ODEs are solved via shooting method with RK-4 algorithms (bvp4c). Behaviors of involved parameters on flow, Nusselt number (heat transfer rate), temperature and skin friction coefficient are analyzed graphically. Velocity of fluid enhances with increment in nanoparticles volume fraction for multi-walled CNTs, nanoparticle volume fraction for Cu and mixed convection parameter, while it can be reduced via higher estimations of velocity slip parameter. Temperature of the fluid varies directly with an increase in nanoparticles volume fraction for multi-walled CNTs, nanoparticle volume fraction for Cu, Eckert number and thermal Biot number. Skin friction coefficient is reduced via higher mixed convection as well as velocity slip parameters. Nusselt number intensifies with increment in nanoparticles volume fraction for multi-walled CNTs, nanoparticle volume fraction for Cu, Eckert and thermal Biot numbers. During comparative study amongst hybrid nanomaterial, nanomaterial and base fluid, efficient behavior is noted for hybrid nanomaterial. [ABSTRACT FROM AUTHOR]

Presented work concerns with investigation of hybrid nanomaterial (SWCNTs + CuO + Ethylene glycol) flow over curved nonlinear stretched sheet. Heat transfer features are emphasized through Newtonian heating and viscous dissipation. Coupled nonlinear ODEs are constructed from the flow field equations (Continuity Eq., Momentum Eq. and Energy Eq.) by mean of adequate transformations. Such resulting nonlinear ODEs are then converted into system of 1st-order ODEs and solved via shooting technique using RK-4 algorithms (bvp4c). Impacts of emerging flow parameters on temperature, skin friction coefficient, velocity and Nusselt number are illustrated graphically. Also comparison among hybrid nanofluid (SWCNTs + CuO + Ethylene glycol), nanofluid (SWCNTs + Ethylene glycol) and basefluid (Ethylene glycol) is performed. [ABSTRACT FROM AUTHOR]