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In this research endeavor, Casson fluid flow and melting heat transfer due to a curved nonlinearly stretching sheet are investigated. The sheet is naturally permeable and the flow is considered in a porous medium. For flow in a porous medium, a modified Darcy's resistance term for Casson fluid is considered in the momentum equation. In the energy equation, heat transport characteristics, including viscous dissipation, are taken into account. Mass transport is also studied together with the impact of chemical reaction of higher order. The governing nonlinear partial differential equations of flow, heat, and mass transport are reduced to nondimensional ordinary differential equations using adequate similarity transformations and then solved numerically employing the bvp4c technique and Runge–Kutta fourth‐order method on MATLAB. The impacts of numerous occurring parameters on relevant fields (velocity field, temperature field, and concentration field) are depicted and discussed by plotting graphs. We concluded the curvature parameter, K $K$ reduces the pace of the flow. The impacts of the stretching index, m $m$ and melting parameter, Me $Me$ are also found to reduce flow and temperature field. Furthermore, we noted that the reaction parameter, Kn ${K}_{n}$ and its order, n $n$ exhibit opposite impacts on the concentration field. Moreover, the numerical values of skin‐friction coefficient and Nusselt number calculated employing bvp4c and Runge–Kutta fourth‐order technique are expressed in tabular mode, and these are found in an excellent match. For validation of the results, skin‐friction coefficient values were computed using the Runge–Kutta fourth‐order technique and bvp4c solver, compared with the existing results, and a good agreement was found. [ABSTRACT FROM AUTHOR]

The convective–radiative magnetohydrodynamic non‐Newtonian second‐grade fluid boundary layer flow from a curved stretching surface has been scrutinized in the present study. The Reiner–Rivlin second‐grade viscoelastic model is deployed which provides a good approximation for certain magnetic polymers. High temperature invokes the presence of radiative heat transfer, which is simulated with the Rosseland diffusion approximation. Viscous dissipation and Joule heating are also featured in the model and hydrodynamic (velocity) slip at the wall is also incorporated in the boundary conditions. The emerging nonlinear coupled dimensionless transport equations are solved with a Runge–Kutta method and a shooting numerical scheme. The influence of emerging multiphysical flow parameters on the dimensionless profiles is examined with the help of plots for comparative analysis of both non‐Newtonian fluid and Newtonian fluid. The numerical solutions are validated for special cases with existing works. The velocity declines for a higher magnetic field, whereas the reverse trend is noted for the temperature function. The augmentation in the thermal field is noted with increments in radiation parameters. Furthermore, the fluid temperature of the second‐grade fluid is higher with increasing Brinkmann number. The wall slip induces deceleration. Contour plots for streamlines and isotherms are also visualized and analyzed. [ABSTRACT FROM AUTHOR]

In boiling phenomena, the heater surface gets covered by a vapor, which results in a decrease in the overall heat transfer coefficient (HTC). The curvature of the surface helps to reduce this vapor blanketing by vapor sliding over the curved surface. The sliding generates fluid circulation and makes the heater surface available for boiling liquid. Therefore, in the present work, the vapor dynamics, nucleation and growth, pinch‐off of the bubble, and heat transfer characteristics over smooth and uniform surfaces with different curvature ratios (δ = 0, 0.01, 0.05, 0.15, and 0.25) are numerically studied. Also, the effect of the degree of superheat (ΔT = 10, 20, 30, and 40 K) on the bubble formation, vapor sliding, and fluid recirculation over the curved surface have been observed. Furthermore, investigated the dome formation and multiple pinch‐off of the bubble on the heated curved surfaces. The dominance of the curvature and degree of superheat on the bubble departure has been investigated using PDF of FFT of vapor void fraction at the surface. At higher curvature of the surface, there is less significance of the degree of superheat on the departure frequency of vapor bubbles. Furthermore, it is found that there is an increase in the average HTC with an increase in the curvature ratio, while the pinch‐off time of the bubble decreases. The HTC is enhanced by 86% with curved surfaces as compared to flat surfaces. Furthermore, the curved surface with a curvature (δ) of 0.15 showed better performance than the curved surface with δ = 0.25. Boiling over a curved surface leads to vapor sliding and recirculation of the fluid, leading to enhancement in surface renewal and an increase in HTC. [ABSTRACT FROM AUTHOR]

The purpose of the study is to discuss the comparison of the linear and nonlinear stretching sheets on the heat transfer over a curved surface spiraling in a circle with radial distance R. Additionally the consequences of Soret–Dufour in the presence of injection velocity and heat source/sink are investigated in the article. Silver and Copper Oxide are taken as hybrid nanoparticles with water as foundation fluid. Leading equations are converted to nonlinear ordinary differential equations taking some relevant transformations and solved with the combination of the shooting method and RK‐4th order method. MAPLE software is used to plot graphs and numerical charts. Flow features are examined for different pertinent parameters. Physical quantities like Sherwood number, Nusselt number, and so forth, are evaluated numerically for different nondimensional numbers. The result substantiates that improving the Dufour number boost the fluid flow and fluid temperature but the opposite behavior is seen in the concentration profile. It is observed that a linearly stretching sheet gives better fluid behaviors compared to nonlinear stretching sheet. [ABSTRACT FROM AUTHOR]

The magnetic nanofluid flow over a curved surface in the presence of heat and mass mixed convection, volumetric heat generation, and higher‐order chemical reaction is studied in this study. The Maxwell Garnetts model of thermal conductivity and the Brinkman model of viscosity are used for working fluid. The numerical method is applied to assess the governing nonlinear equations of the developed model. The influence of parameters, such as buoyancy, chemical reaction, magnetic field, curvature, heat generation, and chemical reaction order are considered in the existing study. The surface diagram for Nusselt number, skin friction coefficient, and Sherwood number are revealed. From the outcomes, it can be noted that with an increase in buoyancy parameters GrT and GrC, the heat and mass transfer (HMT) functions declined. Moreover, the behavior of HMT is reversed when there is an escalation in the values of chemical reaction parameter Kr. A comparison of this study with a previous study is conducted. [ABSTRACT FROM AUTHOR]

An analysis of heat and mass transfer is carried out under the influence of chemical reaction, friction heating, and heat generation/absorption over a curved surface. The impacts of random motion attributes of nanoparticles and thermophoresis are also applied in the expressions of energy and concentration. With the help of assigned transformations, the nonlinear partial differential equations are changed to dimensionless nonlinear ordinary differential equations. Then, the numerical solution is obtained using fourth‐fifth order Runge‐Kutta‐Fehlberg method via the shooting technique. The impacts of relevant parameters on velocity, temperature, and concentration are depicted through graphs and tables. The results illustrate that the lowest concentration distribution of nanofluid is related to the higher value of chemical reaction parameter. Moreover, it is found that thermophoresis and Brownian motion parameters have a propensity to increase the temperature profile while curvature parameter decreases the velocity profile. Also, velocity and temperature fields show a similar behavior for the increasing values of volume fraction of the nanoparticles, while a reverse trend is observed in the concentration profile under the same condition. To authenticate the results of the current study, the obtained data were compared with previously published data. [ABSTRACT FROM AUTHOR]