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This paper introduces fractional Brownian motion into the study of Maxwell nanofluids over a stretching surface. Nonlinear coupled spatial fractional-order energy and mass equations are established and solved numerically by the finite difference method with Newton's iterative technique. The quantities of physical interest are graphically presented and discussed in detail. It is found that the modified model with fractional Brownian motion is more capable of explaining the thermal conductivity enhancement. The results indicate that a reduction in the fractional parameter leads to thinner thermal and concentration boundary layers, accompanied by higher local Nusselt and Sherwood numbers. Consequently, the introduction of a fractional Brownian model not only enriches our comprehension of the thermal conductivity enhancement phenomenon but also amplifies the efficacy of heat and mass transfer within Maxwell nanofluids. This achievement demonstrates practical application potential in optimizing the efficiency of fluid heating and cooling processes, underscoring its importance in the realm of thermal management and energy conservation. [ABSTRACT FROM AUTHOR]

This paper introduces fractional Brownian motion into the study of Maxwell nanofluids over a stretching surface. Nonlinear coupled spatial fractional-order energy and mass equations are established and solved numerically by the finite difference method with Newton’s iterative technique. The quantities of physical interest are graphically presented and discussed in detail. It is found that the modified model with fractional Brownian motion is more capable of explaining the thermal conductivity enhancement. The results indicate that a reduction in the fractional parameter leads to thinner thermal and concentration boundary layers, accompanied by higher local Nusselt and Sherwood numbers. Consequently, the introduction of a fractional Brownian model not only enriches our comprehension of the thermal conductivity enhancement phenomenon but also amplifies the efficacy of heat and mass transfer within Maxwell nanofluids. This achievement demonstrates practical application potential in optimizing the efficiency of fluid heating and cooling processes, underscoring its importance in the realm of thermal management and energy conservation.

The aim of the current analysis is to investigate heat and mass transfer characteristics of single and multi‐walled water‐based carbon nanotubes Maxwell nanofluid flow between continuously rotating stretchable disks under the sway of chemical reaction and radiation. Boundary conditions of the convective type of temperature are employed at both lower and upper rotating disks in the preparation. Similarity variables are employed to transform the governing partial differential equations into the nonlinear ordinary differential equations. The computational finite element method is applied to solve this nonlinear system of equations along with boundary conditions. The sway of different admissible parameters on the profiles of concentration, temperature, and velocity are inspected and revealed through graphs. Furthermore, the numerical solutions for rates of temperature, concentration, and rates of velocity are depicted in tabular form. It is revealed that temperature sketches deteriorate with augmented values of Deborah number at both upper and lower disks of single‐walled carbon nanotubes and multi‐walled carbon nanotubes with water‐based Maxwell nanofluids. [ABSTRACT FROM AUTHOR]

Stagnation-point heat and mass transfer of MHD Maxwell nanofluids over a stretching surface in the presence of thermophoresis have been investigated. Convective heat transfer boundary condition and Brownian motion are both taken into account. The boundary layer momentum, energy and concentration governing equations based on the upper convected Maxwell constitutive model are established. With the proper similarity variables, the nonlinear partial differential equations are transformed into a set of coupled ordinary differential equations. The homotopy analysis method (HAM) with three auxiliary parameters is presented to obtain the analytical solutions in the form of exponential series functions, which shows a good agreement with the previous results. The effects of various parameters on the velocity, temperature and concentration fields are discussed graphically. Results show that the velocity and the skin friction coefficient are decreasing with the increasing of the Maxwell parameter. The larger value of the stagnation parameter is, the thinner velocity boundary layer thickness goes. The thermophoresis restricts the heat and mass transfer. The Brownian motion resists the heat flux, but promotes the mass flux. [ABSTRACT FROM AUTHOR]