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The present study communicates with the thermal analysis of an incompressible micropolar fluid by considering two different prescribed conditions corresponding to two different surfaces. On the porous surface of two different stretchable sheets, the unsteady flow problem of a micropolar fluid is explored by taking the variable impacts of the magnetic field. For both considered sheets, the prescribed thermal analysis is carried out with the contribution of joule heating, viscous dissipation, and radiation. Two prescribed cases of surface temperature and heat flux are discussed for linear stretched surface. Similarly, prescribed cases of exponential surface temperature and exponential heat flux are investigated for the case of an exponential stretchable surface. An effective technique of bvp4c in MATLAB is utilized to numerically tackle the governing equations of the problem. Both the distributions of temperature and velocity and the field of microrotation are graphically scrutinized relative to different geometries and several pertinent parameters. This study of thermal analysis with prescribed conditions elucidates that for an exponential surface, three distributions of flow phenomenon (temperature, microrotation, velocity) manifest more prominent results in comparison to the stretchable surface with linear velocity.

Nanofluids with their excellent thermophysical properties strengthen the thermal performance of an ordinary fluid. Due to the efficacious thermophysical characteristics of nanofluids, the aim of the present study is to discuss the three distinct viscosity models for an incompressible Jeffrey nanofluid relative to its oscillatory oblique stagnation point flow. Three different viscosity models namely Brinkman model, Einstein model, and Reynolds model are discussed to scrutinize the thermophysical attributes of (TiO2-Kerosene oil) nanofluid. The unsteady magnetized flow problem of Jeffrey nanofluid is deliberated over an oscillatory medium corresponding to different frames of references namely fixed frame and moving frame. The thermal analysis is evaluated with the involvement of heat absorption/generation and radiation effects. In both frames of reference, the non-dimensional equations are numerically handled via an efficient technique of bvp4c. The fluid velocity and temperature distribution are graphically compared regarding three distinct viscosity models with numerous pertinent parameters. In the context of all viscosity models, both the distributions of velocity and temperature exhibit excellent behavior in the fixed and moving frame of reference. This study exhibits that the parameter that portrays the ratio of relaxation to retardation times deteriorates the flow field in the fixed frame for all viscosity models.

The scrutinization of entropy optimization in the various flow mechanisms of non-Newtonian fluids with heat transfer has been incredibly enhanced. Through the investigation of irreversibility sources in the steady flow of a non-Newtonian Willaimson fluid, an analysis of entropy generation is carried out in this current work. The current study has an essential aspect of investigating the heat transfer mechanism with flow phenomenon by considering convective-radiative boundary conditions. A horizontal MHD channel is assumed with two parallel plates to develop a mathematical model for the flow phenomenon by considering the variable viscosity of the fluid. The contribution of physical impacts of thermal radiation, Joule heating, and viscous dissipation is interpolated in the constitutive energy equation. The complete flow of the current analysis is established in the form of ordinary differential equations which further take the form of the dimensionless system through the contribution of the similarity variables. A graphical scrutinization of the physical features of the flow phenomenon in relation to the pertinent parameters is proposed. This study reveals that the higher magnitude of radiation parameter and Brinkman number dominates the system's entropy. Moreover, the temperature distribution experiences an increasing mechanism with improved conduction-radiation parameter at the lower plate.

Due to realistic implementations of heat transfer flows, this study communicates with the two cases of the prescribed thermal process. A comparative analysis of the time-dependent flow of a micropolar fluid between two problems of linear stretching sheet and exponential stretching sheet is demonstrated. In the context of the linear stretching sheet, the investigation covers situations involving prescribed surface temperature (PST) and prescribed heat flux (PHF). Likewise, for the exponential stretching sheet, the study examines cases of prescribed exponential order temperature (PEST) and prescribed exponential order heat flux (PEHF). For both problems, the two cases of the thermal process are examined for heat transfer analysis considering joule heating and nonlinear thermal radiation. The two-dimensional flow in the presence of a variable magnetic field is explored for both the linear and exponential stretching sheet problems. Graphical representations are employed to provide a comparative illustration of flow properties concerning relevant parameters for both cases. From the graphical and tabular analysis, we deduce that an exponential stretching sheet provides more consequential results as compared to a linear stretching sheet. Furthermore, the material parameter demonstrates an increase in the velocity field for both of the considered sheets.

Based on both the characteristics of shear thinning and shear thickening fluids, the Sutterby fluid has various applications in engineering and industrial fields. Due to the dual nature of the Sutterby fluid, the motive of the current study is to scrutinize the variable physical effects on the Sutterby nanofluid flow subject to shear thickening and shear thinning behavior over biaxially stretchable exponential and nonlinear sheets. The steady flow mechanism with the variable magnetic field, partial slip effects, and variable heat source/sink is examined over both stretchable sheets. The analysis of mass and heat transfer is carried out with the mutual impacts of thermophoresis and Brownian motion through the Buongiorno model. Suitable transformations for both exponential and nonlinear sheets are implemented on the problem's constitutive equations. As a result, the nonlinear setup of ordinary differential equations is acquired which is further numerically analyzed through the bvp4c technique in MATLAB. The graphical explanation of temperature, velocity, and concentration distributions exhibits that the exponential sheet provides more significant results as compared to the nonlinear sheet. Further, this study revealed that for the shear thickening behavior of Sutterby nanofluid, the increasing values of Deborah number increase the axial velocity.

Fractional calculus yields numerous implementations in different fields such as biological materials, physical memory, oscillation, wave propagation, and viscoelastic dynamics. Due to the significant applications of fractional calculus, the current study deals with the fractional derivative base study of a Brinkman hybrid nanofluid with an inclined magnetic field. A three-parametric Prabhakar fractional derivative with the involvement of the Mittag-Leffler function is implemented. A vertical plate moving with exponential velocity is considered to be the source of the flow mechanism. Moreover, the effects of exponential heating are incorporated into the thermal analysis. An appropriate group of dimensionless ansatz is adopted to get the dimensionless setup of equations. The Prabhakar fractional operator is implemented in the dimensionless equations which are further tackled by an effectual Laplace transform technique. An inverse Stehfest method and Tzou's method are implemented to tackle the inversion of the Laplace transform. This study exhibits that the fractional constraints minimize both the fields of temperature and velocity. Moreover, the velocity distribution deteriorates corresponding to the improved Brinkman parameter. The Brinkman parameter and the fluid's viscosity are directly related to each other. With the improved Brinkman parameter, the viscosity of the fluid increases. As a result, the fluid motion decreases.

This article exhibits a brief comparative study of magnetohydrodynamics stagnant point flow in hybrid nanofluid based on the extended version of two models, known as the Yamada-Ota model and Xue model. The time-dependent and thermally radiative two-dimensional flow is processed with the involvement of a stretchable/shrinking permeable sheet. The suspension of two nanoparticles Aluminum Oxide Al2O3 and Copper Cu into the base fluid water is considered for the formulation of hybrid nanofluid. With the execution of the significant similarity transformation, the nonlinear dimensionless system in the form of ordinary differential equations is developed. The Yamada-Ota and Xue models have been implemented on the dimensionless setup of equations that further are numerically worked out via the bvp4c methodology. The velocity and temperature fields corresponding to the pertinent parameters are figured out and discussed for both concerned models. From this study, we have come up with the result that the heat transfer rate involving the Yamada-Ota model is prominent as contrasted with the Xue model. The larger strength of the stretching parameter boosts up the field of the velocity but develops the deterioration in the temperature distribution. Moreover, the field of the velocity diminishes with the accelerating quantities of the solid nanoparticle.