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The present numerical study is aimed at investigating the effect of rotation on heat transfer to non-Newtonian nanofluid flowing through a pipe. Non-Newtonian fluid flow under laminar condition with heat transfer finds the applications in various industries like food processing, pharmaceutical and polymer etc. Various proportions (1–3%) of copper nanoparticles are mixed with water to study the heat transfer rates non-Newtonian nanofluid flowing through the rotating pipe. Effect of rotation rate on heat transfer rates are also studied. In this study for 1% nanofluid at a constant rotation rate of 0.8, the Nusselt number is increased by 119.45%. The highest thermal performance factor (TPF) is 1.74, observed at N = 0.8, Pe = 5000, and for 1% volume concentration of non-Newtonian nanofluid. [ABSTRACT FROM AUTHOR]

Heat transfer is an important process in many engineering, industrial, residential, and commercial buildings. Thus, this study aims to analyse the effect of MHD and viscous dissipation on radiative heat transfer of Reiner–Philippoff fluid flow over a nonlinearly shrinking sheet. By adopting appropriate similarity transformations, the partial derivatives of multivariable differential equations are transformed into the similarity equations of a particular form. The resulting mathematical model is elucidated in MATLAB software using the bvp4c technique. To determine the impact of physical parameters supplied into the problem, the results are shown in the form of tables and graphs. The findings reveal that the heat transfer rate reduces as the Eckert number and radiation parameter are introduced in the operating fluid. However, increasing the magnetic parameter raises both the skin friction coefficient and the local Nusselt number, which impulsively improves the heat transfer performance. The suction effect has a noticeable influence on the Reiner–Philippoff fluid, since increasing the suction parameter's value is seen to enhance the skin friction coefficient and the heat transfer performance. The dual solutions are established, leading to the stability analysis that supports the first solution's validity. [ABSTRACT FROM AUTHOR]

This work investigates the Ohmic heating, nonuniform heat generation, and Hall effects with Cattaneo-Christov model (CCM) on flow and heat transfer of power-low non-Newtonian fluids (NNFs) past stretching surface embedded in a porous medium. Runge-Kutta method is used to solve non-linear ODEs numerically using a shooting procedure. We study non-Newtonian fluids for power law values of 0.7 and 1.2, respectively. Innovation of this work lies in studying the effect of Hall currents in presence of buoyancy force and an irregular heat source on slip flow of NNFs moving through Darcy porous medium. Varying velocities, surface frictional forces, and Nusselt numbers are examined. Resulting entropy is also examined using computational flow problem investigation. Model-simulated results suggested that various factors play critical role in constructing thermal systems. It is asserted that Hall parameter, mixed convection parameter, Biot numbers, and thermal relaxation time improve heat transference rates by directly affecting fluid molecules temperature. [ABSTRACT FROM AUTHOR]

• Various industrial configurations were simulated and evaluated for optimal heat transfer efficiency. • Nano metal particles were employed in the simulation to enhance heat transfer efficiency. • The results show that the square geometry with a certain amount of nano metals performs better than other common industrial geometries. • The simulation results align well with other researchers' laboratory results in this field. Spiral tube heat exchangers represent a conventional type of exchanger that finds use in industries such as food, chemical reactors, ventilation, and heat recovery systems. The compact structure, high mass, and heat transfer coefficient of spiral tubes have made them popular in many industries as heat exchangers. This article delves into the investigation of the flow of non-Newtonian Nano fluid CuO-CMC within pipes that possess different cross-sections. In order to analyze the heat transfer of the non-Newtonian Nano fluid flow in the spiral channel, both the single-phase model and the ANSYS Fluent commercial software were employed for simulation. In the realm of numerical simulation, investigation has been conducted on the flow of non-Newtonian water-copper oxide Nano fluid through spiral tubes having three distinct cross-sections, namely circular, square, and oval. The study aimed to delve into the effects of varying volume fractions of nanoparticles, inlet velocities, and cross-sectional areas on several parameters, including but not limited to average Nusselt number, local Nusselt number, vorticity, bulk temperature, transferred heat, average friction coefficient, and local friction coefficient. Elevating Re has a greater impact on Nu than adding nanoparticles. Even with 4% nanoparticles, Nu is lower than pure water with Re of 5000. Incorporating nanoparticles enhances fluid's thermal characteristics but disrupts flow. [ABSTRACT FROM AUTHOR]

Porous materials are used in thermal devices such as heat exchangers to improvement the heat transfer. The heat transfer of a non-Newtonian fluid flow in an annular pipe with porous discs is numerically investigated in this paper. The flow regime in both porous medium and clear region are considered to be turbulent. The effects of power-law index of the non-Newtonian fluid and porous discs pitch variationson the heat transfer rate, friction coefficient are studied and compared to each other for two porous layer thicknesses. Finally, the thermal performance is defined which determines the optimum porous media and non-Newtonian fluid characteristics in the annular pipe. [ABSTRACT FROM AUTHOR]

In this study, a numerical investigation on mixed convection inside a trapezoidal cavity with a pair of rotating cylinders has been conducted. Three different power-law fluid indexes (n = 1.4, 1.0, and 0.6) have been considered to model different sets of non-Newtonian fluids. Four separate cases are considered based on the rotational orientation of the cylinders within the cavity. In the first two cases, the cylinders rotate in the same direction, i.e., both counterclockwise (CCW), and both clockwise (CW), whereas, in the other two cases, cylinders rotate in opposite directions (CW-CCW and CCW-CW). Simulations have been carried out over a broad range of Reynolds number (from 0.5 to 500) and angular speeds (a dimensionless value from 0 to 10). The average Nusselt number values at the isothermal hot inclined cavity surface are determined to evaluate heat transfer performance in various circumstances. Streamlines and isotherm contours are also plotted for a better understanding of the effects of different cases for various parameters on thermal and fluid flow fields. It is found that the Nusselt number varies nonlinearly with different angular speeds of the cylinders. The combined effect of the mixing induced by cylinder rotation and viscosity characteristics of the fluid dictates the heat transfer in the system. Predictions from the numerical investigation provide insights into the sets of key parametric configurations that have a dominant influence on the thermal performance of the lid-driven cavity with double rotating cylinders. [ABSTRACT FROM AUTHOR]

This paper simulated the free convective heat transfer (CHT) and generation of entropy (GOE) of a non-Newtonian fluid (NNF) in a square chamber using the FDLBM approach. The NNF is modeled by the power-law method. A magnetic field (MF) is able to take different angles which has affected the chamber. A hot square barrier exists in the middle of the chamber. The side edges of the chamber have sinusoidal temperature profiles, and the top and bottom sides are insulated. The effective studied parameters include the Hartmann number (Ha), angle of MF, exponential function index, and the aspect ratio (AR) of the hot barrier. The results of simulation disclosed that shear-thinning NNF has the highest CHT and shear-thickening NNF has the lowest GOE. Increasing the AR of the hot barrier led to an increase in the Nusselt number (Nu) and GOE and a decrease in the Bejan number (Be). Increasing the angle of the MF at small ARs with Newtonian fluid increases the Nu. Increasing the Ha from 0 to 40 in shear-thinning NNF, shear-thickening NNF, and Newtonian fluid reduced CHT by 43%, 15%, and 43%, respectively. Increasing the Ha also reduces the GOE by 27% for Newtonian fluid and 763% and 4% shear-thinning NNF and shear-thickening NNF, respectively. Eventually, a relation is proposed for the mean Nu, GOE, and Be. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation of power-law fluid flow past and through elliptical porous cylinder, considering heat transfer effects. The study covers a wide range of parameters, including Reynolds number, power-law index, cylinder aspect ratio and Darcy number. The wake pattern, streamline distribution, drag coefficient, pressure distribution, and Nusselt number are analyzed comprehensively for various cases. Within the investigated parameter range, four distinct vortices are observed: an external vortex separated from the cylinder, an external vortex attached to the cylinder, a boundary vortex partially inside and outside the cylinder, and an internal vortex entirely inside the cylinder. The occurrence of the external and separated vortex is limited to AR = 0.2 and = 10 − 3 , while the internal and boundary vortices are exclusively observed at AR = 2.0. Additionally, increasing the aspect ratio of the elliptical cylinder results in shorter vortices at a given Reynolds and Darcy number. For example, at Re = 40 and D a = 10 − 4 , vortex lengths decrease from 5 to 0.6 with increasing aspect ratio from 0.2 to 2. Furthermore, by decreasing aspect ratio, the drag coefficient generally increases and the Nusselt number decreases from 0.2 to 1, but this trend reverses as the aspect ratio rises from 1 to 2. • Four distinct vortices (external separated, external attached, boundary, and internal) are observed. • External separated vortex is limited to AR = 0.2 and D a = 10 − 3 . • Internal and boundary vortices are exclusively observed at AR = 2.0. • Drag coefficient is considerably affected by vortex type. • At high values of Da number (Da = 10−1, 10−2), as the power index increases, the Nusselt number increases. [ABSTRACT FROM AUTHOR]

This paper deals with the melting effect on steady mixed convection flow of a non-Newtonian fluid containing gyrotatic microorganism along a vertical plate embedded in a saturated non-Darcy porous medium. Variable fluid properties are considered in this paper to describe the variation of permeability, porosity, thermal conductivity which is approximated by an exponential function. The changed non-dimensional governing ordinary differential equations via similarity transformation characterize the flow phenomena subjected to melting surface boundary condition are solved numerically by Matlab bvp4c solver. To analyze the consequences of flow influencing parameters to the flow variables are tabulated and visualized graphically. With increasing non-Darcy and mixed convection parameters velocity profiles decays. Temperature escalates for mixed convection parameter and plunges for melting parameter. Concentration slow down for high melting effect and rises for high Lewis number. Bioconvection Lewis number and Peclet number has an increasing impact on the microorganism profiles. Mixed convection parameters show pronouncing impact on Sherwood number, Nusselt number and motile microorganism density profiles but they decrease mostly for pseudo plastic fluid. Comparisons with prior works show splendid agreement between the results. [ABSTRACT FROM AUTHOR]

The current endeavor examines the convective heat transfer characteristics on magnetohydrodynamic stagnation point flow of micropolar fluid past an exponential curved surface. The flow is supposed to be laminar and time-independent. The influence of radiation, irregular heat source/sink, Joule heating, and variable thermal conductivity are supposed. Suitable similarity renovations are considered to transform the original partial differential equations as ordinary ones and then resolved by shooting and fourth-order Runge-Kutta methods. Graphs are drawn to inspect the impacts of sundry nondimensional parameters on the distributions of velocity, microrotation, and temperature. We detect that there is an escalation in temperature with Eckert number and variable heat source/sink parameters. Also, it is motivating to comment that Biot number is an increasing function of local Nusselt number. [ABSTRACT FROM AUTHOR]

The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convection flows, the surface of the cylinder is maintained by the uniform surface temperature (UST) or the uniform heat flux (UHF) condition. The governing equations corresponding to the flow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids (n > 1) than the other fluids (n ⩽ 1). The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature. [ABSTRACT FROM AUTHOR]

• Looking back at the research done in this area, we can see that effective heat transportation is still a major focus, and the sole notion of nanoliquid has proven useful in this way. • The current analysis investigates the three-dimensional flow of MHD Maxwell fluid flow containing gyrotactic microorganisms over a stretching surface. • The influence of the magnetic field is applied normal to the direction of the fluid flow. Additionally, the significance of chemical reaction, thermal radiation, heat source, and activation energy are also considered. • The Cattaneo-Christov heat and mass flux model has been employed to illustrate the energy and mass transmission in viscoelastic flow caused by the stretching sheet. • The modeled equations are reformed into a dimensionless system of differential equations through similarity variables which are further semi-analytically solved through the homotopy analysis method. During the last few decades, researchers have been increasingly interested in non-Newtonian fluid flows due to their practical applications. There is an increasing interest in non-Newtonian fluids due to the wide variety of applications in many disciplines, including biological sciences, geophysics, the chemical industry, and petroleum engineering. Plastics, polymers, pulps, food, fuels, and molten plastics are among the fluids that exhibit non-Newtonian properties. The three-dimensional MHD Maxwell fluid flow comprising gyrotactic microorganisms over a stretching surface is analytically examined in the present analysis. The influence of the magnetic field is applied normal to the direction of the fluid flow. Additionally, the significance of chemical reaction, thermal radiation, heat source, and activation energy are also considered. The Cattaneo-Christov heat and mass flux model has been employed to illustrate the energy and mass transmission in viscoelastic flow caused by the stretching sheet. The modeled equations are reformed into a dimensionless system of differential equations through similarity variables which are further semi-analytically solved through the homotopy analysis method. The nature of velocity, concentration, energy, and motile microorganisms' profiles are graphically presented against the variation of distinct physical constraints. It has been noticed that the velocity of Maxwell fluid declines by the rising influence of Rayleigh number, mixed convection, relaxation factor, magnetic field, and buoyancy ratio constant. The consequence of fluid relaxation term drops the energy profile, while the consequences of velocity ratio factor and magnetic field augment the temperature field. Furthermore, the Nusselt number advances with the rising trend of thermal radiation and heat source, while reducing with the impact of the thermal stratification factor. [ABSTRACT FROM AUTHOR]

• A comprehensive and detailed solution of double-diffusive natural convection of Casson fluids in an enclosure is obtained. • The influence of the governing parameters on fluid flow, morphology of yielded/unyielded regions, and heat and mass transfer are thoroughly examined. • The unyielded regions grow with decreasing buoyancy ratio and increasing the yield number. • The Lewis number has different effects on unyielded areas depending on the flow parameters. • Correlations for average Nusselt and Sherwood numbers are provided. This study investigates the double-diffusive natural convection of the non-Newtonian Casson fluid in a square cavity based on the original viscoplastic stress model without simplification. Therefore, yield stress plays an essential role in understanding fluid behavior. The finite element approach provided a numerical solution to continuity, momentum, energy, and species governing equations. The governing parameters for this problem are Rayleigh number, Ra , yield number, Y , buoyancy ratio number, Nr , and Lewis number, Le. The influence of these parameters on heat and mass transfer, the morphology of yielded/unyielded regions, and fluid flow are thoroughly examined. The results show that unyielded regions increase at high Rayleigh numbers, despite the increase in buoyancy force and consequently increased heat and mass transfer. On the other hand, as the buoyancy ratio drops, the flow's strength and heat and mass transmission diminish, leading to an increase in plug regions. Accordingly, the mechanisms influencing the growth of unyielded regions are complex and follow different patterns. However, the plug regions always grow with increasing Y. The results indicate that increasing the Lewis number (mass transfer) reduces the effect of the buoyancy ratio on flow, heat transfer, and the unyielded regions in every case. Quantitative analysis of the results indicates that, while buoyancy ratio affects heat and mass transfer almost equally, the Lewis number increases mass transfer up to three times the heat transfer. Meanwhile, changing the buoyancy ratio can increase the maximum yield stress to 400%, while changing the Lewis number has a maximum effect of 20%. [Display omitted] [ABSTRACT FROM AUTHOR]

• Viscosity correction factor derived from first principles for constant wall temperature. • Viscosity correction to Nusselt number for convective heat transfer in laminar flow. • Detailed thermal boundary layer analysis for Prandtl number >1. The role of variable viscosity on the heat transfer in non-Newtonian fluid flow has not been adequately explored in the past. Typically, non-Newtonian fluids are described by the power-law type behaviour as τ = K γ ̇ n (τ : shear stress; K : consistency index; γ ̇ : shear rate; n : power-law exponent). The viscosity correction factor in the form of K w K ∞ m (w : wall; ∞ : bulk) is a function of n. Traditionally, the Sieder-Tate correction for Newtonian fluid, μ w μ ∞ - 0.14 was the popular choice (μ w : fluid viscosity at the wall, μ ∞ : bulk) (Metzner et al. 1957). This is the first work on postulating the viscosity correction from the fundamental boundary layer analysis in non-Newtonian fluid. The mathematical predictions are validated with the literature experimental data. Inaccurate estimation of the viscosity correction leads to under- or over-predictions of the heat transfer coefficient, consequently, affects the effective heat transfer area. The correlations developed in this work would help in improved area calculations, thus, better performance and economic benefits. [ABSTRACT FROM AUTHOR]