Free convection of non-Newtonian nanofluids about a vertical truncated cone in a porous medium

This work studies the free convection heat transfer over a truncated cone embedded in a porous medium saturated by a non-Newtonian power-law nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar equations are solved by the cubic spline collocation method. The effects of the power-law index, Brownian motion parameter, thermophoresis parameter and buoyancy ratio on the temperature, nanoparticle volume fraction and velocity profiles are discussed. The reduced Nusselt numbers are plotted as functions of the power-law index, thermophoresis parameter, Brownian parameter, Lewis number, and buoyancy ratio. Results show that increasing the thermophoresis parameter or the Brownian parameter tends to decrease the reduced Nusselt number. Moreover, the reduced Nusselt number increases as the power-law index is increased.     

Lie group analysis of hyperbolic tangent fluid flow in the presence of thermal radiation

The present study is devoted to the flow and heat transfer analysis of the hyperbolic tangent fluid through a stretching sheet by considering the effect of thermal radiation in addition to an applied transverse magnetic field, as well as thermal and velocity slip conditions. The Lie group analysis technique has been utilized for establishing similarity transformations, which effectively transform the governing equations to a system of nonlinear ordinary differential equations (ODEs). These ODEs are numerically solved by utilizing the shooting method. The heat transfer properties and flow features under the influence of various physical parameters are also studied. We noted that by increasing the thermal radiation parameter, the temperature profile increases and also the thermal boundary layer thickens. Furthermore, it is deduced that rising the thermal radiation parameter reduces the local Nusselt number. Moreover, the numerical results obtained are in agreement with the existing results in the literature.     

Effects of viscous dissipation on forced convective heat transfer in a channel embedded in a power-law fluid saturated porous medium

The convective heat transfer analysis in a channel embedded in a power-law fluid saturated porous medium subject to uniform heat flux is presented and compared with a Newtonian fluid concerning the effects of viscous dissipation. Governing momentum and energy equations for non-Newtonian fluids which accounts for the viscous dissipation effects are solved numerically. The temperature profiles of the non-Newtonian fluids are found to relate closely to the velocity profiles. When viscous dissipation is taken account of, Nusselt numbers for non-Newtonian fluid are found to deviate more from Newtonian fluid with increasing Brinkman number for a certain range of the Darcy number.     

Impacts of couple stress with magnetic field and heat absorption on peristaltic flow of a power-law fluid containing nanoparticles

This paper deals with the mathematical examination of the arrangement of incomplete differential conditions which depict the peristaltic movement of a non-Newtonian nanofluid with couple stress through a symmetric channel with flexible walls. The fluid used obeys a power-law model. The system of the nondimensional form of momentum, heat, and concentration of the fluid flow is solved numerically by using a Rung–Kutta–Merson method with the appropriate boundary conditions after using the approximations of long wavelength and low Reynolds number. The obtained arrangements are elements of the physical boundaries of the problem. In this manner, the impacts of these boundaries on the velocity, temperature, and nanoconcentration distributions are concentrated mathematically and shown graphically through many figures. It is discovered that the physical boundaries play a significant role in controlling the arrangements, where the speed field diminishes with expansion of the attractive boundary, while it increments with expanding couple pressure and the non-Newtonian parameter of the non-Newtonian liquid. Additionally, the temperature and nanoconcentration changes with the Brownian parameter and thermophoresis. Moreover, the temperature distribution increases with increase of the magnetic parameter, Prandtl number, Eckert number, and heat source.     

Thermophoresis and Brownian motion effects on Williamson nanofluid flow past a stretching surface with thermal radiation and chemical reaction

The heat transfer mechanism of nanofluids has numerous industrial applications owing to the non-Newtonian behavior and has been exercised as a thermophysical phenomena in presence of thermal radiation. The present paper deals with the thermal transfer characteristics of time-independent magnetohydrodynamics Williamson fluid past a stretching surface in presence of the reaction of chemical equilibrium is dealt. The flow constitutive nonlinear partial differential coupled equations are transmitted into ordinary differential equalities by employing relevant similarity transmutations. These deduced equations are determined by using the Runge–Kutta numerical technique with a shooting approach with the aid of MATLAB software. Influences of distinct pertinent flow parameters like an inclined uniform magnetic field, Soret number, heat generation/absorption, and Schmidt number constrained to convective boundary condition is displayed through graphs with relevant physical interpretations. Computed numerical values for the friction factor coefficient, local Nusselt parameter, and Sherwood number are tabulated.      

Numerical analysis of MHD nanofluid flow over a wedge,including effects of viscous dissipation and heat generation/absorption,using Buongiorno model

The key purpose of this article is to examine magnetohydrodynamics flow, generative/absorptive heat, and mass transfer of nanofluid flow past a wedge in the presence of viscous dissipation through a porous medium. The investigation is completely theoretical, and the present model expresses the influence of Brownian motion and thermophoresis using the nanofluid Buongiorno model. The fundamental model of partial differential equations is reframed into the structure of ordinary differential equations implementing the nondimensional similarity transformation, which are tackled through the fourth–fifth-order Runge–Kutta–Fehlberg algorithm together with the shooting scheme. The analysis of sundry nondimensional controlling parameters, such as magnetic parameter, Eckert number, heat generation/absorption parameter, porosity parameter, Brownian motion parameter, and thermophoresis parameter on velocity, temperature, and concentration profiles are discussed graphically. The effects of the physical factors on the rate of momentum and heat and mass transfer are also determined with appropriate analysis in terms of skin friction, Nusselt number, and Sherwood number. The outcomes illustrate that the local Nusselt number and local Sherwood number are reduced for higher values of the thermophoresis parameter. Besides, it is found that higher estimations of heat generation/absorption and viscous dissipation parameters increase temperature. Moreover, it is found that the temperature profile increases with the involvement of the Brownian motion parameter, while an opposite trend is observed in the concentration profile. A comparison is also provided for limiting cases to authenticate our obtained results.     

Steady magnetohydrodynamic Poiseuille flow of two immiscible non-Newtonian and Newtonian fluids in a horizontal channel with Ohmic heating

In this paper, an analytical study has been carried out on a steady magnetohydrodynamics (MHD) Poiseuille flow of two immiscible fluids in a horizontal channel with ohmic heating in the presence of an applied magnetic field. The channel is divided into two sections, Region I and Region II, respectively. Region I contains an electrically conducting, third grade, non-Newtonian fluid while Region II is a Newtonian fluid. The regular Perturbation series method is used to transform the coupled nonlinear differential equations governing the flow into a system of linear ordinary differential equations in both fluid regions. Suitable interface matching conditions were chosen to obtain separate solutions for each fluid in both regions and the results were displayed graphically for various values of physical parameters, such as pressure gradient, suction parameter, Hartmann number, Prandtl number, viscosity, and conductivity ratios to show their effects on the flow. The effect of skin friction and Nusselt number was shown with the aid of tables. The results obtained among other findings clearly shows that as the value of the magnetic parameter increases, the velocity and temperature of the fluid decrease.     

Laminar Flow and Heat Transfer to a Non-Newtonian Fluid in an Entrance Region of a Square Duct with Prescribed Constant Axial Wall Heat Flux

Abstract

Forced-convection heat transfer information as a function of the pertinent nondimensional numbers is obtained numerically for laminar incompressible non-Newtonian fluid flow in the entrance region of a square duct with simultaneously developing temperature and velocity profiles for constant axial wall heat flux with uniform peripheral wall temperature. The power-law model characterizes the non-Newtonian behavior.

Finite-difference representations are developed for the equations of the mathematical model, and numerical solutions are obtained assuming uniform inlet velocity and temperature distributions. Results are presented for local and mean Nusselt numbers as functions of the Graetz number and the Prandtl number in the entrance region. Comparisons are made with previous analytical work for Newtonian fluids. The results show a strong effect of the Prandtl number on the Nusselt numbers with fully developed and uniform velocity profiles representing the lower and upper limits, respectively. The results provide a new insight into the true three-dimensional character of the pseudoplastlc fluid flow in the entrance region of a square duct and are accurate.     

Energy analysis of non-Newtonian nanofluid flow over parabola of revolution on the horizontal surface with catalytic chemical reaction

Nanofluids are special functional fluids, which are designed to reduce the loss of energy and maximize the transport of heat. The thermophoresis and Brownian motion of the particle are important factors in the transport of heat in these fluids. The rise in heat transport shows encouraging effects in control of dissipation of energy and reduces entropy generation. In the current study, two-dimensional non-Newtonian Casson nanofluid flow on an upper horizontal surface of a parabola is investigated. The impact of catalytic surface chemical reactions has been account also due to its industrial importance. For this flow problem, the governing equations are modeled using the law of conservation of mass, momentum, heat, and concentration equation. The fitting transformations are taken to change governing couple partial differential equations and domain into local similar ordinary differential equation and domain of [0,∞). Using the "RK4" approach with Newton's shooting schemes via MATLAB tools, the numerical solution of dimensionless governing equations is sorted. It is observed that the Casson fluid parameter caused a drop in temperature profile, and the chemical reaction parameter is the source of the rise in the temperature field.     

Local thermal nonequilibrium conjugate natural convection heat transfer of nanofluids in a cavity partially filled with porous media using Buongiorno’s model

The natural convection heat transfer in a cavity filled with three layers of solid, porous medium, and free fluid is addressed. The porous medium and free fluid layers are filled with a nanofluid. The porous layer is modeled using the local thermal nonequilibrium (LTNE) model, considering the temperature difference between the solid porous matrix and the nanofluid phases. The nanofluid is modeled using the Buongiorno’s model incorporating the thermophoresis and Brownian motion effects. The governing equations are transformed into a set of nondimensional partial differential equations, and then solved using finite element method in a nonuniform grid. The effects of various nondimensional parameters are discussed. The results showed that the Brownian motion and thermophoresis effects result in significant concentration gradients of nanoparticles in the porous and free fluid layers. The increase in Rayleigh (Ra), Darcy (Da), the thermal conductivity ratios for the solid wall and solid porous matrix, i.e., K_r and R_k, enhanced the average Nusselt number. The increase in the convection interaction heat transfer parameter between the solid porous matrix and the nanofluid in the pores (H) increases the average Nusselt number in the solid porous matrix but decreases the average Nusselt number in the nanofluid phase of the porous layer.     

Transient natural convection of non-Newtonian fluids about a vertical surface embedded in an anisotropic porous medium

An analytical method is carried out to investigate transient free convection boundary layer flow along a vertical surface embedded in an anisotropic porous medium saturated by a non-Newtonian fluid. The porous medium is anisotropic in permeability with its principal axes oriented in a direction that is non-coincident with the gravity force. A step increase in wall temperature or in surface heat flux is considered. On the basis of the modified Darcy power-law model proposed by Pascal [H. Pascal, Rheological behaviour effect of non-Newtonian fluids on steady and unsteady flow through porous media, Int. J. Numer. Anal. Methods in Geomech. 7 (1983) 207–224] and the generalized Darcy’s law described by Bear [J. Bear, Dynamics of fluids in porous media. Dover Publications, Elsevier, New York (1972)], boundary-layer equations are solved exactly by the method of characteristics. Scale analysis is applied to predict the order-of-magnitudes involved in the boundary layer regime. Analytical expressions are obtained for the limiting time required to reach steady-state, the boundary-layer thickness and the local Nusselt number in terms of the modified-Darcy Rayleigh number, the power-law index, the anisotropic permeability ratio, and the orientation angle of the principal axes. It is demonstrated that both the power-law index and the anisotropic properties have a strong influence on the heat transfer rate.     

Dufour and Soret influence on MHD boundary layer flow of a Maxwell fluid over a stretching sheet with nanoparticles

An analysis has been carried out to examine the heat and mass transfer properties of a two-dimensional incompressible electrically conducting Maxwell fluid over a stretching sheet in the existence of Soret, Dufour, and nanoparticles. In many practical scenarios, such as the polymer extrusion process, the problem presented here is crucial. The flow is examined in terms of the impacts of magnetohydrodynamics and elasticity. Brownian motion and thermophoresis are incorporated into the transport equations. Using adequate similarity variables, the governing partial differential equations and related boundary conditions are non-dimensionalized. The fourth–fifth-order Runge–Kutta–Fehlberg procedure is utilized to solve the consequent transformed ordinary differential equations. The effects of various embedded thermo-physical parameters on the fluid velocity, temperature, concentration, Nusselt number, and Sherwood number have been determined and discussed quantitatively. A comparison of a special case of our results with the one previously reported in the literature shows a very good agreement. An increase in the values of Du and Sr leads to an increase in the temperature and concentration distribution. Nusselt number estimates decrease as Nb estimations increase. Furthermore, this study leads to the study of different flows of electrically conducting fluid over a stretching sheet problem that includes the two-dimensional nonlinear boundary equations.     

Natural convection boundary layer flow over a truncated cone in a porous medium saturated by a nanofluid

This work studies the natural convection boundary layer flow over a truncated cone embedded in a porous medium saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A suitable coordinate transformation is performed, and the obtained nonsimilar equations are solved by the cubic spline collocation method. The effect of the Brownian motion parameter and thermophoresis parameter on the temperature, nanoparticle volume fraction and velocity profiles are discussed. The effects of the thermophoresis parameter, Brownian parameter, Lewis number, and buoyancy ratio on the local Nusselt number have been studied. Results show that an increase in the thermophoresis parameter or the Brownian parameter tends to decrease the local Nusselt number. Moreover, the local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased.     

MHD,thermal radiation,thermophoresis and Soret–Dufour mechanism contributions on unsteady motion of Casson fluid over a semi-infinite porous vertical plate

This paper examined the contribution of MHD, thermal radiation, thermophoresis and Soret–Dufour mechanism on unsteady motion of Casson non-Newtonian fluid. The flow model which resulted in partial differential equations (PDES) was transformed into a dimensionless form of PDES using suitable quantities. The contributions of controlling flow parameters were graphically presented for velocity, temperature, and concentration. The quantities of engineering interest were calculated for flow parameters and presented using table. A considerable value of Soret parameter was noticed to elevate the skin friction and Sherwood number. Impact of the magnetic parameter has great impact on the motion of Casson fluid by lowering its motion. This is because as the value of magnetic parameter increases the Lorentz force added more strength and hereby slow down the motion of an electrically conducting fluids. The present outcomes were examined with previously published work and was in conformity with each other.     

Thermally dependent viscosity and non-Newtonian flow in a double-pipe helical heat exchanger

A double-pipe helical heat exchanger was numerically studied to determine the effects of thermally dependent viscosity and non-Newtonian flows on heat transfer and pressure drop for laminar flow. Thermally dependent viscosities were found to have very little effect on the Nusselt number correlations for Newtonian fluids; however significant effects on the pressure drop in the heat exchanger were predicted. Changing the flow rate in the annulus can significantly affect the pressure drop in the inner tube, since the average viscosity of the fluid in the inner tube would change due to the change in the average temperature.The effects of non-Newtonian power law fluids on the heat transfer and the pressure drop were determined for laminar flow in the inner tube and in the annulus. The Nusselt number was correlated with the Péclet number for heat transfer in the inner tube. For the annulus, the Nusselt number was found to correlate best with the Péclet number and the curvature ratio. Pressure drop data were compared by using ratios of the pressure drop of the non-Newtonian fluid to a Newtonian fluid at identical mass flow rates and consistency indices.     

Heat transfer due to electroosmotic flow of viscoelastic fluids in a slit microchannel

The bio-microfluidic systems are usually encountered with non-Newtonian behaviors of working fluids. The rheological behavior of some bio-fluids can be described by differential viscoelastic constitutive equations that are related to PTT and FENE-P models. In the present work, thermal transport characteristics of the steady fully developed electroosmotic flow of these fluids in a slit microchannel with constant wall heat fluxes have been investigated. The Debye–Huckel linearization is adopted and the effects of viscous dissipation and Joule heating are taken into account. Analytical solutions are obtained for the transverse distributions of velocity and temperature and finally for Nusselt number. Two different behaviors are observed for the Nusselt number variations due to increasing ?_geWe² which are an increasing trend for positive wall heat flux and a decreasing one for negative wall heat flux. However, the influence of ?_geWe² on Nusselt number vanishes at higher values of the dimensionless Debye–Huckel parameter. It is also realized that the effect of viscous heating is more important at small values of both ?_geWe² and the dimensionless Debye–Huckel parameter. Furthermore, the results show a singularity in Nusselt number at higher negative values of the dimensionless Joule heating parameter.     

Thermal characteristics of forced convection in combined pressure and shear-driven flow of a non-Newtonian third-grade fluid through parallel plates

Heat transfer in a non-Newtonian third-grade fluid, flowing under the action of pressure gradient and shear, through two parallel plates, is considered. The upper plate moves with a constant velocity. Constant wall heat fluxes are applied to the plates. Effect of viscous dissipation is included, which has a major role in heat transfer of non-Newtonian fluids. The governing equations are nonlinear and are solved semi-analytically by using the least-square method (LSM). Then, using the solution for velocity in the energy equation, the solution is obtained by a direct integration process. Further, approximate analytical solutions are obtained by the perturbation method, which validates the results generated by the LSM. The effects of the third-grade fluid parameter on the velocity and temperature and also on the physical quantity, such as Nusselt's number, are discussed. Further, viscous dissipation effects on the temperature distribution have been analyzed. Observations show that the movement of the upper plate results in a significant decrease in temperature near the upper plate. For the unit heat flux ratio, the temperature difference between the surface and fluid is more at the upper surface due to the enhanced convective heat transfer caused by the moving upper plate. Nusselt's number increases significantly with an increase in the heat flux ratio.     

Simultaneous effects of radiation,magnetic field on peristaltic flow of Carreau nanofluid submerged in gyrotactic microorganisms with heat and mass transfer

Our study intends to examine the combined effects of radiation, magnetic field, and chemical reaction on the peristaltic flow of a non-Newtonian fluid containing gyrotactic microorganisms and nanoparticles. The system of our equations is understood numerically by using the Rung-Kutta-Merson method with Newton iteration in a shooting and matching procedure. The effect of physical implanted parameters is represented and discussed through a lot of charts for velocity, temperature, nanoparticle concentration, the density of motile microorganisms. From this discussion, we notice that the motile microorganisms profile is affected by the arising with the Brownian motion parameter and radiation parameter but the thermophoresis parameter, traditional Lewis number, and bioconvection of Peclet number are decremented the motile microorganisms profile.     

Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid

This work studies the free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar governing equations are then solved by the cubic spline collocation method. The effects of the Brownian motion parameter and thermophoresis parameter on the profiles of the temperature, nanoparticle volume fraction and velocity profiles are presented. The local Nusselt number is presented as a function of the thermophoresis parameter, Brownian parameter, Lewis number and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). Results show that the local Nusselt number is increased as the thermophoresis parameter or the Brownian parameter is decreased. The local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased. Moreover, the local Nusselt number of the elliptical cylinder with slender orientation is higher than those of the elliptical cylinder with blunt orientation over the lower half cylinder.     

Impacts of Cattaneo–Christov heat flux on the radiative MHD nanofluid flow past a stretched cylinder under multiple slip conditions

This investigation explores the features of velocity distribution, mass and heat transmissions of nanoliquid stream over a permeable cylinder accompanied by Cattaneo–Christov heat model and thermal radiation with nonlinear sort. Multiple slip conditions have been also encountered here. A magnetic force is oriented along vertically upward. The existence of thermophoresis together with Brownian motion has been assumed here. The foremost equations and associated boundary conditions have been normalized through the similarity technique. Then we solve the system numerically along with the fourth-order Runge–Kutta shooting scheme by using the software MAPLE-17 and round it with our preassigned accuracy level. The obtained outcomes are epitomized by tables and graphs. All of the impacts have been compared in suction and injection correspondingly and explained with proper reasoning. In charts, the physical consignments (such as Sherwood number, Nusselt number and skin friction) reveal the transference of mass and temperature and amount of friction by nanoparticles in the nanocomposition. For suction, the nanofluidic temperature gradually diminished due to the advanced thermal relaxation, whereas the contrary fact is exhibited in injection. The relaxation parameter of concentration provides a positive influence on mass transmission. The rates of amplification of this transportation are 1.99% and 3.87%, measured in consideration of injection and suction, respectively. Thermal radiation influenced the fluid's temperature in a positive direction. It increases Nusselt number with 41.75% in suction, and 45.21% is recorded for injection.