Darcy–Forchheimer Radiative Flow of Micropoler CNT Nanofluid in Rotating Frame with Convective Heat Generation/Consumption

Application of Fractional Derivative Without Singular and Local Kernel to Enhanced Heat Transfer in CNTs Nanofluid Over an Inclined Plate

Nanofluids are a novel class of heat transfer fluid that plays a vital role in industries. In mathematical investigations, these fluids are modeled in terms of traditional integer-order partial differential equations (PDEs). It is recognized that traditional PDEs cannot decode the complex behavior of physical flow parameters and memory effects. Therefore, this article intends to study the mixed convection heat transfer in nanofluid over an inclined vertical plate via fractional derivatives approach. The problem in hand is modeled in connection with Atangana–Baleanu fractional derivatives without singular and local kernel with a strong memory. Human blood is considered as base fluid and carbon nanotube (CNTs) (single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs)) are dispersed into it to form blood-CNTs nanofluid. The nanofluid is considered to flow in a saturated porous medium under the influence of an applied magnetic field. The exact analytical expressions for velocity and temperature profiles are acquired using the Laplace transform technique and plotted in various graphs. The empirical results indicate that the memory effect decreases with increasing fractional parameters in the case of both temperature and velocity profiles. Moreover, the temperature profile is higher for blood SWCNTs because of higher thermal conductivity whereas this trend is found opposite in the case of velocity profile due to densities difference.

Unsteady Radiative Natural Convective MHD Nanofluid Flow Past a Porous Moving Vertical Plate with Heat Source/Sink

In this research article, we investigated a comprehensive analysis of time-dependent free convection electrically and thermally conducted water-based nanofluid flow containing Copper and Titanium oxide (Cu and TiO 2 ) past a moving porous vertical plate. A uniform transverse magnetic field is imposed perpendicular to the flow direction. Thermal radiation and heat sink terms are included in the energy equation. The governing equations of this flow consist of partial differential equations along with some initial and boundary conditions. The solution method of these flow interpreting equations comprised of two parts. Firstly, principal equations of flow are symmetrically transformed to a set of nonlinear coupled dimensionless partial differential equations using convenient dimensionless parameters. Secondly, the Laplace transformation technique is applied to those non-dimensional equations to get the close form exact solutions. The control of momentum and heat profile with respect to different associated parameters is analyzed thoroughly with the help of graphs. Fluid accelerates with increasing Grashof number (Gr) and porosity parameter (K), while increasing values of heat sink parameter (Q) and Prandtl number (Pr) drop the thermal profile. Moreover, velocity and thermal profile comparison for Cu and TiO 2 -based nanofluids is graphed.

Darcy–Boussinesq Model of Cilia-Assisted Transport of a Non-Newtonian Magneto-Biofluid with Chemical Reactions

The model developed in this study presents a mathematical approach to the physiological transport of seminal liquid due to ciliary movements, which are attached with the lumen of the ductile efferent in the male reproductive system. The rheological properties of the seminal liquids were described using the Jeffrey liquid model. The problem described an electromagnetic mixed convective flow of a Jeffrey liquid through a vertical channel with heat and mass transfers. The effects of chemical reactions and the external heat generation were included in the formulation. The flow took place through an active porous medium (due to thick cilia mat and other deposits) and was influenced by the Lorentz magnetic force. Four basic conservation laws of mass, momentum, energy, and concentration were utilized in the mathematical modeling. These are highly nonlinear equations, which were simplified due to a physiologically valid approach known as LAT (lubrication approximation theory). Analytical solutions for temperature, concentration, and velocity profiles were evaluated. The expressions describing the pressure–volume flow rate relationships were also obtained. Analysis of various physical and geometrical factors affecting the pressure–volume (pumping) characteristics was also presented. One of the main findings of our study is that the difference between our calculated values of the flow rate and the estimated values of the flow rate in the ductile efferent was negligibly small. Moreover, our results can be implemented in the artificial cilia pumping systems in microchannels.

Brownian Motion and Thermophoresis Effects on MHD Three Dimensional Nanofluid Flow with Slip Conditions and Joule Dissipation Due to Porous Rotating Disk

This paper examines the time independent and incompressible flow of magnetohydrodynamic (MHD) nanofluid through a porous rotating disc with velocity slip conditions. The mass and heat transmission with viscous dissipation is scrutinized. The proposed partial differential equations (PDEs) are converted to ordinary differential equation (ODEs) by mean of similarity variables. Analytical and numerical approaches are applied to examine the modeled problem and compared each other, which verify the validation of both approaches. The variation in the nanofluid flow due to physical parameters is revealed through graphs. It is witnessed that the fluid velocities decrease with the escalation in magnetic, velocity slip, and porosity parameters. The fluid temperature escalates with heightening in the Prandtl number, while other parameters have opposite impacts. The fluid concentration augments with the intensification in the thermophoresis parameter. The validity of the proposed model is presented through Tables.

Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition

The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative).

Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis

In this study, first-order slip effect with viscous dissipation and thermal radiation in micropolar fluid on a linear shrinking sheet is considered. Mathematical formulations of the governing equations of the problem have been derived by employing the fundamental laws of conservations which then converted into highly non-linear coupled partial differential equations (PDEs) of boundary layers. Linear transformations are employed to change PDEs into non-dimensional ordinary differential equations (ODEs). The solutions of the resultant ODEs have been obtained by using of numerical method which is presented in the form of shootlib package in MAPLE 2018. The results reveal that there is more than one solution depending upon the values of suction and material parameters. The ranges of dual solutions are S ≥ S c i , i = 0 , 1 , 2 and no solution is S < S c i where S c i is the critical values of S . Critical values have been obtained in the presence of dual solutions and the stability analysis is carried out to identify more stable solutions. Variations of numerous parameters have been also examined by giving tables and graphs. The numerical values have been obtained for the skin friction and local Nusselt number and presented graphically. Further, it is observed that the temperature and thickness of the thermal boundary layer increase when thermal radiation parameter is increased in both solutions. In addition, it is also noticed that the fluid velocity increases in the case of strong magnetic field effect in the second solution.

Activation Energy and Second Order Slip in Bioconvection of Oldroyd-B Nanofluid over a Stretching Cylinder: A Proposed Mathematical Model

The thermal performances based on the interaction of nanoparticles are the topic of great interest in recent years. In the current continuation, we have utilized the activation energy and thermal radiation consequences in the bioconvection flow of magnetized Oldroyd-B nanoparticles over a stretching cylinder. As a novelty, the second order slip features (Wu’s slip) and convective Nield boundary assumptions are also introduced for the flow situation. The heat performances of nanofluids are captured with an evaluation of the famous Buongiorno’s model which enables us to determine the attractive features of Brownian motion and thermophoretic diffusion. The suggested thermal system is based on the flow velocity, nanoparticles temperature, nanoparticles volume fraction and motile microorganisms. The governing flow equations for the flow problem are constituted with relevant references for which numerically solution is developed via shooting algorithm. A detailed graphically analysis for the assisted flow problem is performed in view of the involved parameters. Although some studies are available in the literature which deals with the flow of various fluids over-stretching cylinder, the phenomenon of bioconvection and other interesting features are not reported yet. Therefore, present scientific computations are performed to fill this gap and the reported results can be more useful for the enhancement of thermal extrusion processes, solar energy systems, and biofuels.

Heat Transfer Analysis of a Magneto-Bio-Fluid Transport with Variable Thermal Viscosity through a Vertical Ciliated Channel

We communicate the responses of various physiological fluids containing hemoglobin and other ionic constituents when they propagate in the presence of an electromagnetic body force field with the mechanisms of heat generation and conduction. A fully developed mixed convective flow of a Newtonian fluid takes place through a 2D vertical channel in the presence of an external magnetic field acting in the direction normal to the flow. The inner surface of the channel is carpeted with a thick mat of cilia, which propagates a sinusoidal metachronal wave travelling in the direction of flow. Coupled, nonlinear governing Naiver-Stokes and temperature equations are simplified by utilizing the creeping flow and long wavelength approximations. This enables us to formulate the exact analytical solution of the temperature distribution; whereas, the velocity distribution is evaluated from the momentum equations by using the Adomian decomposition method. In order to determine the pumping characteristics, the formulae of volume flow rate and the pressure rise are also obtained. Trapping due to the ciliary system is highlighted by graphing the stream function. The findings of the present model have significant outputs, which can be applicable in the physiological transport of human semen through the male reproduction system.