Fluid Prandtl Research Articles

Natural convection effects on heat and mass transfer of slip flow of time-dependent Prandtl fluid

Abstract We proposed a mathematical model for an incompressible, viscous, natural convection, and stagnation point slip flow of MHD Prandtl fluid over an infinite plate. The governing flow equations are constructed using the Prandtl rheological model. In account of physical relevance, we investigated the Soret and Dufour effects on the flow field. The complex natured flow equations are transformed to a set of PDEs using a suitable similarity variables. The non-dimensionalized ruling problem together with physical boundary conditions is numerically analyzed via Crank-Nicolson scheme. The velocity, temperature and concentration of the diffusing species distributions are enhanced for higher values of unsteadiness parameter. It is noted that velocity is slightly decreasing for higher values of Reynolds number while smaller values of Re providing more dominant effects on the velocity, temperature and concentration of the diffusing species profiles and enhanced heat and mass transfer rates is noticed. The physical behavior of reduced Nusselt and Sherwood numbers, friction factor, for distinct values of emerging parameters is examined and representative set of graphs are presented. Highlights Flow model is presented for MHD Prandtl fluid flow over an infinite plate. Mathematical model is performed for unsteady flow with Soret and Dufour effects. The proposed model is solved via crank Nicolson finite difference scheme. Simulations are performed for skin friction, Nusselt and Sherwood numbers.

Boundary layer flow and melting heat transfer of Prandtl fluid over a stretching surface by considering Joule heating effect

PurposeThe purpose of this paper is to study the impact of Joule heating on boundary layer flow and melting heat transfer of Prandtl fluid over a stretching sheet in the presence of fluid particles suspension. The transformed boundary layer equations are solved numerically by RKF-45 method. The influence of the non-dimensional parameters on velocity and temperature growths in the boundary layer region is analyzed in detail and the results are shown graphically. The results indicate that the larger estimation ofαandβreduces for both velocity and temperature profile. Further, the rate of heat transfer decreases by increasing melting parameter.Design/methodology/approachThe converted set of boundary layer equations is solved numerically by RKF-45 method. Obtained numerical results for flow and heat transfer characteristics are deliberated for various physical parameters. Furthermore, the skin friction coefficient and Nusselt number are also presented.FindingsIt is found that the heat transfer rates are advanced in the occurrence of non-linear radiation camper to linear radiation. Also, it is noticed that velocity profile increases by increasing Prandtl parameter but establishes opposite results for temperature profile.Originality/valueThe authors intend to analyze the boundary layer flow and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particles suspension. The governing systems of partial differential equations have been transformed to a set of coupled ordinary differential equations by applying appropriate similarity transformations. The reduced equations are solved numerically. The pertinent parameters are discussed through graphs and plotted graphs. The present results are compared with the existing limiting solutions, showing good agreement with each other.

Effects of coagulation on the two-phase peristaltic pumping of magnetized prandtl biofluid through an endoscopic annular geometry containing a porous medium

In this article, motivated by more accurate simulation of electromagnetic blood flow in annular vessel geometries in intravascular thrombosis, a mathematical model is developed for elucidating the effects of coagulation (i.e., a blood clot) on peristaltically induced motion of an electrically-conducting (magnetized) Prandtl fluid physiological suspension through a non-uniform annulus containing a homogenous porous medium. Magnetohydrodynamics is included owing to the presence of iron in the hemoglobin molecule and also the presence of ions in real blood. Hall current which generates a secondary (cross) flow at stronger magnetic field is also considered in the present study. A small annular tube (endoscopic) with sinusoidal peristaltic waves traveling along the inner and outer walls at constant velocity with a clot present is analyzed. The governing conservation equations which comprise the continuity and momentum equations for the fluid phase and particle phase are simplified under lubrication approximations (long wavelength and creeping flow conditions). The moving boundary value problem is normalized and solved analytically (with appropriate wall conditions) for the fluid phase and particle phase using the homotopy perturbation method (HPM) with MATHEMATICA software. Validation is conducted with MAPLE numerical quadrature. A parametric study of the influence of clot height (δ), particle volume fraction (C), Prandtl fluid material parameters (α, β), Hartmann number (M), Hall parameter (m), permeability parameter (k), peristaltic wave amplitude (φ) and wave number (δ¯) on pressure difference and wall shear (friction forces) is included. Pressure rise is elevated with clot height, medium permeability and Prandtl rheological material parameters whereas it is reduced with increasing particle volume fraction and magnetic Hartmann number. Friction forces on the outer and inner tubes of the endoscope annulus are enhanced with clot height and particle volume fraction whereas they are decreased with Prandtl rheological material parameters, Hall parameter and permeability parameter. The simulations provide a good benchmark for more general computational fluid dynamics studies of magnetic endoscopic multi-phase peristaltic pumping.

Comment on the paper “Three-dimensional flow of Prandtl fluid with Cattaneo-Christov double diffusion, Tasawar Hayat, Arsalan Aziz, Taseer Muhammad, Ahmed Alsaedi, results in physics 9 (2018) 290–296”

Comment on the paper “Three-dimensional flow of Prandtl fluid with Cattaneo-Christov double diffusion, Tasawar Hayat, Arsalan Aziz, Taseer Muhammad, Ahmed Alsaedi, results in physics 9 (2018) 290–296”

Dual Solutions for Unsteady Stagnation-Point Flow of Prandtl Nanofluid Past a Stretching/shrinking Plate

Dual solutions for the time-dependent flow of a Prandtl fluid containing nanoparticles along a stretching/shrinking surface are presented. The nano Prandtl fluid fills the porous stretching/shrinking surface. The Buongiorno model is employed by accounting Brownian motion and thermophoresis slip mechanisms in the analysis. The relevant nonlinear problem is treated numerically via Runge-Kutta-Fehlberg scheme. The flow profiles are scrutinized with respect to the different governing parameters. Results of this study indicate that the temperature boundary layer thickness increased due to the influence of nanoparticles.

A theoretical and comparative analysis of γAl2O3–H2O and γAl2O3–C2H6O2 nanoparticles with entropy generation and nonlinear radiation

Here nonlinear radiation influence in slip flow of viscous nanomaterial is modeled and elaborated. Rate of entropy generation is evaluated employing second thermodynamics relation. Energy equation is modeled via heat generation and thermal stratification aspects. Non-Darcy porous medium is considered. Prandtl number has an essential contribution in momentum and energy equations to control the boundary layer. For this purpose, effective and without effective Prandtl fluid models are utilized in forced convective nanomaterial flow over a stretched surface. Appropriate similarity transformations give the nonlinear systems. Influence of pertinent variables versus Bejan number and entropy rate are elaborated through graphs. Engineering quantities such as Nusselt number and coefficient of skin friction are examined graphically. The main conclusions are presented.

Scrutinization of Chemical Reaction Effect on Flow and Mass Transfer of Prandtl Liquid over a Riga Plate in the Presence of Solutal Slip Effect

AbstractIn the present paper focused on flow and mass transfer of Prandtl fluid over a Riga plate. The effects of chemical reaction and solutal slip are taken into the account. The governing partial differential equations are reduced into a set of coupled non linear ordinary differential equations using suitable similarity transformations. These equations are then solved using Runge-Kutta-Fehlberg-45 method. Behaviour of emerging parameters are presented graphically and discussed for velocity and concentration distribution. Numerical values of reduced skin friction coefficient and Sherwood number are shown in table and are discussed. From the plotted results it can be observed that the solutal boundary layer thickness decreases for larger values of chemical reaction parameter and Schmidt number. Also, momentum boundary layer thickness rise with stronger modified Hartman number.

The impact of impinging TiO2 nanoparticles in Prandtl nanofluid along with endoscopic and variable magnetic field effects on peristaltic blood flow

PurposeThe purpose of this paper is to study the variable magnetic field and endoscope effects on peristaltic blood flow of nanofluid containing TiO2 nanoparticles (NPs) through a porous annulus. The Prandtl fluid model is taken into account for the present flow. The mathematical modelling comprises the temperature, continuity, NP concentration, and equations of motion which are further simplified by taking a long peristaltic wave and creeping flow regime.Design/methodology/approachAfter using the long wavelength approximation, the obtained highly non-linear partial differential equations are solved using the homotopy perturbation scheme. The inclusion of the pertinent parameters is discussed mathematically and graphically for the pressure rise, friction forces, temperature profile, and concentration profile. The trapping phenomenon is also investigated with the help of contours.FindingsResults show that the maximum velocity distribution exists near the centre of the annulus, whereas the average time flow boosts the velocity profile. It has also been shown that flow can pass readily without enormous pressure gradient imposed on the endoscope tube unlike the case of the slim section of the problem.Practical implicationsThe nanofluids containing titanium NPs are increasingly utilised since such type of NPs is used by several manufacturers in sunscreen blockers and different types of endoscopy. In endoscopy, the variable magnetic field is used at the tip in order to detect or treat diseases. The NPs are used since they acquire specific thermal properties as compared with base fluids. The present study provides qualitative results showing the effect of inner tube of annulus on the fluid flow, the effect of variable magnetic field, and the change in the temperature profile on the flow field.Originality/valueA new model is introduced that shows the utmost pressure that works against the positive peristaltic pump. It studies the blood flow that results in extremely non-linear partial differential equations that are solved by the homotopy perturbation method. The titanium NPs are being used in blocking the rays that penetrate the epidermis causing skin burns and short ultraviolet ageing rays that cause visible wrinkles, and thus are used in the manufacturing of sunscreens that are partially absorbed through the skin.

Heat transfer analysis of Prandtl liquid nanofluid in the presence of homogeneous-heterogeneous reactions

Abstract The objective of present research work is to analyze the homogeneous-heterogeneous reactions on the MHD two-dimensional stagnation-point flow of non-Newtonian Prandtl fluid flow and heat transfer towards horizontal linear stretching sheet. The governing boundary layer equations using similarity transformation are reduced to ordinary differential equations suitable to be solved using Finite Difference Method. The quantities of interests are thoroughly analyzed under the effects of various emerging parameters. Comparison of the results obtained from limiting case of present model with already existing literature is in good agreement which shows the validity of the present numerical solution. The study concludes that homogeneous and heterogeneous reaction strength decreases the heat transfer rate. On the other hand, Prandtl fluid parameter and elastic parameter increases heat transfer rate.

Three-dimensional flow of Prandtl fluid with Cattaneo-Christov double diffusion

Abstract This research paper intends to investigate the 3D flow of Prandtl liquid in the existence of improved heat conduction and mass diffusion models. Flow is created by considering linearly bidirectional stretchable sheet. Thermal and concentration diffusions are considered by employing Cattaneo-Christov double diffusion models. Boundary layer approach has been used to simplify the governing PDEs. Suitable nondimensional similarity variables correspond to strong nonlinear ODEs. Optimal homotopy analysis method (OHAM) is employed for solutions development. The role of various pertinent variables on temperature and concentration are analyzed through graphs. The physical quantities such as surface drag coefficients and heat and mass transfer rates at the wall are also plotted and discussed. Our results indicate that the temperature and concentration are decreasing functions of thermal and concentration relaxation parameters respectively.

Soret and Dufour effects on MHD peristaltic flow of Prandtl fluid in a rotating channel

Abstract An analysis has been arranged to study the magnetohydrodynamics (MHD) peristaltic flow of Prandtl fluid in a channel with flexible walls. Both fluid and channel are in a state of solid body rotation. Simultaneous effects of heat and mass transfer with thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects are considered. Convective conditions for heat and mass transfer in the formulation are adopted. Ordinary differential systems using low Reynolds number and long wavelength approximation are obtained. Resulting equations have been solved numerically. The discussion of axial and secondary velocities, temperature, concentration and heat transfer coefficient with respect to emerging parameters embedded in the flow model is presented after sketching plots.

Numerical Investigation of Transient Magnetohydrodynamic Mixed Convection in a Ventilated Cavity Containing Two Heated Circular Cylinders

ABSTRACTA two-dimensional finite volume computation is performed to analyze the transient magnetoconvective transport in a ventilated cavity containing two inner heated circular cylinders with identical shape. An electrically conducting fluid (Prandtl number 0.01) enters the cavity through an opening at the middle of the left wall and is taken away by a similar opening at the middle of the right wall. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. Simulations are performed for the parameters, Richardson number (0, 0.25, 0.5, and 1), Reynolds number (380–550), Hartmann number (0, 10, 20, and 50) and dimensionless gap between the cylinders 0.1, 0.2, and 0.3. The analysis indicates that the transport process is a complex function of the magnetic field strength, mixed convective strength and the cylinder distance. Some typical combinations of these controlling parameters may produce three different transport characteristics such as the steady state, periodic oscillatory, and chaotic. With a lower cylinder distance and higher mixed convective strength, the flow instability increases causing periodic and even chaotic oscillations, whereas the magnetic field due to its damping nature imparts stability to the flow resulting in a steady state flow condition.

Homogeneous–heterogeneous reactions in peristaltic flow of Prandtl fluid with thermal radiation

This attempt is made to look at the influence of homogeneous–heterogeneous reactions on MHD peristaltic flow of Prandtl fluid. The configuration of channel is considered as inclined and asymmetric. Mathematical modelling is developed through consideration of Joule heating, viscous dissipation and thermal radiation. Heat and mass transfer phenomenons are addressed simultaneously. Numerical solutions of problem are attained after employing long wavelength and low Reynolds number assumptions. The results for velocity, temperature, concentration and heat transfer rate have been emphasized through graphical illustration. Physical interpretation for sundry parameters of interest is carried out in detail. Results indicate that concentration decreases during both homogeneous and heterogenous reactions where thermal radiation lessens fluid temperature and rate of heat transfer.

Passive control of nanoparticle due to convective heat transfer of Prandtl fluid model at the stretching surface

The objective of present research work is to establish the non-Newtonian nanofluid flow and heat transfer along a stretching surface. Stagnation point flow of Prandtl nanofluid is purposed over a convective surface where zero normal flux of nanoparticles is considered to disperse the particle away from the surface. Physical problem is governed by mathematical model which consists of continuity, momentum, energy and concentration equations which are adapt to non-linear ordinary differential equations using transformation of variables. Numerical computational is implemented for coupled nonlinear equations using finite difference method (FDM) to analyze the flow and heat transfer characteristics under the influence of various physical parameters namely: Prandtl fluid parameter, elastic parameter, magnetic parameter, stagnation parameter, Prandtl number, Brownian motion parameter, thermophoresis parameter, Lewis number, stretching parameter, and Biot number. Obtained results describe the effects of significant parameters on temperature and nanoparticle volume concentration due to zero flux and convective boundary condition. It is found that due to zero flux, concentration of nanoparticles disperse at the surface within the boundary layer region.

Peristaltic flow of an Eyring Prandtl fluid in a diverging tube with heat and mass transfer

The present article reflects the peristaltic motion of an Eyring Prandtl fluid in a diverging tube in the presence of heat and mass transfer. Mathematical Analysis has been carried out by considering the assumptions of long wave length and low Reynolds number. Under these limitations, we obtain resulted non linear system of small values. These have been evaluated analytically using homotopy Perturbation method. The succeeding complex disparity computations are explained for velocity, temperature, concentration field and pressure gradient. The effects of physical parameters on the flow and heat transfer attributes are investigated in detail. Special attention is given to explain the pumping and trapping phenomena in detail. Convergence of solution is clearly shown in the graphical results. It is found that rate of heat transfer and mass transfer decreases with increasing Brashof number. The consequence of many underdeveloped restraint are explicate for five dissimilar impressions. Streamlines in trust at the terminus point of the objective.

Computational Fluid Dynamics Study on Forced Convective Heat Transfer Phenomena of Spheres in Power-law Liquids with Velocity Slip at the Interface

ABSTRACTNumerical results on combined effects of the slip velocity, power-law fluid behavior index, Reynolds number, and Prandtl number on the forced convective heat transfer characteristics of single spheres in power-law liquids with velocity slip at the fluid-solid interface are reported on the basis of computational fluid dynamics approach. The governing conservation equations of the momentum and energy along with the appropriate boundary conditions are nondimensionalized using appropriate scaling parameters. These dimensionless equations are solved by a segregated approach using a finite difference method based simplified marker and cell algorithm implemented on a staggered grid arrangement in spherical coordinates. The detailed domain and grid independence studies along with appropriate validations are carried out to establish reliability and accuracy of the solver. Further extensive new results obtained in the range of conditions as: Reynolds number, 0.1–200; dimensionless slip number, 0.01–100; power-law index, 0.5–1.6; and Prandtl number, 1–100. The effects of these dimensionless parameters on the isotherm contours and local and average Nusselt numbers are thoroughly delineated. Finally, on the basis of present numerical results, an empirical correlation for the average Nusselt numbers of single spheres in power-law liquids with velocity slip at the interface is proposed.

On the Solution of Boundary Layer Flow of Prandtl Fluid Past a Flat Surface

On the Solution of Boundary Layer Flow of Prandtl Fluid Past a Flat Surface

Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet

Abstract An analysis is performed to explore the effects of homogenous-heterogeneous reactions on two-dimensional flow of Prandtl fluid over a stretching sheet. In present analysis, we used the developed model of homogeneous–heterogeneous reactions in boundary layer flow. The mathematical configuration of presented flow phenomenon yields the nonlinear partial differential equations. Using scaling transformations, the governing partial differential equations (momentum equation and homogenous-heterogeneous reactions equations) are transformed into non-linear ordinary differential equations (ODE’s). Then, resulting non-linear ODE’s are solved by computational scheme known as shooting method. The quantitative and qualitative manners of concerned physical quantities (velocity, concentration and drag force coefficient) are examined under prescribed physical constrained through figures and tables. It is observed that velocity profile enhances verses fluid parameters α and β while Hartmann number reduced it. The homogeneous and heterogeneous reactions parameters have reverse effects on concentration profile. Concentration profile shows retarding behavior for large values of Schmidt number. Skin fraction coefficient enhances with increment in Hartmann number H and fluid parameter α .

Numerical analysis for endoscope and Soret and Dufour effects on peristalsis of Prandtl fluid

This article addresses the effect of endoscope on peristaltic flow of Prandtl fluid in an inclined tube. Simultaneous study of heat and mass transfer is performed by considering thermal-diffusion and diffusion-thermo effects. No-slip conditions for velocity, temperature and concentration are imposed. Tube walls are compliant in nature. Analysis is subject to long wavelength approximation. Impacts of sundry parameters on the physical quantities like velocity, temperature, concentration and heat transfer rate are discussed. A comparative study with existing research is made. The significant feature of this study reveals the activation of temperature and reduction of concentration with larger Soret and Dufour effects. Also the Froude and Reynolds numbers show similar behavior towards velocity.

Effects of mass transfer on MHD three dimensional flow of a Prandtl liquid over a flat plate in the presence of chemical reaction

The present study addresses the three-dimensional flow of a Prandtl fluid over a Riga plate in the presence of chemical reaction and convective condition. The converted set of boundary layer equations are solved numerically by RKF four-fifth method. Obtained numerical results for flow and mass transfer characteristics are discussed for various physical parameters. Additionally, the skin friction coefficient and Sherwood number are also presented. It is found that, the momentum boundary layer thickness is dominant for higher values of α and solutal boundary layer is low for higher Schmidt number and chemical reaction parameter.