Effect Of Prandtl Number Research Articles

Numerical Exploration of Soret and Dufour Effect on Unsteady Free Convective Radiating Nanofluid Past a Vertical Moving Porous Plate

The present paper deals with the numerical investigation of Soret and Dufour effect on free convective heat and mass transfer characteristics of radiating water based nanofluid past a vertically moving porous plate in porous medium. The water based nanofluid with copper as a nanoparticle is considered in the present study. The dimensional governing equations relevant to the present model are transformed into non-dimensional form by using the appropriate parameters. The non-dimensional governing equations with the pertinent boundary conditions are solved numerically by using bvp4c function in Matlab software. The influence of suitable parameters on fluid velocity, temperature, concentration, Sherwood number (rate of mass transfer), Nusselt number (rate of heat transfer) and skin friction are exhibited graphically and discussed. Also, the effect of radiation parameter and Prandtl number in the absence of Dufour number has been compared with the help of contours. It is apparent from this study that fluid velocity increases with the increase in K, , & Du and decreases with increase in The fluid temperature increases with the increase in Du & R while it decreases with Pr. The fluid concentration increases with increase in whereas it decreases with . The rate of mass transfer (Sherwood number) increases with increase in Du and decreases with increase in & while the rate of heat transfer (Nusselt number) increases with increase in Du & Pr and decreases with increase in R. Shear stress (skin friction) decreases with the increase in , , K & Du.

Numerical simulations of convective heat transfer of a viscous fluid inside a rectangular cavity with heated rotating obstacles

With the help of commercial software, we have discussed the novel numerical simulations for a two-dimensional rectangular cavity with two square rotating obstacles, Fig. 1, that has fixed dimensions from the reference point (0, 0) placed in it, and we have interpreted a detailed convection analysis for fluid flow that highlights the physical, mathematical and numerical aspects of this system. The square obstacles having an anti-clockwise rotation are heated to a certain temperature, respectively, where the behavior of the fluid distribution depends upon the values of Reynolds number. We have conducted this research by fixing Reynolds number at four different positions like Reynolds 10, 30, 50 and 80. The prime effects of Reynolds number and Prandtl number are highlighted for convection analysis. Finally, we have analyzed the results of velocity, pressure, vorticity and temperature from the viewpoint of numerical simulations. Heat transfer has a huge dependence on the Reynolds number and Prandtl number.

Numerical investigation of thermo-hydraulic transport characteristics of laminar flow through partially filled porous wavy channel: Effect of Prandtl number

The present study numerically investigates the impact of different Prandtl numbers on thermo-hydraulic transport characteristics of partial porous wavy channel for a laminar flow. The series of simulations are performed for various thicknesses (S = 0, 0.2, 0.3, and 0.4) of the porous slab at different Prandtl numbers (0.72 ≤ Pr ≤ 100), Darcy numbers (10−6≤Da ≤ 10−2), and Reynolds number (Re = 5, 50, 200). Firstly, the variation of the average Nusselt number Nuavg , Enhancement Ratio ER, and Performance Factor PF has been delineated at constant Da for all the geometry configurations, Re, and range of Pr. The result shows a significant increment in the Nuavg and ER with increasing Pr and Re for all geometry configurations. However, the performance factor deteriorates with increasing slab thickness (S = 0.2, 0.3, and 0.4) compared to S = 0. Later, the effect of the various Da is evaluated, which revealed that the Nuavg decreases with increasing Da values, while the ER almost becomes double for Da values between 10−2 to 10−6 at S = 0.4. Streamline contours and temperature field distribution contours are also shown to visualize the physical phenomenon governing fluid flow and heat transfer.

Comparative heat transfer analysis of γ -Al2O3−C2H6O2 and γ -Al2O3−H2O electroconductive nanofluids in a saturated porous square cavity with Joule dissipation and heat source/sink effects

Inspired by the applications in electromagnetic nanomaterials processing in enclosures and hybrid fuel cell technologies, a mathematical model is presented to analyze the mixed convective flow of electrically conducting nanofluids (γ-Al2O3−H2O and γ-Al2O3−C2H6O2) inside a square enclosure saturated with porous medium under an inclined magnetic field. The Tiwari–Das model, along with the viscosity, thermal conductivity, and effective Prandtl number correlations, is considered in this study. The impacts of Joule heating, viscous dissipation, and internal heat absorption/generation are taken into consideration. Strongly nonlinear conservation equations, which govern the heat transfer and momentum inside the cavity with associated initial and boundary conditions, are rendered dimensionless with appropriate transformations. The marker-and-cell technique is deployed to solve the non-dimensional initial-boundary value problem. Validations with a previous study are included. A detailed parametric study is carried out to evaluate the influences of the emerging parameters on the transport phenomena. When 5% γ-Al2O3 nanoparticles are suspended into H2O base-fluid, the average heat transfer rate of γ-Al2O3−H2O nanoliquid is increased by 25.63% compared with the case where nanoparticles are absent. When 5% γ-Al2O3 nanoparticles are suspended into C2H6O2 base-fluid, the average heat transfer rate of γ-Al2O3−C2H6O2 nanofluid is increased by 43.20% compared with the case where nanoparticles are absent. Furthermore, when the heat source is present, the average heat transfer rate of γ-Al2O3−C2H6O2 nanofluid is 194.92% higher than that in the case of γ-Al2O3−H2O nanofluid.

Magnetohydrodynamic Jeffrey Nanofluid Flow Over a Vertical Sheet

Aim: This study focuses on the numerical analysis of Jeffrey nano-fluid bound with magnetic field in presence of convectively heated boundary.
 Study Design: Abstract, introduction, Equations formulation, numerical analysis and conclusion
 Place and Duration of Study: Department of Mathematics and Actuarial Science, Kenyatta University, between 2021-2022
 Methodology: This paper discusses the imposed magnetic field on Jeffrey fluid suspended with nanometre-sized particles moving over a vertical sheet with a convectively heated boundary. The partial differential equations are formulated by considering assumptions and the boundary conditions to describe the continuity, momentum, energy and concentration of the fluid. The similarity transformation technique was applied to convert the partial differential equations into first-order linear differential equations which were simulated in Matlab by invoking the Adam’s-Moulton predictor-corrector scheme in ode113.
 The graphs have been analysed with the effects of Deborah, Dufour-Lewis, Hartman, and Prandtl numbers respectively, solutal stratification, diffusion, thermophoresis, temperature Grashof, mass Grashof, relaxation-retardation parameters on the flow velocity, concentration, temperature, skin friction, heat and mass transfers looked into.
 Results: While Deborah number increased velocity, it reduced concentration, skin friction and thermal boundary layer at lower numbers hence improved mass and heat transfer. Solutal stratification, Retardation-relaxation parameter and diffusion raised temperature thus heat transfer.
 Conclusion: Deborah number, solutal stratification, retardation-relaxation parameter and diffusion improves heat and mass transfer.

Soret and Dufour aspects of the third-grade fluid due to the stretching cylinder with the Keller box approach

The convective transport of the third-grade fluid with thermo-diffusion features has to be worked out. The impact of the Soret and Dufour properties, as well as the radiative phenomena, is noticed. The assumed flow is due to the stretched cylinder. The partial differential equations indicating the flow model are first worked out into the dimensionless nature using similarity variables. The most effective numerical technique (the Keller Box method) has been used to solve nonlinear ODEs for obtaining the numerical data. The solution accuracy is validated using already claimed studies. The exploration subject to the flow pattern against parameters is presented. The simultaneous increase in Dufour and Soret numbers assists the temperature and concentration in the boundary layer region around the cylinder. With the increasing fluctuation in Dufour and reducing Soret numbers, the revised change in heat and mass transportation phenomenon is depicted. Furthermore, the radiation effects are elucidated by varying the effective Prandtl number.

The Influence of Effective Prandtl Number Model on the Micropolar Squeezing Flow of Nanofluids between Parallel Disks

A mathematical model of micropolar squeezing flow of nanofluids between parallel planes is taken into consideration under the influence of the effective Prandtl number using ethyl glycol (C2H6O2) and water (H2O) as base fluids along with nanoparticles of gamma alumina (γAl2O3). The governing nonlinear PDEs are changed into a system of ODEs via suitable transformations. The RKF (Range–Kutta–Fehlberg) technique is used to solve the system of nonlinear equations deriving from the governing equation. The velocity, temperature, and concentration profiles are depicted graphically for emerging parameters such as Hartmann number M, micronation parameter K, squeeze number R, Brownian motion parameter Nb, and thermophoresis parameter Nt. However, physical parameters such as skin friction coefficient, Nusselt number, and Sherwood number are portrayed in tabulated form. The inclusion of the effective Prandtl number model indicated that the effect of the micropolar parameter K on angular velocity h(ξ) in both suction and injection cases is opposite for both nanofluids. It is observed that the increase in angular velocity is rapid for γAl2O3−C2H6O2 throughout the study.

Numerical thermal featuring in γAl2O3-C2H6O2 nanofluid under the influence of thermal radiation and convective heat condition by inducing novel effects of effective Prandtl number model (EPNM)

The investigation of thermal transport in the nanofluid attained much interest of the researchers due to their extensive applications in automobile, mechanical engineering, radiators, aerodynamics, and many other industries. Therefore, a nanofluid model is developed for γAl2O3-C2H6O2 by incorporating the novel effects of Effective Prandtl Number Model (EPNM), thermal radiations, and convective heat condition. The model discussed numerically and furnished the results against the governing flow quantities. It is examined that the nanofluid velocity alters significantly due to combined convection and stretching parameter. Induction of thermal radiation in the model significantly contributed in the temperature of nanofluids and high temperature is observed by strengthen thermal radiation (Rd) parameter. Further, convection from the surface (convective heat condition) provided extra energy to the fluid particles which boosts the temperature of γAl2O3-C2H6O2. The comparison of nanofluid (γAl2O3-C2H6O2) temperature with base fluid (C2H6O2) revealed that γAl2O3-C2H6O2 has high temperature and would be fruitful for future industrial applications. Moreover, the study is validated with previously reported literature and found reliability of the study.

Nonsimilar numerical analysis for the mixed convective flow of Casson fluid with thermal radiations and chemical reactions

The focus of this nonsimilar study is to implore the effects of thermal radiations and chemical reactions on the boundary layer flow of Casson fluid over an exponentially stretching sheet. The appropriate nonsimilar transformations are implemented to convert convection differential equations into a set of coupled dimensionless partial differential equations (PDEs). The dimensionless nonsimilar system is analytically approximated by local nonsimilarity methods up to two truncations levels. The numerical simulations of the local nonsimilar truncations are obtained via Matlab-built-in solver bvp4c. The effects of several parameters, such as, radiation parameter, Schmidt and Prandtl numbers on local skin friction coefficient, local Nusselt and local Sherwood numbers, are given in a table, while velocity, temperature, and concentration distributions are numerically calculated and expressed through graphs. From numerical experiments, it can be concluded that the temperature flow profile escalates by enhancing the radiation parameter and the concentration profile de-escalates by rising values of the reaction rate parameter.

Thermal aspects of radiation in Casson fluid with nonlinear stretching surface: non-similar solutions

A mathematical model is established to peruse the effects of viscous dissipation and thermal radiation on non-Newtonian, incompressible, steady, mixed convective flow next to a nonlinear vertical stretching surface. The Rosseland approximation is used in the energy equation to describe the radiative heat flux. Non-similarity transformation has been used to convert coupled partial differential equations (PDEs) into dimensionless PDEs. For dealing with non-similar problems, the non-similarity method is more effective as compared to similarity transformation. First, this method utilizes transformations to reduce governing equations into dimensionless systems of PDEs, and further, it utilizes different truncation levels to get a detailed set of PDEs. MATLAB built-in solver bvp4c is used to solve obtained dimensionless PDEs. Parameters describing the nature of flow like local Sherwood number, local Nusselt number and local skin friction coefficient are explored in detail after finding the numerical solution. The effects of Casson number, Radiation number, Eckert number, Schmidt number, Prandtl number and Grashof number for heat and mass transfer on concentration, temperature and velocity profiles are specified with the aid of graphs.

Mixed convection heat transfer effects in a lid driven square cavity

This investigation numerically explored the parameters of mixed convection heat transfer in a square cavity with a bottom heated wall. The upper horizontal wall of the cavity is Tc, while the heated lower wall is Th, while the surfaces of the left and right walls are adiabatic. The main approach here is to solve numerically the mass, momentum, and energy flow equation using Galerkin weighted residual finite element method. Here, the Prandtl number (Pr), Richardson number (Ri), and Reynolds number (Re) effects have been investigated. The factors mentioned above have been found to have a significant impact on the temperature and flow fields.

Experimental observation on flow patterns of thermocapillary-buoyancy convection in shallow annular pools with a heated inner cylinder

Experimental observations on flow patterns of thermocapillary-buoyancy convection in shallow annular pools with a hot inner cylindrical wall have been carried out to understand the effect of Prandtl number on the flow pattern bifurcation. The results reveal that the flow could be weakened and the critical Marangoni number increases with the increasing aspect ratio and Prandtl number. With the increasing Marangoni number, both the transition from a stable multicellular flow to an oscillating multicellular flow and the pulsating pattern have been observed. Because the pulsating pattern is superimposed on an oscillating multicellular flow, thermocapillary convection evolves from periodic oscillatory state to quasi-periodic bifurcation state. As Prandtl number increases, both the oscillating multicellular flow and the pulsating pattern become difficult to be observed. Moreover, the pulsating pattern propagates radially from the hot inner cylindrical wall to the colder outer cylindrical wall, which is opposite to the direction of the surface-tension gradient. The underlying physical mechanism of the pulsating pattern is discussed.

Analytical analysis of non-boiling heat transfer during droplet impact on heated wall and the effect of thermophysical properties

Droplet impact process exhibits excellent heat and mass transfer characteristics. Analytical solution with simple explicit form and certain accuracy can clearly reflect the correlation of physical parameters, however the analytical study on droplet impact heat transfer is quite insufficient and limited to flow field analysis. In this paper, the analytical solutions of heat flux and temperature variation of droplet impact on heated wall in non-boiling regime were obtained based on boundary layer asymptotic matching method. Parameter analysis of thermophysical properties was conducted to explore the decisive properties of droplet and wall materials. The results showed that the analytical solutions are appropriate to predict non-boiling heat transfer at low impact velocity and low initial wall temperature. Parameter analysis showed that thermal effusivity is the decisive property rather than the thermal diffusivity. Wall thermal effusivity could independently determine heat flux, but should determine temperature variation together with wall thermal conductivity. Droplet thermal effusivity and Prandtl number were the decisive properties, however the effect of Prandtl number in reality can be ignored. Wall materials and droplet liquids with higher thermal effusivity showed higher heat transfer capacity. The importance of thermal effusivity was demonstrated and high thermal effusivity was preferred in future thermal management.

Instabilities of buoyancy-induced flow along vertical cylinder in thermally stratified medium

In this paper, the instability of the buoyancy-driven boundary layer on a vertical cylinder is considered. We provide a mathematical description of a vertical cylinder immersed in a stably stratified fluid, and the analytical solutions of the basic flow are derived. Based on linear stability analysis, the effects of Prandtl number and transversal curvature have been investigated. It is found that the most unstable mode for Pr = 0.7 is three-dimensional for the cylindrical radii between 0.03 and 46, while the critical modes are axisymmetric for Pr = 7 and 100. All the results for different Pr are consistent with those of the vertical plate when the radius is large enough. Additionally, for absolute instability analysis, there exists absolute instability in the present model when the dimensionless radius is less than 0.31, which is quite different from the results obtained in the vertical plate. These encouraging results revealed in this paper should be helpful for understanding such a buoyancy-driven flow system.

Effect of Heat Generation/Absorption and Radiation on Two-Dimensional Unsteady Magnetohydrodynamic Heat and Mass Transfer Nanofluid Boundary Layer Flow Over a Permeable Shrinking Sheet

The objective of this research is to look into the impact of heat generation/absorption and radiation on twodimensional unsteady magnetohydrodynamic forced convection heat and mass transfer nanofluid boundary layer flow over a permeable shrinking sheet. Similarity transformations are used to translate the governing time-dependent nonlinear PDEs into nonlinear ODEs. The Keller box method is used to solve the transformed equations. The effect of non-dimensional variables is studied and graphically illustrated on velocity, temperature, and concentration. The friction factor, Nusselt, and Sherwood numbers are also investigated and arranged for different values of Unsteadiness parameter, effective Prandtl number, thermophoresis parameter, magnetic field, Grashof number, Modified Grashof number, Lewis number, Heat Source/Sink, and Suction in tabular form. The velocity profiles for dual solutions have improved as the Thermal Grashof number and Modified Grashof number have amplified, but the temperature and concentration profiles have shown the reverse pattern. Temperature profiles are increasing as improving the Heat source/sink. The temperature and concentration profiles decline in the first and opposite pattern in the second solution with improved values of the magnetic field. The findings of this study are very well-acknowledged with current research.

Unsteady MHD Couette flow in a vertical porous channel with effect of thermal radiation and variable temperature

Unsteady MHD Couette flows in a vertical porous channel with effect of thermal radiation and variable temperature have been studied. The governing equations at first were transformed by usual transformation non-dimensional form. The numerical solutions for time dependent velocity, temperature and special concentration are obtained by the implicit finite difference method. The computed values of fluid velocity, temperature and concentrations are analyzed for different flow parameters such as thermal Grashof number Gr, modify Grashof number Gm, Prandtl number Pr, thermal radiation parameter R and Schmidt number Sc. The effect of these parameters depicting physical situation of the flow profile is expressed with the aid of line graphs. Significant results from this study showed that the velocity, temperature and concentration increases with increase in thermal radiation, magnetic field parameters and time, and decreases with the effect of Prandtl number, Schmidt number at increasing values.

Study of Rayleigh-Taylor instability in viscosity-stratified fluid layers

The Rayleigh-Taylor instability in viscosity varying fluid layers is studied. A heavier fluid layer is superimposed on a lighter fluid layer. Both the fluid layers are bounded between two parallel isothermal horizontal walls. Out of the two walls, one wall is isothermally heated, while the other wall is isothermally cooled. The Rayleigh-Taylor instability is studied for axisymmetric configuration. Viscosities of both the fluids are considered to be varying with temperature. The effect of viscosity ratio, temperature ratio, heating location, Prandtl number and Weber number on the instability is studied. When the viscosity of fluid layers vary with temperature, the configuration becomes more unstable compared to that for constant viscosity fluid layers. For varying viscosity fluid layers the spike undergoes large deformations. At lower viscosity ratios, mushroom shaped spike is formed with elongated skirt structure. Whereas, at higher viscosity ratios, spike with fluid column structure is formed. It is found that increasing viscosity ratio shows stabilizing effect. Increasing temperature ratio is found to show destabilizing effect with complex spike structure formation at high temperature ratios. In top wall heating configuration, formation of mushroom shaped spike and skirt of the spike occurs earlier in a thinner and elongated form compared to that of bottom wall heating configuration. Prandtl number showed insignificant effect on the instability. For the parameter values of the study, when Weber is lower than 55 the configuration is stable and does not undergo instability. Overall, surface tension has shown stabilizing effect on the instability.

A flow analysis of gamma-alumina nanoparticles near a solid sphere

ABSTRACT Prandtl number exhibits a primary role in regulating thermal or momentum boundary layer regions. Therefore, keeping such a comprehensive spectrum in view we contemplated the significance of an effective Prandtl number model on natural convection flow of non-uniform viscosity with steady, 2D, incompressible nano-liquids of and towards a solid heated sphere. To renovate the PDEs into a system of ODEs a felicitous transformation has been employed. The converted non-linear equations are executed numerically via BVP4C. Main findings reveal that nanoparticle volume fraction parameter augments the velocity component for both cases of effective and non-effective Prandtl numbers. A comparison reveals that offers better thermal transfer enhancement than . Entropy generation analysis is also perceived and the behavior of Grashof number is also presented.

Numerical simulation of Marangoni Maxwell nanofluid flow with Arrhenius activation energy and entropy anatomization over a rotating disk

The nanofluid flow under the consequences of Brownian motion, thermophoresis, and nonlinear radiation has been numerically studied over a heated rotating disc. Arrhenius activation energy is used to describe the various aspects of heat and mass transition. The problem has been modeled in the form of a system of PDEs consist of the Maxwell and Navier Stokes equations. The system of modeled equations has been reduced to the ordinary system of dimensionless differential equations using a similarity framework. For the problem's quantitative approximation, the results have been obtained through numerical technique boundary value solver (bvp4c). The physical quantities that derive from the modeled equations are displayed and addressed. It has been perceived that the Prandtl number and radiation effect improves the heat transmission rate while improving the magnetic parameter reduces the velocity field. Furthermore, the entropy rate and Bejan number increases with the rising effect of chemical reaction, temperature differential variable, concentration ratio variable and Schmidt number.

Numerical study of heat and mass transfer on the pulsatile flow of blood under atherosclerotic condition

Abstract The present article investigates the effects of heat and mass transfer on the pulsatile flow of blood through a tapered artery under atherosclerotic conditions. The blood is treated as Sutterby fluid. The wall of the artery is considered to be time-invariant having overlapping stenosis in its lumen. The fully coupled momentum, energy and concentration equations in conjunction with the constitutive equation of Sutterby fluid are simplified by applying the mild stenosis assumption. The governing equations together with the prescribed boundary conditions are discretized and solved by using the finite difference method. The results highlighting the effects of various emerging parameters on the heat and mass transfer are also displayed through graphs. The effects of stenosis height and Prandtl number on the axial variation of Nusselt number are also discussed in detail. A comparison of Sutterby fluid with the Newtonian fluid is also presented to highlight the effects of the Prandtl number on the heat and mass transfer. The present study reveals that the distribution of temperature in the constricted region of the blood vessel is closely associated with the viscoelastic nature of blood. It is also observed that the rate of heat transfer at the wall of the artery can be enhanced by reducing the thermal conductivity.