Laminar Free Convection Flow Research Articles

Effect of Viscous Energy Dissipation on Transient Laminar Free Convective Flow of a Dusty Viscous Fluid through a Porous Medium

Effect of Viscous Energy Dissipation on Transient Laminar Free Convective Flow of a Dusty Viscous Fluid through a Porous Medium

Second Law Analysis for Free Convection in an L-Shaped Cavity Filled with Nanofluid

The paper aims to analyze the effects of various Prandtl number and different nanoparticles for heat transfer and entropy generation of free convection laminar fluid flow in an L-shaped cavity filled by nanofluid. To investigate the second law characteristics of free convective flow and heat transfer from an L- shaped geometry filled by water and nanofluids (Cu-water, Ag-water, Al2O3-water), the effects of Prandtl number and various nanoparticles on the average Nusselt number, total entropy generation and Bejan number has been numerically analyzed. Isotherms, stream function and entropy generation caused by heat transfer are also presented for various Prandtl numbers and various nanoparticles. The governing equations are solved using penalty finite element method with Galerkins weighted residual technique. The results reveal that Ag-water nanofluid with highest Prandtl number gives the highest amount of irreversibility as well as rate of heat transfer. Cu-water and Ag-water nanofluid produces more irreversibilities than Al2O3-water nanofluid and base fluid. Also the results show that the Nusselt number and Bejan number increase with the increase of Prandtl number. Therefore, Prandtl number may be an important parameter for desired heat transfer increment with decreasing entropy generation in the given geometry.

Aligned magnetohydrodynamic effect on magnetic nanoparticle with different base fluids past a moving inclined plate

This paper deals with the numerical solutions for the aligned MHD free convection laminar boundary layer flow over a moving inclined plate for two magnetic nanofluids, namely Fe3O4-water and Fe3O4-kerosene. It is assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid is on the right surface. The mathematical model has been constructed and based on the Tiwari-Das model, appropriate similarity transformations are used to convert the governing partial differential equations into nonlinear ordinary differential equations and solved numerically using the Keller-Box method. Numerical results for the skin friction coefficient and local Nusselt number were presented whilst the velocity and temperature profiles were illustrated graphically and analyzed. It is found that the velocity increases and temperature decrease with an increase of aligned magnetic field angle parameter, magnetic strength parameter, and Grashof number while the velocity decreases and temperature increase when inclined plate angle parameter and volume fractions of nanoparticles increase. For the convective parameter, both velocity and temperature profile increase when the Biot number increase. Comparisons with previously published studies are performed and excellent agreement is obtained.

NUMERICAL STUDY OF FREE CONVECTION Ag-WATER NANOFLUID FLOW IN A SQUARE ENCLOSURE WITH VISCOUS DISSIPATION AND HEAT GENERATION/ABSORPTION EFFECTS IN A POROUS MEDIUM WITH COMPLEX WALL CONDITIONS

Nanofluids hold great promise in improving transport processes in energy systems including hybrid fuel cells. In this present work, a mathematical model is developed for laminar free convection flow of Ag-water nano-additives in an enclosure in a porous medium with complex boundary conditions. Additionally, heat generation/absorption and viscous dissipation effects are included. Via appropriate scaling transformations, the conservation equations for mass, primary and secondary momentum, energy, and nanoiparticle vorticity with wall boundary conditions are rendered dimensionless. A finite-difference computational scheme known as the marker and cell (MAC) method, developed by Harlow and Welch, is occupied to solve the dimensionless, nonlinear coupled boundary value problem. A mesh independence study is included. The impact of parameters such as Eckert number (Ec), Darcy number (Da), Grashof number (Gr), Prandtl number (Pr), Reynolds number (Re), and Richardson number (Ri) are observed with physical framework. Graphical plots are presented for the impact of key control parameters on streamline contours, isotherm contours, and local Nusselt number. By heat sink (absorption), the Nusselt number is increased, whereas by heat generation it is reduced since there is a decrease in heat transferred to the boundary. The presence of viscous dissipation effects moves the streamlines toward the blue core and allows the temperature to increase in the neighborhood of the hot wall of the envelope. An increase in Richardson number induces a flip in vortex cell structures from an initially strong circulation cell on the left and weaker cell on the right, to the opposite distribution. Significant cooling is also induced in the core zone with an increasing Richardson number, and a decrease in vorticity is observed.

Unsteady MHD free convective flow past a vertical plate: An automated solution approach

The case of unsteady two-dimensional laminar free convection flow over a vertical plate by an incompressible viscous fluid is analysed in the presence of uniform magnetic field perpendicular to the flow. The governing equations in a vector form are transformed into non- dimensional form. Then, the dimensionless equations are solved using automated solution technique which is FEniCS. The effects of magnetic parameter on the velocity and temperature profiles are obtained and discussed in this paper

CFD simulation of laminar free convection flows of nanofluids in a cubical enclosure

Understanding the physics behind heat transfer within an enclosure especially in the natural convection domain has many important applications. The heat transfer performance of nanofluids inside a cubical enclosure with an internal heat source fixed on the side-wall of the enclosure will be investigated under natural convection flow condition in this paper. A three-dimensional two-phase mixture model will be developed and validated for this investigation. Computational fluid dynamic (CFD) simulations will be undergone using an in-house solver developed on simplified marker and cell (SMAC) algorithm within a collocated grid by finite difference method. The time dependent flow and characteristics of heat transfer for nanofluids will be investigated with pure water as the base fluid dispersed with different nanoparticles. In addition, parametric studies will also be performed by varying the particle volume concentrations (0%≤Φ ≤ 3%), particle diameters (25 nm ≤ Dp ≤ 50 nm) and Grashof numbers (103 ≤ Gr ≤ 106). The particle volume concentration when increased in a nanofluid gives more affinity to heat absorption. Velocity increase of particles leads to the efficient mixing of nanofluid and so an increase in Grashof number also leads to heat transfer enhancement. Decrease in particle diameter is the final parameter which shows a heat transfer increase.

Influence of Heat Source/Sink on Free Convection in Annular Porous Region

The significant interpretation of this model is to explore the influence of temperature-dependent heat source/sink on laminar free-convective flow in an annular porous region such as petroleum engineering, thermal technique and groundwater hydrology. For a unified solution of the Brinkman-Darcy model, the regulatory equations solved analytically by applying the variation of parameter technique in terms of Bessel's functions for the heat source and sink. Moreover, we have investigated the Variations of Darcy number, Heat source/sink and viscosity ratio in the presence of isothermal and constant heat flux sequentially. As a result, we received the critical value of the velocity for the radii ratio (R = 2.05 and 2.92) in both the cases of source and sink (S = 1.0 and Si = 0.1) respectively which is exhibited through the graphs. Further, the numerical outcomes present of the skin friction including volume flow with annular gap by the graphs as well as tables.

Entropy generation and heat transfer analysis in power-law fluid flow: Finite difference method

In this article entropy generation analysis for unsteady laminar free convection flow of power-law fluid is investigated. Fluid flow is in the presence of thermal radiation and magnetic field. The flow and heat transfer are governed by coupled system of PDE's. System of partial differential equation (PDE's) governs the continuity, momentum and energy equations. Using suitable dimensionless parameters, the system of PDE's is transformed into dimensionless form. Numerical computations made employing finite difference method (FDM). This method converts the nonlinear PDE 's to simple algebraic equations and by using variational technique the approximate solution is obtained technique. Impacts of important flow variables on velocity, skin friction and Nusselt number are shown graphically. Skin friction and Nusselt number are discussed for different pertinent flow variables. Velocity, temperature, entropy and Bejan number variations through important variables are discussed in the form of graphs. The obtained results show that velocity decays against Re, Ha and Pr. Temperature is enhanced for higher values of Re, Ec, Tr and Gr. For higher estimation of Ec entropy of the system enhance while show opposite behavior for the Bejan number. Entropy of system boosts for strong magnetic field.

Radiation-absorption, chemical reaction, Hall and ion slip impacts on magnetohydrodynamic free convective flow over semi-infinite moving absorbent surface

The investigation of radiation-absorption, chemical reaction, Hall and ion-slip impacts on unsteady MHD free convective laminar flow of an incompressible viscous, electrically conducting and heat generation/absorbing fluid enclosed with a semi-infinite porous plate within a rotating frame has been premeditated. The plate is assumed to be moving with a constant velocity in the direction of fluid movement. A uniform transverse magnetic field is applied at right angles to the porous surface, which is absorbing the fluid with a suction velocity changing with time. The non-dimensional governing equations for present investigation are solved analytically making use of two term harmonic and non-harmonic functions. The graphical results of velocity, temperature and concentration distributions on the analytical solutions are displayed and discussed with reference to pertinent parameters. It is found that the velocity profiles decreased with an increasing in Hartmann number, rotation parameter, the Schmidt number, heat source parameter, while it increased due to an increase in permeability parameter, radiation-absorption parameter, Hall and ion slip parameters. However, the temperature profile is an increasing function of radiation- absorption parameter, whereas an increase in chemical reaction parameter, the Schmidt number Sc or frequency of oscillations decrease the temperature profile on cooling. Also, it is found that the concentration profile is decreased with an escalating in the Schmidt number or the chemical reaction parameter.

Aligned magnetic field effects on an unsteady MHD free convective Laminar flow past an exponentially infinite vertical porous plate in the presence of radiation absorption, chemical reaction and heat generation.

Aligned magnetic field effects on an unsteady MHD free convective Laminar flow past an exponentially infinite vertical porous plate in the presence of radiation absorption, chemical reaction and heat generation.

MHD natural convective flow of a polar fluid with Newtonian heat transfer in vertical concentric annuli

ABSTRACT A fully developed laminar free convective flow of polar fluid between two concentric vertical cylinders has been considered. The outer surface of the inner cylinders is subjected to Newton’s law of heat transfer in the presence of an adjustable transverse magnetic field. The magnetic lines of force interact with conducting flowing fluid to generate a force act-at-a-distance (control input). The analytic solutions of the governing equations are obtained in the form of modified Bessel function. The important findings are: Newtonian heating/cooling as well as vortex viscosity reduce the velocity distribution; micro-rotation and linear velocity having opposite signs have an experimental bearing; magnetic force, act-at-a-distance, a control input reduce the primary flow which may have a therapeutic application; vortex viscosity is favourable for generating low skin friction coefficient; Reynolds analogy holds good with respect to the annular spacing. Most importantly, high Newtonian heating of the bounding surface may lead to back flow as well as instability to flow and heat transfer processes.

Effect of Newtonian heating/cooling on free convection in an annular permeable region in the presence of heat source/sink

AbstractThe influence of Newtonian heating/cooling in the presence of heat source/sink has been investigated on laminar free convective flow in a vertical annular permeable region. The mathematical model for the problem has been considered as a boundary value problem consisting of two simultaneous ordinary differential equations. The boundary value problem has been transformed to nondimensional form. This has given rise to a number of parameters representing both geometrical and physical features of the problem. Closed‐form analytical solutions of the governing equations have been obtained for two different cases of internal heat generation/absorption. To assess the effects of governing parameters on the fluid velocity and temperature, a number of profiles of these field variables have been presented. The efficacy of the distinct processes on the field variables has been discussed extensively. The main outcome obtained in this study is that the velocity as well as temperature is enhanced in the case of the Newtonian heating while the opposite behavior occurs in the Newtonian cooling for both cases of source and sink. Furthermore, the influence of the governing parameters has been shown on the skin friction, volume flow rate, and the Nusselt number.

Radiation absorption on MHD free convective laminar flow over a moving vertical porous plate, viscous dissipation and chemical reaction with suction under the influence of transverses magnetic field

Abstract The aim of the present chapter is to investigate the problem of Study on MHD boundary layer flow over a moving vertical porous plate with heat generation and chemical reaction in the presence of thermal absorption. The governing equations of the flow are transformed into nonlinear ordinary differential equations and then solved by using Runge-Kutta-fourth order along with shooting method. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The influence of the various parameters like Magnetic parameter (M), thermal Grashof number (Gr), mass Grashof number (Gc), permeability parameter (K), Prandtl number (Pr), Dufour number (Df), Soret number (Sr), Schmidt number (Sc), Heat generation (B), Radiation Parameter (Ra) and Chemical reaction (Ch) on the flow are analyzed and discussed through graphs in detail. The values of the skin friction coefficient, Nusselt number and the Sherwood number for different physical parameters are also tabulated.

Effects of Viscous Dissipation Parameter on Magneto-hydrodynamic Free Convective Flow through a Porous Media of Parallel Plates with a Non-uniform Heat Source for an Unsteady Case

The magnetic hydrodynamic free convective flow past an infinite stretching porous sheet at constant density for electrically conducting fluid with viscous dissipation was numerically studied. The study revolved around an unsteady two-dimensional free convective laminar flow through a porous medium with the interaction of magnetic area standard to the stream. The graphs represented the effects of material parameters on the temperature and velocity profiles across the fluid boundary layer. The solutions of partial differential equations obtained numerically using an implicit finite difference method for various values of (nu), numbers (0.5 to 0.7) at a constant thermal conductivity (kappa=0.1). The velocity and temperature of MHD flow increased with an increase in viscous dissipation and vice versa.

Transient Analysis of Third-Grade Viscoelastic Nanofluid Flow External to a Heated Cylinder with Buoyancy Effects

Nanotechnology is rapidly embracing numerous areas of manufacturing and process engineering. New types of nanomaterials are being exploited to improve, for example, coating integrity, anti-corrosion characteristics and other features of fabricated components. Motivated by these developments, in the current study a mathematical model is developed for unsteady free-convective laminar flow of third-grade viscoelastic fluid (doped with nanoparticles) from a semi-infinite vertical isothermal cylinder, as a model of thermal coating flow of a pipe geometry. Non-Newtonian behavior is simulated with the thermodynamically robust third-grade Reiner–Rivlin model which accurately represents polymer fluids. Nanoscale effects are analyzed with the Buongiorno two-component nanofluid model. The governing equations comprise a set of highly coupled, nonlinear, multi-degree partial differential equations featuring viscoelastic and nanofluid parameters. An implicit Crank–Nicolson numerical scheme is implemented to solve the emerging nonlinear problem with appropriate initial and boundary conditions. Detailed graphical plots for velocity, temperature and nanoparticle volume fraction are presented for a range of different parameters (i.e., third-grade fluid parameter, Brownian motion parameter, thermophoretic parameter, buoyancy ratio parameter, Lewis number). Additionally, distributions of the heat transfer coefficient, skin friction and Sherwood number at the cylinder surface are visualized. Furthermore, streamlines, isotherms and nanoparticle volume fraction contour plots are included for variation of the third-grade parameter. Contour plots for the third-grade nanofluid flow are found to deviate significantly from those corresponding to Newtonian nanofluids. Validation of the numerical solutions with earlier studies is also included.

Natural Convection Between Vertical Walls Due To Point/Line Heat Source/Sink

In the present paper, we have investigated the influence of constant point/line heat source on fully developed free convective laminar flow between two infinite vertical walls of an electrically conducting and viscous incompressible fluid. The Heaviside step function is used to model the constant heat source/sink and further this function can be converted into line heat source/sink. The compact solution has been obtained by using Laplace transform method. The effects of physical parameters such as constant point/line heat source parameter and Hartmann number on the velocity and temperature fields are shown graphically while on skin friction, mass flow rate and Nusselt number of the fluid are presented in tabular form. It is found that the velocity and temperature field of the fluid increases when the point heat source changes into a line heat source. Also, we have observed that the velocity and temperature profiles increase as the value of constant point/line heat source parameter increases.

Comparison of free convection flow around an engineered porous fin with spherical connections and rigid fin under different positioning angles—An experimental and numerical analysis

In this paper, the free convective flow around an engineered porous fin with spherical connections is investigated experimentally and numerically. In addition, the effects of different positioning angles for different fin materials on thermal fin performance are analyzed. First, the copper, aluminum, and brass fins are made and their thermal performances under free convective flow are examined experimentally. Then, in order to extend the results, after validation the numerical analysis is carried out in steady and three-dimensional calculations. Then, at different positioning angles, the formed free convective flow around the porous fin is analyzed numerically and compared with the results of a rigid fin. The results show that the efficiency of the copper fins at all positioning angles is maximal. It was also found that the highest amount of Nusselt number occurs at the angle of 45°. In the numerical investigations, it is determined that the maximum increase in the Nusselt number of the engineered porous fins is about two times that of the rigid fin. Moreover, a relationship between the Nusselt number and the Rayleigh number is presented for a horizontal engineered porous fin in laminar free convection flow.

Fluid-structure interaction analysis of buoyancy-driven fluid and heat transfer through an enclosure with a flexible thin partition

PurposeA numerical model of an unsteady laminar free convection flow and heat transfer is studied in a cavity that comprises a vertical flexible thin partition.Design/methodology/approachThe left and right vertical boundaries are isothermal, while the horizontal boundaries are insulated. Moreover, the thin partition, placed in the geometric centerline of the enclosure, is considered to be hyper elastic and diathermal. Galerkin finite-element methods, the system of partial differential equations along with the appropriate boundary conditions are transformed to a weak form through the fluid-structure interaction and solved numerically.FindingsThe heat transfer characteristics of the enclosure with rigid and flexible partitions are compared. The effect of Rayleigh number and Young’s modulus on the maximum nondimensional stress and final deformed shape of the membrane is addressed.Originality/valueIncorporation of vertical thin flexible membrane in middle of a cavity has numerous industrial applications, and it could noticeably affect the heat and mass transfer in the enclosure.

Transient Natural Convection Heat Transfer to CO2 in the Supercritical Region

Present research paper investigates the transient laminar free convective supercritical carbon dioxide flow past a semi-infinite vertical cylinder using numerical methods. Two new thermodynamic models for the supercritical fluid (SCF) flow are considered. Based on these models, for supercritical carbon dioxide, two new equations for thermal expansion coefficient are obtained on the basis of Redlich–Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). Based on the calculated values of thermal expansion coefficient, it is shown that not only RK-EOS is closer to experimental values but also gives greater accuracy when compared to VW-EOS validating RK-EOS as suitable model for predicting natural convective properties of carbon dioxide under supercritical condition. The governing equations of SCF flow are solved numerically using Crank–Nicolson implicit finite difference scheme. Numerical simulations are performed for carbon dioxide in the region of its critical point. Results in subcritical, supercritical, and near-critical regions are shown graphically and discussed for different physical parameters. From the obtained numerical results, it is clear that the steady-state time increases for the increasing values of reduced temperature and reduced pressure for carbon dioxide in supercritical region.

Radiative Effects on a Free Convective MHD Flow past a Vertically Inclined Plate with with Heat Source and Sink

The impact of thermal radiation on unsteady laminar free convective MHD flow of a incompressible viscous fluid passes through a vertically inclined plate under the persuade of heat source and sink is presented here.Plate surface is considered to have variable wall temperature. The fluid regarded as gray absorbing / emitting, but non dispersing medium. The periphery layer dimensionless equations that administer the flow are evaluated by a finite difference implicit method called Crank Nicolson method. Numerical solutions are carried out for velocity, temperature, local shear stress, heat transfer rate for various values of the parameters (Pr, λ, Δ M, Rd ) are presented.