Nonlinear Boussinesq Approximation Research Articles

Two‐phase Sakiadis flow of a nanoliquid with nonlinear Boussinesq approximation and Brownian motion past a vertical plate: Koo‐Kleinstreuer‐Li model

AbstractThis paper investigates the Sakiadis flow of a Al2O3‐H2O nanoliquid with consistently scattered dust particles over a vertical plate. To account for the effect of the Brownian movement, the Koo‐Kleinstreuer‐Li model is considered. In some thermal systems such as reactor safety areas, and solar collectors, combustion works from moderate to high temperature, making the relationship between the temperature and density nonlinear. To consider this temperature‐dependent density, the nonlinear Boussinesq estimation is utilized. The present physical structure, which includes energy and momentum equations, is converted into a system of ordinary, coupled, and nonlinear differential conditions through the help of similarity transformations. By using the finite difference code, the subsequent equations have been numerically solved. The impact on the velocity and the thermal profiles of the nondimensional parameters is visualized through graphs. Both the Nusselt number and friction factor strengthen with a higher nonlinear thermal parameter in the case of nonlinear Boussinesq approximation compared to the linear Boussinesq case. Growing estimations of nonlinear thermal parameter deteriorate the thermal profile but it boosts the velocity profile of both liquid and dust phases.

APPLICATION OF TAGUCHI EXPERIMENTAL METHOD IN NUMERICAL SIMULATION OF VARIABLE VISCOSITY AND INTERNAL HEAT GENERATION EFFECTS ON NATURAL CONVECTION IN POROUS MEDIA

This study uses an optimization approach representation of the numerical solution for the variable viscosity, the uniform blowing/suction and the internal heat source effects on the free convection flow over a vertical permeable plate in porous media with a non-linear Boussinesq approximation. The internal heat source is of an exponential decaying form. The partial differential equations are transformed into non-similar equations and solved by Keller box method (KBM). Compared with the previously published articles, the results are considered to be very consistent. Numerical results for the local Nusselt number with the four parameters: 1) the blowing/suction parameter , 2) the viscosity-variation parameter , 3) internal heat source coefficient , 4) the non-linear temperature parameter are expressed in tables. Through the Taguchi method to predict the best point of the maximum of local Nusselt number is , , , .

Nonlinear Mixed Convection Flow in an Inclined Channel with Time-Periodic Boundary Conditions

This article scrutinises the role of nonlinear Boussinesq approximation on mixed convection flow in an inclined channel when one of the walls is kept at constant temperature while is other one is periodically heated. By expanding the Boussinesq approximation up to second degree Taylor series expansion, the governing momentum and energy equations are derived and solved analytically. During the course of graphical and numerical simulations, results show that the role of nonlinear Boussinesq approximation is to increase fluid velocity, interval of reverse flow formation at the walls, pressure drop and fanning frictional factor.

Entropy generation of tangent hyperbolic nanofluid flow over a circular cylinder in the presence of nonlinear Boussinesq approximation: a non-similar solution

The analysis of entropy generation has received notable attention in the study of nanofluids because the prime objective of nanofluids is to admit high heat fluxes. The entropy production can be utilized to generate the entropy in any irreversible heat transfer process which is important in thermal machines. This work presents to explore the fluid transport characteristics and entropy generation of a tangent hyperbolic nanofluid over a horizontal circular cylinder with the influence of nonlinear Boussinesq approximation. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. The impacts of active parameters on the flow field like Weissenberg number, power-law index, magnetic field, mixed convection, Brownian motion, thermal convention, thermophoresis and radiation are illustrated with graphs and tables. The current results exposed that the nanofluid velocity enhances for enhancing the mixed convection parameter. Isotherms thickness is escalated with increasing values of radiation parameter. Total entropy generation rises for higher values of dimensionless temperature ratio parameter.

Theoretical and analytical analysis of convective heat transport of radiated micropolar fluid over a vertical plate under nonlinear Boussinesq approximation

PurposeIn heat transfer problems, if the temperature difference is not sufficiently so small then the linear Boussinesq approximation is not adequate to describe thermal analysis. Also, nonlinear density variation with respect to temperature/concentration has a significant impact on heat and fluid flow characteristics. Because of this reason, the impact of nonlinear density variation in the buoyancy force term cannot be neglected. Therefore in this paper, the unsteady flow and heat transfer of radiating magneto-micropolar fluid by considering nonlinear Boussinesq approximation is investigated analytically.Design/methodology/approachThe flow is fully developed and time-dependent. Heat and mass flux boundary conditions are also accounted in the analysis. The governing equations of transport phenomena are treated analytically using regular perturbation method. To analyze the tendency of the obtained solutions, a parametric study is performed.FindingsIt is established that the velocity field is directly proportional to the nonlinear convection parameter and the same trend is observed with the increase of the value of Grashof number. The micro-rotational velocity profile decreases with increase in the nonlinear convection parameter. Further, the temperature profile increases due to the presence of radiative heat aspect.Originality/valueThe effectiveness of nonlinear Boussinesq approximation in the flow of micropolar fluid past a vertical plate in the presence of thermal radiation and magnetic dipole is investigated for the first time.

Sensitivity analysis of nonlinear radiated heat transport of hybrid nanoliquid in an annulus subjected to the nonlinear Boussinesq approximation

The main emphasis of the current study is to analyze the novel feature of the quadratic convective and nonlinear radiative flow of MHD hybrid nanoliquid (Cu–Al2O3–H2O) in an annulus with sensitivity analysis. The significance of exponential space-related heat source, movement of annuli and a new radiation parameter corresponding to an asymptotic nature are also comprehended in the existing study. The dimensionless governing nonlinear equations are treated numerically by employing shooting technique. Impact of effective parameters on the flow and heat transport features has been scrutinized. The optimization procedure is implemented to analyze the influence of three effective parameters $$\left( {1.5 \le R_{\mathrm{f}} \le 5.5,\; 1 \le Q_{\mathrm{E}} \le 3\;{\mathrm{and}}\; 1\% \le \phi_{\mathrm{Cu}} \le 3\% } \right)$$ on skin friction and Nusselt number by utilizing response surface methodology and sensitivity analysis. The obtained results portray that the nonlinear convection parameter is more favorable for the skin friction coefficient. Further, a comparison of sensitivity depicts that the skin friction coefficient is more sensitive to $$R_{\mathrm{f}}$$ and $$Q_{\mathrm{E}}$$ , whereas Nusselt number is more sensitive to $$\phi_{\mathrm{Cu}}$$ .

MHD natural convective flow of [formula omitted] ferrofluids in an inclined partial open complex-wavy-walls ringed enclosures using non-linear Boussinesq approximation

In the current contribution, a numerical investigation of natural convection with nonlinear Boussinesq approximation is considered for a ferrofluid flows inside an inclined, and partial open cavity. The vertical walls of the cavity are wavy where the aperture part lies in the right one. The left wall is considered to be uniformly heated whereas the remaining parts of the cavity are adiabatic. The nonslip boundary condition is assumed for all the boundaries except the aperture part where the directional do-nothing boundary condition is introduced to ensure the theoretical studies which leads to a conservative kinetic energy. The problem is modeled and the resulting partial differential equation system, after converting it to a non-dimensional form using a suitable transformation variables, is solved based on the Galerkin finite element method. The entropy generation analysis is presented for the local entropy generation due to heat transfer, local entropy generation due to fluid friction as well as their contribution to Bejan number. An intensive computation is carried out for wide ranges of the governing parameters namely; the Rayleigh number Ra, Hartmann number Ha, nanoparticle volume fraction ϕ, amplitudes of the two superimposed sinusoidal functions αi, non-linear Boussinesq parameter ξ, length of the aperture BR and its position bR. The obtained results are shown in terms of the streamlines, isotherms, local entropy generation due to heat transfer, local entropy generation due to fluid friction contours as well as average Bejan and Nusselt number. Over all, most of the governing parameters have a significant impacts in the flow and heat transfer rate as shown in the discussion section.

Analysis of activation energy in quadratic convective flow of a micropolar fluid with chemical reaction and suction/injection effects

PurposeThe purpose of this paper is to analyze the combined effects of thermal radiation and activation energy with a chemical reaction on the quadratic convective flow of a micropolar fluid over an inclined plate. Convective thermal boundary condition and suction/injection effects are considered at the surface of an inclined plate.Design/methodology/approachThe convection along with nonlinear Boussinesq approximation (i.e. quadratic convection or nonlinear convection) and usual boundary layer assumptions is employed in the mathematical formulation. Highly coupled nonlinear governing equations are tackled by a combined local non-similarity and successive linearization techniques.FindingsThe behavior of various pertinent parameters on the fluid flow characteristics is conferred through graphs and it reveals that the qualitative behaviors of velocity, temperature, skin friction and heat transfer rates of a micropolar fluid are similar for Biot number and radiation parameters. The suction/injection and activation energy parameters increase the concentration of the micropolar fluid within the boundary layer, while the chemical reaction parameter reduces the concentration in the same region. Further, this quadratic convection shows a strong influence on the fluid flow characteristics and then the impact of pertinent parameters is more prominent on the physical quantities, compared therewith results of the linear convection.Practical implicationsThis kind of investigation is useful in the mechanism of combustion, aerosol technology, high-temperature polymeric mixtures and solar collectors which are operated at moderate to very high temperatures.Originality/valueThis attempt is a unique contribution to the establishment of both micropolar fluid and activation energy. This kind of study even in the absence of quadratic convection is not yet noted.

Theory of fully developed mixed convection including flow reversal: A nonlinear Boussinesq approximation approach

AbstractIn this article, an exact solution is obtained to investigate the role of nonlinear Boussinesq approximation on mixed convection flow in a vertical channel subject to asymmetric wall heating. The nonlinear density variation with temperature (NDT) in the buoyancy term is introduced to the momentum equation and solved exactly by direct integration. During the course of graphical and numerical computations, results show that the role of NDT is to increase fluid velocity as well as skin‐friction while it reduces the rate of heat transfer. In addition, reverse flow formation at the walls is increased due to the inclusion of NDT (nonlinear Boussinesq approximation).

Influence of Non-Linear Boussinesq Approximation and Convective Thermal Boundary Condition on MHD Natural Convection Flow of a Couple Stress-Nanofluid in a Porous Medium

Nonlinear density and temperature variation’s role (NDT) on the magnetohydrodynamic (MHD) natural convective flow of couple stress fluid with nanoparticles through a vertical porous channel modeled as Darcy-Forchheimer flow is the purpose of our work. The nanoparticles volume fraction is taken into consideration (Buongiorno model). The nonlinear partial differential equations governing this flow were transformed into ordinary differential equations via the similarity technique and simulated numerically using Matlab, following boundary value problem (BVP4c) code. Graphical illustrations, including non-dimensional velocity, temperature, concentration, nanoparticle’s concentration and numerical results containing Nusselt and Sherwood numbers were presented for different values of the non-linear part of the Boussinesq approximation; couple stress parameter, and the Biot number on the walls.

Analysis of activation energy and thermal radiation on convective flow of a power‐law fluid under convective heating and chemical reaction

AbstractThe purpose of the present article is to explore the influence of activation energy in the mixed convective flow of a power‐law fluid over a permeable inclined plate. The energy expression is incorporated with thermal radiation effect. Additionally, the suction/injection effect and convective thermal conditions are considered at the surface of the inclined plate. The convection along with a nonlinear Boussinesq approximation (i.e., quadratic or nonlinear convection) and usual boundary‐layer assumptions are used in the mathematical formulation. A combined local non‐similarity and successive linearization techniques are used to evaluate the highly complicated governing equations. The effect of pertinent parameters on the fluid flow characteristics and its solutions are conferred using this study with the help of graphs. This kind of investigation is useful in the mechanism of combustion, aerosol technology, high‐temperature polymeric mixtures, and solar collectors, which operate at moderate to very high temperatures.

MHD free convection in a vertical slit micro-channel with super-hydrophobic slip and temperature jump: non-linear Boussinesq approximation approach

An exact solution is obtained for natural convection flow of electrically conducting fluid in a vertical slit micro-channel with super-hydrophobic slip and temperature jump using non-linear Boussinesq approximation approach. The inner surface of one of the micro-channel surfaces is structurally changed so that it exhibited super-hydrophobic velocity slip and jump in temperature. A transverse magnetic field is applied to the flow direction. A unified solution is derived for two different physical situations. Case I, represents a physical situation when super-hydrophobic surface is heated and no-slip surface is unheated while case II represents a physical situation when no-slip surface is heated and super-hydrophobic surface is unheated. The velocity slip lowers the Nusselt number in Case I and raises it in Case II while the temperature jump co-efficient does the opposite. Velocity and flow rate are higher in case of non-linear density variation with temperature in comparison to linear density variation with temperature.

Effects of Nonlinear Boussinesq Approximation and Double Dispersion on Free Convective Flow of an Ostwald-de Waele Power-Law Fluid Along an Inclined Plate Under Convective Thermal Condition

Effects of Nonlinear Boussinesq Approximation and Double Dispersion on Free Convective Flow of an Ostwald-de Waele Power-Law Fluid Along an Inclined Plate Under Convective Thermal Condition

Effects of nonlinear Boussinesq approximation and double dispersion on a micropolar fluid flow under convective thermal condition

AbstractThis article investigates the effect of double dispersion on the natural convective flow of a micropolar fluid along an inclined plate in the presence of the convective thermal condition. In addition, the nonlinear convection is considered to analyze the heat and mass transfer phenomena of thermal systems, which are performed at moderate‐ and high‐level temperatures. A combination of local nonsimilarity and successive linearization techniques is used to evaluate the associated complicated nondimensional governing equations. This study discusses the impact of relevant factors on the fluid characteristics through graphs. The influence of nonlinear convection parameters on the heat and mass transfer rates seems to be more in Darcy porous media compared with that in non‐Darcy porous media.

Unsteady Flow of a Nanofluid over a Sphere with Nonlinear Boussinesq Approximation

A theoretical study is presented for transient mixed convection flow of a nanofluid in the forward stagnation region of a heated sphere that is rotating with time-dependent angular velocity, taking nonlinear Boussinesq approximation into account. The nanofluid is treated as a two-component mixture (i.e., nanoparticles distributed homogenously in a base fluid). The effects of the Brownian motion and thermophoresis are included for the nanofluid flow. The first and second laws of thermodynamics are employed to study thermophysics as well as heat and mass transfer phenomena. The governing equations are transformed into a system of dimensionless, nonlinear, coupled, differential equations using suitable transformation, which are then solved numerically by applying the Keller box method. The accuracy of the obtained numerical results is validated via comparison to previously published results for special cases. Primary shear stress is boosted with increasing mixed convection parameter and Brownian motion effect, whereas secondary shear stress is depressed. Temperatures are suppressed with increasing nonlinear temperature parameter, whereas nanoparticle concentrations are elevated.

Double dispersion effect on nonlinear convective flow over an inclined plate in a micropolar fluid saturated non-Darcy porous medium

This article explores the influence of double dispersion on micropolar fluid flow past an inclined plate in a homogeneous and isotropic non-Darcy porous medium. Additionally, the effect of nonlinear Boussinesq approximation (i.e., also known as nonlinear convection) with the convective thermal condition is considered to address the heat and mass transfer phenomena in some thermal systems which are operated at moderate to very high temperatures. The governing partial differential equations are transformed into a system of ordinary differential equations using a local non-similarity method, and the resulting boundary value problem is solved using a novel successive linearization method (SLM). The accuracy of the SLM has been established by comparing the results with the shooting technique. This numerical study discusses the influence of pertinent parameters on the fluid flow characteristics through graphs and the salient features are discussed in detail. Heat and mass transfer varies extensively with the increase of nonlinear convection parameters, which depends on aiding and opposing flow situations. In the both aiding and opposing flows, thermal dispersion favors the heat transfer, whereas the solutal dispersion parameter benefits the mass transfer. This kind of investigation is useful in the mechanism of combustion, aerosol technology, high-temperature polymeric mixtures, solar collectors which are operated at moderate to very high temperatures.

Nonlinear Boussinesq Approximation in an Ostwald-de Waele Power-Law Fluid Subject to Cross-Diffusion Effects and Convective Thermal Condition

Nonlinear Boussinesq Approximation in an Ostwald-de Waele Power-Law Fluid Subject to Cross-Diffusion Effects and Convective Thermal Condition

Influence of Non-linear Boussinesq Approximation on Natural Convective Flow of a Power-Law Fluid along an Inclined Plate under Convective Thermal Boundary Condition

Abstract In the present investigation, a problem of natural convective flow of a non-Newtonian power-law fluid over an inclined plate saturated in a non-Darcy porous medium is considered. Also, the nonlinear Boussinesq approximation and convective thermal boundary condition are taken into account to address heat and mass transfer phenomena of thermal systems which are operated at moderate and very high temperatures. The steady-state boundary layer equations are non-dimensionalized into non-similar form and then solved numerically by the local non-similarity method with successive linearisation method (SLM). The effects of various physical parameters on the fluid flow, heat and mass transfer characteristics are depicted graphically and analysed in detail.

Non-Linear Boussinesq Approximation and Cross-Diffusion Effects on an Ostwald-de-Waele Power-Law Fluid Flow with Convective Boundary Condition

Non-Linear Boussinesq Approximation and Cross-Diffusion Effects on an Ostwald-de-Waele Power-Law Fluid Flow with Convective Boundary Condition

Mixed convection from a wavy surface embedded in a thermally stratified nanofluid saturated porous medium with non-linear Boussinesq approximation

In this article, we have made an attempt to study the convective heat transfer in the influence of non-linear Boussinesq approximation, thermal stratification and convective boundary conditions on non-Darcy nanofluid flow over a vertical wavy surface. The surface of the vertical wavy plate, put up at convective temperature and concentration. A coordinate transformation is used to transform the wavy surface into smooth surface. Using local similarity and non-similarity method the governing nondimensional equations are transformed into coupled nonlinear ordinary differential equations. Effects of thermal convective parameter, thermal stratification parameter, Lewis number, Sherwood number on the wave geometry on the heat and mass transfer characteristics have been studied. Numerical results have been obtained for various physical parameters. A comparison of the present results is made with the earlier published results and is found to be in good agreement.