Wavy Vertical Wall Research Articles

Mixed convection heat transfer in a partial porous layered split lid-driven wavy wall cavity with Cu–H2O nanofluid

This numerical study investigates mixed convection heat transfer in a two-dimensional irregularly-shaped enclosure with a nanofluid-saturated porous medium. The enclosure has wavy vertical walls, a centered triangular block, and a lid split into two regions moving in opposite directions. Transport equations are solved using the finite element method under varied Darcy (10−5 to 10−1), Reynolds (50 to 200), Richardson (0.1 to 10), amplitude (0 to 0.2), and nanoparticle volume fraction (0 to 0.1) numbers. Results demonstrate the combined effects of forced convection from lid motion and natural convection from temperature differences significantly enhance heat transfer. The wavy walls induce secondary flows and periodic disruption of thermal boundary layers. Increasing Darcy number enables deeper penetration into the porous block. Copper nanoparticles incrementally improve conductive heat transfer. Richardson number effects are more prominent at higher Reynolds numbers as buoyancy forces influence vertical convection. This study provides novel insights into synergistically utilizing wavy geometries, nanofluids, porous media, and active pumping for optimizing heat transfer in irregular enclosures for electronics cooling and thermal management.

Effect of surface waviness on MHD thermo-gravitational convection of Cu−Al2O3−water hybrid nanofluid in a porous oblique enclosure

This study investigates thermo-fluid phenomena of magnetohydrodynamic (MHD) free convection utilizing Cu-Al2O3/water hybrid nanofluid in a porous oblique enclosure consisting of a heated wavy vertical wall. The coupled transport equations are solved numerically by implementing the dimensionless governing equations and using an indigenous FORTRAN-based CFD code and the finite volume approach (FVM). The flow physics along with heat transfer characteristics are explored thoroughly by varying the number of peaks (n) of the wavy wall at different Darcy-Rayleigh numbers (Ram), Darcy numbers (Da), Hartmann numbers (Ha), and nanoparticle volumetric fractions (ϕ) for different inclinations (γ) of the enclosure. The study findings indicate that the wavy curved wall does not always guarantee heat transfer boosting even with the increase in the effective heating surface area. An increase in active length of the wavy heated wall by the undulations (which is ∼320% with 8 undulations) leads to the heat transfer enhancement of ∼20% compared to a no-undulated cavity. The average heat transfer rate is maximum when n = 4, beyond which heat transfer decreases. Depending upon the setting of the value of Ram, Da, Ha, ϕ and γ, the flow-structure and associated heat transfer characteristics are severely altered. Cavity inclination angle has a significant role in controlling the overall thermal performance.

Natural Convection and Entropy Generation in a Porous Enclosure Filled with Non-Newtonian Nanofluid

In the present work, the analysis of natural convection and entropy generation in a square porous cavity, having either a flat or a wavy vertical wall, filled with a non-Newtonian nanofluid is reported. The effect of Rayleigh number (), non-Newtonian power-law index (0.6–1.4), Darcy number (0.0001–0.01), Hartmann number (0–90), and volume fraction of CuO nanoparticles (0–0.12) on heat transfer characteristics has been thoroughly examined. It is found that the average surface Nusselt number for an undulated wall is less than that of a plane wall. for all the cases increases with and and decreases with . The mixing of the nanoparticles with both Newtonian and non-Newtonian fluids enhances the heat transfer only for of 0.01 and less than 30 for all . When is low at 0.0001, the addition of nanoparticles to a fluid enhances the heat transfer for all the cases except of at less than 1. The entropy generation is significant near the vertical wall because of the higher temperature and velocity gradient. The magnitude of is found to be very less as compared with and . , , and increase with an increase in for all cases; however, for a of 60 or 90, there exists an optimum for for a ranging from 0.0005 to 0.001. Finally, the correlation for the average surface as a function of the pertinent input parameters has been proposed for both Newtonian and non-Newtonian fluids, which can be referred in the academics and the industrial world.

Conjugate effect on flow boiling instability in wavy microchannel

Three-dimensional numerical study on two-phase flow boiling in rectangular microchannel with wavy vertical wall configuration is considered that can be utilized for heat dissipation in high flux electronics devices. Straight and wavy microchannels are considered for comparison and analysis. Under conjugate heat transfer situation, effect of flow boiling instability in straight and wavy microchannel is numerically studied using water as the working fluid. Behaviour of bubble growth rate and two-phase flow pattern in straight and wavy microchannel are investigated for a wide range of parameters such as waviness (γ ~ 0 - 0.267), substrate thickness to channel height ratio (δsf ~ 1 and 5), wall to fluid conductivity ratio (ksf ~ 22 - 646), and mass flux (G ~ 118 - 590 kg/m2s). It is found that smaller bubbles are formed in wavy microchannel while confined and elongated bubbles are formed in straight microchannel which often causes flow clogging and premature dryout. The work also presents a comparative analysis between single-phase and two-phase flow boiling cooling technique in straight and wavy microchannel under same geometrical parameters and applied heat flux.

Numerical investigation of natural convection of [formula omitted]-water nanofluid in a wavy cavity with conductive inner block using Buongiorno’s two-phase model

By employing the finite element method, thermophoresis and Brownian diffusion are studied numerically relating to the natural convection in a wavy cavity that is filled with an Al2O3-water nanofluid possessing a central heat-conducting solid block that is influenced by the local heater located on the bottom wall. An isothermal condition is established in the two wavy vertical walls, while adiabatic condition is for the top horizontal wall. Partial heating is applied to the bottom of the horizontal wall, while the remaining part remains in the adiabatic condition. Empirical correlations are employed for the thermal conductivity and dynamic viscosity of the nanofluid. The number of oscillations (1⩽N≤4), Rayleigh number (103⩽Ra≤106), nanoparticles volume fraction (0⩽ϕ≤0.04) and dimensionless length of the bottom heater (0.2⩽H⩽0.8) govern the parameters in this study. The grid independency test, as well as experimental and numerical data from other published works, was employed to validate the developed computational code comprehensively. Based on the obtained results, it was found that the heat transfer inside the cavity is enhanced by introducing nanoparticles as well as a selection of optimal number of oscillations.

Natural convection in a wavy open porous cavity filled with a nanofluid: Tiwari and Das’ nanofluid model

Natural convective heat transfer and fluid flow in an open porous cavity filled with a nanofluid is studied numerically using the Tiwari and Das nanofluid model. The transport equations for mass, momentum and energy formulated in dimensionless stream function and temperature are solved numerically using a second-order accurate finite difference method. Particular efforts are focused on the effects of the governing parameters on the heat and fluid flow. It is found that an increase in undulation number of the wavy vertical wall leads to an attenuation of convective flow and a decrease in the heat transfer rate.

Numerical Study of Natural Convection in a Heated Enclosure with Two Wavy Vertical Walls Using Finite Element Method

The effects of wavy geometry on natural convection in an enclosure with two wavy vertical walls and filled with fluid saturated porous media are investigated numerically by using finite element method. The wavy enclosure is transformed to a unit square in the computational domain and the finite element formulations are solved in terms ofξη-coordinate based on iterative method. In order to investigate the effects of interested parameters, the values of wave amplitude (λ= 0.05 and 0.1) and number of undulations (n= 1 and 2) are chosen with constants Ra = 105, Da = 10−3, and Pr = 0.71. It is found that the increase in number of undulations has small effect on natural convection inside the enclosure whereas the increase in wave amplitude reduces the strength of convection because higher wave volume plays a barricade role.

Natural Convection Heat Transfer Performance of Non-Newtonian Power-Law Fluids Enclosed in Cavity With Complex-Wavy Surfaces

Numerical simulations are performed to investigate the natural convection heat transfer performance of non-Newtonian power-law fluids in a cavity bounded by wavy vertical walls with different temperatures and flat horizontal walls under adiabatic conditions. The results show that for Rayleigh numbers greater than 103, the mean Nusselt number has a significantly increase as the flow behavior index is decreased. Moreover, it is shown that in the convection-dominated regime, the mean Nusselt number increases with an increasing Rayleigh number, while in the conduction-dominated regime, the mean Nusselt number remains approximately constant. Finally, it is shown that for a given fluid, the heat transfer performance can be optimized via an appropriate tuning of the wavelength and amplitude of the wavy surface depending on the Rayleigh number.

Natural convection heat transfer and entropy generation in wavy-wall enclosure containing water-based nanofluid

A numerical investigation is performed into the natural convection heat transfer characteristics and entropy generation of water-based nanofluids in an enclosure bounded by wavy vertical walls and flat upper and lower surfaces. In performing the analysis, it is assumed that the left wall is heated by a constant heat flux while the right wall is maintained at a constant low temperature. In addition, the upper and lower walls are both assumed to be insulated. The analysis considers three different nanofluids, namely Cu–water, Al2O3–water and TiO2–water. The governing equations are modeled using the Boussinesq approximation and are solved using the finite-volume numerical method. The analysis examines the effects of the nanoparticle volume fraction, the type of nanofluid, the Rayleigh number and the wavy surface geometry parameters on the mean Nusselt number and total entropy generation. The results show that for all values of the Rayleigh number considered in the present study (Ra=104∼106), the mean Nusselt number increases and the total entropy generation reduces as the volume fraction of nanoparticles increases. In addition, it is shown that the Cu–water nanofluid yields the best heat transfer performance and the lowest total entropy generation of the three nanofluids. Finally, it is shown that for a given nanofluid, the mean Nusselt number can be maximized and the total entropy generation minimized via an appropriate tuning of the wavy surface geometry parameters. Overall, the results presented in this study provide a useful source of reference for enhancing the natural convection heat transfer performance in wavy-wall enclosures while simultaneously reducing the entropy generation.

Finite element simulation of MHD combined convection through a triangular wavy channel

The present paper implements the analysis of magnetohydrodynamic (MHD) combined convective flow and heat transfer characteristics through a triangular wavy vertical channel using the Galerkin weighted residual finite element method. The flow enters at the bottom and exits from the top surface. The wavy vertical walls are at constant temperature and the cold flow enters the channel from the inlet. The numerical model is based on a 2D Navier–Stokes incompressible flow and energy equation. The effects of Grashof number, Reynolds number and Prandtl number on flow and thermal fields are investigated. The variation of local Nusselt number along the vertical walls for the mentioned parameters is also presented. The study reveals that the flow as well as thermal field strongly depends on the aforesaid parameters.

NUMERICAL STUDY OF NATURAL CONVECTION IN A CAVITY WITH WAVY VERTICAL WALLS

This paper describes a numerical study of natural convection heat transfer and fluid flow characteristics inside a cavity with wavy vertical walls. The bottom wall is heated by spatially varying temperature and other three walls are kept at cooled temperature. Governing equation was discretized using the finite volume-method with staggered variables arrangement in curvilinear coordinates. Two geometrical configurations were used in this study for symmetrical and unsymmetrical wavy vertical walls (total of 132 cases) for range of Ra=100 to 106 and fixed Prandtl number (0.71). The effects of the wave geometry, wave amplitude, number of undulation, and Rayliegh number on flow behavior, thermal field, local Nusselt number and Nusselt number ratio (NNR) factor have been studied. Streamline, velocity vector, and isothermal contour are used to present the corresponding flow and thermal field inside the cavity. The Results show that the enhanced of heat transfer rate seems to depend on geometrical configuration.

Influence of variable heat flux on natural convection along a corrugated wall in porous media

In this work the coupled non-linear partial differential equations, governing the free convection from a wavy vertical wall under a power law heat flux condition, are solved numerically. For both Darcy and Forchheimer extended non-Darcy models, a wavy to flat surface transformation is applied and the governing equations are reduced to boundary layer equations. A finite difference scheme based on the Keller Box approach has been used in conjunction with a block tri-diagonal solver for obtaining the solution. Detailed simulations are carried out to investigate the effect of varying parameters such as power law heat flux exponent m, wavelength–amplitude ratio a and the transformed Grashof number Gr′. Both surface undulations and inertial forces increase the temperature of the vertical surface while increasing m reduces it. The wavy pattern observed in surface temperature plots, become more prominent with increasing m or a but reduces as Gr′ increases.

Combined Influence of Mass and Thermal Stratification on Double-Diffusion Non-Darcian Natural Convection From a Wavy Vertical Wall to Porous Media

Abstract In this study we analyze the combined influence of mass and thermal stratification on non-Darcian double-diffusive natural convection from a wavy vertical wall to a porous media. A finite difference scheme based on the Keller box approach is derived for the boundary layer equations resulting from the use of nonsimilarity transformation on the coupled nonlinear partial differential equations. Extensive numerical simulations are carried out to analyze the influence of wave amplitude a, Grashof number Gr*, thermal stratification parameter ST, concentration stratification parameter SC, buoyancy ratio B, and Lewis number Le on the double-diffusive natural convection process. Increasing a and Gr* or decreasing B is seen to favor the heat and mass transport in the porous region thereby reducing the heat and mass fluxes along the vertical heated surface. Increasing ST or decreasing Le leads to an enhanced mass transfer process. Presence of surface waviness brings in a wavy pattern in the local heat and mass fluxes with decreasing magnitudes in the streamwise direction in the presence of stratification terms.