Solid Fluid Thermal Conductivity Ratio Research Articles

Numerical Simulation for Nanofluid Flow in a Wall Driven Cavity with Solid Hindrance: Impact of Thermal Conductivity Ratio and Heat Generation

The current work performs the heatline revelation for combined convection of nanofluid within an enclosure with two moving walls at several thermal conductivity ratios plus heat generation parameter. A solid obstacle that produces uniform heat q per unit area is positioned at the middle of the domain. Sliding lids are assigned to the opposite side walls. Two cases: (I) vertical lids are moving in the same directions and (II) horizontal lids are moving in the opposite directions are analyzed. The computational fluid throughout the enclosed space is water-alumina nanofluid. The Finite Element Method of Galerkin’s weighted residual technique is used to solve the governing nonlinear partial differential equations. Numerical estimations are conducted for a wide range of solid fluid thermal conductivity ratio (0.2 ≤ K ≤ 50) and heat generation parameter (1 ≤ Q ≤ 4) for both cases. Outcomes are obtained as streamlines, isothermal lines, heatlines, heat transfer rate and average heat flow. The results show that the heat flux magnitude is higher for case II than case I but the rate of heat transfer stays nearly same for both cases which increase for the increment of Q and decrement of K. Finally, correlations have been established between the heatfunction with parameters K and Q. There exist strong correlations between the variables which measured from the R-squared values.

Conjugate Natural Convection: A Study of Optimum Fluid Flow and Heat Transfer in Eccentric Annular Channels

Laminar natural convection-conduction heat transfer in vertically positioned annular channels with inherent eccentricity is investigated for optimum solid-fluid thermal conductivity ratio and optimum cylinder walls thicknesses allowing maximum induced fluid flow rate and heat transfer under varying geometry parameters, i.e., annulus eccentricity and radius ratio. A finite-difference technique is employed to solve the coupled momentum and energy equations for the cylindrical annulus walls and the annular fluid with Prandtl number 0.7. As part of the results, fluctuations in the induced fluid flow rate and heat transfer in the eccentric annular channel due to the conjugate effect, governed by the ratios of the solid and fluid thermal conductivities and thicknesses of outer and inner circular cylinder walls, are obtained for the boundary conditions of one wall heated isothermally and the other kept adiabatic. Commonly encountered ratios of the solid and fluid thermal conductivities and cylinder walls thicknesses are utilized in the present analysis. Results reveal that the optimum conductivity ratio and cylinder walls thicknesses increase nonlinearly with eccentricity and radius ratio. Such results can be very useful in effectively designing the heat transfer equipment for optimum performance.

Entropy generation analysis due to MHD natural convection flow in a cavity occupied with hybrid nanofluid and equipped with a conducting hollow cylinder

The main objective of this numerical investigation was to analyze the entropy generation and natural convection flow under magnetic field in a square enclosure filled with Cu–Al2O3/water hybrid nanofluid. The enclosure is equipped with a conducting hollow cylinder. The free convective flow in the enclosure is created by a horizontal temperature difference between the vertical left hot wall and the right cold wall under the Boussinesq approximation. The dimensionless equations of steady laminar natural convection flow for Newtonian and incompressible mixture are discretized using the finite volume method. The effective thermal conductivity and viscosity of the hybrid nanofluid are calculated using Corcione correlations taking into consideration the Brownian motion of nanoparticles. Numerical solutions were performed for different values of the nanoparticles volumic concentration, Hartmann number, Rayleigh number, radius ratio, and solid–fluid thermal conductivity ratio. The analyzed results show that inserting a hollow conducting cylinder plays an important role in controlling flow characteristic and heat transfer rate as well as irreversibilities within the cavity.

Experimental quantification of natural convective heat transfer within annulus space filled with a H2O-Cu nanofluid saturated porous medium. Application to electronics cooling

ABSTRACTThis experimental study deals with cooling electronics contained in a hemispherical cavity whose cupola is maintained isothermal, being its base inclined at an angle varying from 0° (horizontal disc with the cupola oriented upwards) to 135°. The active component is a dome centered on this base. The space between the differentially heated elements of the assembly is filled with a porous medium of high porosity saturated by a water–copper nanofluid whose volume fraction varies between 0% (pure water) and 7%. The Rayleigh number based on the radius of the cupola reaches high values up to 7.29 × 1010 given the important surface heat flux generated by the device during operation. The ratio between the thermal conductivity of the solid matrix and that of the base fluid ranges between 0 (interstitial volume without porous medium) and 41.4 corresponding to the intended applications. This experimental study done with an industrial prototype at scale 1 quantifies the natural convective heat transfer via the Nusselt number determined for many configurations obtained by varying the solid-fluid thermal conductivity ratio, the inclination angle, the Rayleigh number, and the volume fraction. The study clearly shows that the cooling performance of the Cu-H2O nanofluid degrades with its age and the number of times it has been used. Analysis of the results reproducibility also proves the irreversibility of the performance. The measured values were compared with those obtained in a recent numerical study based on the volume control method. The observed deviations taking into account the experimental uncertainty margins validate the mathematical model implemented in the numerical approach.

Lattice Boltzmann Pore Scale Simulation of Natural Convection in a Differentially Heated Enclosure Filled with a Detached or Attached Bidisperse Porous Medium

In this research, pore scale simulation of natural convection in a differentially heated enclosure filled with a conducting bidisperse porous medium is investigated using the thermal lattice Boltzmann method. For the first time, the effect of connection of the bidisperse porous medium to the enclosure walls is studied by considering the attached geometry in addition to the detached one. Effect of most relevant parameters on the streamlines and isotherms as well as hot wall average Nusselt number is studied for two of the bidisperse porous medium configurations. It is observed that effect of geometrical and thermo-physical parameters of the bidisperse porous medium on the heat transfer characteristics is more complicated for the attached configuration. To assess the validity of the local thermal equilibrium condition in the micro-porous media, the pore scale results are used to compute the percentage of the local thermal non-equilibrium for two of the bidisperse porous medium configurations. It is concluded that for the detached configuration, the local thermal equilibrium condition is confirmed in the entire micro-porous media for the ranges of the parameters studied here. However, for the attached geometry, it is shown that departure from the local thermal equilibrium condition is observed for the higher values of the Rayleigh number, micro-porous porosity, solid–fluid thermal conductivity ratio, and the smaller values of the macro-pores volume fraction.

Investigation of Mixed Convection in a Ventilated Cavity in the Presence of a Heat Conducting Circular Cylinder

The study is aimed to investigate the mixed convective transport within a ventilated square cavity in presence of a heat conducting circular cylinder. The fluid flow is imposed through an opening at the bottom of the left cavity wall and is taken away by a similar opening at the top of the right cavity wall. The cylinder is placed at the center of the cavity. Two cases are considered depending on the thermal conditions of the cavity walls. In the first case, the left and right vertical walls are kept isothermal with different temperatures and the top and bottom horizontal walls are considered as thermally insulated. For the second case, the top and bottom walls are maintained at different constant temperatures and the left and right walls are considered adiabatic. Heat transfer due to forced flow, thermal buoyancy, and conduction within the cylinder are taken into account. Effect of the cylinder size (0.1 ≤ D ≤ 0.5) and the solid–fluid thermal conductivity ratio (0.1 ≤ K ≤ 10) are explored for various values of Richardson number (0 ≤ Ri ≤ 5) at fixed Reynolds (Re = 100) and Prandtl (Pr = 0.71) numbers. The fluid dynamic and thermal transport phenomena are depicted through streamline and isotherm plots. Additionally, the global thermal parameters such as the average Nusselt number and average fluid temperature of the cavity are presented. It is found that the aforementioned parameters have significant influences on the fluid flow and heat transfer characteristics in the cavity.

Hydromagnetic Mixed Convective Transport in a Nonisothermally Heated Lid-Driven Square Enclosure Including a Heat-Conducting Circular Cylinder

A two-dimensional numerical study is performed in an effort to understand the fundamental characteristics of hydromagnetic mixed convective transport in a nonisothermally heated vertical lid-driven square enclosure filled with an electrically conducting fluid in the presence of a heat-conducting solid circular cylinder. Additionally, entropy generation due to heat transfer, fluid friction, and magnetic effect is also determined. Simulations are performed for various controlling parameters such as the Richardson number (1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50), Prandtl number (0.02 ≤ Pr ≤ 7), Reynolds number based on the lid velocity (Re = 100, 150, and 200), and amplitude of the sinusoidal function (A = 0.25, 0.5, and 1), keeping the solid–fluid thermal conductivity ratio fixed as K = 5. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, Ri, Re, and Pr. Furthermore, the drag coefficient on the moving lid and Nusselt numbers on heated surfaces are also computed to understand the effects of Ha, Ri, Re, Pr, and n on them. It is observed that the drag on the moving lid decreases with Re and increases with Ri and Ha, however, remains insensitive with Pr. The heat-transfer rate from the hot right wall increases as usual with Re, Pr, and Ri but decreases with Ha. The sinusoidally heated bottom wall shows a decrease in the heat-transfer rate with increasing Pr, and at higher Pr, it also decreases with Re. Furthermore, increasing magnetic field strength causes an increase in the heat-transfer rate from the bottom wall. It also decreases with decreasing value of the amplitude of the sinusoidal function.

Numerical Investigation of Natural Convection in Heterogeneous Rectangular Enclosures

The aim of this study is to investigate numerically the steady natural convection resulting from horizontally heating a rectangular enclosure filled with a fluid and containing uniformly distributed, conducting, fixed and disconnected solid blocks (i.e., not touching each other). In particular, the effects of solid volume fraction, solid–fluid thermal conductivity ratio, and total number of blocks on the heat transfer process are determined by solving the mass, momentum, and energy conservation equations using the finite-volume method. The enclosure aspect ratio is varied from 0.25 to 4, the Rayleigh number from 105 to 108, and the Prandtl number is set as unity. Results of the numerical simulations are presented in terms of the surface-averaged Nusselt number, streamfunction, and streamline and isotherm distributions. The interference phenomenon caused by the solid blocks on the natural convection process is considered in detail and used to explain and predict the surprising and complex behavior of surface-averaged Nusselt number.

Numerical Study on Conjugate Conduction–Convection in a Cubic Enclosure Submitted to Time-Periodic Sidewall Temperature

The laminar conjugate conduction-natural convection heat transfer in a cubic enclosure of finite thickness conductive walls and central cavity filled with fluid is comprehensively studied by using recently developed high accuracy temporal-spatial multidomain pseudospectral method. The enclosure is assumed to have one sidewall submitted to time-periodic pulsating temperature and the opposing sidewall constant temperature, and the top, bottom and two lateral sidewalls are adiabatic. The present study is devoted to explore the fluid mechanics and heat transfer mechanisms of the time-periodic conjugate conduction-natural convection in the enclosure, with particular highlights on the heat transfer resonance and back heat transfer phenomena, the perturbation propagation patterns and the three-dimensional characteristics. The computations are performed for wide ranges of controlling parameters of engineering significance, i.e., the dimensionless wall thickness 0 ≤ s ≤ 0.10, the solid–fluid thermal conductivity ratio 10 ≤ k ≤ 50 and diffusivity ratio 0.001 ≤ a ≤ 0.1, and the sidewall temperature pulsating period 1 ≤ P ≤ 103. Numerical results reveal that the time-periodic fluid flow and conjugate heat transfer performances of the enclosure system are greatly affected by the conductive walls and complexly dependent on the controlling parameters. The thickness and thermophysical properties of the conductive walls, together with the pulsating period of the sidewall temperature, govern the sidewall temperature disturbance propagation patterns (amplitude, phase position and speed) within the enclosure. The heat transfer resonance only appears in cases of large diffusivity ratio, but the variation of period-averaged heat transfer rate with respect to the pulsating period is quite different from that of the zero wall thickness enclosure. The back heat transfer exists in region close to the corners formed by either the top or bottom walls and the enclosure hot sidewall, and the former is more remarkable in both scale and duration and is gradually disappearing as the pulsating period increases.

Laminar combined magnetoconvection in a wavy enclosure with the effect of heat conducting cylinder

In the current work, a numerical study of the flow characteristics on combined magnetoconvection in a lid-driven square enclosure, differentially heated, is carried out. This problem is solved by using finite element method of the partial differential equations, which are the heat transfer and stream function in Cartesian coordinates. The tests are performed for different solid–fluid thermal conductivity ratio, cylinder location and Richardson number while the Prandtl number, Reynolds number, magnetic and Joule heating parameters are kept constant. One geometrical configuration is used namely two undulations. The outcome obtained shows that the heat conducting inner square cylinder affects the flow and the heat transfer rate in the enclosure. The trend of the local heat transfer is found to follow a wavy pattern. Results are presented in terms of streamlines, isotherms, average Nusselt number at the heated wavy wall, average temperature of the fluid in the enclosure and dimensionless temperature at the cylinder center for different combinations of the governing parameters.

Numerical analysis of fluid flow due to mixed convection in a lid-driven cavity having a heated circular hollow cylinder

Mixed convection heat transfer in a lid-driven cavity along with a heated circular hollow cylinder positioned at the center of the cavity has been analyzed numerically. The present study simulates a realistic system such as air-cooled electronic equipment with a heat component or an oven with heater. A Galerkin weighted residual finite element method with a Newton–Raphson iterative algorithm is adopted to solve the governing equations. The computation is carried out for wide ranges of the Richardson numbers, cylinder diameter and solid fluid thermal conductivity ratio. Results are presented in the form of streamlines, isothermal lines, average Nusselt number at the heated surface and fluid temperature in the cavity for the mentioned parameters. It is found that the flow field and temperature distribution strongly depend on the cylinder diameter and also the solid–fluid thermal conductivity ratio at the three convective regimes.

Critical Conductivity Ratio and Wall Thickness for Conjugate Natural Convection Heat Transfer in Vertical Eccentric Annuli

Combined conduction-free convection heat transfer in vertical eccentric annuli is numerically investigated using a finite-difference technique. The effects of geometrical parameters, such as eccentricity and radius ratio, on very practical parameters known as critical values of conductivity ratio above which and wall thickness below which the conjugate effect can be neglected, are presented. Solid-fluid thermal conductivity ratio is varied over a range covering practical cases with commonly encountered wall thicknesses. The obtained results can be of value in many industrial applications. The numerical results show that conjugate effects can be increased or decreased by controlling the geometrical parameters.

A numerical study on the effect of a heated hollow cylinder on mixed convection in a ventilated cavity

The present work is aimed to study mixed convection heat transfer characteristics within a ventilated square cavity having a heated hollow cylinder. The heated hollow cylinder is placed at the center of the cavity. In addition, the wall of the cavity is assumed to be adiabatic. Flows are imposed through the inlet at the bottom of the left wall and exited at the top of the right wall of the cavity. The present study simulates a practical system such as air-cooled electronic equipment with a heat component or an oven with heater. Emphasis is sited on the influences of the cylinder diameter and the thermal conductivity of the cylinder in the cavity. The consequent mathematical model is governed by the coupled equations of mass, momentum and energy and solved by employing Galerkin weighted residual method of finite element formulation. A wide range of pertinent parameters such as Reynolds number, Richardson number, cylinder diameter and the solid-fluid thermal conductivity ratio are considered in the present study. Various results such as the streamlines, isotherms, heat transfer rates in terms of the average Nusselt number and average fluid temperature in the cavity are presented for different aforesaid parameters. It is observed that the cylinder diameter has significant effect on both the flow and thermal fields but the solid-fluid thermal conductivity ratio has significant effect only on the thermal field.

Heat generation effects in natural convection inside a porous annulus

The interplay between internal heat generation and externally driven natural convection inside a porous medium annulus is studied in detail using numerical methods. The axisymmetric domain is bounded with adiabatic top and bottom walls and differentially heated side walls sustaining steady natural convection of a fluid with Prandtl number, Pr = 5, through a porous matrix of volumetric porosity, ϕ = 0.4. The generalized momentum equation with Brinkman–Darcy–Forchheimer terms and the local thermal non-equilibrium based two-energy equation model are solved to determine the flow and the temperature distribution. Beyond a critical heat generation value defined using an internal Rayleigh number, Ra I,cr ⁎, the convection transits from unicellular to bicellular mode, as the annulus T max becomes higher than the fixed hot-wall temperature. The Ra I,cr ⁎ increases proportionately when the permeability based external Rayleigh number Ra E ⁎ and the solid–fluid thermal conductivity ratio γ are independently increased. A correlation is proposed to predict the overall annulus Nu as a function of Ra E ⁎, Ra I ⁎, Da and γ. It predicts the results within ± 20% accuracy.

Effect of the Presence of a Heat Conducting Horizontal Square Block on Mixed Convection inside a Vented Square Cavity

Finite element method is used to solve two-dimensional governing mass, momentum and energy equations for steady state, mixed convection problem inside a vented square cavity. The cavity consists of adiabatic left, top and bottom walls and heated right vertical wall; but it also contains a heat conducting horizontal square block located somewhere inside the cavity. Forced flow conditions are imposed by providing an inlet at the bottom of the left wall and an exit at the top of the right wall, through which the working fluid escape out of the cavity. The aim of the study is to describe the effect of such block on the flow and thermal fields. The investigations are conducted for various values of geometric size, location and thermal conductivity of the block under constant Reynolds and Prandtl numbers. Various results such as the streamlines, isotherms, heat transfer rates in terms of the average Nusselt number, average fluid temperature in the cavity and the temperature at the center of solid block are presented for different parameters. It is observed that the block size and location have significant effect on both the flow and thermal fields but the solid-fluid thermal conductivity ratio has insignificant effect on the flow field. The results also indicate that the average Nusselt number at the heated surface, the average temperature of the fluid inside the cavity and the temperature at the center of solid block are strongly dependent on the configurations of the system studied under different geometrical and physical conditions.

Effect of Conjugate Heat Transfer on MEMS-Based Thermal Shear Stress Sensor

ABSTRACT The effect of conjugate heat transfer resulting from a microelectromechanical systems (MEMS)-based thermal shear stress is investigated. Due to the length-scale disparity and large solid–fluid thermal conductivity ratio, a two-level computation is used to examine the relevant physical mechanisms and their influences on wall shear stress. The substantial variations in transport properties between the fluid and solid phases and their interplay with regard to heat transfer and near-wall fluid flow structures are investigated. It is demonstrated that for state-of-the-art sensor design, the buoyancy effect can noticeably affect the accuracy of the shear stress measurement.

Heat transfer in laminar flow through circular tubes accounting for two-dimensional wall conduction

This paper examines the influence of a finite heated length on the heat transfer characteristics of laminar flows through thick-walled circular tubes. Under the assumption of temperature-invariant properties, this kind of conjugate problem is governed by four dimensionless groups : the length of the heated region, the Peclet number, the solid-fluid thermal conductivity ratio, and the radii ratio of the solid wall. From numerical solutions via the control volume approach, it was found that the two-dimensional wall offers a heat flow path into the fluid flow controlling the parameters of interest such as, the bulk temperature of fluid and both internal and external surface temperatures of the solid wall. From a set of typical cases analysed, it was concluded that both surface temperatures exhibited a substantial variation in the axial direction and lesser and more gradual variations were exhibited for the distribution of bulk temperature. A radical limiting solution based on a one-dimensional domain approximation of the conduction equation for the wall is also explained in detail.