Unsteady conjugate water/air mixed convection in a square cavity

Transient natural convection inside an inner thin walled container caused by external mixed convection in a square cavity has been analyzed numerically. Air and water were chosen alternatively as internal and external working fluids. Fluid mechanics and conjugate heat transfer, described in terms of continuity, linear momentum and energy equations, were predicted by using the finite volume method. Streamlines, isotherms, velocity profiles and local Nusselt number time evolution are presented for external flows, of either air or water, with Ri = 1, in two cases: Re = 200 and 500.     

Numerical investigation of mixed convection of non-Newtonian fluid in a vented square cavity with fixed baffle

This paper numerically investigates mixed convective heat transfer in a vented square cavity incorporated with a baffle that is subjected to external non-Newtonian fluids (NNFs). Adiabatic conditions are imposed on the top and bottom walls, while cold temperature conditions are applied to the right and left solid boundaries. Heated NNF enters the cavity through the inlet and goes out through the outlet at three different locations, and it passes on a vertical baffle fixed at the base placed at different lengths. To examine the impact of the inlet and outlet positions, three different shapes of the outlet port located on the right wall and the inlet port on the left bottom wall were investigated. The impacts of Reynolds number (Re) of 100 ≤ Re ≤ 1000, Richardson number (Ri) of 0.1 ≤ Ri ≤ 3, power law index (n) of 0.6 ≤ n ≤ 1.4, length of baffle (L_b) of 0.2 ≤ L_b ≤ 0.6 and the outlet hole positions (S) of $0\le S\le 0.9$ on the thermal and flow distributions in the cavity are taken into consideration in this paper. The results demonstrated that the flow's intensity and heat transfer increase with improvement in the Re and n at any baffle length. When the Ri increased from 0.1 to 3, $N{u}_{\mathrm{avg}}$ increased by 23.3% at $n=0.6$, and 13.8% at $n=1.2$. Also, the Ri increment results in the augmentation of the average heat transfer.     

Non-Darcy natural convection of a non-Newtonian fluid in a porous cavity

A numerical study of non-Darcy natural convection in a porous enclosure saturated with a power-law fluid is presented. Hydrodynamic and heat transfer results are reported for the configuration in which the enclosure is heated from a side-wall while the horizontal walls are insulated. The flow in the porous medium is modeled using the modified Brinkman–Forchheimer-extended Darcy model for power-law fluids, which accounts for both inertia and boundary effects. The results indicate that when the power law index is decreased, the circulation within the enclosure increases leading to a higher Nusselt number and these effects are enhanced as the Darcy number is increased. Consequently as the power law index decreases, the onset of the transitions from Darcy regime to Darcy–Forchheimer–Brinkman regime to asymptotic convection (boundary layer) regime shift to higher corresponding values of the Darcy number. An increase in Rayleigh number produces similar effects as a decrease in power law index.     

Unsteady conjugate natural convection in a square enclosure filled with a porous medium

Mathematical simulation of unsteady natural convection modes in a square cavity filled with a porous medium having finite thickness heat-conducting walls with local heat source in conditions of heterogeneous heat exchange with an environment at one of the external boundaries has been carried out. Numerical analysis was based on Darcy–Forchheimer model in dimensionless variables such as a stream function, a vorticity vector and a temperature. The special attention was given to analysis of Rayleigh number effect Ra = 10⁴, 10⁵, 10⁶, of Darcy number effect Da = 10^?5, 10^?4, 10^?3, ∞, of the transient factor effect 0 < τ < 1000 and of the heat conductivity ratio k_2,1 = 3.7 × 10^?2, 5.7 × 10^?4, 6.8 × 10^?5 on the velocity and temperature fields. The influence scales of the defining parameters on the average Nusselt number have been detected.     

Numerical conjugate air mixed convection/non-Newtonian liquid solidification for various cavity configurations and rheological models

Unsteady 2D natural convection/phase change of a non-Newtonian liquid inside a square container caused by external mixed convection of a Newtonian fluid with various cavity configurations has been studied numerically. Air was chosen as external cooling fluid and modified non-Newtonian water as the internal solidifying fluid. Conjugate convective fluid and heat transport, described in terms of non-linear coupled continuity, momentum, and energy equations, were solved by using the finite volume method with the SIMPLE algorithm. Effects of four external fluid inlet/outlet locations and four non-Newtonian rheological models were studied. Results for the time evolution of streamlines, isotherms and freezing curves are analyzed. The effect of the cavity inlet/outlet configuration on streamlines of the external fluid is remarkable, near the region close to the non-Newtonian liquid filled container.     

Numerical investigation on mixed convection in a non-Newtonian fluid inside a vertical duct

This paper reports a numerical study of the thermal and fluid-dynamic behaviour of laminar mixed convection in a non-Newtonian fluid inside a vertical duct enclosed within two vertical plates that are plane and parallel, having linearly varying wall temperatures. The other inlet conditions consist of a parabolic distribution of the velocity field and a constant fluid temperature. The problem is assumed to be steady and two-dimensional. The formulation of a mathematical model in dimensionless co-ordinates and the discretisation of the governing equations by means of the finite difference method, have made it possible to create a numerical code developed in Matlab environment. The study was focused on the simultaneous presence and on the mutual interaction of natural and forced convection, starting from the effects of the re-circulation on the heat transfer. The quantitative results of the analysis, which are strongly affected by the variation of the Grashof number and of the exponent of the power law, are given in terms of graphic visualisations of the fluid velocity profiles and, when the governing parameters vary, of the various geometries characterising the heat transfer.     

Unsteady mixed convection heat transfer from a solid sphere: The conjugate problem

Heat transfer associated with a spherical particle under simultaneous free and forced convection is numerically investigated using a combined Chebyshev Legendre spectral method. Both internal and external thermal resistances are taken into consideration by means of a conjugate model consisting of the full Navier -Stokes equations for external flow and the energy equations for both inside and outside the sphere. An influence matrix technique is employed to resolve the difficulties created by the lack of vorticity boundary conditions and to decouple the energy equations from interfacial couplings. Simulation results reveal that effects due to natural convection are most remarkable in the wake where the flow structure is changed. The overall Nusselt number and the drag coefficient show an increase or decrease in magnitude depending on whether gravity-induced flow aids or opposes the main flow. However, the change does not exceed 17% for the cases Gr/Re2 40. When the buoyancy and the free stream are in the same direction, the effects are less pronounced than when they are in the opposite direction.     

Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid

A numerical investigation of laminar mixed convection flows through a copper–water nanofluid in a square lid-driven cavity has been executed. In the present study, the top and bottom horizontal walls are insulated while the vertical walls are maintained at constant but different temperatures. The study has been carried out for the Rayleigh number 10⁴ to 10⁶, Reynolds number 1 to 100 and the solid volume fraction 0 to 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics have been investigated and discussed. It is found that at the fixed Reynolds number, the solid concentration affects on the flow pattern and thermal behavior particularly for a higher Rayleigh number. In addition it is observed that the effect of solid concentration decreases by the increase of Reynolds number.     

Unsteady conjugate natural convection in a porous cavity boarded by two vertical finite thickness walls

The objective of this study is to investigate unsteady conjugate natural convection in a porous cavity sandwiched by finite conductive walls considering time-periodic boundary conditions and local thermal non-equilibrium. The top and bottom boundaries are assumed to be isolated and the continuity of temperature and heat transfer are considered in interface boundaries. The effect of varying a plethora of parameters such as Rayleigh number, Thermal conductivity ratio, wall thickness, and non-dimensional frequency on the streamlines, isotherms, and Nusselt number has been studied. It is shown that, apart from non-dimensional frequency and wall thickness, the amplitude of periodic fluid Nusselt number is an increasing function of all aforementioned parameters. Furthermore, aside from Rayleigh number and heat transfer coefficient, the behavior of the solid Nusselt number is the same as fluid Nusselt number. Eventually, the time-averaged Nusselt number and heat transfer through the vertical walls for different values of non-dimensional frequencies are calculated.     

Numerical study on the conjugate effect of joule heating and magnato-hydrodynamics mixed convection in an obstructed lid-driven square cavity

Conjugate effect of joule heating and magnetic force, acting normal to the left vertical wall of an obstructed lid-driven cavity saturated with an electrically conducting fluid have been investigated numerically. The cavity is heated from the right vertical wall isothermally. Temperature of the left vertical wall, which has constant flow speed, is lower than that of the right vertical wall. Horizontal walls of the cavity are adiabatic. The physical problem is represented mathematically by sets of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. To see the effects of the presence of an obstacle on magnetohydrodenamic mixed convection in the cavity, we considered the cases of with and without obstacle for different values of Ri varying in the range 0.0 to 5.0. Results are presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the magnetic parameter, Ha and Joule heating parameter J. The results showed that the obstacle has significant effects on the flow field at the pure mixed convection region and on the thermal field at the pure forced convection region. It is also found that the parameters Ha and J have notable effect on flow fields; temperature distributions and heat transfer in the cavity. Numerical values of average Nusselt number for different values of the aforementioned parameters have been presented in tabular form.     

Laminar mixed convection in an eccentric annular horizontal duct for a thermodependent non-Newtonian fluid

The present work focuses on the study of mixed convection of a purely viscous shear-thinning fluid in a horizontal annular eccentric duct. The inner and outer cylinders are heated with constant and uniform heat flux densities. The objective of this work is to study the effect of the variation of eccentricity, rheological behavior of the fluid as well as the thermodependency of the rheological parameters on the reorganization of the flow and thermal stratification caused by the buoyancy forces. At the entrance of the heating zone, the dynamic regime is assumed to be established and the temperature profile uniform. The conservation equations are solved numerically using a finite difference method with implicit schemes. A secondary azimuthal flow, induced by natural convection, develops downstream of the inlet section. This flow creates a stratification of the thermal field on a given section of the duct, which intensifies downstream from the entrance. On the other hand, the decrease in consistency with increasing temperature near the heated walls produces a centrifugal radial flow towards the walls. The presence of an eccentricity induces in turn a significant effect on the main dynamic field and the stratification of the thermal field. Two cases of upward and downward eccentricity are treated. These show that an upward shift increases the stratification of the thermal field, while the stratification begins to weaken from a certain amount of eccentricity in the case of downward shift. This represents an important result in terms of possible industrial applications. We may indeed conclude that an appropriate choice of downward eccentricity can reduce the thermal stratification, observed experimentally in the case of a concentric heated annular duct [1], when this stratification is undesirable. The choice of this eccentricity depends on rheological and thermal properties of the fluid.     

Projection- and characteristic-based operator-splitting simulation of mixed convection flow coupling heat transfer and fluid flow in a lid-driven square cavity

ABSTRACT

Mixed convection flow in a 2D rectangular cavity is simulated by a novel finite element method, namely the projection- and characteristic-based operator-splitting algorithm. In each time step, the Navier–Stokes equations are split as follows: the diffusion part, the convection part by applying operator-splitting method, and the Poisson’s equation by adopting projection method. The implicit diffusion part is solved by the preconditioned conjugate gradient (PCG) method, whereas characteristic method is applied for the convection part in a multistep explicit scheme. The characteristic Galerkin approach is used to solve the energy equation. To validate the model, lid-driven cavity flow and natural convection flow are simulated.     

Heat and mass transfer under MHD mixed convection in a four-sided lid-driven square cavity

This paper investigates the heat and mass transfer under magnetohydrodynamic mixed convection flow of a binary gas mixture in a four-sided lid-driven square cavity. The enclosure's left wall is sinusoidally heated and acts as a source term, while the right wall functions as a sink. The cavity's horizontal walls are adiabatic and impermeable to mass transfer. The governing equations under Boussinesq approximation and stream function-vorticity formulation are solved using the alternating-direction-implicit scheme, a finite-difference method. The numerical scheme's consistency and stability are demonstrated using the matrix method. The MATLAB code is written, validated against some existing studies, and used to perform numerical simulations. The numerical solutions are graphically examined by visualizing the streamline, isotherm, and concentration contours for nondimensional parameters, such as Hartmann number $\left(0\le Ha\le 100\right)$, heat absorption or generation coefficient $\left(-2\le \varphi \le 2\right)$, Richardson number $\left(0.01\le Ri\le 100\right)$, and buoyancy ratio $\left(-6\le N\le 6\right)$. The magnetic field modifies the temperature and concentration distribution in the cavity, depending on the convection mode. The magnetic field forces the fluid to stagnate in different regions of the cavity, depending on the mode of convection. It was found that the difference between the maximum and minimum temperature and concentration at the cavity's midpoint increases up to 13 and 10 times, respectively, in the natural convection compared with the forced convection. The average Nusselt number on the vertical walls of the cavity is maximum in natural convection in the absence of a magnetic field but reaches a minimum value at $Ha=100$ in forced and mixed convection. The average Sherwood number on the cavity's vertical walls decreases with the magnetic field in mixed and natural convection.     

Magneto hydrodynamic buoyant convection of an electrically conducting fluid in a tilted square cavity

A numerical investigation of steady‐natural convection of an electrically conducting fluid, enclosed in a tilted square cavity, subjected to a uniform magnetic field applied perpendicular to the plane of cavity is presented. A comprehensive understanding of the effects of controlling parameters on the flow and heat transfer is delineated for a wide range of parameters. Correlations for the average Nusselt number are presented specifically for fluids with low Prandtl numbers pertaining to liquid metals. It is made known that when the applied magnetic field is perpendicular to the plane of the cavity, the magneto hydrodynamic drag is greatest as compared to any other direction of the applied magnetic field and consequently the suppression of convection is also at its maximum, irrespective of all other controlling parameters. 8 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20326     

Unsteady MHD mixed convection flow of a micropolar fluid along an inclined stretching plate

In this research, the unsteady magnetohydrodynamic mixed convection flow of a micropolar fluid over an inclined plate has been investigated. The problem is reduced to a system of non‐dimensional partial differential equations, which are solved numerically using the implicit finite‐difference scheme. Velocity profiles, temperature profiles, concentration profiles, the skin friction coefficient, the rate of heat transfer, and the rate of mass transfer are computed numerically for various values of different physical parameters. In this study, we consider both assisting and opposing flow. It is found that in the assisting flow case, a solution could be obtained for all positive values of the buoyancy parameter λ, while in the opposing flow case the solution terminated at $\lambda = {\lambda _c}(\lambda < 0)$ . © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21034     

Numerical simulation of natural convection heat transfer from a heated square cylinder in a square cavity filled with micropolar fluid

A numerical investigation has been performed to visualize the magnetohydrodynamic natural convective heat transfer from a heated square cylinder situated within a square enclosure subjected to nonuniform temperature distributions on the left wall. The flow inside the enclosure is unsteady, incompressible, and laminar and the working fluid is micropolar fluid with constant Prandtl number (Pr = 7). The governing equations of the flow problem are the conservation of mass, energy, and linear momentum, as well as the angular momentum equations. Governing equations formulated in dimensionless velocity and pressure form has been solved by Marker and Cell method with second-order accuracy finite difference scheme. Comprehensive verification of the utilized numerical method and mathematical model has shown a good agreement with numerical data of other authors. The results are discussed in terms of the distribution of streamlines and isotherms and surface-averaged Nusselt number, for combinations of Rayleigh number, Ra (10³–10⁶), Vortex viscosity parameter, K (0–5), and Ha parameter (0–50). It has been shown that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside the cavity.     

Study on local resistance of non-Newtonian power law fluid in elbow pipes

This paper focuses on the flow characteristic and local resistance of non-Newtonian power law fluid in a curved90° bend pipe with circular cross-sections,which are widely used in industrial applications.By employing numerical simulation and theoretical analysis the properties of the flow and local resistance of power law fluid under different working conditions are obtained.To explore the change rule the experiment is carried out by changing the Reynolds number,the wall roughness and different diameter ratio of elbow pipe.The variation of the local resistance coefficient with the Reynolds number,the diameter ratio and the wall roughness is presented comprehensively in the paper.The results show that the local resistance force coefficient hardly changes with Reynolds number of the power law fluid;the wall roughness has a significant impact on the local resistance coefficient.As the pipe wall roughness increasing,the coefficient of local resistance force will increase.The main reason of the influence of the roughness on the local resistance coefficient is the increase of the eddy current region in the power law fluid flow,which increases the kinetic energy dissipation of the main flow.This paper provides theoretical and numerical methods to understand the local resistance property of non-Newtonian power law fluid in elbow pipes.     

Unsteady mixed convection flow over a vertical wedge

The behavior of unsteady mixed convection flow of an incompressible viscous fluid over a vertical wedge with constant suction/injection have been investigated. The unsteadiness is due to the time-dependent free stream velocity. The governing boundary layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations is solved by an implicit finite-difference scheme in combination with the quasi-linearization technique. Numerical results for the effects of various parameters on velocity, temperature and concentration profiles and on their gradient at the wall are reported in the present study. The buoyancy force causes considerable velocity overshoot for low Prandtl number (Pr) fluids. Skin friction coefficient, heat and concentration transfer rates are found to alter significantly due to injection/suction for both accelerating and decelerating flow.     

Natural convection and entropy generation in a square cavity

A natural convection in a square cavity finds considerable interest in thermal engineering applications. However, the use of entropy generation concept enables to identify the optimum conditions for its practical application. Consequently, in the present study, natural convection in a square cavity with differential top and bottom wall temperatures is investigated. A numerical scheme using the control volume approach is introduced when discretizing the governing flow and energy equations. The study is extended to include the analysis of the entropy in the cavity. It is found that the local rise of temperature occurs at the right bottom of the cavity due to vertical circulation developed in the cavity. The entropy generation amplifies when circulation along the x-axis increases and, the entropy generation becomes minimum for a particular Rayleigh number. © 1998 John Wiley & Sons, Ltd.