A numerical study of mixed convection in a horizontal channel with a discrete heat source in an open cavity

This article aims to numerically investigate mixed convection heat transfer in a two-dimensional horizontal channel with an open cavity. A discrete heat source is considered to be located on one of the walls of the cavity. Three different heating modes are considered which relate to the location of the heat source on three different walls (left, right and bottom) of the cavity. The analysis is carried out for a range of Richardson numbers and cavity aspect ratios. The results show that there are noticeable differences among the three heating modes. When the heat source is located on the right wall, the cavity with an aspect ratio of two has the highest heat transfer rate compared to other cavity heating modes. Moreover, when the heat source is located on the bottom wall, the flow field in the cavity with an aspect ratio of two experiences a fluctuating behaviour for Richardson number of 10. The results also show that at a fixed value of Richardson number, all three different heating modes show noticeable improvements in the heat transfer mechanism as the cavity aspect ratio increases.     

Influence of buoyancy in a mixed convection liquid metal flow for a horizontal channel configuration

This article presents the direct numerical simulation (DNS) of mixed convection turbulent heat transfer in a horizontal channel case for liquid lead. Cartesian mesh is used and the incompressible Navier-Stokes equations are discretized with highly accurate finite difference sixth-order compact schemes to perform the DNS. The influence of mixed convection in liquid metal with Prandtl number equal to 0.025 and Reynolds number equal to 4667 has been studied by varying the Richardson number (Ri = 0, 0.25, 0.50, 1.00). The obtained results are extensively analyzed and discussed in this article. In particular, large-scale circulation is observed under the influence of buoyancy. Compared to the forced convection case (Ri = 0), stronger velocity fluctuations are noticed that highlight the fact that turbulence is strongly enhanced with the increasing buoyancy. It also proves that the thermal plumes rising up from the hot wall of the channel activate the cross-stream eddies. Moreover, temperature fluctuations are found to be more homogeneously distributed with increasing buoyancy effects and mixing is more effective in the center of the channel. In addition, compared with forced convection, mixed convection has shown enlargement of the large-scale structures that only appear in the temperature field for low Prandtl number fluids. Extensive results of flow and temperature fields are analyzed and presented.     

Characterization of fluid flow patterns and heat transfer in horizontal channel mixed convection

Two mechanisms of roll initiation are highlighted in a horizontal channel flow, uniformly heated from below, at constant heat flux (Γ = 10, Pr = 7, 50 ≤ Re ≤ 100, 0 ≤ Ra ≤ 10⁶). The first mechanism is the classical one, it occurs for low Rayleigh numbers and is initiated by the lateral wall effect. The second occurs for higher Rayleigh numbers and combines the previous effect with a supercritical vertical temperature gradient in the lower boundary layer, which simultaneously triggers pairs of rolls in the whole zone in between the two lateral rolls. We have found that in the present configuration, the transition between the two roll initiation mechanisms occurs for Ra/Re ² ≈ 18. Consequently, the heat transfer is significantly enhanced compared to the pure forced convection case owing to the flow pattern responsible of the continuous flooding the heated wall with cold fluid.     

Mixed convection flow in a horizontal rectangular channel subjected to a horizontal thermal gradient

This paper deals with a mixed convection water flow in a horizontal rectangular duct, uniformly heated from one lateral vertical wall and thermally insulated elsewhere. The supplied heat flux induces a secondary flow, which structure is constituted of one longitudinal roll in the considered aspect ratio (Γ = 1.9), embedded into a return flow of possibly large stream wise extension (up to twenty channel heights). Such situation induces helicoidal trajectories for the fluid flow particles, which contributes to a heat transfer enhancement compared to purely forced convection flow.     

Three-dimensional numerical simulation of free convection in a plane-parallel flow

The results are given of numerical simulation of convection in Couette and Poiseuille flow for stationary (T*/t = 0) and uniformly increasing (T*/t = = const) mean temperature of the convective layer. Numerical experiments were made for air (Prandtl number Pr = 0.7) in the range of Rayleigh numbers 2 000 Ra 44 000. The results confirm the conclusion drawn in earlier studies that at slightly supercritical Ra the dominant forms in the convection are cylindrical rolls with helical circulation. The rolls are oriented along the direction of the flow and are stationary formations. When a certain value of Ra, which depends on the vertical distribution of the temperature and velocity, is reached, the roll structure is deformed by transverse perturbations. All the considered flow forms have a stabilizing influence on the transverse modes, occurring at larger Rayleigh numbers than is the case for convection in a fluid at rest. The perturbations are displaced at a phase velocity close to the mean velocity of the undisturbed flow. In the considered range of Rayleigh numbers, a shear flow does not have an appreciable influence on the heat transfer, although there is a certain tendency for the Nusselt number to be larger in a shear flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 127–135, May–June, 1979.We thank N. M. Sazanovich and L. I. Derevich for assistance in the calculations.     

Transient mixed convection flow arising due to thermal and mass diffusion over porous sensor surface inside squeezing horizontal channel

The double diffusion effect on the mixed convection flow over a horizontal porous sensor surface placed inside a horizontal channel is analyzed.With the appropriate transformations,the unsteady equations governing the flow are reduced to non-similar boundary layer equations which are solved numerically for the time-dependent mixed convection parameter.The asymptotic solutions are obtained for small and large values of the time-dependent mixed convection parameter.The results are discussed in terms of the skin friction,the heat transfer coefficient,the mass transfer coefficient,and the velocity,temperature,and concentration profiles for different values of the Prandtl number,the Schmidt number,the squeezing index,and the mixed convection parameter.     

Experimental and numerical study of mixed convection and flow pattern in a lid-driven arc-shape cavity

Experimental and numerical study has been performed to investigate the combined effects of lid movement and buoyancy on flow and heat transfer characteristics for the mixed convective flow inside a lid-driven arc-shape cavity. The numerical methodology is based on a numerical grid generation scheme that maps the complex cross section onto a rectangular computation domain. The discretization procedure for the governing equations is based on the finite-volume method. In experiments, steady-state temperature data are measured by T-type thermocouples, and the flow field is visualized by using kerosene smoke. Reynolds number and Grashof number are two major independent parameters representing the effects of lid movement and buoyancy, respectively. Flow pattern, friction factor, and Nusselt numbers are investigated in wide ranges of these independent parameters. Close agreement in the comparison between the predicted and the visualized flow patterns shows the validity of the numerical methods.     

Experimental and numerical study of mixed convection with flow reversal in coaxial double-duct heat exchangers

Velocity vectors in a vertical coaxial double-duct heat exchanger for parallel ascending flow of water under conditions of laminar mixed convection have been determined experimentally using the particle image velocimetry technique. The measured velocity distributions for large annular flow rates, resulting in an essentially isothermal environment for the stream in the inner tube, are in very good agreement with corresponding numerical predictions. For flow rates of the same order of magnitude in the inner tube and the annulus, and corresponding temperature differences of about 20 °C, experimental observations show that flow reversal occurs simultaneously in both streams over large axial distances for both heating and cooling of the flow in the inner tube.     

Radiation effect on mixed convection from a horizontal surface in a porous medium

The effect of thermal radiation on the non-Darcy mixed convection flow over a non-isothermal horizontal surface immersed in a saturated porous medium has been studied. The wall temperature is assumed to have a power-law variation with the distance measured from the leading edge of the plate. The non-linear coupled parabolic partial differential equations governing the flow have been solved numerically using a finite-difference scheme. For some particular cases, the self-similar solution has also been obtained. The heat transfer is found to be strongly influenced by the radiative flux number, buoyancy parameter, variation of wall temperature, non-Darcy parameter and the nature of the free stream velocity.     

On the effect of flow direction on mixed convection from a horizontal cylinder

The influence of free stream direction on mixed (natural and forced) convective heat transfer from a circular cylinder is investigated. The cylinder, which has an isothermal surface, is placed with its axis horizontal and normal to the oncoming flow. The free stream direction varies between the vertically upward (parallel flow) and the vertically downward (contraflow) directions. The investigation is based on the time integration of the unsteady, two-dimensional equations of motion and energy until reaching steady conditions. The study is limited to Reynolds numbers up to Re = 40 and Grashoff numbers of Gr = Re². The results are compared with the available experimental data and the agreement is satisfactory.     

Integral solution for Forchheimer free convection over a horizontal flat surface

The aim of the present paper is to study the non-Darcy free convection from a horizontal flat surface in a fluid saturated porous medium using integral method for the case when the heat flux from the surface remains constant. The thermal dispersion effects are taken into consideration. The linear relation between the dispersion thermal diffusivity and the streamwise velocity component has been adopted. Exponential profiles are choosen for the velocity and temperature distributions. The Nusselt number results are in good agreement with the existing similarity solution.     

Experimental investigation of helicoidal rolls in an advective flow over a hot horizontal surface

A digital tracer technique is applied to reconstruct the velocity fields in a convective flow developing in a rectangular cavity filled with a layer of fluid and having a bottom consisting of two heat exchangers kept at different temperatures. The upper boundary of the fluid is free. The structure of the secondary flows in the form of streamwise helicoidal rolls generated in the boundary layer over a hot plate is studied. It is shown that the centers of roll rotation coincide with temperature minima in the boundary layer, while the roll shape and dimensions vary with the distance from the temperature jump. With increase in the temperature difference the roll dimensions decrease but the velocity of their rotation increases.     

Application of the wavelet transform for a channel flow in a mixed convection phenomenon

The aim of this paper is to investigate laminar-turbulent transition in a mixed convection phenomenon occurring in a horizontal rectangular duct. Indeed, laminar-turbulent transition is well known in the case of forced convection but the presence of secondary flow induced by natural convection on this transition is not well highlighted. In this study, we will not be concerned by determining a critical threshold value of a Reynolds number of transition but only to estimate the degree of turbulence in the transition regime, i.e. weak turbulence in the case of a mixed convection phenomenon. This is possible thanks to the application of the wavelet transform. The calculation of the Hölder exponent, associated with the maximum value of the singularity spectrum for various experimental conditions allows the degree of turbulence to be measured. The variation of the Hölder exponent versus heat flux and Reynolds number enables us to show that there are two ways to go towards turbulence: thermal by increasing heat flux and hydrodynamic by increasing fluid velocity.     

Experimental investigation of mixed convection heat transfer in a horizontal and inclined rectangular channel

 Mixed convection heat transfer in rectangular channels has been investigated experimentally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Experiments were conducted for Pr=0.7, aspect ratios AR=5 and 10, inclination angles 0° ≤ θ ≤ 30°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr*=7.0 × 10⁵ to 4.0 × 10⁷. From the parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results related to the buoyancy affected secondary flow and the onset of instability have been discussed. Some of the results obtained from the experimental measurements are also compared with the literature, and a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number and increasing aspect ratio. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle. Received on 19 March 2001 / Published online: 29 November 2001     

Mixed convection boundary-layer flow on a horizontal flat surface with a convective boundary condition

The steady mixed convection boundary-layer flow on an upward facing horizontal surface heated convectively is considered. The problem is reduced to similarity form, a necessary requirement for which is that the outer flow and surface heat transfer coefficient are spatially dependent. The resulting similarity equations involve, apart from the Prandtl number, two dimensionless parameters, a measure of the relative strength of the outer flow M and a heat transfer coefficient γ. The free convection, M=0, case is considered with the asymptotic limits of large and small γ being derived. Results for the general, M>0, case are presented and the asymptotic limit of large M being treated.     

Laminar mixed convection on a horizontal plate of finite length in a channel of finite width

The steady two-dimensional laminar mixed-convection flow past a horizontal plate of finite length is analysed for large Péclet numbers, small Prandtl numbers and weak buoyancy effects. The plate is placed in a channel of finite width, with the plane walls of the channel being parallel to the plate. The temperature of the plate is assumed to be constant. The hydrostatic pressure difference across the wake behind the plate is compensated by a perturbation of the inviscid channel flow. This outer flow perturbation affects the temperature distribution in the thermal boundary layer at the plate and the heat transfer rate, respectively. Solutions in closed form are given. The forces acting on the plate due to the potential flow perturbation are also determined.     

Magnetohydrodynamic mixed convection in a vertical channel

The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε.     

Free convection boundary-layer flow above a nearly horizontal surface in a porous medium with newtonian heating

In this paper the steady free convection boundary-layer along a semi-infinite, slightly inclined (both positive and negative) to the horizontal plate embedded in a porous medium with the flow generated by Newtonian heating has been investigated. The asymptotic solution near the leading edge and the full numerical solution along the whole plate domain have been obtained numerically, whilst the asymptotic solution far downstream along the plate has been obtained analytically. For a positive inclination the full numerical solution is in agreement with the asymptotic solutions. However, for a negatively inclined plate, only the small asymptotic solution near the leading edge of the plate can be predicted giving an insight that the model for a negatively inclined plate, whilst mathematically interesting, is not physically realistic.