An experimental investigation on the effects of surface gravity waves on the water evaporation rate in different air flow regimes

Estimating rate of evaporation from undisturbed water surfaces to moving and quiet air has been the topic a vast number of research activities. The obvious presence of various shapes of gravity waves on the water body surfaces was the motivation of this experimental investigation. In this investigation experimental measurements have been done to quantify evaporation rate from wavy water surfaces in free, mixed and forced convection regimes. The effects of a wide range of surface gravity waves from low steepness, round shaped crest with slow celerity, to steep and very slight spilling crest waves, on the water evaporation rate have been investigated. A wide range of ${\text{Gr}}/{\text{Re}}^{2} (0.01 \le {\text{Gr}}/{\text{Re}}^{2} \le 100)$ was achieved by applying different air flow velocities on a large heated wave flume equipped with a wind tunnel. Results reveal that wave motion on the water surface increase the rate of evaporation for all air flow regimes. For free convection, due to the effect of wave motion for pumping rotational airflows at the wave troughs and the dominant effect of natural convection for the air flow advection, the maximum evaporation increment percentage from wavy water surface is about 70 %. For mixed and forced convection, water evaporation rate increment is more sensitive to the air flow velocity for the appearance of very slight spilling on the steep wave crests and the leeward air flow structures.     

Convection of a viscous incompressible gas in rectangular regions with inlet and outlet channels

A study is made of two-dimensional problems of thermal convection of a viscous incompressible gas in rectangular regions that have gas inlet and outlet channels in the presence of a temperature difference between the bottom and the top (the bottom is heated). In contrast to the well-studied case of natural convection, when no-slip conditions are specified on all boundaries of the region and motion in the region occurs only through the temperature difference [1–4], the heat transfer in the investigated flows is complicated by the additional influence of the forced convection of the gas due to the motion of gas through the inlet and outlet channels. Flows of such type simulate well the processes that take place in many heat transfer devices and in ventilated and air-conditioned industrial premises. Two formulations of the problem are considered. In the first, the gas flow through the inlet and outlet channels is assumed given, and the solution of the problem is determined by the dimensionless Prandtl, Grashof, and Reynolds numbers. In the second case, this flow rate is not given but determined during the solution of the problem. The motion in the region arises from the difference between the temperatures of the bottom and the top of the region, and the motion, in its turn, causes a flow of gas through the inlet and outlet channels. As in the case of natural convection, the solution of the problem in this case is determined by only two dimensionless numbers — the Grashof and Prandtl numbers. By numerical solution of the boundary-value problems for the equations of heat transfer a study is made of the influence of the characteristic dimensionless numbers on the hydrodynamic and temperature fields and the heat fluxes through the boundaries of the region. The solutions of the problems in the two formulations are compared for different positions of the outlet channels.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 126–131, September–October, 1979.We thank G. I. Petrov for discussing the results.     

Conjugate heat exchange and hydrodynamics for a viscous incompressible fluid moving in a rectangular cavity

Numerical simulation was performed of the motion of a viscous incompressible nonisothermal fluid in an open rectangular cavity under conditions of forced convection and conjugate heat exchange. The effect of the jet dynamic parameter (Reynolds number) and fluid flow conditions on the character of motion and heat exchange of viscous incompressible nonisothermal fluids in rectangular cavities is studied. A hydrodynamic pattern of viscous flow in an open cavity under forced convection conditions (in the conjugate and nonconjugate formulations of the problem) is obtained. The effect of parameters of the model on the character of motion is studied. Temperature profiles for the solid and fluid phases are obtained. The effect of parameters of the model on the character of temperature distribution in both phases is studied.     

Thermoconvective instability of longitudinal flow in a vertical layer

An experimental study has been made of convection in a vertical slit cavity heated from below and with longitudinal horizontal forced flow. It was shown that the convective stability of such flow increases appreciably when the velocity of the forced flow is raised. In the case of slow pumping, an increase in the pressure difference leads to superposition on the rectilinear flow of first monotonic convection and then auto-oscillatory convection. At high flow velocities, the instability is immediately of an oscillatory nature. A diagram of the flow regimes is constructed, and the evolution of the supercritical structures described.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhikosti i Gaza, No. 2, pp. 28–33, March–April, 1984.     

On the second fundamental problem of combined free and forced convection through vertical noncircular ducts

Analysis of combined free and forced convection through vertical noncircular ducts is carried out using a variational technique. Fully developed flow with uniform axial heat input and uniform peripheral heat flux is assumed. All fluid properties are considered invariant with temperature except the variation of density in the buoyancy term of the equation of motion. The condition of uniform peripheral heat flux is utilized in deriving the variational expression. This procedure releases the thermal boundary condition from satisfying exactly the condition at the wall. A finite-difference procedure is carried out. For pure forced convection case, a particularly simple variational expression is presented. Nusselt numbers for combined free and forced convection are computed for rectangular, rhombic and elliptical ducts. An exact solution is presented for laminar forced convection through elliptic ducts. Variational results are in agreement with this exact solution. The present results are compared with those in the published literature wherever possible, and good agreement is obtained.     

Mixed convection from a cylinder oscillating vertically in a quiescent fluid

 The problem of heat convection from a vertically oscillating cylinder in a quiescent fluid is investigated. The governing equations of motion and energy are solved numerically in a non-inertial frame of references to determine the flow field and heat transfer characteristics under different conditions. The main dominating parameters are Keulegan–Carpenter number, KC, frequency parameter, β, Grashof number, Gr and Prandtl number, Pr. The ranges considered for these parameters are KC ≤ 10, β≤40 and Gr ≤ 10⁵ while Prandtl number is kept constant. The study revealed that the effect of amplitude and frequency of oscillation on heat transfer is strongly influenced by the Grashof number range. In the forced convection regime (Gr = 0), the increase of KC creates extensive vortex motion at all cylinder positions that leads to a significant increase in heat transfer. A similar trend, but with a lesser extent, is also observed for the increase of β. However, at high Grashof numbers, the effect of oscillation on heat convection is only significant at large values of KC. Received on 5 June 2000 / Published online: 29 November 2001     

Numerical simulation of convective flows in a soil during the evaporation of water containing a dissolved admixture

The concentration profile is investigated for a solution that saturates a low-permeability soil. The simulation results showed the presence of three flow regimes. The salt accumulated near the phase transition boundary increases the solution density and may lead to the development of natural concentration-induced convection which interacts with the rising flow (forced convection). The stability threshold of the forced flow and the effect on it of natural convection that arises are determined. It is shown that at intense flow to the evaporation surface the admixture concentration increases at this boundary rapidly and reaches the saturation concentration. In this case, the admixture precipitates. In the slow evaporation regime the admixture diffuses from the high-concentration region, which prevents the development of convective flow.     

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.     

Entropy generation in parallel plate microchannels

In this study the entropy generation in microchannels in microdevices induced by the transient laminar forced convection in the combined entrance region between two parallel plates has been investigated numerically. The study considers the microscales in the region of Kn < 0.001. The effects of aspect ratio, Reynolds number, Prandtl number, Brinkman number, and the motion of the lower plate on the entropy generation during the simultaneously developing flow in a parallel-plates channel are investigated. The obtained results addressing all cases are thoroughly in good agreement with the expectations that the entropy generation has its highest value at channel with the smallest aspect ratio at counter motion of the lower plate with the highest Re, Pr and Br/Ω values considered in the problem. An erratum to this article can be found at     

A general treatment for non-Darcy film condensation within a porous medium in the presence of gravity and forced flow

Non-Darcy film condensation over a vertical flat plate within a porous medium is considered. The Forchheimer extended Darcy model is adopted to account for the non-Darcy effects on film condensation in the presence of both gravity and externally forced flow. A general similarity transformation is proposed upon introducing a modified Peclet number based on the total velocity of condensate, resulting from both gravitational force and externally forced flow. This general treatment makes it possible to obtain all possible similarity solutions including the asymptotic results in the four different limiting regimes, namely, Darcy forced convection regime, Forchheimer forced convection regime, Darcy body force predominant regime and Forchheimer body force predominant regime. Appropriate dimensionless groups for distinguishing these asymptotic regimes are found to be the micro-scale Grashof and Reynolds numbers based on the square root of the permeability of the porous medium. Correspondingly, the non-Darcy effect on the heat transfer rate are investigated in terms of these micro-scale dimensionless numbers.     

Interaction of mixed convection in two-sided lid driven differentially heated square enclosure with radiation in presence of participating medium

The current study addresses the mathematical modeling aspects of transport phenomena in steady, two-dimensional, laminar flow accompanied by heat transfer in a lid-driven differentially heated cavity in presence of radiatively absorbing, emitting and scattering gray medium. The walls of the enclosure are considered to be opaque, diffusive and gray. Mixed convection is the outcome of the interaction of forced convection induced by the moving vertical hot and cold wall with the natural convection induced due to the differentially heated enclosure. Two different orientations of the wall movement have been considered to simulate opposing and aiding mixed convection phenomenon and to study its interaction with radiation. Vorticity-stream function formulation of N–S equation has been employed. The discrete ordinate method has been used in modeling the radiative transport equation followed with finite volume method as discretisation technique. The effect of influencing parameters on fluid flow and heat transfer has been studied.     

Heat convection from a cylinder performing steady rotation or rotary oscillation – Part II: Rotary oscillation

This paper deals with the problem of combined (forced and natural) convection from a horizontal cylinder performing oscillating rotary motion in a quiescent fluid of infinite extent. While forced convection is caused by cylinder oscillation, the natural convection is caused by the buoyancy driven flow. The heat transfer process is governed by Rayleigh number, Ra, Reynolds number, Re, and the dimensionless frequency of oscillation, S. The study covers Ra up to 10³, Re up to 400 and S up to 0.8. The results showed that, for the same Ra, the time-averaged rate of heat transfer lies in between two limiting values. The first, is the steady state heat rate due to natural convection from a fixed cylinder and the second is the steady state heat rate from a cylinder rotating steadily at a speed equal to the maximum speed of rotational oscillation. The smaller the value of Re the nearer the time-averaged Nusselt number to that of fixed cylinder at the same Ra and the higher Re the lower the average Nusselt number. The effect of frequency is only limited to changing the amplitude of the fluctuating Nusselt number. Received on 15 December 1997     

Combined free and forced convection in a porous medium between two vertical walls with viscous dissipation

Viscous dissipation effects in the problem of a fully-developed combined free and forced convection flow between two symmetrically and asymmetrically heated vertical parallel walls filled with a porous medium is analyzed. The equation of motion contains the modified Rayleigh number for a porous medium and the small-order viscous dissipation parameter. Particular attention is given to the solutions near the critical Rayleigh numbers at which infinite flow rates are predicted. Information concerning the multiplicity of solutions at critical Rayleigh numbers is also deduced from perturbation solutions of the governing equation.     

Non-Darcy mixed convection from a vertical plate in saturated porous media-variable surface heat flux

Nonsimilarity solutions for non-Darcy mixed convection from a vertical impermeable surface embedded in a saturated porous medium are presented for variable surface heat flux (VHF) of the power-law form. The entire mixed convection region is divided into two regimes. One region covers the forced convection dominated regime and the other one covers the natural convection dominated regime. The governing equations are first transformed into a dimensionless form by the nonsimilar transformation and then solved by a finite-difference scheme. Computations are based on Keller Box method and a tolerance of iteration of 10⁻⁵ as a criterion for convergence. Three physical aspects are introduced. One measures the strength of mixed convection where the dimensionless parameter Ra^* _x /Pe^3/2 _x characterizes the effect of buoyancy forces on the forced convection; while the parameter Pe _x /Ra^*2/3 _x characterizes the effect of forced flow on the natural convection. The second aspect represents the effect of the inertial resistance where the parameter K′U _∞/ν is found to characterize the effect of inertial force in the forced convection dominated regime, while the parameter (K′U _∞/ν)(Ra^*2/3 _x /Pe _x ) characterizes the effect of inertial force in the natural convection dominated regime. The third aspect is the effect of the heating condition at the wall on the mixed convection, which is presented by m, the power index of the power-law form heating condition. Numerical results for both heating conditions are carried out. Distributions of dimensionless temperature and velocity profiles for both Darcy and non-Darcy models are presented. Received on 26 May 1997     

Numerical investigation of flow and combined natural-forced convection from an isothermal square cylinder in cross flow

Unsteady flow and heat transfer from a horizontal isothermal square cylinder is studied numerically using a three-dimensional computational model to investigate the influence of buoyancy on the forced flow and heat transfer characteristics. The numerical model is based on a horizontal square cylinder subjected to laminar fluid flow in an unconfined channel. The governing equations in 3D form are solved using a fractional step method based on the finite difference discretization in addition to a Crank–Nicholson scheme employed to the convective and the viscous terms. Two working fluids–air (Pr = 0.7) and water (Pr = 7)–are considered, and the flow and heat transfer simulations were carried out for the Reynolds and Richardson numbers in the intervals 55 ≤ Re ≤ 250 and 0 ≤ Ri ≤ 2, respectively. The flow characteristics such as time-averaged drag/lift, rms drag/rms lift coefficients as well as Strouhal number were computed. The heat transfer from the cylinder is assessed by mean Nusselt number (and rms Nusselt number) over the total heated cylinder walls. As the buoyancy increases, the mass and the velocity of the fluid flowing underneath the cylinder increases. The fluid is injected into the near wake region with an upward motion which significantly alters the flow field in the downstream as well as upstream regions. The effects of Reynolds, Richardson and Prandtl numbers on the flow field and temperature distributions are discussed in detail. It is shown that the flow and heat transfer characteristics are influenced more for air than water. To fill the void in the literature, useful empirical correlations of practical importance are derived for pure forced and pure natural as well as mixed convection. The mixed convection correlations, in terms of the ratio of pure forced convection, are also developed, and their implications are discussed.     

Similarity conditions for heat transfer in incompressible two-dimensional laminar boundary layer flow

Summary Similarity conditions are presented for the solution of some problems of heat transfer in incompressible two-dimensional boundary layer flow. The treatment holds for forced convection as well as for free convection. For free convection no a priori restriction is made with respect to geometry or temperature distribution of the solid surface. For forced convection the treatment is restricted to uniform bulk flow parallel to a flat surface of non-uniform temperature or heat flux. The results are summarized in some tables that facilitate comparison with older work.     

Higher order stability effects in a natural convection boundary layer over a vertical heated wall

 The stability of a laminar boundary layer flow under natural convection on a vertical isothermally heated wall is studied analytically. The analysis is performed by using two different two-dimensional linear models: (1) The non-parallel flow model in which the steady mean flow as well as the disturbance amplitude functions can change in the streamwise direction; (2) The parallel flow model in which the effects of the mean flow and disturbance changes in the streamwise direction are neglected. The linear non-parallel stability analysis is based on the so-called parabolised stability equations (PSEs) which have been successfully applied to the stability analysis of forced convection boundary layers. In this study the PSE equations are applied to natural convection boundary layers in order to show the difference between parallel and non-parallel stability analysis. A second part of this study deals with the effects of variable properties, which are always present in natural convection flows. They are analysed by an extended version of the Orr–Sommerfeld equation (EOSE). Received on 31 May 2000     

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.     

On pattern selection in mixed convection in rectangular ducts

Mixed convection in a horizontal rectangular duct has the same critical Rayleigh number as natural convection in a rectangular cavity for the onset of convection. The linear stability analysis predicts either an odd or an even number of convective rolls to appear depending on the aspect ratio of the cross section. However, it has been shown both experimentally and numerically that an even number of convective rolls appears under supercritical conditions for fully developed mixed convection. The paper first presents an analytical solution for the buoyancy-induced mainstream velocity, w ^b , at the onset of buoyancy-induced motion in a forced convective flow. Then, a comparison in the initial growth rate of w ^b is made between the case of an odd and an even number of rolls; which shows the selection of an even number of rolls over an odd number in mixed convection except for low aspect ratio ducts.     

Mixed convection unsteady stagnation point flow over a stretching sheet with heat transfer in the presence of variable free stream

An analysis is performed for the unsteady mixed convection flow of an incompressible viscous fluid about a stagnation point on a stretching sheet in the presence of a variable free stream. The equations of motion and energy are transformed into the ordinary differential equations by using similarity transformations. Homotopy analysis method is used for the solution of the governing problem. The results have been discussed by plots. The present values of the function are shown very close to the previous limiting solutions. Copyright © 2011 John Wiley & Sons, Ltd.