Combined heat and mass transfer in natural convection between vertical parallel plates

Abstract

This study is to examine the effects of latent heat transfer associated with liquid film vaporization on heat transfer in the natural convection flows driven by the simultaneous presence of combined buoyancy forces of thermal and mass diffusion. Results are especially presented for an air‐water system under various conditions. The influences of channel length and system temperatures on the momentum, heat and mass transfer in the flow are investigated in great detail. The important role of transport of latent heat of vaporization under the situations of buoyancy‐aiding and opposing flows is clearly demonstrated.     

Effect of discrete flow distribution on heat transfer at a vertical surface in natural convection

The influence of a discrete distribution of injection and suction of air on heat transfer at a vertical flat surface under free convection has been investigated experimentally. The results are presented together with empirical formulas for the heat transfer coefficients.     

Combined heat and mass transfer in MHD free convection from a vertical surface with Ohmic heating and viscous dissipation

The problem of combined heat and mass transfer of an electrically conducting fluid in MHD natural convection adjacent to a vertical surface is analyzed, taking into account the effects of Ohmic heating and viscous dissipation. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference technique. The solution is found to be dependent on the governing parameters including the magnetic field parameter, the buoyancy ratio between species and thermal diffusion, the Eckert number, the Prandtl number, and the Schmidt number. Effects of these major parameters on the transport behaviors are investigated methodically and typical results are illustrated to reveal the tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions, as well as the local skin-friction coefficient, local Nusselt number, and the local Sherwood number.     

Evaporation heat and mass transfer in natural convection pipe flow

Abstract

A numerical analysis has been performed to examine film evaporation on natural convection heat and mass transfer in a vertical pipe. Coupled governing equations for liquid film and induced gas flow were simultaneously solved by the implicit finite difference method. Results for interfacial heat and mass transfer coefficients are specifically presented for ethanol film and water film vaporization. The predicted results indicate that the heat transfer from gas‐liquid interface to the gas flow is predominated by the transport of latent heat in association with film evaporation. The results are also contrasted with those of zero film thickness and show that the assumption of extremely thin film thickness made by Chang et al. [5] and Yan and Lin [19] is only valid for a system with a low liquid Reynolds number Re _l1. But as the liquid Reynolds number is high, the assumption becomes inappropriate.     

Free convection heat and mass transfer along a vertical surface in a porous medium

Summary This study deals with free convection heat and mass transfer from a vertical plate embedded in a fluid saturated porous medium with constant wall temperature and concentration. The temperature and concentration variations across the boundary layer produce a buoyancy effect which gives rise to flow field. Integral method of Von-Karman type is applied to obtain the analytical solution of this fundamental problem.     

Combined momentum, heat and mass transfer in vertical slug flow absorbers

Numerical solutions have been obtained for the system of equations of momentum, heat and mass transfer describing the absorption of a refrigerant vapour from a Taylor bubble into the refrigerant-absorbent solution film around the bubble. The numerical results are compared with Nusselt's solution of the energy equation and with the penetration theory solution of the mass diffusion variation. Experimental data have been collected in vertical tubular absorbers in the slug flow region with the systems ammonia-lithium nitrate and ammonia-sodium thiocyanate. Four different absorber tubes have been tested with internal diameters of 10, 15, 20, and 25 mm. These data are compared with the numerical and theoretical results. The effect of the bubble nose on mass transfer is studied. Typical temperature profiles during the absorption process in absorption cooling/heating systems are shown.     

Heat and mass transfer in a binary turbulent boundary layer with natural convection at vertical surface

An approximate solution is given for binary turbulent natural convection, with allowance for diffusive heat conduction. Analytic expressions are obtained for the boundary-layer outlet characteristics (coefficients of heat exchange and mass transfer). The solution is compared with experiments on heat and mass transfer during condensation of vapors from mixtures with various gases.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.17, No. 2, pp. 226–232, August, 1969.     

Experimental investigation of heat and mass transfer during condensation of water vapor from humid air on a vertical surface under natural convection conditions

Results are presented of an experimental investigation of the heat and mass transfer accompanying condensation of water vapor from vapor-air mixtures with low volumetric vapor contents (_o.v 2.1%). Empirical formulas are proposed for the heat transfer coefficient and the rate of condensation.     

Numerical study of Soret and Dufour effects on heat and mass transfer from natural convection flow over a vertical porous medium with variable wall heat fluxes

A study has been carried out to obtain the solutions for heat and mass transfer from natural convection flow along a vertical surface with variable heat fluxes embedded in a porous medium due to thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. The buoyancy induced boundary layer adjacent to a vertical surface is analyzed using a non-Darcy flow model. The parameters for inertia, buoyancy ratio, exponent of heat flux, position and diffusion have been examined. The governing differential equations of continuity, momentum, energy and concentration are transformed into a set of coupled equations and solved using similarity analysis with numerical technique. Results show the velocity, temperature and concentration profiles related to local Nusselt and Sherwood numbers at different magnitude of Soret and Dufour numbers.     

Combined heat and mass transfer in natural convection on horizontal and inclined plates with variable surface temperature/concentration or heat/mass flux

Summary An analysis is presented to study the heat and mass transfer characteristics of natural convection flow along horizontal and inclined plates with variable surface temperature/concentration or heat/mass flux under the combined buoyancy effects of thermal and mass diffusion. Numerical results are obtained for two values of Schmidt number covering the range of diffusion species of common interest like water vapour, carbon dioxide and naphthalene in air.     

Heat transfer response of free convection flow from a vertical heated plate to an oscillating surface heat flux

Summary An investigation is undertaken of the unsteady response of two-dimensional laminar free convection boundary layer flow of a viscous incompressible fluid along a semi-infinite vertical heated plate where the mean surface heat flux oscillates with a small amplitude about a steady profile. The buoyancy forces are favourable, resulting from a positive flux of heat from the surface of the plate into the fluid. The interaction of the time-periodic heat flux with the usual boundary-layer flow is examined by using a linearized theory. Solutions are obtained using three distinct methods, namely an extended series expansion method for low frequencies, an asymptotic series expansion method for high frequencies and a fully numerical finite difference method for general frequencies. Calculations have been carried out for a wide range of parameters to examine the solutions in terms of the amplitude and phase angle of the fluctuating parts of the surface shear stress and the surface temperature. It has been found that the amplitude and phase angle of both the shear stress and the surface temperature predicted by these three methods are in very good agreement in their respective ranges of validity.     

Mixed convection of micropolar fluids along a vertical wavy surface

Summary This paper presents numerical results for the steady-state mixed convection in micropolar fluids along a vertical wavy surface. The problem has been formulated by a simple trnasposition theorem, and the spline alternating-direction implicit method has been applied to solve the governing momentum, angular momentum and energy equations. The influence of the micropolar parameters (R and ), the amplitude-wave length ratio and the Gr/Re² number on the skin-friction coefficient and Nusselt number have been studied. Results demonstrate that the skin friction coefficient and local Nusselt number consist of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases but the skin friction increases. In addition, when the spin gradient viscosity parameter () increases, the heat transfer rate and the skin friction decreases. However, the heat transfer rate of a micropolar fluid is smaller than a Newtonian fluid, but the skin friction of a micropolar fluid is larger than a Newtonian fluid under all circumstances.     

Hydromagnetic flow and heat transfer on a continuously moving vertical surface

Summary A theoretical solution for hydromagnetic convection over a continuously moving vertical surface with uniform suction is obtained. A flow of this types represents a new class of boundary-layer flow at a surface of finite length. The solutions for the velocity and temperature profiles are obtained. It is observed that the velocity decreases considerably in the presence of a magnetic field, as compared to its absence.     

Heat and mass transfer in MHD flow by natural convection from a permeable, inclined surface with variable wall temperature and concentration

Summary. An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation. Power-law temperature and concentration variations are assumed at the inclined surface. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference method. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Eckert number, the buoyancy ratio between species and thermal diffusion, Prandtl number, Schmidt number, wall temperature and concentration exponent, the inclination angle from the vertical direction, and the injection parameter. A parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions as well as the local friction coefficient, local Nusselt number, and the local Sherwood number.     

Fluid flow and heat transfer in horizontal wavy channels

Summary The equations governing the fluid flow and heat transfer have been solved subject to the relevant boundary conditions by assuming that the solution consists of two parts: a mean part and a perturbed part. To obtain the perturbed part of the solution, use has been made of the long-wave approximation. The mean part of the solution has been found to be in good agreement with that of the plane Poiseuille flow. The perturbed part of the solution is the contribution from the waviness of the walls. The mean part, the perturbed part and the total solution of the problem have been evaluated numerically for several sets of values of the parameters. Certain qualitatively interesting properties of the fluid flow and heat transfer, along with the changes in the fluid pressure on the wavy walls, are recorded in § § 5 and 6.

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Strömung und Wärmeübergang in horizontalen, welligen Kanälen

Zusammenfassung Die Grundgleichungen des Problems werden für das Stromfeld und den Wärmeübergang unter den gegebenen Randbedingungen gelöst. Dabei wird angenommen, daß die Lösung aus zwei Anteilen besteht: einem Mittelwert und den Störgrößen. Der Störanteil wird ermittelt durch eine Approximation im Sinne langer Wellen. Der Mittelwert des Stromfeldes stimmt gut mit der ebenen Poiseuille-Strömung überein. Der Störanteil rührt von der Welligkeit der Wände her. Die Gesamtströmung wurde numerisch für zahlreiche Werte der eingehenden Parameter bestimmt. Zahlreiche interessante Eigenschaften der Strömungsgrößen sowie des Wärmeüberganges sowie der Druckverteilung längs der welligen Wand werden in § § 5 und 6 besprochen.

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With 12 Figures     

Transient natural convection flow over vertical cylinder with variable surface temperatures

An analysis is made for transient natural connective flow over a vertical cylinder with surface temperature of the cylinder varying as x ⁿ , a power function of distance from the leading edge. A Crank-Nicolson type of implicit finite difference method is used to solve the governing non-linear set of equations. Numerical results are obtained and presented for air and water with various n. The transient velocity and temperature profiles, local and average skin-friction and Nusselt numbers are shown graphically. The effects of exponent n on velocity and temperature profiles, skin-friction and rate of heat transfer have been analysed. The velocity and temperature profiles are compared with the available results in the literature and it is found to be in good agreement.     

Experimental study of laminar natural convection heat transfer from a vertical cylinder to slush nitrogen under constant heat flux conditions

Natural convection heat transfer from a vertical cylinder immersed in slush and subcooled liquid nitrogen and subjected to constant heat fluxes was investigated in order to determine the relative merits of slush nitrogen (SlN₂) for immersion cooling. A glass dewar was used as a test vessel in which a cylindrical heater was mounted vertically, and heat transfer measurements were carried out for SlN₂ and subcooled liquid nitrogen (LN₂) in the laminar flow range. The results revealed advantages of SlN₂ over subcooled LN₂ in natural convection cooling. The local temperatures of the heated surface surrounded by solid nitrogen particles are measured to increase at much slower rates than in subcooled LN₂, which is due to the latent heat of fusion of solid nitrogen. Even after the solid nitrogen particles surrounding the heater are apparently depleted, the average heat transfer coefficients for SlN₂ are still found to be greater than those for LN₂ with the improvement in heat transfer being larger for lower Grashof number regime. Our analysis also indicates that solid nitrogen particles in close proximity to heated surface do not discourage local convection due to the porous nature of SlN₂, making the heat transfer in SlN₂ more effective than in the case of solid–liquid phase change of nitrogen involving melting and conduction processes.