Coupled heat and mass transfer in mixed convection over a vertical flat plate embedded in saturated porous media: PST/PSC or PHF/PMF

A boundary layer analysis is used to investigate the heat and mass transfer characteristics of mixed convection about a vertical flat plate embedded in a saturated porous medium under the coupled effects of thermal and mass diffusion. The plate is maintained at prescribed surface temperature/concentration (PST/PSC) or prescribed heat/mass flux (PHF/PMF). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results for the local heat transfer rate and the local mass transfer rate are presented for various parameters. The local heat and mass transfer rates increase with increasing n and m and buoyancy parameter ξ. When buoyancy parameter ξ is very small (large) the value of local Nusselt and the local Sherwood number correspond with the pure forced (free) convection, respectively. Increasing buoyancy ratio N (or N ^*) increases the local heat and mass transfer rates. It is apparent that Lewis number has a pronounced effect on the local mass transfer rate than it does on the local heat transfer rate. Furthermore, increasing Lewis number decreases (increases) the local heat (mass) transfer rate. Received on 8 December 1997     

Experimental results of pure and simultaneous heat and mass transfer by free convection about a vertical cylinder for Pr=0.71 and Sc=0.63

In this paper experimental results are given concerning stationary heat and mass transfer in the laminar boundary layer of a vertical cylinder placed in still air. The combined effect is considered as well as the two separate effects. Measurements are carried out on heat transfer and evaporation of water. Results are in close agreement with the classical free convection boundary layer theory for a vertical flat plate, if only a small cylinder correction is applied.     

Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium

Unsteady laminar mixed convection flow (combined free and forced convection flow) along a vertical slender cylinder embedded in a porous medium under the combined buoyancy effect of thermal and species diffusion has been studied. The effect of the permeability of the medium as well as the magnetic field has been included in the analysis. The partial differential equations with three independent variables governing the flow have been solved numerically using a implicit finite difference scheme in combination with the quasilinearization technique. Computations have been carried out for accelerating, decelerating and oscillatory free stream velocity distributions. The effects of the permeability of the medium, buoyancy forces, transverse curvature and magnetic field on skin friction, heat transfer and mass transfer have been studied. It is found that the effect of free stream velocity distribution is more pronounced on the skin friction than on the heat and mass transfer. The permeability and magnetic parameters increase the skin friction, but reduce the heat and mass transfer. The skin friction, heat transfer and mass transfer are enhanced due to the buoyancy forces and curvature parameter. The heat transfer is strongly dependent on the viscous dissipation parameter and the Prandtl number, and the mass transfer on the Schmidt number.     

Friction and heat transfer with simultaneous convection on a permeable surface

The velocity and heat transfer fields near a vertical permeable surface with simultaneous convection are investigated. A solution is found for the boundary layer equations with known laws of surface temperature and flow velocity change. The transformed boundary layer equations contain the parameter G/R², which determines the effect of free convection on friction and heat transfer for constrained motion. Calculations of friction and heat transfer as functions of draft (suction) with simultaneous convection are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 96–100, March–April, 1973.     

Effect of vapor condensation on forced convection heat transfer of moistened gas

The forced convection heat transfer with water vapor condensation is studied both theoretically and experimentally when wet flue gas passes downwards through a bank of horizontal tubes. Extraordinarily, discussions are concentrated on the effect of water vapor condensation on forced convection heat transfer. In the experiments, the air–steam mixture is used to simulate the flue gas of a natural gas fired boiler, and the vapor mass fraction ranges from 3.2 to 12.8%. By theoretical analysis, a new dimensionless number defined as augmentation factor is derived to account for the effect of condensation of relatively small amount of water vapor on convection heat transfer, and a consequent correlation is proposed based on the experimental data to describe the combined convection–condensation heat transfer. Good agreement can be found between the values of the Nusselt number obtained from the experiments and calculated by the correlation. The maximum deviation is within ±6%. The experimental results also shows that the convection–condensation heat transfer coefficient increases with Reynolds number and bulk vapor mass fraction, and is 1∼3.5 times that of the forced convection without condensation.     

Turbulent mixed convection heat transfer to liquid sodium

The influences of buoyancy on turbulent heat transfer to a liquid metal flowing in a vertical pipe are considered. A theoretical model is presented which provides a criterion for the conditions under which such influences become significant and which predicts the impairment of heat transfer for upward flow and enhancement for downward flow. The variation with Peclet number of the maximum impairment of heat transfer and conditions under which it occurs are established. A generalization of the model leading to an equation for the entire mixed convection region is proposed. From this an equation for turbulent free convection to liquid metals is obtained.     

Turbulent free convection heat transfer to power-law fluids from arbitrary geometric configurations

The problem of turbulent free convection heat transfer from curved surfaces to non-Newtonian power-law fluids has been investigated using the Nakayama-Koyama solution methodology. The scheme is designed to deal with bodies of arbitrary geometric configurations and hence can be viewed as a generalized version of the Shenoy-Mashelkar approach for turbulent free convection heat transfer from a flat vertical plate to a power-law fluid. The surface wall temperature is allowed to vary in the streamwise direction in an arbitrary fashion, and calculations are carried out for the turbulent free convection about the horizontal circular cylinder and sphere for illustrative purposes. Available theoretical and experimental data have been compared with the predictions of the present analysis and the comparison of results has been found to be reasonably good.     

Three dimensional free convection flow and heat transfer along a porous vertical plate

The free convection flow along a vertical porous plate with transverse sinusoidal suction velocity distribution is investigated. Due to this type of suction velocity at the plate the flow becomes three dimensional one. For the asymptotic flow condition, the wall shear stress in the direction of main flow for different values of buoyancy parameter G is obtained. For G=0, the skin friction in the direction of free stream and the rate of heat transfer from the plate to the fluid are given. It is found that these results differ from those obtained by Gersten and Gross.     

Heat transfer enhancement for laminar natural convection along a vertical plate due to sub-millimeter-bubble injection

Sub-millimeter-bubble injection is one of the most promising techniques for enhancing heat transfer for the laminar natural convection of liquids. However, flow and heat transfer characteristics for laminar natural convection of water with sub-millimeter bubbles have not yet been fully understood. The purpose of this study is to experimentally clarify the effects of sub-millimeter-bubble injection on the laminar natural convection of water along a heated vertical plate. The use of thermocouples and a particle tracking velocimetry (PTV) technique are applied to temperature and velocity measurements, respectively. The temperature measurement shows that the ratio of the heat transfer coefficient with sub-millimeter-bubble injection to that without injection increases with an increase in the bubble flow rate or a decrease in the wall heat flux and that the ratio ranges from 1.35 to 1.85. Moreover, it is concluded from simultaneous measurement of temperature and velocity that the heat transfer enhancement is directly affected by flow modification due to bubbles rising near the heated vertical plate.     

Three dimensional unsteady convection and mass transfer flow through porous medium

The problem of three dimensional unsteady convection flow through a porous medium, with effect of mass transfer bounded by an infinite vertical porous plate is discussed, when the suction at the plate is transverse sinusoidal and the plate temperature oscillates in time about a constant mean. Assuming the free stream velocity to be uniform, approximate solutions are obtained for the flow field, the temperature field, the skin-friction and the rate of heat transfer. The dependence of solution on Pr (Prandtl number), Gr (Grashof number based on temperature), Gc (modified Grashof number based on concentration difference), Sc (Schimdt number), the frequency and the permeability parameter is also investigated.     

Combined heat and mass transfer by laminar natural convection from a vertical plate with uniform heat flux and concentration

This paper studies combined heat and mass transfer by laminar natural convection from a vertical plate maintained with uniform surface heat flux and species concentration. Very accurate finite-difference solutions of a set of nonsimilarity equations have been obtained for most practical gaseous solutions (Pr?=?0.7, 0.21 ≤ Sc ≤ 2.1) and aqueous solutions (Pr?=?7, 140 ≤ Sc ≤ 1400). Variations of heat and mass transfer rates with buoyancy ratio and Lewis number are presented. Precise correlations have been developed for predicting heat and mass transfer rates of natural convection arising from single (solutal or thermal) buoyancy force and dual buoyancy forces.     

An experimental investigation on performance of rectangular fins on a horizontal base in free convection heat transfer

This paper reports an experimental study of free convection heat transfer from rectangular fin-arrays on a horizontal base. An experimental set-up was constructed and calibrated, 15 sets of fin-arrays and a base plate without fins were tested in atmosphere. Fin height was varied from 6 mm to 26 mm, fin spacing was varied from 6.2 mm to 83 mm. The base-to-ambient temperature difference was also varied independently and systematically with the power supply to heater ranging from 8 W to 50 W. Fin length and fin thicknesses were fixed at 100 mm and 3 mm, respectively. The experimental program was conducted so as to clearly delineate the separate roles of fin height, fin spacing and base-to-ambient temperature difference. It was found that for a given base-to-ambient temperature difference the convection heat transfer rate from fin-arrays takes on a maximum value as a function of fin spacing and fin height. For a given base-to-ambient temperature difference the enhancement of the convection heat transfer rate of fin-arrays relative to that for base plate without fins is strongly dependent on the fin spacing to fin height ratio and number of fins. A correlation was also presented relating the convection heat transfer rate of fin-arrays relative to that for base plate without fins with the relevant non-dimensional parameters. Received on 7 August 1997     

Free convection heat and mass transfer with Hall current, Joule heating and thermal diffusion

A boundary layer analysis has been presented to study the combined effects of viscous dissipation, Joule heating, transpiration, heat source, thermal diffusion and Hall current on the hydromagnetic free convection and mass transfer flow of an electrically conducting, viscous, homogeneous, incompressible fluid past an infinite vertical porous plate. The governing partial differential equations of the hydromagnetic free convective boundary layer flow are reduced to non-linear ordinary differential equations and solutions for primary velocity, secondary velocity, temperature and concentration field are obtained for large suction. The expressions for the skin-friction, the heat transfer and the mass transfer are also derived. The results of the study are discussed through graphs and tables for different numerical values of the parameters entered into the equations governing the flow.     

Numerical estimation of mixed convection heat transfer in vertical helically coiled tube heat exchangers

A numerical investigation of the mixed convection heat transfer from vertical helically coiled tubes in a cylindrical shell at various Reynolds and Rayleigh numbers, various coil‐to‐tube diameter ratios and non‐dimensional coil pitches was carried out. The particular difference in this study compared with other similar studies is the boundary conditions for the helical coil. Most studies focus on constant wall temperature or constant heat flux, whereas in this study it was a fluid‐to‐fluid heat exchanger. The purpose of this article is to assess the influence of the tube diameter, coil pitch and shell‐side mass flow rate on shell‐side heat transfer coefficient of the heat exchanger. Different characteristic lengths were used in the Nusselt number calculations to determine which length best fits the data and finally it has been shown that the normalized length of the shell‐side of the heat exchanger reasonably demonstrates the desired relation. Copyright © 2010 John Wiley & Sons, Ltd.     

Interaction between heat and mass transfer in simultaneous natural convection about an isothermal vertical flat plate

In order to investigate how simultaneous heat and mass transfer by free convection interact, some numerical theoretical results are presented and discussed. The total flow rate appears to be an essential element in obtaining some insight into this interaction.     

Convection and heat transfer near the critical point of carbon dioxide

A study has been made of convective heat transfer between carbon dioxide and electrically heated wires in horizontal and vertical channels. The heat-transfer and convection coefficients have been and a dimensionless correlation determining the onset of convection verified.     

Non-darcy double-diffusive mixed convection from heated vertical and horizontal plates in saturated porous media

The non-darcy mixed convection flows from heated vertical and horizontal plates in saturated porous media have been considered using boundary layer approximations. The flows are considered to be driven by multiple buoyancy forces. The similarity solutions for both vertical and horizontal plates have been obtained. The governing equations have been solved numerically using a shooting method. The heat transfer, mass transfer and skin friction are reduced due to inertial forces. Also, they increase with the buoyancy parameter for aiding flow and decrease for the opposing flow. For aiding flow, the heat and mass transfer coefficients are found to approach asymptotically the forced or free convection values as the buoyancy parameter approaches zero or infinity.     

Experimental studies on mixed convection heat transfer in laminar flow through a plain square duct

This paper reports the findings of experimental studies on combined free and forced convection through a plain square duct in laminar region. The test fluid flows through an inner square duct, hot water at high flow rate circulated through a annular channel formed between square duct and circular tube, in counter current fashion to attain a nearly uniform wall temperature conditions. The importance of mixed convection is judged by the value of the Richardson number (Ri). It was observed that at low Reynolds number, heat transfer was mainly governed by mixed convection. However at higher values of Reynolds number, heat transfer was significantly dominated by forced convection. It was found that Reynolds number higher than 1050 for water and 480 for ethylene glycol resulted in laminar forced convention heat transfer. The empirical correlation developed for Nusselt number in terms of Grashoff number and Graez number, was found to fit with experimental Nusselt number within ±11 and ±12?% for water and ethylene glycol respectively.     

Heat transfer by combined free and forced convection in vertical tubes

The influence of free convection on forced convection heat transfer becomes important in laminar flows. Numerical methods have been applied for a study of mixed convection in vertical tubes for the following conditions: temperature-dependent fluid density, constant wall temperature and parabolic profile of axial velocity at the tube entrance. Both cases: heating and cooling have been considered.     

The Effect of Double Dispersion on Natural Convection Heat and Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

The effect of power law index parameter of the non-Newtonian fluid on free convection heat and mass transfer from a vertical wall is analyzed by considering double dispersion in a non-Darcy porous medium with constant wall temperature and concentration conditions. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. In this case a similarity solution is possible. The variation of heat and mass transfer coefficients with the governing parameters such as power law index, thermal and solutal dispersion parameters, inertia parameter, buoyancy ratio, and the Lewis number is discussed for a wide range of values of these parameters.