An Interferometric Study of Mass Transfer From a Vertical Plate at Low Reynolds Numbers

1966 ◽  
Vol 88 (4) ◽  
pp. 399-406 ◽  
Author(s):  
M. M. El-Wakil ◽  
G. E. Myers ◽  
R. J. Schilling
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Natural Convection ◽  
Free Convection ◽  
Forced Convection ◽  
Boundary Layers ◽  
Reynolds Numbers ◽  
Perturbation Solutions

Experimental concentration profiles in steady-state, two-component boundary layers formed by the evaporation of a volatile liquid from a porous vertical flat plate into a heated airstream were obtained by an interferometric technique. Tests were conducted with benzene and n-heptane as the evaporating fluids with airstream temperatures ranging from 70 to 94 F and airstream velocities ranging from 90 to 120 fpm. The Reynolds number range, based on the distance from the leading edge of the plate, was from 75 to 1800. It was experimentally observed that transition from laminar flow occurred at Reynolds numbers between 300 and 600. These values, much lower than generally reported in the literature for heat transfer alone, are believed to be related to the relatively thick boundary layers induced by mass transfer of the heavier-than-air fluid from the plate and the associated free-convection effects. While the flow was primarily forced convection, the experimental data indicated a strong natural-convection effect when compared with analytical predictions based on forced convection alone. This was due primarily to the mass transfer into the boundary layer. An attempt was made to analytically account for the effects of mass transfer and natural convection on the Sherwood-Reynolds numbers relationship by utilizing perturbation solutions for the analogous heat transfer problem. The trends shown by this analysis agreed with the experimental data in the laminar portion of the boundary layer. The absolute magnitudes, however, still differed significantly, showing that first-order perturbation solutions of the mass transfer and free-convection effects are inadequate and pointing to the need for more theoretical work.

Temperature Scalings and Profiles in Forced Convection Turbulent Boundary Layers

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Xia Wang ◽  
Luciano Castillo ◽  
Guillermo Araya
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Pressure Gradient ◽  
Temperature Profile ◽  
Forced Convection ◽  
Boundary Layers ◽  
Heat Mass Transfer ◽  
Turbulent Boundary Layers ◽  
Similarity Analysis

Based on the theory of similarity analysis and the analogy between momentum and energy transport equations, the temperature scalings have been derived for forced convection turbulent boundary layers. These scalings are shown to be able to remove the effects of Reynolds number and the pressure gradient on the temperature profile. Furthermore, using the near-asymptotic method and the scalings from the similarity analysis, a power law solution is obtained for the temperature profile in the overlap region. Subsequently, a composite temperature profile is found by further introducing the functions in the wake region and in the near-the-wall region. The proposed composite temperature profile can describe the entire boundary layer from the wall all the way to the outer edge of the turbulent boundary layer at finite Re number. The experimental data and direct numerical simulation (DNS) data with zero pressure gradient and adverse pressure gradient are used to confirm the accuracy of the scalings and the proposed composite temperature profiles. Comparison with the theoretical profiles by Kader (1981, “Temperature and Concentration Profiles in Fully Turbulent Boundary Layers,” Int. J. Heat Mass Transfer, 24, pp. 1541–1544; 1991, “Heat and Mass Transfer in Pressure-Gradient Boundary Layers,” Int. J. Heat Mass Transfer, 34, pp. 2837–2857) shows that the current theory yields a higher accuracy. The error in the mean temperature profile is within 5% when the present theory is compared to the experimental data. Meanwhile, the Stanton number is calculated using the energy and momentum integral equations and the newly proposed composite temperature profile. The calculated Stanton number is consistent with previous experimental results and the DNS data, and the error of the present prediction is less than 5%. In addition, the growth of the thermal boundary layer is obtained from the theory and the average error is less than 5% for the range of Reynolds numbers between 5×105 and 5×106 when compared with the empirical correlation for the experimental data of isothermal boundary layer conditions.

Effects of Free Convection and Axial Conduction on Forced-Convection Heat Transfer Inside a Vertical Channel at Low Peclet Numbers

1984 ◽  
Vol 106 (2) ◽  
pp. 297-303 ◽  
Author(s):  
L. C. Chow ◽  
S. R. Husain ◽  
A. Campo
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Forced Convection ◽  
Convection Heat Transfer ◽  
Vertical Channel ◽  
Reynolds Numbers ◽  
Convection Heat ◽  
Constant Property ◽  
Axial Conduction ◽  
Forced Convection Heat Transfer

A numerical investigation was conducted to study the simultaneous effects of free convection and axial conduction on forced-convection heat transfer inside a vertical channel at low Peclet numbers. Insulated entry and exit lengths were provided in order to assess the effect of upstream and downstream energy penetration due to axial conduction. The fluid enters the channel with a parabolic velocity and uniform temperature profiles. A constant-property (except for the buoyancy term), steady-state case was assumed for the analysis. Results were categorized into two main groups, the first being the case where the channel walls were hotter than the entering fluid (heating), and the second being the reverse of the first (cooling). For each group, heat transfer between the fluid and the walls were given as functions of the Grashof, Peclet, and Reynolds numbers.

Closed-Form Analytical Solutions for Laminar Natural Convection on Horizontal Plates

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Abhijit Guha ◽  
Subho Samanta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Natural Convection ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Temperature Profiles ◽  
Integral Analysis ◽  
Laminar Natural Convection

A boundary layer based integral analysis has been performed to investigate laminar natural convection heat transfer characteristics for fluids with arbitrary Prandtl number over a semi-infinite horizontal plate subjected either to a variable wall temperature or variable heat flux. The wall temperature is assumed to vary in the form T¯w(x¯)-T¯∞=ax¯n whereas the heat flux is assumed to vary according to qw(x¯)=bx¯m. Analytical closed-form solutions for local and average Nusselt number valid for arbitrary values of Prandtl number and nonuniform heating conditions are mathematically derived here. The effects of various values of Prandtl number and the index n or m on the heat transfer coefficients are presented. The results of the integral analysis compare well with that of previously published similarity theory, numerical computations and experiments. A study is presented on how the choice for velocity and temperature profiles affects the results of the integral theory. The theory has been generalized for arbitrary orders of the polynomials representing the velocity and temperature profiles. The subtle role of Prandtl number in determining the relative thicknesses of the velocity and temperature boundary layers for natural convection is elucidated and contrasted with that in forced convection. It is found that, in natural convection, the two boundary layers are of comparable thickness if Pr ≤ 1 or Pr ≈ 1. It is only when the Prandtl number is large (Pr > 1) that the velocity boundary layer is thicker than the thermal boundary layer.

Bouyancy Effect on Forced Convection in Vertical Tubes at High Reynolds Numbers

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
LiDong Huang ◽  
Kevin J. Farrell
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Natural Convection ◽  
Mixed Convection ◽  
Transfer Coefficient ◽  
Flow Regime ◽  
Forced Convection ◽  
Reynolds Numbers ◽  
Buoyancy Effect ◽  
Vertical Tubes

The complex interaction of forced and natural convections depends on flow regime and flow direction. Aiding flow occurs when both driving forces act in the same direction (heating upflow fluid and cooling downflow fluid), opposing flow occurs when they act in different directions (cooling upflow fluid and heating downflow fluid). To evaluate mixed convection methods, Heat Transfer Research, Inc. (HTRI) recently collected water and propylene glycol data in two vertical tubes of different tube diameters. The data cover wide ranges of Reynolds, Grashof, and Prandtl numbers and differing ratios of heated tube length to diameter in laminar, transition, and turbulent forced flow regimes. In this paper, we focus the buoyancy effect on forced convection of single-phase flows in vertical tubes with Reynolds numbers higher than 2000. Using HTRI data and experimental data in literature, we demonstrate that natural convection can greatly increase or decrease the convective heat transfer coefficient. In addition, we establish that natural convection should not be neglected if the Richardson number is higher than 0.01 or the mixed turbulent parameter Ra1/3/(Re0.8 Pr0.4) is higher than 0.05 even in forced turbulent flow with Reynolds numbers greater than 10,000. High resolution Reynolds-averaged Navier–Stokes simulations of several experimental conditions confirm the importance of the buoyancy effect on the production of turbulence kinetic energy. We also determine that flow regime maps are required to predict the mixed convection heat transfer coefficient accurately.

scholarly journals EXPERIMENTAL STUDY OF HEAT TRANSFER OF A SINGLE-ROW BUNDLE OF FINNED TUBES IN MIXED CONVECTION OF AIR

2017 ◽  
Vol 60 (4) ◽  
pp. 352-366 ◽  
Author(s):  
A. B. Sukhotskii ◽  
G. S. Sidorik
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Reynolds Number ◽  
Free Convection ◽  
Mixed Convection ◽  
Forced Convection ◽  
Reynolds Numbers ◽  
Convection Flow ◽  
Single Bundle ◽  
Single Row

The technique and results of experimental study of heat transfer of a single bundle consisting of bimetallic tubes with helically knurled edges, in natural and mixed convection of air are presented. Mixed convection, i.e. a heat transfer, when the contribution of free and forced convection is comparable, was created with the help of the exhaust shaft mounted above the heat exchanger bundle and forced air movement was created by the difference in density of the air in the shaft and the environment. The experimental dependence of the heat transfer of finned single row of bundles in the selected ranges of Grashof and Reynolds numbers has been determined. It is demonstrated that heat transfer in the mixed convection is 2.5−3 times higher than in free one and the growth rate of heat transfer with increasing Reynolds number is more than in the forced convection. Different forms of representation of results of experiments were analyzed and it was determined that the Nusselt number has a single power dependence on the Reynolds number at any height of the exhaust shafts. A linear dependence of the Reynolds number on the square root of the Grashof number was determined as well as the proportionality factors for different shaft heights. It is noted that the characteristics of the motion of air particles in the bundle in free convection is identical to the motion of particles in forced convection at small Reynolds numbers, i.e. a free convection flow smoothly flows into a forced convection one without the typical failures or surges if additional driving forces arise.

Heat Transfer Due to Combined Free and Forced Convection in a Horizontal and Isothermal Tube

1971 ◽  
Vol 93 (4) ◽  
pp. 380-384 ◽  
Author(s):  
C. A. Depew ◽  
S. E. August
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Natural Convection ◽  
Forced Convection ◽  
Tube Flow ◽  
Heating And Cooling ◽  
Free And Forced Convection ◽  
Heated Length

The influence of natural convection due to buoyancy has been studied both experimentally and analytically for many cases, but the existing correlations are not accurate for horizontal, isothermal tube flow when the heated length is relatively short. The research reported in this paper was undertaken to alleviate this shortcoming by deriving a correlation to include new experimental data on a tube with L/D = 28.4. The experimental data from this and other investigations represents a variety of fluids, heating and cooling, and various apparatus and conditions. The equation which correlates the present and previous data to within ±40 percent is Nuaμwμb0.14=1.75[Gz+0.12(GzGr1/3Pr0.36)0.88]1/3

scholarly journals Impact of Binary Chemical Reaction and Activation Energy on Heat and Mass Transfer of Marangoni Driven Boundary Layer Flow of a Non-Newtonian Nanofluid

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 702
Author(s):  
Ramanahalli Jayadevamurthy Punith Gowda ◽  
Rangaswamy Naveen Kumar ◽  
Anigere Marikempaiah Jyothi ◽  
Ballajja Chandrappa Prasannakumara ◽  
Ioannis E. Sarris
Keyword(s):  
Heat Transfer ◽  
Activation Energy ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Velocity Gradient ◽  
Boundary Layer Flow ◽  
Biological Fluids ◽  
Porosity Parameter ◽  
Layer Flow

The flow and heat transfer of non-Newtonian nanofluids has an extensive range of applications in oceanography, the cooling of metallic plates, melt-spinning, the movement of biological fluids, heat exchangers technology, coating and suspensions. In view of these applications, we studied the steady Marangoni driven boundary layer flow, heat and mass transfer characteristics of a nanofluid. A non-Newtonian second-grade liquid model is used to deliberate the effect of activation energy on the chemically reactive non-Newtonian nanofluid. By applying suitable similarity transformations, the system of governing equations is transformed into a set of ordinary differential equations. These reduced equations are tackled numerically using the Runge–Kutta–Fehlberg fourth-fifth order (RKF-45) method. The velocity, concentration, thermal fields and rate of heat transfer are explored for the embedded non-dimensional parameters graphically. Our results revealed that the escalating values of the Marangoni number improve the velocity gradient and reduce the heat transfer. As the values of the porosity parameter increase, the velocity gradient is reduced and the heat transfer is improved. Finally, the Nusselt number is found to decline as the porosity parameter increases.

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