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.

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jinhu Zhao ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fawang Liu ◽  
Xuehui Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Prandtl Number ◽  
Fractional Derivative ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Elastic Effect

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities With Different Aspect Ratios

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Wenjiang Wu ◽  
Chan Y. Ching
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Vertical Wall ◽  
Flow Region ◽  
Temperature Profiles ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
C And N ◽  
Laminar Natural Convection

The effect of the top wall temperature on the laminar natural convection in air-filled rectangular cavities driven by a temperature difference across the vertical walls was investigated for three different aspect ratios of 0.5, 1.0, and 2.0. The temperature distributions along the heated vertical wall were measured, and the flow patterns in the cavities were visualized. The experiments were performed for a global Grashof number of approximately 1.8×108 and nondimensional top wall temperatures from 0.52 (insulated) to 1.42. As the top wall was heated, the flow separated from the top wall with an undulating flow region in the corner of the cavity, which resulted in a nonuniformity in the temperature profiles in this region. The location and extent of the undulation in the flow are primarily determined by the top wall temperature and nearly independent of the aspect ratio of the cavity. The local Nusselt number was correlated with the local Rayleigh number for all three cavities in the form of Nu=C⋅Ran, but the values of the constants C and n changed with the aspect ratio.

Paradoxes of Heat Transfer on a Permeable Wall

2010 ◽  
Author(s):  
A. I. Leontiev ◽  
V. G. Lushchik ◽  
A. E. Yakubenko
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Modeling ◽  
Turbulent Boundary Layer ◽  
Prandtl Number ◽  
Wall Temperature ◽  
Gas Injection ◽  
Gas Mixtures ◽  
Permeable Wall ◽  
Gas Temperature

Numerical modeling of a turbulent boundary layer on a permeable wall with gas injection is performed. New effects are discovered. It is shown in particular that the wall temperature in the region of the gas film may be lower than the injected gas temperature. This effect is especially essential for gas mixtures with low values of the Prandtl number.

Condensation of Flowing Vapor on a Horizontal Tube—Numerical Analysis as a Conjugate Heat Transfer Problem

1984 ◽  
Vol 106 (4) ◽  
pp. 841-848 ◽  
Author(s):  
H. Honda ◽  
T. Fujii
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Flux Density ◽  
Wall Temperature ◽  
Heat Flux Density ◽  
Tube Wall ◽  
Horizontal Tube ◽  
Uniform Wall

Condensation of flowing vapor on a horizontal tube is numerically analyzed under given conditions of vapor and coolant. Besides the usual boundary layer concept, some approximations are introduced for the determination of shear stress at the vapor-liquid interface. The conjugation of the two-phase boundary layer equations and the heat conduction equation within the tube wall is achieved by using an iterative scheme at the outer surface of the tube wall. The solution thus obtained reveals the effects of vapor velocity, tube material, heat transfer of coolant side, etc., upon circumferential distributions of temperature, heat flux density, and Nusselt number at the outer tube surface. Also the solution compared well with available experimental results for the wall temperature distribution and average Nusselt number. The heat transfer characteristics of steam and refrigerant vapors resemble those of the tubes with uniform wall heat flux density and uniform wall temperature, respectively.

scholarly journals Heat transfer for two types of viscoelastic fluid over an exponentially stretching sheet with variable thermal conductivity and radiation in porous medium

2014 ◽  
Vol 18 (4) ◽  
pp. 1079-1093 ◽  
Author(s):  
V. Singh ◽  
Shweta Agarwal
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Wall Temperature ◽  
Stretching Sheet ◽  
Variable Thermal Conductivity ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

An Analysis has been carried out to study the boundary layer flow and heat transfer characteristics of second order fluid and second grade fluid with variable thermal conductivity and radiation over an exponentially stretching sheet in porous medium. The basic boundary layer equations governing the flow and heat transfer in prescribed surface temperature (PST) and prescribed heat flux (PHF) cases are in the form of partial differential equations. These equations are converted to non-linear ordinary differential equations using similarity transformations. Numerical solutions of the resulting boundary value problem are solved by using the fourth order Runge-Kutta method with shooting technique for various values of the physical parameters. The effect of variable thermal conductivity, porosity, Prandtl number, radiation parameter and viscoelastic parameters on velocity and temperature profiles (in PST and PHF cases) are analyzed and discussed through graphs. Numerical values of wall temperature gradient in PST case and wall temperature in PHF case are obtained and tabulated for various values of the governing parameters. In this study Prandtl number also treated as variable inside the boundary layer because it depends on thermal conductivity. The results are also verified by using finite difference method.

Paper 27: Heat Transfer to Steam-Water Mixtures Flowing in Uniformly Heated Tubes in which the Critical Heat Flux has been Exceeded

1967 ◽  
Vol 182 (8) ◽  
pp. 258-267 ◽  
Author(s):  
A. W. Bennett ◽  
G. F. Hewitt ◽  
H. A. Kearsey ◽  
R. K. F. Keeys
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Wall Temperature ◽  
Heat Transfer Process ◽  
High Mass ◽  
Uniform Heat Flux ◽  
Wall Region ◽  
Temperature Profiles ◽  
Axial Temperature ◽  
Dry Out

Experiments are described on evaporative heat transfer to boiling water in upflow in a vertical electrically heated 0·497-in inside diameter tube at 1000 lbf/in2 (abs.). The main objects were to measure the surface temperature profiles in the region beyond the dry-out point in the channel where liquid ceased to flow on the channel wall, and to investigate the behaviour of the dry-out ‘interface’ between the ‘wetted wall’ and the ‘dry wall’ regions. The test section was made from ‘Nimonic’ as this can withstand the highest temperatures in the ‘dry wall’ region and also has a low temperature coefficient of electrical resistivity, thus allowing a uniform heat flux to be maintained with wide axial temperature variation. The temperature in the ‘dry wall’ region first increased rapidly with distance from the dry-out point, after which it either increased at a slower rate or, at high mass velocities, even decreased. The dry-out ‘interface’ moved reversibly down and up the channel as the heat flux was increased and decreased. Local surface temperatures showed no hysteresis with cycling of heat flux, in contrast with the pool boiling situation. A method of predicting the wall temperature profile in the ‘dry wall’ region has been developed. In this method, the heat-transfer process is considered as being in two steps: wall to superheated steam continuum, and steam continuum to water droplets. The first step was calculated from standard single-phase steam heat-transfer correlations, and the second step was calculated on the basis of simultaneous heat transfer to, and steam diffusion from, the droplets. It was important to take account of the slip between the droplets and the steam. Satisfactory agreement was obtained between measured and predicted wall temperature profiles.

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