scholarly journals Temperature boundary layer on a rotating surface - the problem of the constant temperature wall

2006 ◽  
Vol 33 (2) ◽  
pp. 91-106 ◽  
Author(s):  
Milos Pavlovic
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Working Fluid ◽  
Dimensionless Temperature ◽  
Governing Equations ◽  
Constant Wall Temperature ◽  
Temperature Boundary Layer ◽  
Temperature Boundary ◽  
Rotating Surface ◽  
Dimensionless Heat

Introducing the group of Loitskanskii [1] form-parameters and transformations of Saljnikov [2], the set of governing equations of the in compressible laminar temperature boundary layer was transformed in the universal form, with Prandtl number as parameter, for the case of the constant wall temperature. Using the universal results for air (Pr=0.72) the procedure for calculation of the Nusselt number (dimensionless heat transfer coefficient) on the particular contour (airfoil NACA 0010-34) was developed. The dimensionless temperature profiles within the boundary layer were presented also. The parameter of rotation ?0, as well as Eckert number, was varied, and their influences on the heat transfer from the surface to the working fluid were presented and analyzed. .

scholarly journals Fractional Boundary Layer Flow and Heat Transfer Over a Stretching Sheet With Variable Thickness

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Lin Liu ◽  
Liancun Zheng ◽  
Yanping Chen ◽  
Fawang Liu
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Governing Equations ◽  
Velocity Boundary Layer ◽  
Flow And Heat Transfer ◽  
Temperature Boundary ◽  
Layer Flow ◽  
Fractional Parameter

The paper gives a comprehensive study on the space fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness, and the variable magnetic field is applied. Novel governing equations with left and right Riemann–Liouville fractional derivatives subject to irregular region are formulated. By introducing new variables, the boundary conditions change as the traditional ones. Solutions of the governing equations are obtained numerically where the shifted Grünwald formulae are applied. Good agreement is obtained between the numerical solutions and exact solutions which are constructed by introducing new source items. Dynamic characteristics with the effects of involved parameters on the velocity and temperature distributions are shown and discussed by graphical illustrations. Results show that the velocity boundary layer is thicker for a larger fractional parameter or a smaller magnetic parameter, while the temperature boundary layer is thicker for a larger fractional parameter, a smaller exponent parameter, or a larger magnetic parameter. Moreover, it is thicker at a smaller y and thinner at a larger y for the velocity boundary layer with a larger exponent parameter while for the velocity and temperature boundary layers with a smaller weight coefficient.

Investigation of Heat Transfer Efficiency of Improved Intermig Impellers in a Stirred Tank Equipped with Vertical Tubes

2020 ◽  
Vol 18 (3) ◽  
Author(s):  
Leizhi Wang ◽  
Yongjun Zhou ◽  
Zhaobo Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Heat Exchange ◽  
Convective Heat Transfer Coefficient ◽  
Simulation Software ◽  
Related Factors ◽  
Temperature Boundary Layer ◽  
Temperature Boundary ◽  
Vertical Tubes

AbstractThe heat transfer of a reactor with improved Intermig impellers was numerically investigated by the finite element method (FEM) simulation software Fluent (V.19). A turbulence model utilized the standard k-ε model, and the turbulent flows in two large vortexes between vertical tubes were collided to form a strong convection. The influence of heat and mass transfer developing from the impeller diameters, the distance between the two impellers (C1), the rotational speed and the installation height of the bottom impeller (C2) were studied. The reactor was equipped with special structure vertical tubes to increase the heat exchange areas. The rate of heat transfer, including criteria such as the convective heat transfer coefficient, the Nusselt number of outside vertical tubes, and the temperature boundary layer thickness, assured the accurate control of the heat exchange mixing state. The experimental testing platform was designed to validate the simulated results, which revealed the influence order of related factors. The Nusselt number Nu was affected by various related factors, resulting in the rotation and diameter of impellers extending far beyond the distance between the two impellers (C1) and the installation height of the impeller (C2). The average temperature boundary layer thicknesses of the symmetrical and middle sections were 3.24 mm and 3.48 mm, respectively. Adjusting the appropriate parameters can accurately control the heat exchange process in such a reactor, and the conclusions provide a significant reference for engineering applications.

scholarly journals Incompressible laminar temperature boundary layer on a body of revolution: The adiabatic case

2003 ◽  
pp. 247-264 ◽  
Author(s):  
Mira Miric-Milosavljevic ◽  
Milos Pavlovic
Keyword(s):  
Boundary Layer ◽  
Body Of Revolution ◽  
Improved Method ◽  
Governing Equations ◽  
Temperature Boundary Layer ◽  
Temperature Boundary ◽  
General Similarity ◽  
Universal Solutions ◽  
Adiabatic Case ◽  
Parametric Approximation

In the paper the universal governing equations of incompressible laminar temperature boundary layer on the sphere are obtained using the improved method of general similarity for the case of adiabatic boundary conditions. Universal solutions in one parametric approximation for Pr=1 and Pr=0.72 are obtained by numerical integration. Calculated universal functions for temperature boundary layer are presented graphically. As an example eigen-temperature of the sphere are calculated and discussed.

Laminar-Diffusion Boundary Layer—A Review

1955 ◽  
Vol 22 (2) ◽  
pp. 197-203
Author(s):  
Kurt Berman
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transport ◽  
Diffusion Theory ◽  
Transport Phenomena ◽  
Diffusion Boundary ◽  
Temperature Boundary Layer ◽  
Flow And Heat Transfer ◽  
Temperature Boundary ◽  
Laminar Diffusion

Abstract Diffusion theory has not assumed as yet the degree of organizational elegance accorded to fluid-flow and heat-transfer theories. In this paper mass-transport phenomena and their nondimensional correlation are summarized. In order that the similarities between energy, momentum, and mass-transport phenomena may be exhibited, the discussion of diffusion is preceded by brief summaries of dynamic and temperature boundary-layer theories.

Unsteady heat transfer for flow over a flat plate

1963 ◽  
Vol 17 (1) ◽  
pp. 97-104 ◽  
Author(s):  
N. Riley
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flat Plate ◽  
Thermal Boundary Layer ◽  
Unsteady Heat Transfer ◽  
Velocity Boundary Layer ◽  
Temperature Boundary Layer ◽  
Temperature Boundary ◽  
Layer Flow ◽  
Steady Velocity

The boundary-layer flow over a semi-infinite flat plate is investigated. For time t < 0 there is the usual steady velocity boundary layer and, neglecting viscous dissipation, no thermal boundary layer. At t = 0 a temperature boundary layer is initiated without altering the velocity, and the subsequent temperature distributionn is studied for large and small t.

The solution of heat-transfer problems by the Wiener—Hopf technique II. Trailing edge of a hot film

1974 ◽  
Vol 337 (1610) ◽  
pp. 395-412 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Half Plane ◽  
Dimensionless Temperature ◽  
Fluid Temperature ◽  
Trailing Edge ◽  
Boundary Layer Solution ◽  
Leading Term ◽  
Hot Film ◽  
Layer Solution

An incompressible fluid of constant thermal diffusivity k , flows with velocity u = Sy in the x -direction, where S is a scaling factor for the velocity gradient at the wall y = 0. The region — L ≤ x ≤ 0 is occupied by a heated film of temperature T 1 , the rest of the wall being insulated. Far from the film the fluid temperature is T 0 < T 1 . The finite heated film is approximated by a semi-infinite half-plane x < 0 by assuming that the boundary-layer solution is valid somewhere on the finite region upstream of the trailing edge. Exact solutions in terms of Fourier inverse integrals are obtained by using the Wiener-Hopf technique for the dimensionless temperature distribution on the half-plane x > 0 and the heat transfer from the heated film. An asymptotic expansion is made in inverse powers of x and the coefficient of the leading term is used to calculate the exact value of the total heat-transfer as a function of the length L . It is shown that the boundary layer solution differs from the exact solution by a term of order L -1/3 for large L . An expansion in powers of x for the heat transfer upstream of the trailing edge is also found. Application of the theory, together with that of Springer & Pedley (1973), to hot films used in experiments are discussed for the range of values of L(S/K) ½ , up to 20.

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