Laminar Mixed Convection in a Shrouded Fin Array

1981 ◽  
Vol 103 (3) ◽  
pp. 559-565 ◽  
Author(s):  
S. Acharya ◽  
S. V. Patankar
Keyword(s):  
Secondary Flow ◽  
Forced Convection ◽  
Tip Clearance ◽  
Base Surface ◽  
Nusselt Numbers ◽  
Laminar Mixed Convection ◽  
Friction Factors ◽  
Wide Range ◽  
Laminar Forced Convection ◽  
The Heat Transfer Coefficient

An analytical study is made to investigate the effect of buoyancy on laminar forced convection in a shrouded fin array. Two heating conditions are considered; in one, the fins and the base surface are hotter than the fluid, and in the other, they are colder. The results are obtained numerically for a wide range of the governing buoyancy parameter. It is found that with a hot fin and base, the secondary flow pattern is mostly made up of a single eddy. The influence of buoyancy is significant and leads to Nusselt numbers and friction factors which are much higher than for pure forced convection. With a cold fin and base, the presence of a tip clearance between the fins and the shroud generates a multiple eddy pattern. The resulting stratification is responsible for the existence of high axial velocity and temperature in the clearance region relative to that in the inter-fin space. Compared to the hot fin case, the secondary flow is weaker, and therefore a relatively smaller increase in the friction factor is obtained. The Nusselt number is found to increase only in the absence of tip clearance. The distribution of the heat transfer coefficient along the fin and the base for both heating situations is found to be highly nonuniform.

Effect of Circumferentially Nonuniform Heating on Laminar Combined Convection in a Horizontal Tube

1978 ◽  
Vol 100 (1) ◽  
pp. 63-70 ◽  
Author(s):  
S. V. Patankar ◽  
S. Ramadhyani ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Forced Convection ◽  
Horizontal Tube ◽  
Nonuniform Heating ◽  
Convection Flow ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Bottom Heating ◽  
Over The Top

An analytical study has been made of how the circumferential distribution of the wall heat flux affects the forced/natural convection flow and heat transfer in a horizontal tube. Two heating conditions were investigated, one in which the tube was uniformly heated over the top half and insulated over the bottom, and the other in which the heated and insulated portions were reversed. The results were obtained numerically for a wide range of the governing buoyancy parameter and for Prandtl numbers of 0.7 and 5. It was found that bottom heating gives rise to a vigorous buoyancy-induced secondary flow, with the result that the average Nusselt numbers are much higher than those for pure forced convection, while the local Nusselt numbers are nearly circumferentially uniform. A less vigorous secondary flow is induced in the case of top heating because of temperature stratification, with average Nusselt numbers that are substantially lower than those for bottom heating and with large circumferential variations of the local Nusselt number. The friction factor is also increased by the secondary flow, but much less than the average heat transfer coefficient. It was also demonstrated that the buoyancy effects are governed solely by a modified Grashof number, without regard for the Reynolds number of the forced convection flow.

Laminar Forced Convection of Liquids in Tubes With Variable Viscosity

1962 ◽  
Vol 84 (4) ◽  
pp. 353-361 ◽  
Author(s):  
Kwang-Tzu Yang
Keyword(s):  
Forced Convection ◽  
Variable Viscosity ◽  
Step Change ◽  
Temperature Dependent Viscosity ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Tube Wall Temperature ◽  
Integral Procedure ◽  
Dependent Viscosity ◽  
Laminar Forced Convection

Analytical solutions for laminar forced convection of liquids flowing in circular tubes with temperature-dependent viscosity are obtained for both step change in tube-wall temperature and step change in wall heat flux by using an improved integral procedure. The accuracy of this analytical procedure is demonstrated by comparing results for the isothermal problems with that from the exact solutions. Results for the nonisothermal cases are presented in graphical forms in terms of Nusselt numbers, velocity variations at tube center line, and friction factors. Tabulated Nusselt numbers are also given.

Analysis of Combined Forced and Free Flow in a Vertical Channel With Viscous Dissipation and Isothermal-Isoflux Boundary Conditions

1999 ◽  
Vol 121 (2) ◽  
pp. 349-356 ◽  
Author(s):  
A. Barletta
Keyword(s):  
Boundary Conditions ◽  
Parallel Plate ◽  
Vertical Channel ◽  
Uniform Heat Flux ◽  
Viscous Heating ◽  
Perturbation Expansions ◽  
Nusselt Numbers ◽  
Buoyancy Parameter ◽  
Laminar Mixed Convection ◽  
Friction Factors

Fully developed and laminar mixed convection in a parallel-plate vertical channel is investigated in the case of non-negligible viscous heating. The channel walls are subjected to asymmetric boundary conditions: One wall experiences a constant and uniform heat flux, while the other is kept at a uniform and constant temperature. The velocity field and the temperature field are evaluated analytically by means of perturbation expansions with respect to a buoyancy parameter, i.e., the ratio between the Grashof number and the Reynolds number. The Nusselt numbers and the friction factors are obtained as functions of the buoyancy parameter.

Exact Solutions to the Thermal Entry Problem for Laminar Flow Through Annular Ducts

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
T. D. Bennett
Keyword(s):  
Separation Of Variables ◽  
Outer Wall ◽  
Series Solutions ◽  
Eigenvalues And Eigenfunctions ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Flow Through ◽  
Laminar Forced Convection ◽  
Thermal Entrance ◽  
Annular Tube

Abstract The thermal entrance region for laminar-forced convection of a Newtonian fluid in an annular tube is solved by separation of variables using as many eigenvalues and eigenfunctions as needed to report exact results for a specified range of Graetz numbers. Results for the local and average Nusselt numbers are calculated for a wide range of inner to outer wall radius ratios and for convection to either the inner or outer wall, when the opposing wall is adiabatic. The present benchmark results are utilized to critically examine the accuracy of previous extended Lévêque series solutions that are convergent for short axial distances, and Graetz series solutions that are convergent for long axial distances, and to examine the performance of a new correlation for convection in annular tubes.

Recent Research on Cascade-Flow Problems

1966 ◽  
Vol 88 (1) ◽  
pp. 221-228 ◽  
Author(s):  
H. Schlichting ◽  
A. Das
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
High Speed ◽  
Research Work ◽  
Reynolds Numbers ◽  
Tip Clearance ◽  
Flow Problems ◽  
Flow Losses ◽  
Cascade Flow ◽  
Wide Range

A survey is given of extensive research work on cascade-flow problems carried out in recent years in Germany. A considerable part of this work was done in the Variable Density High Speed Cascade Wind Tunnel of the Deutsche Forschungsanstalt fu¨r Luftfahrt at Braunschweig, in which the Reynolds number and the Mach number of the cascade can be varied independently. For compressor cascades with blades of different thickness ratio extensive measurements of the aerodynamic coefficients have been carried out in a wide range of Mach numbers and Reynolds numbers. For very low Reynolds numbers, as they occur for jet engines in high-altitude flight, the influence of turbulence level on loss coefficients has been investigated. Furthermore, comprehensive investigations on secondary-flow losses are reported. The most important parameters in this connection are the ratio of blade length to blade chord, the tip clearance, the Reynolds number, and the deflection of the flow in the cascade. The influence of all these parameters on the secondary-flow losses has been clarified to a certain extent.

scholarly journals Numerical Analysis of Water Forced Convection in Channels with Differently Shaped Transverse Ribs

2011 ◽  
Vol 2011 ◽  
pp. 1-25 ◽  
Author(s):  
Oronzio Manca ◽  
Sergio Nardini ◽  
Daniele Ricci
Keyword(s):  
Heat Transfer ◽  
Forced Convection ◽  
High Heat ◽  
Constant Heat Flux ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
High Heat Transfer ◽  
Friction Factors ◽  
Turbulent Water

Heat transfer enhancement technology has the aim of developing more efficient systems as demanded in many applications. An available passive method is represented by the employ of rough surfaces. Transversal turbulators enhance the heat transfer rate by reducing the thermal resistance near surfaces, because of the improved local turbulence; on the other hand, higher losses are expected. In this paper, a numerical investigation is carried out on turbulent water forced convection in a ribbed channel. Its external walls are heated by a constant heat flux. Several arrangements of ribs in terms of height, width, and shape are analyzed. The aim is to find the optimal configuration in terms of high heat transfer coefficients and low losses. The maximum average Nusselt numbers are evaluated for dimensionless pitches of 6, 8, and 10 according to the shape while the maximum friction factors are in the range of pitches from 8 to 10.

scholarly journals Laminar forced convection at low Péclet number

1972 ◽  
Vol 6 (1) ◽  
pp. 83-94 ◽  
Author(s):  
A.S. Jones
Keyword(s):  
Forced Convection ◽  
Peclet Number ◽  
Asymptotic Form ◽  
Circular Tube ◽  
Physical Parameters ◽  
Heat Sources ◽  
Temperature Changes ◽  
Péclet Number ◽  
Nusselt Numbers ◽  
Laminar Forced Convection

This work is concerned with the forced convection of heat in a circular tube. The fluid flow is assumed to be laminar Poiseuille flow, and the physical parameters; viscosity, density, conductivity; are assumed to be independent of temperature changes. Viscous dissipation terms are also ignored, and there are no heat sources in the fluid. The problem is treated for the case of a step change in the wall temperature, and the eigenvalues have been obtained as an expansion in powers of the Péclet number for the smaller values, and in an asymptotic form for the larger values. The temperature distribution in the fluid in the neighbourhood of the temperature jump has been calculated for two values of the Péclet number, as have the Nusselt numbers.

Developing Forced and Free Convection for Inclined Semicircular Ducts

2008 ◽  
Author(s):  
Yousef M. F. El. Hasadi
Keyword(s):  
Boundary Condition ◽  
Free Convection ◽  
Thermal Boundary Condition ◽  
Entrance Region ◽  
Nusselt Numbers ◽  
Simpler Algorithm ◽  
Laminar Mixed Convection ◽  
Wide Range ◽  
Inclination Angles ◽  
Semicircular Ducts

Laminar mixed convection in the entrance region for inclined semicircular ducts with the flat wall in the vertical position has been investigated numerically. The governing momentum and energy equations were solved numerically using a marching technique with finite control volume approach following the SIMPLER algorithm. Results were obtained for the thermal boundary condition of uniform heat input axially and uniform wall temperature circumferentially (H1 thermal boundary condition), with Pr = 7.0 (i. e. water), Reynolds number equals 500, inclination angles 0°, 20°, 40°, 60°, 80°, and a wide range of Grashof numbers. These results include velocity, and temperature distributions, at different axial locations, as well as, the axial development of the Nusselt numbers, and the wall friction factor a long the duct length. It was found that the Nusselt numbers were close to the forced convection values near the entrance region and then decreases to a minimum as the distance from the entrance increases and than rises up due to the effect of free convection before reaching a constant value (fully developed value). It is observed that at inclination angles 0° and 20° the values of Nusselt number are higher in the developing and fully developed regions, than those corresponding to 40°, 60°, and 80° at the same Grashof number, however, it was found that at the same Grshof number the values of friction factors increases in the developing and fully developed regions with the increase of the inclination angle.

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