Transient Natural Convection From Vertical Elements—Appreciable Thermal Capacity

1963 ◽  
Vol 85 (1) ◽  
pp. 10-14 ◽  
Author(s):  
B. Gebhart
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Boundary Layer Flow ◽  
Present Author ◽  
Thermal Capacity ◽  
Generalized Variables ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Layer Flow

Natural convection transients are considered for laminar boundary-layer flow on vertical surfaces by the method previously presented by the present author. Cases are solved for elements having finite thermal capacity as, e.g., electric heaters or reactor elements. A wide range of thermal capacity is considered for fluid Prandtl numbers in the range 0.01 to 1000; for a step in internal energy generation rate. The Prandtl number effect is shown to be very small, in the generalized variables employed, and the range of thermal capacity which results in true convection transients is clearly delineated.

Radiation effect on natural convection boundary layer flow over a vertical wavy frustum of a cone

2009 ◽  
Vol 223 (7) ◽  
pp. 1605-1614 ◽  
Author(s):  
M M Molla ◽  
M A Hossain ◽  
R S R Gorla
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Boundary Layer Flow ◽  
Average Rate ◽  
Local Heat Transfer ◽  
Convection Boundary Layer ◽  
Local Skin ◽  
Wide Range ◽  
Layer Flow

The effect of thermal radiation on a steady two-dimensional natural convection laminar boundary layer flow of a viscous incompressible optically thick fluid over a vertical wavy frustum of a cone has been investigated. The boundary layer regime when the Grashof number Gr is large is considered. Using appropriate transformations, the basic governing equations are transformed into a dimensionless form and then solved numerically employing two efficient methods, namely: (a) implicit finite difference method together with Keller-box scheme and (b) direct numerical scheme. Numerical results are presented by streamline, isotherms, velocity and temperature distribution of the fluid, as well as the local shearing stress in terms of the local skin-friction coefficient, the local heat transfer rate in terms of local Nusselt number, and the average rate of heat transfer for a wide range of the radiation—conduction parameter or Planck number Rd and the surface heating parameter θw.

Free convection in an open thermosyphon, with special reference to turbulent flow

1955 ◽  
Vol 230 (1183) ◽  
pp. 502-530 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Boundary Layer Flow ◽  
Radius Ratio ◽  
Tube Length ◽  
Prandtl Numbers ◽  
Layer Flow ◽  
Rayleigh Numbers

This paper describes an experimental investigation of heat transfer by free convection of a fluid in a heated vertical tube, sealed at its lower end. Heated fluid adjacent to the wall is discharged from the open end into a suitably cooled large reservoir, while a central core of cool fluid is continuously drawn into the tube by way of replacement. The system constitutes an unusual case of natural convection because the two streams of fluid, moving in opposite directions, are compelled to create their own internal boundary. Such an arrangement forms a static simulation of the Schmidt system (1951) for cooling high-temperature gas turbine blades, where sealed radial passages in the blades communicate with a reservoir in the rotor drum, and large centrifugal accelerations replace that due to gravity in the static system. The use of a scaled-up static tube in large measure compensates for the relatively small gravitational acceleration, when determining the working range of Rayleigh numbers, in this case from 10 7 to 10 13 . These are based on tube length, the fluid property values being referred to tube-wall temperature. Separate assessments are made of the effect of fluid Prandtl number (covering values from 7600 to 0·69) and tube length radius ratio (ranging from 7·5 to 47·5). In laminar flow the former is not found to be significant, but the quotient of the Rayleigh number (based on radius) and tube length-radius ratio determines the ranges of three laminar flow régimes. High values of the quotient correspond to 'boundary-layer flow’ and greatest heat transfer. This is followed first by ‘impeded non-similarity flow’ and then by ‘impeded similarity flow’ as the quotient becomes smaller, where the two streams of fluid mingle. These findings are in close agreement with theoretical prediction (Lighthill 1953). Turbulence arises in two ways. For Prandtl numbers near unity, transition occurs during the laminar impeded-flow régimes, resulting in a mixing effect and reduced heat transfer. This is predicted by Lighthill, but his discussion of turbulent flow is restricted to a Prandtl number of unity. For larger Prandtl numbers, transition takes place during laminar boundary-layer flow, yielding a conventional turbulent boundary-layer régime with increased heat transfer. The mean transitional Grashof numbers (based on radius) are in the range 10 4.4 to 10 4.6 ; they compare favourably with a pre­dicted range of from 10 4.0 to 10 4.3 . The tendency for the cool entering fluid to become turbulent renders turbulent boundary-layer flow potentially unstable. Both modes of transition eventually lead to a stable ‘fully mixed' régime where the two turbulent streams mix. This causes reduced circulation and heat transfer, the extent of the reduction varying directly with length-radius ratio and inversely with Prandtl number. The régime was predicted by Lighthill, but there are considerable dis­crepancies between estimated and experimental heat-transfer rates, and in the duration of the régime. In practice it appears to persist indefinitely, whereas Lighthill forecasts its replace­ment at high Rayleigh numbers by a stable boundary-layer flow. Empirical correlations show that fully mixed flow yields optimum heat transfer at a length-radius ratio, which is determined by the Rayleigh number. The suitability of the Schmidt system for blade cooling is briefly discussed in the light of the investigation.

NATURAL CONVECTION BOUNDARY LAYER FLOW PAST A FLAT PLATE OF FINITE DIMENSIONS

2012 ◽  
Vol 15 (6) ◽  
pp. 585-593
Author(s):  
M. Jana ◽  
S. Das ◽  
S. L. Maji ◽  
Rabindra N. Jana ◽  
S. K. Ghosh
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Flat Plate ◽  
Boundary Layer Flow ◽  
Convection Boundary Layer ◽  
Flow Past ◽  
Convection Boundary ◽  
Layer Flow

Compressibility Effects on the Extended Crocco Relation and the Thermal Recovery Factor in Laminar Boundary Layer Flow

2004 ◽  
Vol 126 (1) ◽  
pp. 32-41 ◽  
Author(s):  
B. W. van Oudheusden
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Pressure Gradient ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Thermal Recovery ◽  
Recovery Factor ◽  
Perturbation Approach ◽  
Layer Flow ◽  
Compressibility Effects

The relation between velocity and enthalpy in steady boundary layer flow is known as the Crocco relation. It describes that for an adiabatic wall the total enthalpy remains constant throughout the boundary layer, when the Prandtl number (Pr) is one, irrespective of pressure gradient and compressibility. A generalization of the Crocco relation for Pr near one is obtained from a perturbation approach. In the case of constant-property flow an analytic expression is found, representing a first-order extension of the standard Crocco relation and confirming the asymptotic validity of the square-root dependence of the recovery factor on Prandtl number. The particular subject of the present study is the effect of compressibility on the extended Crocco relation and, hence, on the thermal recovery in laminar flows. A perturbation analysis for constant Pr reveals two additional mechanisms of compressibility effects in the extended Crocco relation, which are related to the viscosity law and to the pressure gradient. Numerical solutions for (quasi-)self-similar as well as non-similar boundary layers are presented to evaluate these effects quantitatively.

scholarly journals THERMAL RADIATION EFFECT ON MHD NATURAL CONVECTION BOUNDARY LAYER FLOW OVER A PLATE WITH SUCTION (INJECTION) AND VARIABLE VISCOSITY

2017 ◽  
Vol 5 (4RAST) ◽  
pp. 52-58
Author(s):  
Jalaja P ◽  
Venkataramana B.S ◽  
Naveen V ◽  
K.R. Jayakumar
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Natural Convection ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Variable Viscosity ◽  
Convection Boundary Layer ◽  
Implicit Finite Difference Scheme ◽  
Convection Boundary ◽  
Layer Flow

The effect of thermal radiation on steady natural convection boundary layer flow over a plate with variable viscosity and magnetic field has been studied in this paper. The effect of suction and injection is also considered in the investigation. The system of partial differential equations governing the nonsimilar flow has been solved numerically using implicit finite difference scheme along with a quasilinearization technique. The thermal radiation has significant effect on heat transfer coefficient and thermal transport in presence of viscosity variation parameter and magnetic field in case of suction and injection.

scholarly journals Magnetohydrodynamic (MHD) Boundary Layer Flow Past a Wedge with Heat Transfer and Viscous Effects of Nanofluid Embedded in Porous Media

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Wubshet Ibrahim ◽  
Ayele Tulu
Keyword(s):  
Boundary Layer ◽  
Porous Media ◽  
Brownian Motion ◽  
Prandtl Number ◽  
Boundary Layer Flow ◽  
Boundary Layer Thickness ◽  
Lewis Number ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

The problem of two-dimensional steady laminar MHD boundary layer flow past a wedge with heat and mass transfer of nanofluid embedded in porous media with viscous dissipation, Brownian motion, and thermophoresis effect is considered. Using suitable similarity transformations, the governing partial differential equations have been transformed to nonlinear higher-order ordinary differential equations. The transmuted model is shown to be controlled by a number of thermophysical parameters, viz. the pressure gradient, magnetic, permeability, Prandtl number, Lewis number, Brownian motion, thermophoresis, and Eckert number. The problem is then solved numerically using spectral quasilinearization method (SQLM). The accuracy of the method is checked against the previously published results and an excellent agreement has been obtained. The velocity boundary layer thickness reduces with an increase in pressure gradient, permeability, and magnetic parameters, whereas thermal boundary layer thickness increases with an increase in Eckert number, Brownian motion, and thermophoresis parameters. Greater values of Prandtl number, Lewis number, Brownian motion, and magnetic parameter reduce the nanoparticles concentration boundary layer.

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