Natural Convection in Enclosures

1988 ◽  
Vol 110 (4b) ◽  
pp. 1175-1190 ◽  
Author(s):  
S. Ostrach
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Driving Force ◽  
Numerical Solutions ◽  
Scaling Analysis ◽  
Interest In Science ◽  
Flow And Transport ◽  
Mathematical Problems ◽  
Buoyancy Flows ◽  
Core Flows

There exists a great diversity of buoyancy flows in enclosures that are of interest in science and technology. These buoyancy flows pose new and challenging physical and mathematical problems. Emphasis is given to the complexities of the phenomena, viz., the coupling of the flow and transport and of the boundary-layer and core flows, the interaction between the flow and the driving force, which alters the regions in which the buoyancy acts, and the occurrence of flow sub-regions (cells and layers). The importance of scaling analysis and experiments to determine flow details are discussed and the essentials of scaling techniques are outlined. The implications of these for numerical methods are presented, and the inadequacies of purely numerical solutions are pointed out. Representative works covering a broad range of problems are discussed.

Unsteady natural convection in a cavity with internal heating and cooling

1984 ◽  
Vol 140 ◽  
pp. 135-151 ◽  
Author(s):  
John C. Patterson
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Transient Flow ◽  
Scaling Analysis ◽  
Steady State Flow ◽  
Internal Heating ◽  
Sources And Sinks ◽  
Heating And Cooling ◽  
Unsteady Natural Convection

The problem of transient natural convection in a cavity of aspect ratio A < 1 driven by internal buoyancy sources and sinks distributed linearly in the horizontal and uniformly in the vertical is considered. Scaling analysis is used to show that a number of possible transient flow regions are possible, collapsing ultimately onto one of conductive, transitional, or convective steady-state flow regimes. A number of numerical solutions are obtained, and their relationships to the scaling analysis are discussed.

A scaling analysis of transient natural convection in a reservoir model induced by iso-flux heating

2014 ◽  
Vol 764 ◽  
pp. 219-249 ◽  
Author(s):  
Peng Yu ◽  
John C. Patterson ◽  
Chengwang Lei
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Water Depth ◽  
Thermal Boundary Layer ◽  
Scaling Analysis ◽  
Horizontal Temperature Gradient ◽  
Reservoir Model ◽  
Transient Behaviour ◽  
Final Steady State

AbstractThis study presents a detailed scaling analysis quantifying the transient behaviour of natural convection in a reservoir model induced by iso-flux surface heating. It is found that horizontal conduction, which has often been neglected in previous analyses, plays an important role in the development of the flow. Depending on the Rayleigh number, three possible pathways through which the flow develops towards the final steady state are identified. A thermal boundary layer initially grows downwards from the surface. When the thermal boundary layer reaches the sloping bottom and becomes indistinct, a horizontal temperature gradient establishes due to the increasing water depth in the offshore direction. A flow is then driven towards the offshore direction by a buoyancy-induced horizontal pressure gradient, which convects away the heat input from the water surface. On the other hand, the horizontal temperature gradient also conducts heat away. The flow behaviour is determined by the interaction between the horizontal conduction and convection. An interesting flow feature revealed by the present scaling analysis is that the region across which the thermal boundary layer encompasses the full water depth shrinks over time at a certain stage of the flow development. The shrinking process eventually stops when this region coincides with a conduction-dominated subregion. The present scaling results are verified by corresponding numerical simulations.

scholarly journals Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

1974 ◽  
Vol 65 (2) ◽  
pp. 231-246 ◽  
Author(s):  
D. E. Cormack ◽  
L. G. Leal ◽  
J. H. Seinfeld
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Excellent Agreement ◽  
Asymptotic Theory ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Shallow Cavity

Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6·983, 10 ≤ Gr 2 × 104 and 0·05 [les ] A [les ] 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A [lsim ] 0·1 and Gr2A3Pr2 [lsim ] 105. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.

Natural Convection Near a Cold Plate Facing Upward in a Porous Medium

1985 ◽  
Vol 107 (4) ◽  
pp. 819-825 ◽  
Author(s):  
S. Kimura ◽  
A. Bejan ◽  
I. Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Cold Plate ◽  
Flow Features ◽  
Sharp Edges ◽  
Layer Flow ◽  
Heat And Fluid Flow

It is shown that the phenomenon of natural convection driven in a porous medium by a cold plate facing upward or by a warm plate facing downward consists of a finite-length boundary layer flow chopped off by the sharp edges of the plate. The heat and fluid flow features of the boundary layer are determined analytically employing scale analysis and integral analysis. The overall heat transfer rate between porous medium and plate is found to vary as Nu/Ra1/3 = 0(1), where Ra is the Darcy-modified Rayleigh number based on plate half-length. The boundary layer features of the flow and the heat transfer effected by it are confirmed in the Ra range 100–700 by numerical solutions of the complete partial differential equations.

A singularity in thermal boundary-layer flow on a horizontal surface

1992 ◽  
Vol 242 ◽  
pp. 419-440 ◽  
Author(s):  
P. G. Daniels
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Rational Numbers ◽  
Velocity Fields ◽  
Boundary Layer Equations ◽  
Layer Flow ◽  
Buoyancy Flows ◽  
Temperature And Velocity Fields

A thermal boundary layer, in which the temperature and velocity fields are coupled by buoyancy, flows along a horizontal, insulated wall. For sufficiently low local Froude number the solution terminates in a singularity with rising skin friction and falling pressure. The structure of the singularity is obtained and the results are compared with numerical solutions of the horizontal boundary-layer equations. A novel feature of the analysis is that the powers of the streamwise coordinate involved in the structure of the singularity do not appear to be simple rational numbers and are determined from the solution of a pair of ordinary differential equations which govern the flow in an inner viscous region close to the wall. Modifications of the theory are noted for cases where either the temperature or a non-zero heat transfer are specified at the wall.

Unsteady nearshore natural convection induced by constant isothermal surface heating

2012 ◽  
Vol 707 ◽  
pp. 342-368 ◽  
Author(s):  
Yadan Mao ◽  
Chengwang Lei ◽  
John C. Patterson
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Flow Velocity ◽  
Thermal Boundary Layer ◽  
Scaling Analysis ◽  
Local Flow ◽  
Entire Flow ◽  
Flow Domain

AbstractThe present investigation is concerned with natural convection in a wedge-shaped domain induced by constant isothermal heating at the water surface. Complementary to the study of daytime heating by solar radiation relevant to nearshore regions of lakes and reservoirs previously reported by the same authors, this study focuses on sensible heating imposed by the atmosphere when it is warmer than the water body. A semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to resolve the problem. Two flow regimes are identified depending on the comparison between the Rayleigh number and the inverse of the square of the bottom slope. For the lower Rayleigh number regime, the entire flow domain eventually becomes isothermal and stationary. For the higher Rayleigh number regime, the flow domain is composed of two distinct subregions, a conductive subregion near the shore and a convective subregion offshore. Within the conductive subregion, the maximum local flow velocity occurs when the thermal boundary layer reaches the local bottom, and the subregion eventually becomes isothermal and stationary. In the offshore convective subregion, a steady state is reached with a distinct thermal boundary layer below the surface and a steady flow velocity. The dividing position between the two subregions and the major time and velocity scales governing the flow development in both subregions are proposed by the scaling analysis and validated by corresponding numerical simulation.

scholarly journals Scaling Analysis of the Unsteady Natural Convection Boundary Layer Adjacent to an Inclined Plate for Pr > 1 Following Instantaneous Heating

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Suvash C. Saha ◽  
Feng Xu ◽  
Md Mamun Molla
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Convection Boundary Layer ◽  
Scaling Analysis ◽  
Inclined Plate ◽  
Wide Range ◽  
Convection Boundary ◽  
Unsteady Natural Convection

The unsteady natural convection boundary layer adjacent to an instantaneously heated inclined plate is investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer following instantaneous heating may be classified into three distinct stages including a start-up stage, a transitional stage, and a steady state stage, which can be clearly identified in the analytical and numerical results. Major scaling relations of the velocity and thicknesses and the flow development time of the natural convection boundary layer are obtained using triple-layer integral solutions and verified by direct numerical simulations over a wide range of flow parameters.

Natural convection from a Plane Vertical Porous Surface in Non Isothermal

2004 ◽  
Vol 9 (2) ◽  
pp. 151-170
Author(s):  
S. C. Saha
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Vertical Surface ◽  
Convection Flow ◽  
Boundary Layer Equations ◽  
Solution Methods ◽  
Distinct Solution ◽  
Perturbation Solutions

In this paper, laminar natural convection flow from a permeable and isothermal vertical surface placed in non-isothermal surroundings is considered. Introducing appropriate transformations into the boundary layer equations governing the flow derives non-similar boundary layer equations. Results of both the analytical and numerical solutions are then presented in the form of skin-friction and Nusselt number. Numerical solutions of the transformed non-similar boundary layer equations are obtained by three distinct solution methods, (i) the perturbation solutions for small ξ (ii) the asymptotic solution for large ξ (iii) the implicit finite difference method for all ξ where ξ is the transpiration parameter. Perturbation solutions for small and large values of ξ are compared with the finite difference solutions for different values of pertinent parameters, namely, the Prandtl number Pr, and the ambient temperature gradient n.

Pseudosteady-State Natural Convection Inside Spheres

1975 ◽  
Vol 97 (1) ◽  
pp. 54-59 ◽  
Author(s):  
M. Y. Chow ◽  
R. G. Akins
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Driving Force ◽  
Numerical Solutions ◽  
Convection Heat Transfer ◽  
Flow Patterns ◽  
Natural Convection Heat Transfer ◽  
Constant Flow ◽  
Convection Heat ◽  
Rayleigh Numbers

Natural convection heat transfer to water contained within five different sized spheres was studied. Pseudosteady-state was maintained by keeping the driving force for convection constant, i.e., the temperature outside the sphere was increased steadily so that the temperature difference between the outside and the center remained constant. Flow visualization was used to determine flow patterns within the spheres. Laminar flow was found to exist below Rayleigh numbers of about 107. The flow patterns along with the position of the circulation centers are presented and compared with recent numerical solutions. The overall heat transfer in the laminar region was fitted by least squares and the following correlation obtained: Nu=0.80Ra0.30

Combined Heat and Mass Transfer by Natural Convection With Opposing Buoyancies

1993 ◽  
Vol 115 (3) ◽  
pp. 606-612 ◽  
Author(s):  
R. L. Mahajan ◽  
D. Angirasa
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Natural Convection ◽  
Heat And Mass Transfer ◽  
Numerical Solutions ◽  
Boundary Layer Analysis ◽  
Layer Analysis ◽  
Wide Range ◽  
Schmidt Numbers ◽  
Buoyancy Ratio

A numerical study is presented for combined heat and mass transfer by natural convection from a vertical surface with opposing buoyancy effects. A comparison with similarity solutions shows that boundary layer analysis is suitable only when the two buoyant forces aid each other. For opposing flows the boundary layer analysis does not predict the transport rates accurately. A detailed comparison with experimental data with opposing buoyancies shows good agreement between the data and the numerical solutions. The heat and mass transfer rates follow complex trends depending on the buoyancy ratio and the Prandtl and Schmidt numbers. Comprehensive Nusselt and Sherwood number data are presented for a wide range of thermal Grashof number, buoyancy ratio, and Prandtl and Schmidt numbers.

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