scholarly journals Transient and steady state, free and natural convection, numerical solutions: Part I. The isothermal, vertical plate

AIChE Journal ◽  
1962 ◽  
Vol 8 (5) ◽  
pp. 690-692 ◽  
Author(s):  
J. D. Hellums ◽  
S. W. Churchill
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Transient And Steady State

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.

Modified Method of Characteristics for Simulating Microscale Energy Transport

2004 ◽  
Vol 126 (5) ◽  
pp. 735-743 ◽  
Author(s):  
Laurent Pilon ◽  
Kamal M. Katika
Keyword(s):  
Steady State ◽  
Numerical Scheme ◽  
Method Of Characteristics ◽  
Energy Transport ◽  
Numerical Solutions ◽  
Computational Cost ◽  
Phonon Transport ◽  
Coupled Equations ◽  
Heat Carriers ◽  
Transient And Steady State

This paper presents a new numerical scheme for simulating multidimensional transient and steady-state microscale energy transport. The new method is based on the method of characteristics that follows heat carriers along their pathline. Unlike traditional methods, it uses a fixed computational grid and follows the heat carriers backward in time. The method 1) is accurate, 2) is unconditionally stable, 3) can deal with complex geometries without a large increase in computational cost, and 4) can be used for solving coupled equations using other numerical schemes. First, the numerical scheme is described. Then, simulations for transient and steady-state phonon transport in dielectric thin films are discussed. Numerical results are compared with analytical and reported numerical solutions and good agreement is obtained.

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