Free convection in a trench with radiative wall conditions
Abstract
Free convection is considered in a rectangular trench with an assigned temperature distribution at the bottom and radiative vertical walls. Following a domain perturbation technique, the problem reduces to the Stokes' equation. After proving the existence and uniqueness of the solution, from a functional point of view, the stream function is expressed in closed form via a biharmonic series and the shape of the free surface is also given. An application follows in order to show the convergence characteristics of the solution of the flow structure.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 January 1980
 DOI:
 10.1002/zamm.19800600106
 Bibcode:
 1980ZaMM...60...31D
 Keywords:

 Convective Heat Transfer;
 Free Convection;
 Radiative Heat Transfer;
 Temperature Distribution;
 Wall Temperature;
 Convergence;
 Laplace Equation;
 Operators (Mathematics);
 Stokes Law Of Radiation;
 Stream Functions (Fluids);
 Fluid Mechanics and Heat Transfer