The effect of axial radiation on the Cartesian Graetz problem
Abstract
The problem of heat transfer for a radiating fluid flowing in plane Poiseuille flow from left to right between infinite parallel plates is formulated with allowance for the effect of radiation on the incoming fluid in a system of Cartesian coordinates at the middle plane. The major consideration in formulating this problem is to investigate the contribution of axial heat transfer by radiation. Temperature distributions for the regions x less than zero and x greater than zero (x = xl/L, where xl is the coordinate in horizontal direction and L is the halfdistance between plates) are obtained for mirror boundaries and black boundaries. A parameter survey is carried out to study the thermal effects of optical thickness, nongrayness and Planck number (ratio of conduction to black body radiation) on the nonscattering, absorbing, and emitting fluid. It is shown that for mirror boundaries axial radiation is negligible even at low Peclet numbers and that for black boundaries axial radiation is negligible only when radiation effects are small and the Peclet number is large.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 February 1976
 DOI:
 10.1016/00179310(76)901083
 Bibcode:
 1976IJHMT..19..157D
 Keywords:

 Axial Flow;
 Black Body Radiation;
 Laminar Flow;
 Parallel Plates;
 Radiation Effects;
 Radiative Heat Transfer;
 Boundary Layer Flow;
 Cartesian Coordinates;
 Eigenvalues;
 Peclet Number;
 Temperature Distribution;
 Wall Flow;
 Fluid Mechanics and Heat Transfer