1. Same value of uniform surface heat flux (4.5e+05) is applied to the same model with different mesh sizes as shown in the attached figure. Convection boundary condition is applied to all the surfaces except the surface where heat flux is applied. The heat flux (HFL) value however seems to be different for the two cases, Can someone explain what's happening?
2. Constant heat flux is applied over the whole flux application area, why is the maximum HFL value at the inner boundary of the flux application area where there is no edge nearby?
Any comments/resources would be appreciated. Thanks.
Waseem Akhtar 1. Theoretically, difference in types of BCs may cause a singularity of heat flux value at the vicinity of the boundary of flux application area. So, the finer mesh, the higher max flux value.
2. Try to plot normal component of heat flux vector instead of magnitude.
Victor J. Аdlucky Thank you for your reply. When I plot the heat flux normal to the surface, it is constant over the whole flux application area and it is same (not much different) for all mesh sizes too. But I am still trying to understand why the overall/total flux value (or flux in directions other than normal to the surface) is different for different mesh sizes with same geometry and convection BC in the light of your comment at sr. 1. Could the explanation at sr.1 be more detailed or is there some related literature/resource.
Thanks once again.
Waseem Akhtar It is known that solutions of partial differential equations with mixed boundary conditions may contain singularities in the vicinity of lines where the type of boundary conditions changes. As a rule, these singularities are investigated by solving two-dimensional problems in sections normal to the lines of change of the boundary conditions. In the theory of elasticity, classical results of this kind belong to M.L.Williams (1952), Stress singularities resulting from various boundary conditions in angular corners of plates in extension, ASME J. Appl. Mech.19, 526–528. https://authors.library.caltech.edu/47672/1/382785.pdf Note that his results for the angle alpha=180 deg. correspond to the case of smooth boundary. Unfortunately, I am not aware of such studies for thermal conductivity, but I think they exist.
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