A note on the free convection boundary-layer flow over a vertical surface with spatial internal heat generation

• Published in: Meccanica (Milan) Vol. 57; no. 5; pp. 1047 - 1053
• Main Author: Merkin, J. H.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2022; Springer Nature B.V
• Subjects: Automotive Engineering; Boundary layer flow; Civil Engineering; Classical Mechanics; Engineering; Free convection; Heat; Heat flux; Heat generation; Heat transfer; Mechanical Engineering; Porous media; Reversed flow; Temperature; Wall temperature; Porous media; Internal heat generation; Natural convection; Similarilty solutions
• ISSN: 0025-6455; 1572-9648
• DOI: 10.1007/s11012-021-01468-3

The model proposed by Postelnicu et al. [ 17 , 18 ] for the natural convection boundary-layer flow on a vertical surface in a porous medium driven by spatially-dependent localised internal heating is discussed further. Their results for a prescribed wall temperature characterised by the parameter λ are extended to a consideration of the singularity seen in the solution as λ → - 1 2 and to the asymptotic limit λ → ∞ , where convection resulting from the wall temperature becomes more important near the wall and showing a region of reversed flow/temperatures below ambient away from the wall. The case, not treated by Postelnicu et al., when there is a prescribed surface heat flux is also treated, finding that the solution became singular as λ → - 1 3 , the nature of which is discussed. The large λ limit is also obtained again finding that the dominant effect is the convection resulting from the wall heat transfer though here the temperature within the boundary layer remains above ambient.