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Scale analysis and asymptotic solution for natural convection over a heated flat plate at high Prandtl numbers

dc.contributor.authorAdewumi, O.O
dc.contributor.authorAdebusoye, A.
dc.contributor.authorAdeniyan, A.
dc.contributor.authorOgbonna, N.
dc.contributor.authorOyediran, A.A
dc.identifier.citationAdewumi, O. O., Adebusoye, A., Adeniyan, A., Ogbonna, N., & Oyediran, A. A. (2018). Scale analysis and asymtotic solution for natural convection over a heated flat plate at high Prandtl number. Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science, 19, 189-194.en_US
dc.descriptionStaff publicationsen_US
dc.description.abstractThis study presents a free convection flow over a heated flat plate using Bejan’s method of scale analysis for balancing forces. For Newtonian fluids of large Prandtl numbers, two different layers which are the thermal and velocity boundary layers exist. The thermal boundary layer is thinner than the velocity boundary layer. The method of matched asymptotic expansion is used to obtain the velocity and temperature within the two layers and these quantities are then matched at the interface. A 5–5 matching is used to obtain both inner and outer solutions for velocity and temperature. A natural small parameter in this problem is the inverse of the square root of the Prandtl number multiplying the highest derivative. In the Bejan formulation for large Prandtl number flows, the two dimensionless quantities that emerge are the Rayleigh and Prandtl numbers as opposed to the Grashof and Prandtl numbers obtained in previous works. The results of velocities, temperature, shear stress and Nusselt number presented in this study are for fluids that have Prandtl numbers ranging 10 to 100,000. The Nusselt number predicted as Prandtl number goes to infinity, approaches the same asymptote as in previous works, while there's about 30% difference in the skin friction predicted when the differences in scaling used are not taken into consideration.en_US
dc.publisherProceedings of the Romanian Academyen_US
dc.subjectLarge Prandtl numberen_US
dc.subjectScale analysisen_US
dc.subjectAsymptotic expansionen_US
dc.subjectBoundary layeren_US
dc.subjectFree convectionen_US
dc.subjectResearch Subject Categories::TECHNOLOGY::Engineering mechanicsen_US
dc.titleScale analysis and asymptotic solution for natural convection over a heated flat plate at high Prandtl numbersen_US

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