%0 Journal Article %1 mcbain2004natural %A McBain, G. D. %A Armfield, S. W. %D 2003 %J ANZIAM Journal %K 35p20-asymptotic-distribution-of-eigenvalues-and-eigenvectors 65f15-numerical-eigenvalues-eigenvectors 65l60-odes-finite-elements-rayleigh-ritz-galerkin-and-collocation-methods 76e05-parallel-shear-flows 76e06-hydrodynamic-stability-convection 76r10-free-convection usyd %P C92--C105 %R 10.21914/anziamj.v45i0.875 %T Natural Convection in a Vertical Slot: Accurate Solution of the Linear Stability Equations %U https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/875 %V 45(E) %X The linear stability of natural convection in a fluid between vertical hot and cold walls was studied using a collocation method. Seven figure accurate results for monotonic disturbances were obtained by Ruth (1979) using numerical power series, but this method is intrinsically limited and failed for Pr > 10 . In contrast, Chebyshev collocation converges more rapidly and allows the computation of results at higher Pr for which oscillatory disturbances dominate. Accurate results are now obtained across the entire Prandtl number range. These match the zero and infinite Pr asymptotes which are also refined here.

@article{mcbain2004natural, abstract = {The linear stability of natural convection in a fluid between vertical hot and cold walls was studied using a collocation method. Seven figure accurate results for monotonic disturbances were obtained by Ruth (1979) using numerical power series, but this method is intrinsically limited and failed for Pr > 10 . In contrast, Chebyshev collocation converges more rapidly and allows the computation of results at higher Pr for which oscillatory disturbances dominate. Accurate results are now obtained across the entire Prandtl number range. These match the zero and infinite Pr asymptotes which are also refined here.}, added-at = {2017-06-29T07:13:07.000+0200}, author = {McBain, G. D. and Armfield, S. W.}, biburl = {https://www.bibsonomy.org/bibtex/2d788a81b5c3182647dfb30c751d4d7f3/gdmcbain}, citeulike-article-id = {2442062}, citeulike-attachment-1 = {mcbain_04_natural_33500.pdf; /pdf/user/gdmcbain/article/2442062/33500/mcbain_04_natural_33500.pdf; ee612149a981f55f26ed478fbd25f0d4f4184a67}, citeulike-linkout-0 = {http://dx.doi.org/10.21914/anziamj.v45i0.875}, citeulike-linkout-1 = {http://anziamj.austms.org.au/V45/CTAC2003/McB2/}, comment = {(private-note)I had some correspondence about this in June 2008 from Marcello Lappa, wanting to reproduce some of the figures in his book. He was confused about the definition of the Grashof number; he used g beta DeltaT d^3 / nu^2, where d is the width of the slot and DeltaT the temperature difference across it. This is the same as what we used, but the original paper does not explicitly define the Grashof number. ---=note-separator=--- The Grashof number is not explicitly defined in the paper. It is g beta DeltaT d^3 / nu^2, where d is the width of the slot and DeltaT the temperature difference across it. The other symbols are g gravitational field strength, beta volumetric expansion coefficient, nu kinematic viscosity. Many or most authors use the same definition, possibly with the exception of the Russians.}, doi = {10.21914/anziamj.v45i0.875}, file = {mcbain_04_natural_33500.pdf}, interhash = {6ec1eda8ee43014a377e34c86ef79523}, intrahash = {d788a81b5c3182647dfb30c751d4d7f3}, journal = {ANZIAM Journal}, keywords = {35p20-asymptotic-distribution-of-eigenvalues-and-eigenvectors 65f15-numerical-eigenvalues-eigenvectors 65l60-odes-finite-elements-rayleigh-ritz-galerkin-and-collocation-methods 76e05-parallel-shear-flows 76e06-hydrodynamic-stability-convection 76r10-free-convection usyd}, pages = {C92--C105}, posted-at = {2008-02-28 10:10:54}, priority = {2}, timestamp = {2020-06-18T01:09:06.000+0200}, title = {Natural Convection in a Vertical Slot: Accurate Solution of the Linear Stability Equations}, url = {https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/875}, volume = {45(E)}, year = 2003 }