TY - JOUR
T1 - Linear stability of a developing thermal front induced by a constant heat flux
AU - Noghrehabadi, Aminreza
AU - Rees, D. Andrew S.
AU - Bassom, Andrew P.
PY - 2013/9
Y1 - 2013/9
N2 - A developing thermal front is set up by suddenly imposing a constant heat flux on the lower horizontal boundary of a semi-infinite fluid-saturated porous domain. The critical time for the onset of convection is determined using two main forms of analysis. The first of these is an approximate method which is effectively a frozen-time model while the second implements a set of parabolic simulations of monochromatic disturbances placed in the boundary layer at an early time. Results from the two approaches are compared and it is found that instability only occurs when the nondimensional disturbance wavenumber, {Mathematical expression}, is less than unity. The neutral curve for the primary mode possesses a vertical asymptote at {Mathematical expression} in wavenumber/time parameter space which is in contrast to the more usual teardrop shape which occurs when the surface is subject to a constant temperature. Asymptotic analyses are performed for the frozen-time model which yield excellent predictions for both branches of the neutral curve and the locus of the maximum growth rate curve at late times.
AB - A developing thermal front is set up by suddenly imposing a constant heat flux on the lower horizontal boundary of a semi-infinite fluid-saturated porous domain. The critical time for the onset of convection is determined using two main forms of analysis. The first of these is an approximate method which is effectively a frozen-time model while the second implements a set of parabolic simulations of monochromatic disturbances placed in the boundary layer at an early time. Results from the two approaches are compared and it is found that instability only occurs when the nondimensional disturbance wavenumber, {Mathematical expression}, is less than unity. The neutral curve for the primary mode possesses a vertical asymptote at {Mathematical expression} in wavenumber/time parameter space which is in contrast to the more usual teardrop shape which occurs when the surface is subject to a constant temperature. Asymptotic analyses are performed for the frozen-time model which yield excellent predictions for both branches of the neutral curve and the locus of the maximum growth rate curve at late times.
UR - http://www.scopus.com/inward/record.url?scp=84880033585&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1007/s11242-013-0197-z
U2 - 10.1007/s11242-013-0197-z
DO - 10.1007/s11242-013-0197-z
M3 - Article
SN - 0169-3913
VL - 99
SP - 493
EP - 513
JO - Transport in Porous Media
JF - Transport in Porous Media
IS - 3
ER -