Instability in Walters B' Viscoelastic Dusty Fluid through Porous Medium

摘要

The thermal instability of Walters B′ viscoelastic fluid in the presence of uniform horizontal magnetic field and suspended particles through porous medium is considered. It is found that Walters B′ viscoelastic fluid behaves like a Newtonian fluid for stationary convection. Further, the medium permeability and suspended particles hasten the onset of convection whereas the magnetic field postpones the onset of convection, for the case of stationary convection. A sufficient condition for the invalidity of the ‘Principle of exchange of stabilities’ is derived, in the context, which states that the exchange principle is not valid provided the thermal Rayleigh number R MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGsb aaaa@375C@ , medium permeability P l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGqb qcfa4aaSbaaKqaGeaajugWaiaadYgaaSqabaaaaa@3A5D@ ?and suspended particles parameter H ′ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaceWGib Gbauaaaaa@375E@ are restricted by the inequality H ′ P l R π 2 < 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGabmisayaafaGaamiuaKqbaoaaBaaajeaibaqcLbmacaWG SbaaleqaaKqzGeGaamOuaaGcbaqcLbsacqaHapaCjuaGdaahaaWcbe qcbasaaKqzadGaaGOmaaaaaaqcLbsacqGH8aapcaaIXaaaaa@44B7@ . Further it is found that the magnetic field and viscoelasticity introduce oscillatory modes in the system which was non-existent in their absence.