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M.VENKATESWARLU,G. VENKATA RAMANA REDDY,D. VENKATA LAKSHMI 한국산업응용수학회 2015 Journal of the Korean Society for Industrial and A Vol.19 No.1
The present paper analyses the radiation effects of mass transfer on steady nonlinear MHD boundary layer flow of a viscous incompressible fluid over a nonlinear porous stretching surface in a porous medium in presence of heat generation. The liquid metal is assumed to be gray, emitting, and absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations are solved numerically using Runge?Kutta fourth order method along with shooting technique. Comparison with previously published work is obtained and good agreement is found. The effects of various governing parameters on the liquid metal fluid dimensionless velocity, dimensionless temperature, dimensionless concentration, skin-friction coefficient, Nusselt number and Sherwood number are discussed with the aid of graphs.
BOUNDS ON THE GROWTH RATE FOR THE KUO PROBLEM
S. LAVANYA,V. GANESH,G. VENKATA RAMANA REDDY The Korean Society for Computational and Applied M 2023 Journal of applied mathematics & informatics Vol.41 No.2
We consider Kuo problem of hydrodynamic stability which deals with incompressible, inviscid, parallel shear flows in the 𝛽-plane. For this problem, we derived instability region without any approximations and which intersects with Howard semi-circle region under certain condition. Also, we derived upper bound for growth rate and amplification factor of an unstable mode and proved Howard's conjecture.
On homogeneous shear flows with bottom cross section
S. Lavanya,V. Ganesh,G. Venkata Ramana Reddy 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.5
We consider inviscid, incompressible homogeneous shear flows of variable cross section known as extended Rayleigh problem. For this extended Rayleigh problem, we derived instability region which intersect with semi-circle instability region under some condition. Also we derived condition for stability , upper bound for amplification factor and growth rate of an unstable mode.
On the bounds for Wave Stability of Stratified Shear Flows
S. Lavanya,V. Ganesh,G. Venkata Ramana Reddy 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.1
We consider incompressible, inviscid, stratified shear flows in $\beta $ plane. First, we obtained an unbounded instability region intersect with semi-ellipse region. Second, we obtained a bounded instability regions depending on Coriolis, stratification parameters and basic velocity profile. Third, we obtained a criterion for wave stability. This has been illustrated with standard examples. Also, we obtained upper bound for growth rate.