Chandra Shekara Guruva Reddy

The stability of thermal convection in a nanofluid-saturated porous layer with impermeable boundaries is investigated by considering the unsteady Darcy’s model along with the horizontal pressure gradient. The analysis employs linear stability theory, with water as the base fluid in thermal equilibrium with the porous matrix under a single thermal phase. The governing stability equations are formulated as an eigenvalue problem and solved using one-term and higher-order Weighted Residual Galerkin Methods (WRGM). Critical values of the Darcy-Rayleigh number, wave number and wave speed are examined for varying horizontal pressure gradients, Prandtl numbers, nanoparticle volume fractions and thermal diffusivity ratios. The findings indicate that higher thermal diffusivity ratios and pressure gradients stabilize the system, while increased nanoparticle volume fractions and higher Prandtl numbers promote instability. The time evolution of streamlines and isotherms is simulated by solving a nonlinear system of PDEs using the method of lines, combined with regularization and finite difference techniques. Nonlinear stability analysis reveals that nanofluids demonstrate enhanced stability compared to the base fluid. Notably, the analysis identifies a subcritical region between the convection onsets predicted by linear and nonlinear methods, showing that convection begins earlier in the nonlinear regime. These insights are crucial for optimizing nanoparticle concentrations in thermally driven systems, ultimately enhancing heat transfer efficiency.

This study investigates the stability of a mixed convective flow of a nanofluid through a horizontal porous layer using an unsteady Jeffrey-Darcy model. Linear stability theory is employed to assess the stability of a system, where the base fluid is modeled as a Jeffrey fluid with dispersed nanoparticles in a state of thermal equilibrium. The stability equations are derived as an eigenvalue problem using Fourier decomposition, solved using the higher order Weighted Residual Galerkin Method (WRGM), and validated analytically. The results are presented in terms of critical values of the Darcy-Rayleigh number, wave number, and wave speed over nondimensional parameters. Further, the impact of nondimensional numbers like horizontal pressure gradient, thermal diffusivity ratio, and nanoparticle volume fraction has stabilizing effects, whereas the Jeffrey parameter and the Vadasz number have the opposite effect. Moreover, it has been observed that the increase in the Jeffrey parameter reduces the stability region. The variation Jeffrey parameter causes a change in the flow and thereby discards the analytical proof of stability even under the limit of an infinite Vadasz number. The inquiry into the stability or instability of the fundamental flow is addressed by solving the eigenvalue problem numerically over a finite range of the Jeffrey parameter and horizontal pressure gradient. These results indicate that the oscillatory convection mode is advantageous for estimating the required volume fraction of nanoparticles in the base fluid to improve the thermal efficiency of Jeffrey nanofluids. Numerical and graphical analyses explore the impacts of dimensionless parameters on physical systems, providing insights into the system’s stability properties under varying conditions.

The present work is concerned with the study of the Kelvin-Helmholtz Instability (KHI) at the interface between a poorly conducting fluid saturated porous layer of large extent which is in relative motion with a poorly conducting fluid in a thin shell with an applied transverse magnetic field and an electric field. Linear instability theory is applied based on fully developed flow approximations to derive the dispersion relation for the growth rate of KHI. The cutoff and the maximum wave numbers and the corresponding maximum frequencies are obtained. It is shown that the effects of the magnetic field, the electric field, permeability and slip parameter reduces the growth rate of KHI considerably compared to a non-conducting fluid in the absence of permeability, magnetic field and electric field. These are favorable to control the surface instabilities in many practical applications.

The pseudo-spectral collocation solution of time dependent nonlinear system of partial differential equations with Dirichlet's boundary conditions is presented in this paper. The nonlinear systems of partial differential equations are reduced to linear form by using quasi-linearization along with the Taylor's series of multi-variables. Then the spectral collocation algorithm is developed by using Lagrange interpolating polynomials as basis of the solution at the Chebyshev-Gauss-Labatto grid points. This algorithm is implemented using MATLAB for test case problems and the results are presented graphically. Error analysis is done by comparing the numerical solution and analytical solution. Solution found by the said method is more accurate compared to the finite difference method with uniform grid points.