Linear and Weak Nonlinear Double Diffusive Convection in a Viscoelastic Fluid Saturated Anisotropic Porous Medium with Internal Heat Source

Abstract

This paper deals linear and weak nonlinear stability analysis of double-diffusive convection in an anisotropic porous layer with internal heat source saturated by viscoelastic fluid. For linear stability analysis we use normal mode technique and obtained the expression for oscillatory thermal Rayleigh number which is used to plot neutral stability curve for oscillatory case. For nonlinear analysis truncated representation of Fourier series upto two terms is used. The system of time dependent nonlinear equation is solved numerically and plot the curve for heat transfer and mass transfer with respect to time for different parameters. Effect of thermal anisotropy parameter, mechanical anisotropy parameter, relaxation parameter, retardation parameter, internal heat source parameter, solute Rayleigh number, diffusivity ratio, Darcy-Prandtl number on the onset of convection, heat and mass transfers have been discussed. We also draw the stream lines, isotherms, isohalines at different times.

The Effect of Thermal Modulation on Double Diffusive Convection in the Presence of Applied Magnetic Field and Internal Heat Source

“…The corresponding stability curves are presented in Figs 2a and 2b. These are the results were obtained by Srivastava et al [35] and Manjula et al [48,56,57] for convection in porous media. The effect of the Hartmann number and solutal Rayleigh number on 0c R versus wavenumber is presented in Fig.…”

“…In general, Rs effect must reduce heat/mass transfer, due to the effect of i R and nonlinearity there is a reverse trend of Rs . The corresponding results may be observed in the following studies [35][36][37][38]. The effect of amplitude and frequency of modulation is presented in Figs 8 and 9.…”

“…Kiran et al [32,33] investigated the effect of internal heating on nanofluid convection h. The effect of internal heating on magneto-double diffusive convection in a viscoelastic fluid-saturated porous layer was studied by Altawallbeh et al [34]. The study of linear and weakly nonlinear thermohaline convection in a viscoelastic fluid-saturated anisotropic porous medium with internal heat source was investigated by Srivastava and Singh [35]. The onset of thermal instability was investigated through the critical Rayleigh number.…”

Effects of Magnetic Field and Internal Heat Generation on Triple Diffusive Convection in an Oldroyd-B Liquid

“…This model can be regarded as an extension of the Upper Convected Maxwell model and gets reduced to it when the solvent viscosity is zero. Owing to the unique properties several researchers have studied viscoelastic liquids including Mahantesh and Sidram [11], Sumathi and Aiswarya [12], Srivastava and Singh [13], Malashetty et al [14] and Banyal [15].…”