Heat and mass transfer of triple diffusive convection in viscoelastic liquids under internal heat source modulations

Abstract

The influence of sinusoidal (trigonometric cosine [TC]) and nonsinusoidal waveforms (square, sawtooth, and triangular) of internal heat source modulation on triple diffusive convection in viscoelastic liquids is investigated. An Oldroyd-B type model is taken into account for viscoelastic liquids. Nonlinear analysis is carried out using a truncated representation of the Fourier series. To analyze the heat and mass transfer over a triply diffusive liquid layer, expressions for average Nusselt and average Sherwood numbers are derived using 8-mode generalized Lorenz equations. The transient behavior of Nusselt and Sherwood numbers is analyzed on different parameters of the problem. From the results, it is found that the internal heat source enhances the heat transfer and diminishes the mass transfer while the heat sink diminishes the heat transfer and enhances the mass transfer. The results for respective waveforms are obtained for each parameter and it is found that the maximum heat and mass transfer occurs due to TC waveform. The limiting cases of viscoelastic liquids (Newtonian, Oldroyd-B, Maxwell, and Rivlin-Ericksen) have been tabulated and corresponding results for each of the waveforms on heat and mass transfer have been shown.

Comparative study of sinusoidal and non‐sinusoidal two‐frequency internal heat modulation in a Rayleigh‐Bénard system

“…As a result, we conclude that the heat source facilitates the greatest heat transfer in the system compared to the heat sink. Further, on comparison with the most recent study of heat transfer under internal heat modulation by Noor et al, 47 the limiting case, i.e., single‐frequency internal heat modulation () for a Newtonian liquid () are seen to be in great agreement with each other (Table 6).…”

“…Although many studies are available on RBC with an internal heat source, not much attention was given to studying time‐dependent internal heat source in RBC. To the best of our knowledge, the only work existing work on internal heat modulation are by Shu et al 45 and Bazylak et al 46 The most recent work by Noor et al 47 is another piece of evidence for the same. However, the authors have focused only on the impact of single‐frequency time‐dependent heat source on the amount of heat transfer in the system and have not discussed possible effect of this on the onset of convection.…”

Influence of Temperature Gradients and Heat Source in a Combined Layer on Double Component-Magneto-Marangoni-Convection

“…Te efects of magnetic feld and heat source on doubledifusive convection two layer system studied by Manjunatha and Sumithra [22]. Te efects of waveforms of internal heat source modulation on triple difusive convection in viscoelastic liquids were investigated by Arshika et al [23]. Kumar Pundir et al [24] investigated the linear stability of a fuid layer with nanoparticles in the presence of a solute gradient.…”