Effect of Time Periodic Boundary Temperature on Nonlinear Convection in Viscoelastic Dielectric Liquids

The paper is a study on the nonlinear analysis of convection in viscoelastic dielectric liquids in the presence of alternating current(AC) and temperature modulation. The intrinsic viscoelasticity as in gel-based dielectric liquids and induced viscoelasticity due to electric field combined with the modulated boundary temperature has significant effect on heat transfer. The constituent equation for the viscoelasticity is the Oldroyd-B model. An elegant, generalised Lorenz model for viscoelastic dielectric liquid has been derived by normal mode analysis using a truncated double Fourier series. The classical Lorenz model can be obtained as a limiting case of the present study. A numerical procedure in Scilab, an open source software, is used to solve the non-autonomous, nonlinear electric Khayat-Lorenz model. This solution is used to compute Nusselt number. The average Nusselt number is evaluated using Simpson’s 3/8th rule. Heat transfer is discussed for various viscoelastic models and parameters which are limiting cases of the generalized Lorenz model. It is found that the modulation of boundary temperature is a controlling mechanism to regulate heat transfer.