Articles written in Sadhana
Volume 43 Issue 7 July 2018 Article ID 0106
The magnetohydrodynamic (MHD) flow of a third grade fluid through a rectangular channel, considering the effect of aspect ratio, has been investigated. The flow considered is steady, laminar, incompressible and hydro-dynamically fully developed. The equation, describing the flow, is a highly non-linearpartial differential equation (PDE) with remote possibility of having an exact solution and even numerical solution also is very difficult to obtain. A combination of the homotopy perturbation method (HPM) and integral method (IM) has been employed to solve the non-linear PDE which is scarce in open literature. The results of the present study are compared with the results obtained by the least square method (LSM) of the MHD third grade fluid flow through a rectangular channel, without the effect of aspect ratio and are found to be in closeagreement. The results indicate that the flow field is significantly affected by the aspect ratio which should be considered for practical applications. In all the available literatures of the third grade fluid flow, the aspect ratioeffect is neglected and this simplifying assumption reduces the highly complicated non-linear PDE to a nonlinear ordinary differential equation (ODE). The novelty of the subject work lies in the inclusion of the effects of aspect ratio in the governing equation describing the flow of a third grade fluid through a channel and solvingthis by a combined analytical method (HPM and IM). Further, the effects of the Hartmann number and non-Newtonian third grade fluid parameter on the flow filed are discussed.
Volume 45 All articles Published: 2 July 2020 Article ID 0171
Pressure driven flow of a Sisko fluid through rectangular parallel plates, having different wall temperatures is investigated considering the effect of viscous dissipation. The nonlinear momentum and energy conservation equations are solved employing homotopy perturbation method (HPM) and analytical solutions for the velocity, flow rate and temperature distributions are obtained. The analytical solution of pressure-driven flow and heat transfer characteristics of Sisko fluids flowing through parallel plates, taking into account viscousdissipation effect, has not been addressed earlier. For a special case of a typical Sisko fluid, the HPM solution exhibits an excellent agreement with the exact solution. Effects of various parameters such as Sisko fluid parameter, non-Newtonian index and Brinkman numbers on the variation of velocity and temperature are discussed. Further, temperature distribution in flow of Sisko fluids through parallel plates with both the plates maintained at same temperature is also obtained by a suitable substitution in the expression for temperaturedistribution. It is observed that the velocity decreases significantly with an increase in Sisko fluid parameter. Temperature of the fluid decreases with an increase in Sisko fluid parameter and displays an increasing trend with an increase in Brinkman number. Results of the present study are useful for designing thermal systems handling polymer flows. For the typical case of two plates having same temperature, the maximum temperature is observed to occur at the centre, which is attributed to the effect of viscous dissipation acting as an internal source. The theoretical framework developed and analytical solution provided for the problem under consideration may be taken as benchmark result for validation of future work