Thermodynamically Consistent Limiting Nusselt Number in the Viscous Dissipative Non-Newtonian Couette Flows

Abstract

The present study attempts to explore the effects of viscous dissipation on the heat transfer characteristics in the conduction limit for the Couette flow of power-law fluids between asymmetrically heated parallel plates. Here, two types of power-law fluids are considered (e.g., the pseudoplastic (n < 1) and dilatants (n > 1)) along with the special case of n = 1 (i.e., the Newtonian fluid). Utilizing the assumptions routinely employed in the literature, a semianalytical framework is devised to explore the effects of viscous dissipation on the limiting heat transfer characteristics. The shear produced by the movement of the upper plate in the dynamics of flow is emphasized; hence, a weak pressure gradient in the flow field is considered, which could otherwise create a complicated situation in the derivation of velocity distribution for the non-Newtonian Couette flows considered in this study. Despite the effect of viscous dissipation on the limiting heat transfer, the effect of asymmetrical wall heating on the same is shown for all the cases under consideration. Using these results, the possibilities of obtaining different temperature profiles and the variation of Nusselt number for different types of power-law fluid are aptly highlighted in view of the energy balance and analysis of the second-law of thermodynamics.

Limiting thermal characteristics for flow of non-Newtonian fluids between asymmetrically heated parallel plates: An analytical study

“…The point of discontinuity in the variation of Nu1 is similar to the results available in the literature. 6,10,11,23 In order to get insight of the variation of Nu1 with Br other than the point of discontinuity, variation of Nu1 with Br is shown on the inset of Figure 6. As can be seen from the inset of Figure 6(a), the variation of Nu1 with Br is not significant for S=0.5, while for S=-0.5 there is a significant change in Nu1 with Br (<0).…”

“…Mondal 10 presented the limiting forced convection heat transfer characteristics for flow of Newtonian fluid between two asymmetrically heated parallel plates filled with saturated porous media. Mondal and Mukherjee 11 explored the viscous dissipation effects on the limiting heat transfer characteristics for the Couette flow of power law fluids between asymmetrically heated parallel plates using a semi-analytical approach. The implications of asymmetric heating on heat transfer characteristics in the limiting condition for flow of non-Newtonian fluids between two parallel plates, with the consideration of viscous heating have not yet been studied.…”

“…The study of thermo-fluidic transport characteristics in narrow-confinement with asymmetric heating has aroused a serious attention in the literature due to its widespread practical applications, such as fuel cells, thermal management of electronic devices, catalytic converters, solar absorbers, journal bearing, to name a few. Considering the technological importance of asymmetric heating on the thermal characteristics in confinements, a great deal of research work [1][2][3][4][5][6][7][8][9][10][11] has been performed by the researchers over the last few decades. Nield 1 analytically obtained Nusselt number for forced convective flow through asymmetrically heated parallel plate channel under different flow conditions, namely, slug flow, Poiseuille flow, and Couette flow and figured out that Nusselt number is independent of the asymmetry only when the velocity profile is symmetric with respect to channel centerline.…”

Thermal characteristics of forced convection in combined pressure and shear‐driven flow of a non‐Newtonian third‐grade fluid through parallel plates

“…The primary focus of the study was again the viscous dissipation effect of the shear produced by the moving upper plate, apart from the viscous dissipation effect produced by the internal fluid friction. Mondal and Mukherjee 15 studied the effect of viscous dissipation, highlighting the effect of viscous dissipative effect of shear, in the Couette flow of a non-Newtonian powerlaw fluid. Analysis was made for both shear-thinning and shear-thickening fluids.…”

Assesment of Thermodynamic Irreversibility in a Micro-Scale Viscous Dissipative Circular Couette Flow

“…Thermal systems and devices are required to sustain different thermal conditions because of their widespread application in different fields. Taking this into consideration, researchers have also investigated the influence of viscous heating developed by a moving surface on the convective transport of heat in a thermal asymmetrical heating environment [ 8 , 22 , 23 ]. On the other hand, the rotation-induced effect of shear heating may alter thermo-fluidic transport by changing the temperature distribution in the field and hence the thermodynamic efficiency of the systems/devices.…”