Different Values Of Power-law Index Research Articles

Numerical study of unsteady natural convection heat transfer of Newtonian and non-Newtonian fluids in a square enclosure under oscillating heat flux

This paper presents a numerical study on the unsteady natural convective flow of Newtonian and non-Newtonian fluids in a square enclosure. A heat source with oscillating heat flux is located on the bottom wall of the enclosure. The top wall is thermally insulated and the other walls are at a relatively low temperature. The continuity, momentum, and energy equations for a computational domain encompassing the enclosure are solved numerically using the SIMPLE algorithm. The flow and temperature fields and the heat transfer performance are examined for different non-Newtonian fluids and heat source locations. The results are presented for different values of power-law index, Rayleigh number, and fluctuation period. It is found that the flow and temperature fields vary as the oscillating heat flux is changed. The pseudoplastic non-Newtonian fluid $$(n < 1)$$ is associated with a higher heat transfer, and the dilatant non-Newtonian fluid $$(n > 1)$$ is associated with a lower heat transfer with respect to the Newtonian fluid. The heat source oscillation period significantly affects the maximum flow temperature in the enclosure. This study provides useful information for the designers of electronic cooling systems using non-Newtonian fluids.

Implication of fluid rheology on the hydrothermal and entropy generation characteristics for mixed convective flow in a backward facing step channel with baffle

The present study numerically investigates a two-dimensional, steady, laminar, incompressible and mixed convective flow of non-Newtonian fluid through a backward facing step channel with different baffle configurations. The power-law model is used to capture the confluence of fluid rheology and buoyancy for varying step to baffle distance, varying number of baffles and different arrangement (inline and staggered) of baffles. Different values of power-law index viz. n = 0.5, 0.8, 1, 1.2 and 1.5 are considered to encompass the shear-thinning (n < 1), shear-thickening (n > 1) as well as Newtonian fluids (n = 1) as a special case. The Reynolds number is fixed equal to 100 whereas the Richardson number has been varied within the range of 0.1–1 in the present investigation. The results obtained from the present investigation reveal the implications of power-law index, Richardson number and baffle configuration on the reattachment length, Nusselt number, pressure drop and entropy generation. The results show that the length of the recirculation zones formed in the backward facing step channel increases with increase in Richardson number and decreases with increase in power-law index. It is also found that the variation of heat transfer rate, pressure drop and entropy generation characteristics for varying step to baffle distance, different number of baffles and different arrangement and number of pairs of baffle is dictated by the interplay of power-law index and Richardson number. The findings of this study bear utility towards designing efficient thermodynamic system that can deliver maximum heat transfer with minimum irreversibility.

Numerical Simulation of Non-Newtonian Power-Law Fluid Flow in a Lid-Driven Skewed Cavity

Non-Newtonian laminar fluid flow in a lid-driven skewed cavity has been studied numerically using power-law viscosity model. The governing two-dimensional unsteady incompressible Navier–Stokes equations were initially non-dimensionalized using appropriate transformation, and then the dimensionless form is transformed to generalized curvilinear coordinates to simulate complex geometry. The transformed equations are discretized using finite volume method with the collocated grid arrangement. The code is first validated against the existing benchmark results for two-dimensional lid-driven square cavity problem considering both Newtonian and non-Newtonian fluids. The validation has also been carried out for a lid-driven skewed cavity in the case of a Newtonian fluid. Then the code is applied to the skewed cavity problem involving non-Newtonian fluid flow which can be described by the power-law viscosity model. Moreover, grid independence test has been performed for a skewed cavity for different values of power-law index. In the present case, the skewness of the geometry has been changed by changing the skew angle for both shear-thinning and shear-thickening fluids. The consequent numerical results are presented in terms of the velocity as well as streamlines for the different values of the power-law index $$n=0.5$$ , 1 and 1.5, Reynolds number $$Re = 100, 200, 300$$ and 500 as well as for the different angles of the skewed cavity ( $$\alpha =15^{\circ }$$ to $$165^{\circ }$$ ).

Lattice Boltzmann model of gas-liquid two-phase flow of incomprssible power-law fluid and its application in the displacement problem of porous media

A new incompressible gas-liquid two-phase flow model for non-Newtonian power-law fluid is proposed based on an incompressible lattice Boltzmann model. And the fundamental physical mechanism of Newtonian fluid displacing non-Newtonian power-law fluid liquid in porous medium is studied by using the proposed model. The effects of capillary number &lt;i&gt;Ca&lt;/i&gt;, dynamic viscosity ratio &lt;i&gt;M&lt;/i&gt;, surface wettability &lt;i&gt;θ&lt;/i&gt;, porous medium geometry, and power law index &lt;i&gt;n&lt;/i&gt; on the displacement process are investigated. The comprehensive results show that with the increase of capillary number, the displacement process turns faster, the fingering phenomenon becomes more obvious and the displacement efficiency decreases. However, for different values of power-law index &lt;i&gt;n&lt;/i&gt;, the effects of the &lt;i&gt;Ca&lt;/i&gt; on the displacement process have some differences. Specially, the decrease rate of displacement efficiency becomes slow if the displaced fluid is shear thickening fluid as compared with that if the displaced fluid is shear thinning fluid. On the other hand, the displacement efficiency decreases as dynamic viscosity ratio &lt;i&gt;M&lt;/i&gt; increases. And the effect of the viscosity ratio on the displacement process becomes more obvious for the low value of the power-law index &lt;i&gt;n&lt;/i&gt;. Moreover, the effect of the surface wettability of the porous medium on the displacement process is also related to the size of the power-law index. With the increase of the contact angle of the porous medium, the fingering phenomenon turns less obvious, and the displacement efficiency increases. However, with the increase of power-law index &lt;i&gt;n&lt;/i&gt;, the influence of the contact angle on the displacement process decreases. Besides, the displacement processes with different geometric types of the porous media are also studied in the work. The results show that comparing with the case of porous medium denoted by circle shape and square shape, the fingering phenomenon obtained by the case of triangular shape is most obvious, and the displacement efficiency is lowest.

Supersonic flutter prediction of functionally graded cylindrical shells

The supersonic flutter analysis of simply supported FG cylindrical shell for different sets of in-plane boundary conditions is performed. The aeroelastic equations of motion are constructed using Love’s shell theory and von Karman–Donnell-type of kinematic nonlinearity coupled with linearized first-order potential (piston) theory. The material properties are assumed to be temperature-dependant and graded across the thickness of the shell according to a simple power law. The temperature distribution is assumed to vary in the thickness direction and is obtained by solving the steady-state heat conduction equation . The pre-stresses due to the thermal and mechanical loadings are obtained by exact solution of the equilibrium equations . The Galerkin method is used to solve the aeroelastic equations of motion employing appropriate displacement functions. The effects of internal pressure and temperature rise on the flutter boundaries of the simply supported FG cylinder with different values of power-law index are investigated.

Unsteady boundary layer flow of power-law fluid on stretching sheet surface

Two-dimensional unsteady boundary layer equations of non-Newtonian fluids are treated. Flow of a thin fluid film of a power-law caused by stretching of surface is investigated by using a similarity transformation. By using this transformation, we reduce the unsteady boundary layer equations to a non-linear ordinary differential equation system. Numerical solutions of outcoming nonlinear differential equations are found by using a combination a Runge–Kutta algorithm and shooting technique. Boundary layer thickness is explored numerically for different values of power-law index.

Hydromagnetic flow of generalized Newtonian fluid through a uniform tube with peristalsis

We have analyzed the mechanics of peristaltic pumping of a non-Newtonian fluid through an axisymmetric conduit subjected to a constant transverse magnetic field. The material represented by the constitutive equation for a power-law fluid. A perturbation series in dimensionless Hartmann number (M<1) was used to obtain explicit forms for the velocity field and relation between the flow rate and pressure gradient, in terms of the dimensionless power-law index and the occlusion. The expressions for the pressure rise and friction force on the wall of tube (small intestine) were computed numerically and were plotted with variation of the flow rate for different values of power-law index, Hartmann number and amplitude ratio. The results were compared with other studies, in both Newtonian and non-Newtonian cases.

Forced Convection Heat Transfer to Power-Law Non-Newtonian Fluids Inside Triangular Ducts

A hybrid analytical-numerical approach based on the Generalized Integral Transform Technique is employed to simulate the laminar forced convection (hydrodynamically fully developed and thermally developing laminar flow) of power-law non-Newtonian fluids inside ducts with arbitrary shaped cross-sections. The analysis is illustrated through consideration of both right angularly and isosceles triangular ducts subjected to constant wall temperature as thermal boundary condition. Reference results for quantities of practical interest such as dimensionless average temperature and Nusselt numbers within the thermal entry region were produced for different values of power-law index and apex angles. Finally, critical comparisons are performed with results available in the literature for direct numerical and approximate approaches.

Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts

The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical–analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.