The linear stability of a liquid layer flowing down an inclined plane lined with a deformable, vi... more The linear stability of a liquid layer flowing down an inclined plane lined with a deformable, viscoelastic solid layer is analyzed in order to determine the effect of the elastohydrodynamic coupling between the liquid flow and solid deformation on the free-surface instability in the liquid layer. The stability of this two-layer system is characterized by two qualitatively different interfacial instability modes: In the absence of the deformable solid layer, the free surface of the liquid film undergoes a long-wave instability due to fluid inertia. With the presence of the deformable solid layer, the interface between the fluid and the solid undergoes a finite-wavelength instability when the deformable solid becomes sufficiently soft. The effect of the solid layer deformability on the free-surface instability of the liquid film flow is analyzed using a long-wave asymptotic analysis. The asymptotic results show that for a fixed Reynolds number and inclination angle, the free-surface instability is completely suppressed in the long-wave limit when the nondimensional ͑inverse͒ solid elasticity parameter ⌫ = V a / ͑GR͒ increases beyond a critical value. Here, V a is the average velocity of the liquid film flow, is the viscosity of the liquid, G is the shear modulus of the solid layer, and R is the thickness of the liquid layer. The predictions of the asymptotic analysis are verified and extended to finite wavelengths using a numerical solution, and this indicates that the suppression of the free-surface instability indeed continues to finite wavelength disturbances. Further increase of ⌫ is found to have two consequences: first, the interface between the liquid and the deformable solid layer could become unstable at finite wavelengths; second, the free-surface interfacial mode could also become unstable at finite wavelengths due to an increase in solid layer deformability. However, our numerical results demonstrate that, for a given average velocity, there exists a sufficient window in the value of shear modulus G where both the unstable modes are absent at all wavelengths. Our study therefore suggests that soft solid layer coatings could potentially provide a passive method of suppressing free-surface instabilities in liquid film flows.
Forced convection heat transfer to incompressible power law type non-Newtonian fluids from a heat... more Forced convection heat transfer to incompressible power law type non-Newtonian fluids from a heated square cylinder in the unsteady cross-flow regime has been studied numerically by solving the relevant momentum and thermal energy equations using a finite-volume method for the range of conditions 0.7 ≤ Pr ≤ 50, 60 ≤ Re ≤ 160, and 0.5 ≤ n ≤ 1.8. Over this range of Reynolds numbers, the flow is truly periodic for Newtonian and
The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylind... more The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylinder are investigated numerically in the unsteady two-dimensional periodic flow regime, for the range of conditions 60 6 Re 6 160 and 0.7 6 Pr 6 50 (the maximum value of Peclet number being 4000). A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. Using the present numerical results, simple heat transfer correlations are obtained for the constant temperature and constant heat flux conditions on the solid square cylinder. In addition, the variation of the time averaged local Nusselt number on the each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the unsteady flow regime.
Numerical Heat Transfer, Part A: Applications, 2010
Forced convection heat transfer characteristics of a long, heated square cylinder blocking the fl... more Forced convection heat transfer characteristics of a long, heated square cylinder blocking the flow of a power-law fluid in a channel is numerically investigated in this study. In particular, the role of the power-law index n, Reynolds number Re, Prandtl number Pr, and blockage ratio β(=B/H) on the rate of heat transfer from a square cylinder in a channel has been studied over the following ranges of conditions: 0.5 ≤ n ≤ 1.8, 60 ≤ Re ≤ 160, β = 1/4, 1/2, and 0.7 ≤ Pr ≤ 50. A semi-explicit finite-volume method is used on a nonuniform collocated grid arrangement. The third-order QUICK and the second-order central difference schemes are used to discretize the convective and diffusive terms, respectively, in the momentum and energy equations. Irrespective of the type of behavior of fluid (different values of n), the average Nusselt number increases as the blockage ratio increases. Similar to the unconfined flow configuration, the average Nusselt number increases monotonically with Reynolds and Prandtl numbers for both values of the blockage ratio and for all values of power-law index considered here. Further insights into the heat transfer phenomenon are provided by presenting isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power-law index for the two values of β considered in this work.
The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder... more The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder has been investigated numerically in the range of conditions 60 ≤ Re ≤ 160 and 0.5 ≤ n ≤ 2.0. Over this range of Reynolds numbers, the flow is periodic in time. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The global quantities such as drag coefficients, Strouhal number and the detailed kinematic variables like stream function, vorticity and so on, have been obtained for the above range of conditions. While, over this range of Reynolds number, the flow is known to be periodic in time for Newtonian fluids, a pseudo-periodic flow regime displaying more than one dominant frequency in the lift is observed for shear-thinning fluids. This seems to occur at Reynolds numbers of 120 and 140 for n = 0.5 and 0.6, respectively. Broadly speaking, the smaller the value of the power law index, lower is the Reynolds number of the onset of the pseudoperiodic regime. This work is concerned only with the fully periodic regime and, therefore, the range of Reynolds numbers studied varies with the value of the power law index. Not withstanding this aspect, in particular here, the effects of Reynolds number and of the power law index have been elucidated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening fluid behaviour delays this separation and shows the lowering of the drag coefficient with the Reynolds number. Also, the preliminary results suggest the transition from the steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thinning fluids than that in Newtonian fluids.
... Two-dimensional laminar flow of power-law fluids past a long square cylinder confined in a pl... more ... Two-dimensional laminar flow of power-law fluids past a long square cylinder confined in a planar channel is ... upon the value of blockage ratio, power-law index and Reynolds number, the nature of flow in the above range of conditions is either steady or unsteady (periodic in ...
ABSTRACT Extensive numerical simulations for the 2-D laminar flow of power-law fluids over an equ... more ABSTRACT Extensive numerical simulations for the 2-D laminar flow of power-law fluids over an equilateral triangular cylinder are performed to elucidate the role of power-law index (0.2 ≤ n ≤ 1.8) on the critical Reynolds number denoting the onset of flow separation and of vortex shedding. Results are presented for both orientations of the triangular cylinder, namely, its apex facing in the upstream and the downstream directions. For shear-thinning fluids, the onset of wake formation and vortex shedding both are seen to be delayed than that in Newtonian and shear-thickening fluids. After delineating the limits of the steady flow regime, the effects of the Reynolds and Prandtl numbers and the power-law index on drag phenomena and heat transfer characteristics of triangular cylinder for shear-thinning fluids have been studied in the steady flow regime. The results reported herein embrace the following ranges of conditions: 0.2 ≤ n ≤ 1; 1 ≤ Re ≤ 30 and 1 ≤ Pr ≤ 100. Detailed results on isotherm contours, local Nusselt number and its surface-averaged values are presented. Finally, the present numerical values of the critical Reynolds numbers and Nusselt number have been correlated using simple forms which are convenient for interpolating the present results for the intermediate values of the governing parameters in a new application.
International Journal of Heat and Mass Transfer, 2009
The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylind... more The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylinder are investigated numerically in the unsteady two-dimensional periodic flow regime, for the range of conditions 60 6 Re 6 160 and 0.7 6 Pr 6 50 (the maximum value of Peclet number being 4000). A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. Using the present numerical results, simple heat transfer correlations are obtained for the constant temperature and constant heat flux conditions on the solid square cylinder. In addition, the variation of the time averaged local Nusselt number on the each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the unsteady flow regime.
... P. Koteswara Rao, Akhilesh K. Sahu and RP Chhabra ... reliable results on drag and wake chara... more ... P. Koteswara Rao, Akhilesh K. Sahu and RP Chhabra ... reliable results on drag and wake characteristics are now available on the flow of power-law fluids past a circular cylinder in the steady-flow regime.(26-30) The role of planar confining walls has been examined by Bharti et ...
The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder... more The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder has been investigated numerically in the range of conditions 60≤Re≤160 and 0.5≤n≤2.0. Over this range of Reynolds numbers, the flow is periodic in time. A semi-explicit finite ...
The linear stability of a liquid layer flowing down an inclined plane lined with a deformable, vi... more The linear stability of a liquid layer flowing down an inclined plane lined with a deformable, viscoelastic solid layer is analyzed in order to determine the effect of the elastohydrodynamic coupling between the liquid flow and solid deformation on the free-surface instability in the liquid layer. The stability of this two-layer system is characterized by two qualitatively different interfacial instability modes: In the absence of the deformable solid layer, the free surface of the liquid film undergoes a long-wave instability due to fluid inertia. With the presence of the deformable solid layer, the interface between the fluid and the solid undergoes a finite-wavelength instability when the deformable solid becomes sufficiently soft. The effect of the solid layer deformability on the free-surface instability of the liquid film flow is analyzed using a long-wave asymptotic analysis. The asymptotic results show that for a fixed Reynolds number and inclination angle, the free-surface instability is completely suppressed in the long-wave limit when the nondimensional ͑inverse͒ solid elasticity parameter ⌫ = V a / ͑GR͒ increases beyond a critical value. Here, V a is the average velocity of the liquid film flow, is the viscosity of the liquid, G is the shear modulus of the solid layer, and R is the thickness of the liquid layer. The predictions of the asymptotic analysis are verified and extended to finite wavelengths using a numerical solution, and this indicates that the suppression of the free-surface instability indeed continues to finite wavelength disturbances. Further increase of ⌫ is found to have two consequences: first, the interface between the liquid and the deformable solid layer could become unstable at finite wavelengths; second, the free-surface interfacial mode could also become unstable at finite wavelengths due to an increase in solid layer deformability. However, our numerical results demonstrate that, for a given average velocity, there exists a sufficient window in the value of shear modulus G where both the unstable modes are absent at all wavelengths. Our study therefore suggests that soft solid layer coatings could potentially provide a passive method of suppressing free-surface instabilities in liquid film flows.
Forced convection heat transfer to incompressible power law type non-Newtonian fluids from a heat... more Forced convection heat transfer to incompressible power law type non-Newtonian fluids from a heated square cylinder in the unsteady cross-flow regime has been studied numerically by solving the relevant momentum and thermal energy equations using a finite-volume method for the range of conditions 0.7 ≤ Pr ≤ 50, 60 ≤ Re ≤ 160, and 0.5 ≤ n ≤ 1.8. Over this range of Reynolds numbers, the flow is truly periodic for Newtonian and
The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylind... more The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylinder are investigated numerically in the unsteady two-dimensional periodic flow regime, for the range of conditions 60 6 Re 6 160 and 0.7 6 Pr 6 50 (the maximum value of Peclet number being 4000). A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. Using the present numerical results, simple heat transfer correlations are obtained for the constant temperature and constant heat flux conditions on the solid square cylinder. In addition, the variation of the time averaged local Nusselt number on the each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the unsteady flow regime.
Numerical Heat Transfer, Part A: Applications, 2010
Forced convection heat transfer characteristics of a long, heated square cylinder blocking the fl... more Forced convection heat transfer characteristics of a long, heated square cylinder blocking the flow of a power-law fluid in a channel is numerically investigated in this study. In particular, the role of the power-law index n, Reynolds number Re, Prandtl number Pr, and blockage ratio β(=B/H) on the rate of heat transfer from a square cylinder in a channel has been studied over the following ranges of conditions: 0.5 ≤ n ≤ 1.8, 60 ≤ Re ≤ 160, β = 1/4, 1/2, and 0.7 ≤ Pr ≤ 50. A semi-explicit finite-volume method is used on a nonuniform collocated grid arrangement. The third-order QUICK and the second-order central difference schemes are used to discretize the convective and diffusive terms, respectively, in the momentum and energy equations. Irrespective of the type of behavior of fluid (different values of n), the average Nusselt number increases as the blockage ratio increases. Similar to the unconfined flow configuration, the average Nusselt number increases monotonically with Reynolds and Prandtl numbers for both values of the blockage ratio and for all values of power-law index considered here. Further insights into the heat transfer phenomenon are provided by presenting isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power-law index for the two values of β considered in this work.
The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder... more The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder has been investigated numerically in the range of conditions 60 ≤ Re ≤ 160 and 0.5 ≤ n ≤ 2.0. Over this range of Reynolds numbers, the flow is periodic in time. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The global quantities such as drag coefficients, Strouhal number and the detailed kinematic variables like stream function, vorticity and so on, have been obtained for the above range of conditions. While, over this range of Reynolds number, the flow is known to be periodic in time for Newtonian fluids, a pseudo-periodic flow regime displaying more than one dominant frequency in the lift is observed for shear-thinning fluids. This seems to occur at Reynolds numbers of 120 and 140 for n = 0.5 and 0.6, respectively. Broadly speaking, the smaller the value of the power law index, lower is the Reynolds number of the onset of the pseudoperiodic regime. This work is concerned only with the fully periodic regime and, therefore, the range of Reynolds numbers studied varies with the value of the power law index. Not withstanding this aspect, in particular here, the effects of Reynolds number and of the power law index have been elucidated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening fluid behaviour delays this separation and shows the lowering of the drag coefficient with the Reynolds number. Also, the preliminary results suggest the transition from the steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thinning fluids than that in Newtonian fluids.
... Two-dimensional laminar flow of power-law fluids past a long square cylinder confined in a pl... more ... Two-dimensional laminar flow of power-law fluids past a long square cylinder confined in a planar channel is ... upon the value of blockage ratio, power-law index and Reynolds number, the nature of flow in the above range of conditions is either steady or unsteady (periodic in ...
ABSTRACT Extensive numerical simulations for the 2-D laminar flow of power-law fluids over an equ... more ABSTRACT Extensive numerical simulations for the 2-D laminar flow of power-law fluids over an equilateral triangular cylinder are performed to elucidate the role of power-law index (0.2 ≤ n ≤ 1.8) on the critical Reynolds number denoting the onset of flow separation and of vortex shedding. Results are presented for both orientations of the triangular cylinder, namely, its apex facing in the upstream and the downstream directions. For shear-thinning fluids, the onset of wake formation and vortex shedding both are seen to be delayed than that in Newtonian and shear-thickening fluids. After delineating the limits of the steady flow regime, the effects of the Reynolds and Prandtl numbers and the power-law index on drag phenomena and heat transfer characteristics of triangular cylinder for shear-thinning fluids have been studied in the steady flow regime. The results reported herein embrace the following ranges of conditions: 0.2 ≤ n ≤ 1; 1 ≤ Re ≤ 30 and 1 ≤ Pr ≤ 100. Detailed results on isotherm contours, local Nusselt number and its surface-averaged values are presented. Finally, the present numerical values of the critical Reynolds numbers and Nusselt number have been correlated using simple forms which are convenient for interpolating the present results for the intermediate values of the governing parameters in a new application.
International Journal of Heat and Mass Transfer, 2009
The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylind... more The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylinder are investigated numerically in the unsteady two-dimensional periodic flow regime, for the range of conditions 60 6 Re 6 160 and 0.7 6 Pr 6 50 (the maximum value of Peclet number being 4000). A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. Using the present numerical results, simple heat transfer correlations are obtained for the constant temperature and constant heat flux conditions on the solid square cylinder. In addition, the variation of the time averaged local Nusselt number on the each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the unsteady flow regime.
... P. Koteswara Rao, Akhilesh K. Sahu and RP Chhabra ... reliable results on drag and wake chara... more ... P. Koteswara Rao, Akhilesh K. Sahu and RP Chhabra ... reliable results on drag and wake characteristics are now available on the flow of power-law fluids past a circular cylinder in the steady-flow regime.(26-30) The role of planar confining walls has been examined by Bharti et ...
The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder... more The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder has been investigated numerically in the range of conditions 60≤Re≤160 and 0.5≤n≤2.0. Over this range of Reynolds numbers, the flow is periodic in time. A semi-explicit finite ...
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