Forced convection of non-Newtonian fluids on a heated flat plate (original) (raw)
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Mixed convection of non-Newtonian fluids along a heated vertical flat plate
"Mixed convective heat transfer of non-Newtonian fluids on a flat plate has been investigated using a modified power-law viscosity model. This model does not contain physically unrealistic limits of zero or infinite viscosity as are encountered in the boundary-layer formulation with traditional models of viscosity for power-law fluids. These unrealistic limits can introduce an irremovable singularity at the leading edge; consequently, the model is physically incorrect. The present modified model matches well with the measurement of viscosity, and does not introduce irremovable singularities. Therefore, the boundarylayer equations can be solved by marching from the leading edge downstream as for Newtonian fluids. The numerical results are presented for a shear-thinning fluid in terms of the velocity and temperature distribution, and for important physical properties, namely the wall shear stress and heat transfer rates."
The Flow of Non-Newtonian Fluids on a Flat Plate With a Uniform Heat Flux
Forced convective heat transfer of non-Newtonian fluids on a flat plate with the heating condition of uniform surface heat flux has been investigated using a modified power-law viscosity model. This model does not restrain physically unrealistic limits; consequently, no irremovable singularities are introduced into a boundary-layer formulation for powerlaw non-Newtonian fluids. Therefore, the boundary-layer equations can be solved by marching from leading edge to downstream as any Newtonian fluids. For shear-thinning and shear-thickening fluids, non-Newtonian effects are illustrated via velocity and temperature distributions, shear stresses, and local temperature distribution. Most significant effects occur near the leading edge, gradually tailing off far downstream where the variation in shear stresses becomes smaller
Non-Newtonian Fluid Flow on a Flat Plate Part 2: Heat Transfer
"Forced convective heat transfer of non-Newtonian fluids on a flat plate is investigated using a recently proposed modified power-law model. For a shear-thinning fluid, non-Newtonian effects are illustrated via local temperature distributions, heat transfer rate, and surface temperature distribution. Most significant effects occur near the leading edge, gradually tailing off far downstream."
Non-Newtonian Natural Convection Along a Vertical Plate with Uniform Surface Heat Fluxes
"Natural convection of non-Newtonian fluids along a vertical flat plate with the heating condition of uniform surface heat flux was investigated using a modified power-law viscosity model. In this model, there are no physically unrealistic limits in the boundary-layer formulation for power-law non-Newtonian fluids. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge is removed; hence, the boundarylayer equations can be solved straightforwardly by marching from the leading edge downstream. Numerical results are presented for the case of shear-thinning as well as shear-thickening fluids for two limits. The numerical results demonstrate that a similarity solution for natural convection exists near the leading edge, where the shear rate is not large enough to trigger non-Newtonian effects. After the shear rate increases beyond a threshold value, non- Newtonian effects start to develop and a similarity solution no longer exists. This indicates that the length scale is introduced into the boundary-layer formulation by the classical power-law correlation."
Non-Newtonian Fluid Flow on a Flat Plate Part 1: Boundary Layer
Amodified power-law viscosity for non-Newtonian fluids based on actual measurements is proposed. This realistic model allows removal of the singularities at the leading edge of a flat-plate boundary layer for either shear-thinning or shear-thickening fluids. Under this condition, the boundary-layer equations can be solved numerically by simple finite difference methods that march downstream from the leading edge, as is usually done for Newtonian fluids. Numerical results are presented for the case of a shear-thinning fluid; applying the model to a shear-thickening fluid is straightforward. The effects of this new variable viscosity are explicitly demonstrated by comparing plots of isolines of viscosity and shear rate, the velocity distribution, and the wall shear stress for non-Newtonian and Newtonian fluids.
"Natural convection of non-Newtonian fluids along a vertical wavy surface with uniform surface temperature has been investigated using a modified power-law viscosity model. An important parameter of the problem is the ratio of the length scale introduced by the power-law and the wavelength of the wavy surface. In this model there are no physically unrealistic limits in the boundary-layer formulation for power-law, non-Newtonian fluids. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge removed; hence, the boundary-layer equations can be solved straightforwardly by marching downstream from the leading edge. Numerical results are presented for the case of shear-thinning as well as shear-thickening fluid in terms of the viscosity, velocity, and temperature distribution, and for important physical properties, namely, the wall shear stress and heat transfer rates in terms of the local skin-friction coefficient and the local Nusselt number, respectively. Also results are presented for the variation in surface amplitude and the ratio of length scale to surface wavelength. The numerical results demonstrate that a Newtonian-like solution for natural convection exists near the leading edge where the shear-rate is not large enough to trigger non- Newtonian effects. After the shear-rate increases beyond a threshold value, non- Newtonian effects start to develop."
Unsteady thermal boundary layer flow of a non-newtonian fluid over a flat plate
International Journal of Engineering Science, 1981
The transient thermal response of a power law type non-Newtonian, laminar boundary layer flow past a flat plate is investigated. Consideration is given to the case of a step change in surface temperature. The transient heat flux and details of the temperature field are obtained and have been illustrated graphically. The range of Prandtl numbers investigated was 5-1000 while the viscosity index was allowed to vary 0.1-5.0. Unsteady thermal boundary layer Row of a non-Newtonian fluid over a flat plate n= 1.0 1397 10 -
Applied Mathematics and Computation, 2004
A numerical study of the laminar mixed free-forced convection of non-Newtonian power law fluid with mass transfer is presented. The flow in boundary layer includes the temperature which dependent on viscosity with thermal-diffusion and diffusion-thermo effects. The equations of momentum, energy and concentration are solved numerically with the aid of the Chebyshev finite difference method. The computation is carried out for wide range of the various material parameters associated with the power law non-Newtonian fluid. The results indicate that all the flow, thermal and concentration fields depend on the material parameters of the problem. During the course of discussion, the skin-friction, the rate of heat and mass transfer are obtained and discussed numerically and illustrated graphically.
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1996
The steady laminar free convection in the flow of a non‐Newtonian power‐law fluid along a vertical wavy surface with constant heat flux has been investigated in this paper. The transformed boundary layer equations are solved by using a very efficient implicit finite‐difference method. A sinusoidal surface is used to elucidate the amplitude of the wavy surface effects. Along with the wall temperature, representative velocity and temperature profiles are presented. Numerical results show that the wall temperature decreases as the power‐law index increases, while it increases with the amplitude of the wavy surface. Comparisons with earlier work are also made for a flat plate immersed in a Newtonian fluid. The results are found to compare very well.
Non-Newtonian fluid flow with natural heat convection through vertical flat plates
Natural heat convection for the flow of a third grade fluid through two parallel vertical infinite flat plates is considered. Similarity transforms combined with conservation laws are used to obtain the set of coupled nonlinear ordinary differential equations that govern the flow. Variation of Parameters Method (VPM) is used to determine the semi-exact solution to the problem. A numerical solution is also sought using Runge-Kutta (RK-4) method. Both the solutions are compared and an excellent agreement has been found. Effects of different dimensionless physical parameters on the flow are demonstrated graphically coupled with comprehensive discussions at the end of the article.