Mixed convection of non-Newtonian fluids along a heated vertical flat plate (original) (raw)
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Forced convection of non-Newtonian fluids on a heated flat plate
"Forced convective heat transfer due to a non-Newtonian fluid flowing past a flat plate has been investigated using a modified power-law viscosity model. This model does not contain physically unrealistic limits; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. Therefore, the boundary-layer equations can be solved by (numerically) marching downstream from the leading edge as is common for boundary layers involving Newtonian fluids. For shearthinning and shear-thickening fluids, non-Newtonian effects are illustrated via velocity and temperature distributions, shear stresses, and heat transfer rates. The most significant effects occur near the leading edge, gradually tailing off far downstream where the variation of shear stresses becomes smaller."
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."
"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."
Mixed convection of a viscous dissipating fluid about a vertical flat plate
Applied Mathematical Modelling, 2007
In this study, the effect of the viscous dissipation in steady, laminar mixed convection heat transfer from a heated/ cooled vertical flat plate is investigated in both aiding and opposing buoyancy situations. The external flow field is assumed to be uniform. The governing systems of partial differential equations are solved numerically using the finite difference method. A parametric study is performed in order to illustrate the interactive influences of the governing parameters, mainly, the Richardson number, Ri (also known as the mixed convection parameter) and the Eckert number, Ec on the velocity and temperature profiles as well as the friction and heat transfer coefficients. Based on the facts the free stream is either in parallel or reverse to the gravity direction and the plate is heated or cooled, different flow situations are identified. The influence of the viscous dissipation on the heat transfer varied according to the situation. For some limiting cases, the obtained results are validated by comparing with those available from the existing literature. An expression correlating Nu in terms of Pr, Ri and Ec is developed.
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."
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.
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.
PLoS ONE, 2013
The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.
Mixed convection boundary layer flow on a continuous flat plate with variable viscosity
Heat and Mass Transfer, 1996
The influences of variable viscosity and buoyancy force on laminar boundary layer flow and heat transfer due to a continuous flat plate are examined. The deviation of the velocity and temperature fields as well as of the skin friction and heat transfer results from their constant values are determined by means of similarity solutions.