Similarity solutions of three-dimensional boundary layer equations of non-Newtonian fluids

Timol, M. G.; Kalthia, N. L.

doi:10.1016/0020-7462(86)90043-0

Cited by 34 publications

(8 citation statements)

References 2 publications

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“…The RP fluid model behave like Newtonian type when shear stress disappears or huge whereas at other condition, this fluid can work like the non-Newtonian characteristics. Many works have been reported on this fluid and the contributions are highlighted on the external effect considered to the flow and also the assumption of the flow of fluid moving too [37][38][39][40]. A fascinating study has been performed by Ahmad et al, [41] where the flow of RP fluids flow prompted by the nonlinearly stretched surface and variable thickness effects.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions on Reiner–Philippoff (RP) Fluid Model with Velocity and Thermal Slip Boundary Condition

Ariffin

Waini

Kasim

et al. 2022

CFDL

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Non-Newtonian fluid model was created against the Newton’s Law of viscosity where the viscosity is no more constant and dependent on the shear rate. The existing such fluid can be found in many industrial claims especially in food manufacturing, lubrication, biomedical flows and oil and gas. Besides, the used of non-Newtonian fluid occurs in mining industry where the slurries and muds are often handled. There are many models on non-Newtonian fluid available in literature where some of them capture the specific properties. The Reiner–Philippoff (RP) fluid model is considered in this endeavour due to the capabilities of the model which can be acted in three different family of fluid which are viscous, shear thickening and the shear-thinning. Mathematical model is constructed using continuity, momentum and energy equations where in form of partial differential equations (PDEs). The complexity of the proposed model is abridged by deduced the equations into ordinary differential equations (ODEs) by adopting similarity variables before the computation is done by bvp4c function drive in MATLAB software. To ratify the validity of the proposed model as well as numerical outputs, the comparative study is performed and it found to be in very strong agreement under limiting case where the present model is condensed to be identical with the reported model previously. The consequences of pertinent parameters on fluid’s characteristics are analyzed in details through the plotted graphic visuals and tabular form.

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Section: Introductionmentioning

confidence: 99%

Numerical Solutions on Reiner–Philippoff (RP) Fluid Model with Velocity and Thermal Slip Boundary Condition

Ariffin

Waini

Kasim

et al. 2022

CFDL

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“…Our aim in this study is to apply scaling transformation to the equation and determine the specific forms of k(θ) and f(x) for which the fin equation admits this transformation. For applications of scaling symmetries as well as other types of special Lie Group transformations, and determining specific forms of functions for which these symmetries exist, see [12][13][14][15][16] for example. In the degenerate case of equation 1with f(x)=0, a complete group classification has been presented previously [17].…”

Section: Theoretical Analysis For Scaling Transformationmentioning

confidence: 99%

A Similarity Solution of Fin Equation with Variable Thermal Conductivity and Heat Transfer Coefficient

Pakdemi̇rli̇

Şahin

2006

MCA

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A nonlinear fin equation in which thermal conductivity is an arbitrary function of temperature and, heat transfer coefficient is an arbitrary function of spatial variable is considered. Scaling transformation is applied to the equations to determine the specific forms of these functions for which the equation admits such type of transformation. It is found that for arbitrary heat conduction function, scaling transformation exists for an inverse square heat transfer coefficient. Selecting also the conductivity as an exponential function, the partial differential equation is transferred to an ordinary differential equation via similarity transformations. The resulting equation is solved numerically and temperature distribution is determined for various heat conductivity parameters.

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“…They have also obtained similarity solution for small cross flow geometry. Timol and Kalthia [6] have carried out similarity analysis of three dimensional boundary layer equations of non-Newtonian fluids and integrated similarity equations for Reiner Philippoff fluids. Pakdemirli [7,8] and his co-workers have worked out similarity solutions for three dimensional boundary layer flow of non-Newtonian Power law fluids using scaling and spiral group of transformations.…”

Section: Introductionmentioning

confidence: 99%

Similarity solutions of quasi three dimensional power law fluids using the method of satisfaction of asymptotic boundary conditions

Jain¹,

Timol

2015

Alexandria Engineering Journal

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The work presented in this paper is focused on deductive group-theoretic transformations to develop the similarity solution of steady, laminar, incompressible quasi three dimensional boundary layer flow governing power law fluid. The application of one-parameter group reduces the number of independent variables to one and consequently the system of governing, highly non-linear partial differential equations reduces to a self similar, non-linear ordinary differential equation with appropriate auxiliary conditions. The numerical solution for a power law fluid considered for small cross flow is obtained systematically using MSABC in dimensionless form. ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Similarity solutions of three-dimensional boundary layer equations of non-Newtonian fluids

Cited by 34 publications

References 2 publications

Numerical Solutions on Reiner–Philippoff (RP) Fluid Model with Velocity and Thermal Slip Boundary Condition

Numerical Solutions on Reiner–Philippoff (RP) Fluid Model with Velocity and Thermal Slip Boundary Condition

A Similarity Solution of Fin Equation with Variable Thermal Conductivity and Heat Transfer Coefficient

Similarity solutions of quasi three dimensional power law fluids using the method of satisfaction of asymptotic boundary conditions

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