Similarity Solution for Free Convection Flow of a Micropolar Fluid under Convective Boundary Condition via Lie Scaling Group Transformations

RamReddy, Ch.; Pradeepa, T.; Srinivasacharya, D.

doi:10.1155/2015/650813

Cited by 17 publications

(11 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We assumed, the size of holes in the porous plate plays an important role to simplify the formulation of the boundary conditions. By taking the aforesaid assumptions into consideration the governing boundary layer equations with corresponding boundary conditions for steady convective flow are as follows:

\frac{\partial u^{'}}{\partial x^{'}} + \frac{\partial v^{'}}{\partial y^{'}} = 0,

u \frac{\partial u^{'}}{\partial x^{'}} + v^{'} \frac{\partial u^{'}}{\partial y^{'}} = (\frac{μ + k}{ρ}) \frac{\partial^{2} u^{'}}{\partial {y^{'}}^{2}} + g β_{T} false(T - T_{\infty} false) cos α + g β_{c} false(C - C_{\infty} false) cos α + \frac{k}{ρ} \frac{\partial N^{'}}{\partial y^{'}},

u^{'} \frac{\partial N^{'}}{\partial x^{'}} + v^{'} \frac{\partial N^{'}}{\partial y^{'}} = \frac{γ}{ρ j^{'}} \frac{\partial^{2} N^{'}}{\partial {y^{'}}^{2}} - \frac{k}{ρ j^{'}} (\frac{\partial u^{'}}{\partial y^{'}} + 2 N^{'}),

u^{'} \frac{\partial T}{\partial x^{'}} + v^{'} \frac{\partial T}{\partial y^{'}} = \frac{κ}{ρ C_{p}} \frac{\partial^{2} T}{\partial}

…”

Section: Reactive Radiative Micropolar Thermo‐solutal Modelmentioning

confidence: 93%

Lie symmetry analysis and numerical solutions for thermosolutal chemically reacting radiative micropolar flow from an inclined porous surface

Shamshuddin

Mishra

Bég

et al. 2018

Heat Trans. Asian Res.

View full text Add to dashboard Cite

Steady, laminar, incompressible thermosolutal natural convection flow of micropolar fluid from an inclined perforated surface with convective boundary conditions is studied. Thermal radiative flux and chemical reaction Nomenclature: , buoyancy ratio parameter; , Biot number; , Concentration of the solute (mol m −3 ); , skin friction coefficient; , real numbers; , wall couple stress; , specific heat at constant pressure (J Kg −1 K −1 ); ∞ , free stream concentration (mol m −3 ); , molecular diffusivity of reactive species (m 2 s −1 )

show abstract

\frac{\partial u^{'}}{\partial x^{'}} + \frac{\partial v^{'}}{\partial y^{'}} = 0,

u \frac{\partial u^{'}}{\partial x^{'}} + v^{'} \frac{\partial u^{'}}{\partial y^{'}} = (\frac{μ + k}{ρ}) \frac{\partial^{2} u^{'}}{\partial {y^{'}}^{2}} + g β_{T} false(T - T_{\infty} false) cos α + g β_{c} false(C - C_{\infty} false) cos α + \frac{k}{ρ} \frac{\partial N^{'}}{\partial y^{'}},

u^{'} \frac{\partial N^{'}}{\partial x^{'}} + v^{'} \frac{\partial N^{'}}{\partial y^{'}} = \frac{γ}{ρ j^{'}} \frac{\partial^{2} N^{'}}{\partial {y^{'}}^{2}} - \frac{k}{ρ j^{'}} (\frac{\partial u^{'}}{\partial y^{'}} + 2 N^{'}),

u^{'} \frac{\partial T}{\partial x^{'}} + v^{'} \frac{\partial T}{\partial y^{'}} = \frac{κ}{ρ C_{p}} \frac{\partial^{2} T}{\partial}

…”

Section: Reactive Radiative Micropolar Thermo‐solutal Modelmentioning

confidence: 93%

Lie symmetry analysis and numerical solutions for thermosolutal chemically reacting radiative micropolar flow from an inclined porous surface

Shamshuddin

Mishra

Bég

et al. 2018

Heat Trans. Asian Res.

View full text Add to dashboard Cite

show abstract

“…The values in (16) are used in the recurrence relations (11)- (15) and 1 , 2 , 3 , 4 , 5 , and 6 are calculated such that they satisfy the boundary conditions at = 1; then we obtain nondimensional velocity components, temperature distribution, and concentration for various parameters by substituting these constants into the respective Taylor series.…”

Section: Re Pr Cosmentioning

confidence: 99%

“…Yao et al [15] analyzed an incompressible laminar viscous fluid flow and heat transfer over a stretching/shrinking sheet with convective boundary conditions and have found that the convective boundary condition results in a temperature slip at the wall. RamReddy et al [16] studied an incompressible laminar free convective micropolar fluid flow along a permeable vertical plate with the convective boundary condition and obtained a numerical solution using spectral quasilinearization method. Postelnicu [17] examined the effects of Soret and Dufour on a two-dimensional steady stagnation point flow of a free convective Darcian fluid with suction/injection and the governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformations and then solved by the Keller box method.…”

Section: Introductionmentioning

confidence: 99%

Influence of Cross-Diffusion on Slip Flow and Heat Transfer of Chemically Reacting UCM Fluid between Porous Parallel Plates with Hall and Ion Slip Currents

Ojjela

Kambhatla

Kumar

et al. 2016

Journal of Computational Engineering

View full text Add to dashboard Cite

The present paper deals with the Hall and ion slip currents on an incompressible unsteady free convection flow and heat transfer of an upper convected Maxwell fluid between porous parallel plates with Soret and Dufour effects by considering the velocity slip and convective boundary conditions. Assume that there are periodic injection and suction at the lower and upper plates, respectively. The temperature and concentration at the lower and upper plates change periodically with time. The flow field equations are reduced to nonlinear ordinary differential equations by using similarity transformations and a semi-analytical-numerical solution has been obtained by the differential transform method. The velocity components, temperature distribution, and concentration with respect to different fluid and geometric parameters are discussed in detail and presented in the form of graphs. It is observed that the Biot number increases the temperature and concentration of the fluid. Further, the concentration of the fluid is enhanced whereas the temperature decreases with increasing slip. The present results are compared with the existing literature and are found to be in good agreement.

show abstract

“…(Chamka et al, 2014) studied the effects of viscous dissipation and magnetic field on free convection flow in a non Darcy porous medium saturated with a nanofluid under convective boundary condition. (RamReddy et al, 2015) analyzed the similarity solution of free convection flow of an incompressible micropolar fluid with convective boundary condition using lie group transformations. investigated the influence of convective boundary condition on MHD mixed convection flow of micropolar fluid towards nonlinear stretched sheet.…”

Section: Introductionmentioning

confidence: 99%

Influence of Convective Boundary Condition on Nonlinear Thermal Convection Flow of a Micropolar Fluid Saturated Porous Medium With Homogeneous-Heterogeneous Reactions

RamReddy¹,

Pradeepa²

2017

Frontiers in Heat and Mass Transfer

View full text Add to dashboard Cite

A numerical approach has been used to analyze the effects of homogeneous-heterogeneous reaction and nonlinear density temperature variation over a vertical plate in an incompressible micropolar fluid flow saturated Darcy porous medium. In addition, convective boundary condition is incorporated in a micropolar fluid model. The similarity representation for the set of partial differential equations is attained by applying Lie group transformations. The resulting non-dimensional equations are worked out numerically by spectral quasi-linearization method. Less temperature and wall couple stress coefficient, but more velocity, skin friction, species concentration, and heat transfer rate are noticed by enhancing the nonlinear convection parameter. It is also observed that as the strength of homogeneous and heterogeneous reaction parameters increases, the species concentration and mass transfer rate reduces.

show abstract

Similarity Solution for Free Convection Flow of a Micropolar Fluid under Convective Boundary Condition via Lie Scaling Group Transformations

Cited by 17 publications

References 30 publications

Lie symmetry analysis and numerical solutions for thermosolutal chemically reacting radiative micropolar flow from an inclined porous surface

Lie symmetry analysis and numerical solutions for thermosolutal chemically reacting radiative micropolar flow from an inclined porous surface

Influence of Cross-Diffusion on Slip Flow and Heat Transfer of Chemically Reacting UCM Fluid between Porous Parallel Plates with Hall and Ion Slip Currents

Influence of Convective Boundary Condition on Nonlinear Thermal Convection Flow of a Micropolar Fluid Saturated Porous Medium With Homogeneous-Heterogeneous Reactions

Contact Info

Product

Resources

About