Influence of Soret and Dufour on Free Convective Second Grade Fluid Flow Between Porous Parallel Plates with Chemical Reaction

Ramesh, K.; Ojjela, Odelu

doi:10.1007/s40819-018-0535-5

Cited by 2 publications

(4 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The equations that govern the second‐grade MHD fluid flow and heat and mass transfer in the absence of body forces are

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

\begin{matrix} 0.33emtrue \\ left ρ true(\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} true) & left = & left - \frac{\partial p}{\partial x} + μ true(\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} true) + a_{1} true(\frac{\partial^{3} u}{\partial x^{2} \partial t} + \frac{\partial^{3} u}{\partial y^{2} \partial t} + u \frac{\partial^{3} u}{\partial x^{3}} + v \frac{\partial^{3} u}{\partial x^{2} \partial y} \\ left & left & left + v \frac{\partial^{3} u}{\partial y^{3}} + 3 \frac{\partial u}{\partial x} \frac{\partial^{2} u}{\partial y^{2}} + \frac{\partial v}{\partial x} \frac{\partial^{2} u}{\partial x \partial y} + 4 \frac{\partial v}{\partial x} \frac{\partial^{2} v}{\partial x^{2}} - 4 \frac{\partial u}{\partial y} \frac{\partial^{2} u}{\partial y \partial x} - 2 \frac{\partial v}{\partial x} \frac{\partial^{2} v}{\partial y^{2}} \\ left & left & left - 2 \frac{\partial v}{\partial y} \frac{\partial^{2} v}{\partial y \partial x} - \frac{\partial v}{\partial y} \frac{\partial^{2} u}{\partial} \end{matrix}

…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…According to

u (x, λ, t) = true(\frac{U_{0}}{a} - \frac{V_{1} x}{h} true) f^{/} (λ) e^{i ω t},

v (x, λ, t) = V_{1} f (λ) e^{i ω t},

T (x, λ, t) = true(T_{1} + \frac{μ V_{1}}{ρ h c} true(ϕ_{1} (λ) + {(\frac{U_{0}}{a V_{1}} - \frac{x}{h})}^{2} ϕ_{2} (λ) true) true) e^{i ω t},

C (x, λ, t) = true(C_{1} + \frac{\overset{n_{A}}{true}}{h υ} true(g_{1} (λ) + {(\frac{U_{0}}{a V_{1}} - \frac{x}{h})}^{2} g_{2} (λ) true) true) e^{i ω t},

where

λ = y / h

U_{0}

‐average velocity at entrance,

a = V_{2} / V_{1} - 1

, that is, suction/injection ratio,

…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…Homotopy analysis is used to solve a second‐grade fluid by Raftari et al The problems on MHD second‐grade fluid flow on two different geometries are considered by Ariel . Recently, Ramesh and Ojjela examined the effects of chemical reaction and double diffusion on heat and mass transfers. There are many methods developed to solve nonlinear boundary value problems emerging in the field of fluid mechanics.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effects of double stratification on MHD chemically reacting second‐grade fluid through porous medium between two parallel plates

Kumar

Ojjela

Sastry

2019

Heat Trans. Asian Res.

Self Cite

View full text Add to dashboard Cite

The present study focuses on the study of heat transfer in a magnetohydrodynamic double stratification fluid flow through porous channel. In getting the solution of Navier-Stokes equations, we have adapted the similarity transformation technique to convert the partial differential equations into a coupled system of nonlinear ordinary differential equations. We further applied the fourth-order Runge-Kutta method with shooting technique to solve the problem numerically. The results are exhibited via graphs, and the analysis has been addressed for various flow characteristics with respect to the parameters concerned. It is found that thermal stratification enhances both temperature and heat transfer rates, and solutal stratification enhances concentration and mass transfer rates. Concentration decreases with increasing chemical reaction and it increases with stratification. A significant variation is observed between concentration profiles in the presence of stratification. K E Y W O R D S double stratification, magnetohydrodynamic, second-grade fluid, shooting method | INTRODUCTIONConvection with porous boundaries has a significant importance in science and technology. For example, heat exchangers, solar collectors, drying processes, geothermal and oil recoveries, aircraft cabin insulations, and so forth. Raptis 1 has considered a two-dimensional laminar flow over an infinite vertical plate. Taking heat source into account, Rana et al 2 solved the problem of free convection flow in a porous channel. Sacheti and Singh 3 studied the effects of viscous and Darcy dissipations in a convection fluid flow through a rotating vertical porous channel. The effects of heat source and slip on the natural convection oscillatory viscous fluid flow between porous parallel plates with mass transfer are presented by Sharma and Sharma. 4 Job and Gunakala 5 investigated the Joule dissipations on free convective magnetohydrodynamic (MHD) nanofluid flow in a wavy trapezoidal enclosure.As growth rate of cultured species is affected by the variations in temperature and concentration levels of oxygen and hydrogen, so it is very important to have control over the thermal and solutal stratification. This is mostly occurs in ground water reservoirs, oceans, and so forth. Neagu 6 analyzed the effects of double stratifications on the natural convective flow over a wavy channel in the presence of viscous forces along with heat and mass fluxes. Convection in a viscous fluid over thermally stratified porous medium along a vertical plate is discussed by Tewari and Singh. 7 Ibrahim and Makinde 8 employed finite difference method for the problem of boundary layer nanofluid flow with double stratification. Rathish Kumar and Singh 9 noticed the impact of double diffusion on the free convection viscous fluid flow in a thermally stratified vertical porous enclosure.From the above studies, one can analyze the natural convective Newtonian fluids with and without stratification. It is also important to study of the aforementioned properties with non-Newtoni...

show abstract

“…The equations that govern the second‐grade MHD fluid flow and heat and mass transfer in the absence of body forces are

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

\begin{matrix} 0.33emtrue \\ left ρ true(\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} true) & left = & left - \frac{\partial p}{\partial x} + μ true(\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} true) + a_{1} true(\frac{\partial^{3} u}{\partial x^{2} \partial t} + \frac{\partial^{3} u}{\partial y^{2} \partial t} + u \frac{\partial^{3} u}{\partial x^{3}} + v \frac{\partial^{3} u}{\partial x^{2} \partial y} \\ left & left & left + v \frac{\partial^{3} u}{\partial y^{3}} + 3 \frac{\partial u}{\partial x} \frac{\partial^{2} u}{\partial y^{2}} + \frac{\partial v}{\partial x} \frac{\partial^{2} u}{\partial x \partial y} + 4 \frac{\partial v}{\partial x} \frac{\partial^{2} v}{\partial x^{2}} - 4 \frac{\partial u}{\partial y} \frac{\partial^{2} u}{\partial y \partial x} - 2 \frac{\partial v}{\partial x} \frac{\partial^{2} v}{\partial y^{2}} \\ left & left & left - 2 \frac{\partial v}{\partial y} \frac{\partial^{2} v}{\partial y \partial x} - \frac{\partial v}{\partial y} \frac{\partial^{2} u}{\partial} \end{matrix}

…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…According to

u (x, λ, t) = true(\frac{U_{0}}{a} - \frac{V_{1} x}{h} true) f^{/} (λ) e^{i ω t},

v (x, λ, t) = V_{1} f (λ) e^{i ω t},

T (x, λ, t) = true(T_{1} + \frac{μ V_{1}}{ρ h c} true(ϕ_{1} (λ) + {(\frac{U_{0}}{a V_{1}} - \frac{x}{h})}^{2} ϕ_{2} (λ) true) true) e^{i ω t},

C (x, λ, t) = true(C_{1} + \frac{\overset{n_{A}}{true}}{h υ} true(g_{1} (λ) + {(\frac{U_{0}}{a V_{1}} - \frac{x}{h})}^{2} g_{2} (λ) true) true) e^{i ω t},

where

λ = y / h

U_{0}

‐average velocity at entrance,

a = V_{2} / V_{1} - 1

, that is, suction/injection ratio,

…”

Section: The Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effects of double stratification on MHD chemically reacting second‐grade fluid through porous medium between two parallel plates

Kumar

Ojjela

Sastry

2019

Heat Trans. Asian Res.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Astanina et al have investigated transient free convective with a temperature based viscosity inside a square cavity. Ramesh and Ojjela have discussed natural convective chemical reacting second grade fluid flow confined between parallel plates channnel with Dufor and Soret effects. Rehman et al have studied mixed convective stagnation point flow of Williamson fluid flow by an inclined stretching cylinder.…”

Section: Introductionmentioning

confidence: 99%

Entropy generation analysis of natural convective chemically reacting squeezing flow of Casson fluid between parallel disks with Hall and Ion slip currents

Ramesh

Ojjela

2019

Heat Trans. Asian Res.

Self Cite

View full text Add to dashboard Cite

This paper concerns the second law analysis of free convective squeezing flow of a chemically reacting Casson fluid confined between two parallel disks with Hall and Ion slip effects. The upper one is impermeable and the lower disk is porous. The linear momentum, energy balance and mass partial differential equations converted as system of ODEs by similarity transformations and tackled with shooting method via fourth order Runge-Kutta scheme. The impact of various dimensionless geometric and fluid parameters on the velocity fields, temperature and concentration fields, entropy generation and Bejan numbers are studied and presented in the form of pictorially. The present results are correlated with already published outcomes for viscous case and found to be good agreement. The Bejan number of the fluid enhances with Ion slip parameter, whereas the concentration profile of the fluid is decreases with increasing of the Casson fluid parameter. The entropy generation of the fluid is enhanced with Eckert number whereas the Bejan number is decreased with suction/blowing parameter K E Y W O R D S chemical reaction, entropy generation, free convection, Hall and Ion slip effects

show abstract

Influence of Soret and Dufour on Free Convective Second Grade Fluid Flow Between Porous Parallel Plates with Chemical Reaction

Cited by 2 publications

References 33 publications

Effects of double stratification on MHD chemically reacting second‐grade fluid through porous medium between two parallel plates

Effects of double stratification on MHD chemically reacting second‐grade fluid through porous medium between two parallel plates

Entropy generation analysis of natural convective chemically reacting squeezing flow of Casson fluid between parallel disks with Hall and Ion slip currents

Contact Info

Product

Resources

About