Startseite Numerical study of chemically reacting unsteady Casson fluid flow past a stretching surface with cross diffusion and thermal radiation
Artikel Open Access

Numerical study of chemically reacting unsteady Casson fluid flow past a stretching surface with cross diffusion and thermal radiation

  • K. Pushpalatha , J.V. Ramana Reddy , V. Sugunamma EMAIL logo und N. Sandeep EMAIL logo
Veröffentlicht/Copyright: 2. April 2017
Artikel downloaden (PDF)
Veröffentlichen auch Sie bei De Gruyter Brill
Manuskript einreichen Informationen für Autor*innen
Open Engineering
Aus der Zeitschrift Open Engineering Band 7 Heft 1

Abstract

The problem of an unsteady MHD Casson fluid flow towards a stretching surface with cross diffusion effects is considered. The governing partial differential equations are converted into a set of nonlinear coupled ordinary differential equations with the help of suitable similarity transformations. Further, these equations have been solved numerically by using Runge-Kutta fourth order method along with shooting technique. Finally, we studied the influence of various non-dimensional governing parameters on the flow field through graphs and tables. Results indicate that Dufour and Soret numbers have tendency to enhance the fluid velocity. It is also found that Soret number enhances the heat transfer rate where as an opposite result is observed with Casson parameter. A comparison of the present results with the previous literature is also tabulated to show the accuracy of the results.

Keywords: thermal radiation; MHD; unsteady; chemical reaction; cross diffusion effects; stretching surface

1 Introduction

The problems of heat and mass transfer effects on MHD flow have become more important in many engineering processes. The effect of radiation can be quite significant at high operating temperature. The fluid not fulfilling the Newton’s rule of cooling is termed as non-Newtonian. A few of them comprise shampoos, sauce, pastes, paints, colloidal solutions, ketchup etc. Casson fluid is also a non-Newtonian fluid. Presently, most of the researchers of fluid mechanics are concentrating their research on this type of fluids due to their rheological applications in chemical and mechanical engineering. The unsteady free convection of non-Newtonian flows over a stretching surface have received much attention in recent days due to its wide applications in many studies like geophysical, geothermal, oil reservoir engineering and astrophysical.

Ibrahim et al. [1] discussed the effects of radiation and chemical reaction on an unsteady hydrodynamic free convection flow over an oscillating vertical plate with heat source. Ishak et al. [2] investigated the heat transfer characteristics of the boundary layer flow past an unsteady vertical stretching sheet. Through this study, it is found that increase in unsteadiness parameter decreases the velocity, temperature profiles. Furthermore, Bhargava et al.[3] studied the Soret and Dufour effects on MHD free convection flow past a semi infinite vertical plate in the presence of thermal radiation. The influence of mass transfer and radiation on MHD unsteady flow past a stretching sheet was reported by Hayat et al. [4]. Vempati and Laxmi-Narayana-Gari [5] analyzed cross-diffusion effects on unsteady hydrodynamic flow over an infinite vertical flat plate with thermal radiation. Chamkha and Aly [6] studied the stagnation point flow of a polar fluid over a stretching surface in a porous medium with thermo diffusion and diffusion thermo effects. Pal and Mondal [7] discussed the unsteady MHD non-Darcy mixed convective flow towards a stretching surface with heat and mass transfer effects. In this study, they concluded that temperature profiles increases with Dufour number. The stagnation point flow of a micropolar fluid past a stretching sheet with Soret and Dufour effects was investigated by Hayat et al. [8]. Mustafa et al.[9] studied the unsteady boundary layer flow of a Casson fluid due to an impulsively oscillating flat plate. From this paper, it is found that an increase in Casson parameter reduces the velocity. The influence of thermal radiation on chemically reacting MHD free convective flow past a vertical plate was studied by Sandeep et al. [10].

The boundary layer flow of non-Newtonian fluids over a stretching surface in presence of Lorentz force has magnetized the attention of many authors owing to its significance in many engineering processes like oil exploration, nuclear reactors, plasma studies, MHD generators and boundary layer control in aerofoil. In view of this, Hayat et al. [11] reported the cross-diffusion effects on MHD steady flow of a Casson fluid past a stretched surface. The study of an unsteady magneto hydrodynamic mixed convection flow through a radiative vertical plate in a porous medium with Dufour and Soret and effects was carried out by Sharma et al. [12] and concluded that velocity and concentration profiles decreases with increasing values of chemical reaction parameter. Zheng et al.[13] analyzed the unsteady MHD flow over a moving stretching surface with Soret and Dufour effects. Mukhopadhyay [14] studied the flow characteristics of Casson fluid towards an unsteady stretching surface with thermal radiation. Further, similar type of study on the stagnation point flow was carried out by Bhattacharya [15].

The flow due to stretching of a sheet has countless scientific and industrial applications such as spinning of fiber, glass blowing, metal continuous casting, manufacturing of plastic covers, paper plates production, cooling of a big magnetite plates in a bath and suspension of particles and so on.The impact of cross-diffusion on unsteady MHD mixed convection flow past a stretching surface was discussed by Alsaadi et al. [16]. Abbasi et al. [17] reported the Soret and Dufour effects on peristaltic transport of magneto hydrodynamic fluid with variable viscosity and found that an increase in Soret number reduces the concentration profiles. The effect of thermo diffusion on chemically reacting dusty viscous flow was studied by Reddy et al. [18]. In that paper, it is found that increasing values of Soret number enhances the fluid velocity. Sugunamma et al. [19] analyzed the influence of magnetic field and thermal radiation on heat transfer of the nanofluid flow towards a rotating frame. Pramanik [20] investigated the heat transfer effects on the Casson fluid past an exponentially stretching surface with suction/blowing and found that friction factor is higher for suction than that of blowing. Mean while, the unsteady free convection flow of MHD Casson fluid over a moving vertical plate in a porous medium was studied by Khalid et al. [21]. Krishna et al. [22] studied the influence of chemical reaction and thermal radiation on free convective MHD flow through a permeable stretching sheet with Soret and Dufour effects. The study of mixed convection flow of incompressible Eyring-Powell nanofluid past a stretching surface was carried out by Malik et al. [23]. The presence of Soret and Dufour effects on nanofluid flow past an exponentially stretching sheet under the influence of aligned magnetic field was discussed by Sulochana et al. [24].

Raju et al. [25] reported the unsteady MHD flow of a nanofluid towards an oscillating vertical plate embedded in a porous medium with radiation and Soret effects. Mythili et al. [26] investigated the effect of chemical reaction on Casson fluid flow through a permeable vertical cone with non-uniform heat source/sink using the finite difference method of Crank-Nicolson type. In that paper they concluded that temperature dependent heat source/sink parameters play a pivotal role in controlling the heat transfer. The influence of thermal radiation and variable permeability on mixed convective flow of MHD fluid over a vertical wavy channel with travelling thermal waves was analyzed by Narayana [27]. Recently, Raju and Sandeep [28] discussed the Soret and Dufour effects on bio-convection flow of a non-Newtonian fluid past a rotating cone with heat and mass transfer. Very recently, the influence of non uniform heat source/sink on nanofluid due to an unsteady permeable stretching surface was reported by Raju et al. [29].

The main aim behind the present study is to analyze the effects of cross diffusion on Casson fluid over an unsteady stretching surface. To the best of author’s knowledge none of the researchers carried out this type of study. So, by making use of all the references mentioned above we make an attempt to study the unsteady flow behavior of Casson fluid over a stretching surface with buoyancy effects.

2 Mathematical modeling

Consider an unsteady two dimensional laminar flow of electrically conducting non-Newtonian Casson fluid over a stretching surface. It is assumed that the unsteady fluid flow, heat and mass transfer begins at t = 0. It is also assumed that the surface is being stretched with velocity Uw(x, t) = ax/1 - ct along the x–axis as shown Figure 1. Here a is the initial stretching rate and B=B0/1−ct is the magnetic field applied along the y– axis, which is perpendicular to the x– axis. Here B0 is the strength transverse magnetic field. The mass transfer vw(t) assumed to be perpendicular to the stretching surface. When the sheet starts to move with velocity Uw(x, t) the surface temperature Tw(x, t) and concentration Cw(x, t) will suddenly raise to T∞, C∞ respectively. Also, it is assumed that Tw > T∞, which corresponds to an assisting flow.

Figure 1 Physical configuration and coordinate system
Figure 1

Physical configuration and coordinate system

The rheological equation of state for the Cauchy stress tensor of Casson fluid can be written as [20, 21]

τij=2(μB+py/2π)eij,π>πc2(μB+py/2πc)eij,π<πc

Where π = eijeij and eij is the (i,j)th component of the deformation rate with itself, πc is the critical value of this product based on the non-Newtonian model, µB is the plastic dynamic viscosity of the non -Newtonian fluid and py is yield stress of the fluid.

Under above made assumptions the governing equations of the flow are given by,

(1)∂ll∂x+∂v∂y=0,
(2)ρ∂u∂t+u∂ll∂x+v∂u∂y=μ1+1β∂2u∂y2+g(ρβT)(T−T∞)+g(ρβC)(C−C∞)−σB2u,
(3)∂T∂t+u∂T∂x+v∂T∂y=α∂2T∂y2−1ρcp∂qr∂y+DmKTcscp∂2C∂y2,
(4)∂C∂t+u∂C∂x+v∂C∂y=Dm∂2C∂y2−kl(C−C∞)+DmKTTm∂2T∂y2,

With the boundary conditions

(5)u=Uw(x,t),v=vw(t),T=Tw(x,t),C=Cw(x,t)

at y = 0,

(6)u→0,T→T∞,C→C∞,asy→∞

where u and v are the velocity components in the x, y directions, t refers to the time, β=μB2πc/py is the Casson parameter, ρ and µ are density and the dynamic viscosity of the Casson fluid respectively, βT and βC are the coefficients of volumetric expansion due to temperature and concentration differences respectively, g is the acceleration due to gravity, T, C are the fluid temperature and concentration, σ is the electrical conductivity, α is the thermal diffusivity, Dm is the species diffusivity, KT is the thermal diffusion ratio, cs is the concentration susceptibility, cp is the specific heat at constant pressure, kl is the chemical reaction parameter and Tm is the mean fluid temperature.

The quantity qr on the right hand side of temperature equation (3) represents the radiative flux and is given by,

(7)qr=−16σ⋆T∞⋆3k⋆∂T∂y,

In eqn. (7), σ* is the Stephan-Boltzmann constant, k* is the mass absorption coefficient, T∞ is the free stream temperature.

Also,

(8)Uw(x,t)=ax1−ct,vw(t)=v0(1−ct)1/2,Tw(x,t)=T∞+bx(1−ct)2,Cw(x,t)=C∞+bx(1−ct)2,

Here a, c are constants (a > 0 and c ≥ 0 with ct < 1). Also, b is a constant and has dimension temperature/concentration length (b = 0 refers to absence of buoyancy forces).

We now introduce the similarity transformation as,

(9)η=av(1−ct)1/2y,ψ(x,y)=va1−ct1/2xf(η)T=T∞+bx(1−ct)2θ(η),C=C∞+bx(1−ct)2ϕ(η),

Here ψ(x, y) is the stream function that satisfies the continuity equation (1) with

(10)u=∂ψ∂y=ax1−ctf′(η),v=−∂ψ∂x=−va1−ct1/2f(η),

Using equations (7)–(10) the equations (2)–(5) can be transformed into

(11)1+1βf−f′(f′+A)−f″12Aη−f+λθ+λ⋆ϕ−Mf′=0
(12)1Pr1+4R3θ″+Duϕ″−θ(2A+f′)−θ′12Aη−f=0,
(13)1Scϕ″−Krϕ+Srθ″−ϕ(2A+f′)−ϕ′12Aη−f=0,

The transformed boundary conditions are

(14)f(η)=fw,f′(η)=1,θ(η)=1,ϕ(η)=1,f′(η)=1,ϕ(η)=1,θ(η)=1atη=0
(15)f′(η)→0,θ(η)→0,ϕ(η)→0asη→∞

Where primes denotes differentiation with respect to η, here η is the similarity variable, A = c/a is the unsteadiness parameter, M = σB02/ ρa is the magnetic field parameter, λ = gβTb/a2 is the thermal buoyancy parameter, λ* = gβCb/a2 is concentration buoyancy parameter, R=4σ⋆T∞3kk⋆ is the radiation parameter, Dn=DmKTcscpv is the Dufour number, Pr=ρcpvk is the Prandtal number, Sc = υf/Dm is the Schmidt number, Kr = kl(1 - ct)/a is the chemical reaction parameter and Sr=DmKTTmv is the Soret number.

The physical quantities of engineering interest are Skin friction coefficient (Cfx), local Nusselt number (Nux) and Sherwood number (Shx).These are given by,

(16)CfXReX1/2=1+1βf″(0),NuXReX−1/2=−1+4R3θ′(0),ShXReX−1/2=−ϕ′(0),

In the above equation Rex = xUw(x, t)/υ is the Reynolds number.

3 Results and discussion

Equations (11)–(13) subject to the boundary conditions (14)–(15) have been solved numerically by adopting Runge-Kutta fourth order method along with shooting technique. Further, the effects of a few pertinent parameters on velocity, temperature and concentration fields have been discussed through figures 2–11.

Figure 2 Velocity profiles for different values of Casson parameter β
Figure 2

Velocity profiles for different values of Casson parameter β

Figure 3 Temperature and concentration profiles for different values of Casson parameter β
Figure 3

Temperature and concentration profiles for different values of Casson parameter β

Figure 4 Velocity profiles for different values of Dufour number Du
Figure 4

Velocity profiles for different values of Dufour number Du

Figure 5 Temperature and concentration profiles for different values of Dufour number Du
Figure 5

Temperature and concentration profiles for different values of Dufour number Du

Figure 6 Velocity profiles for different values of Soret number Sr
Figure 6

Velocity profiles for different values of Soret number Sr

Figure 7 Temperature and concentration profiles for different values of Soret number Sr
Figure 7

Temperature and concentration profiles for different values of Soret number Sr

Figure 8 Velocity profiles for different values of radiation parameter R
Figure 8

Velocity profiles for different values of radiation parameter R

Figure 9 Temperature and concentration profiles for different values of radiation parameter R
Figure 9

Temperature and concentration profiles for different values of radiation parameter R

Figure 10 Velocity profiles for different values of unsteadiness parameter A
Figure 10

Velocity profiles for different values of unsteadiness parameter A

Figure 11 Temperature and concentration profiles for different values of unsteadiness parameter A
Figure 11

Temperature and concentration profiles for different values of unsteadiness parameter A

Then after, we presented the effects of same parameters on skin friction coefficient, Nusselt and Sherwood numbers in table 1. Table 2 depicts the comparison of present results within the existed literature (Ishak etal. [2]). This shows the correctness of our results and the numerical technique we adopted. For the results, we considered the values of physical parameters as β = 0.3, η = 0.1, fw = 0.2, R = 1, M = 2, Pr = 0.7 (air), Sr = Du = 0.5, A = 1, λ = λ* = 1.5, Sc = 0.6 and Kr = 0.5. These values have been kept in common for the complete study of results unless otherwise specified in respective figures and tables.

Table 1

The influence of various physical parameters on skin friction, heat and mass transfer coefficients.

DuSrβRAf′′(0)-θ′(0)-ϕ′(0)
0.5-0.65270.85561.4484
3.0-0.60330.02731.6373
6.0-0.5348-1.58182.0287
0.2-0.65740.84811.5076
1.8-0.63180.89201.1655
4.0-0.59330.97240.5505
0.1-0.44950.87131.4631
0.2-0.57350.86131.4538
0.3-0.65270.85561.4484
0.5-0.66681.01411.4158
2.5-0.62610.62871.4906
5.0-0.60210.47401.5157
1.0-0.65270.85561.4484
2.0-0.81881.09631.7615
3.0-0.95281.29042.0234

Table 2

Comparison of the values of (-θ'(0)) with the previous work Ishak et al. [2], When λ* = Du = Sr = Sc = R = 0 and β → ∞.

AλPr-θ′(0) Ishak et al. [2]-θ′(0) Present values
000.720.80860.808871
001.01.00001.000010
011.01.08731.087641
031.01.18531.185812
101.01.68201.682101
111.01.70391.703990

Figures 2–3 are plotted to examine the influence of Casson parameter (β) on velocity, temperature and concentration profiles. In figure 2, we see that velocity increases with β, because, an increase in β increases in plastic dynamic viscosity, which creates a resistance in the fluid motion. From figure 3, one can easily say that increasing values of Casson parameter (β) enhances the temperature as well as concentration distribution. The reason behind this is Casson parameter enhances the thermal and concentration boundary layer thicknesses. Also, it is worth to mention that β significantly affects the temperature profiles while compared with concentration profiles.

The effect of Dufour number (Du) on velocity, temperature and concentration profiles ispresented in figures 4–5. From figure 4, we may conclude that Dufour number enhances the fluid velocity. We observe the same behavior in temperature profiles. But reverse trend is followed by concentration profiles with an increase in the values of Du. Generally, increase in Dufour number produces heat flux in the fluid. This leads to an enhancement in the thermal boundary layer thickness. Figures 6–7 illustrate the influence of Soret number (Sr) on the flow field. From figure 6, we observe that velocity is an increasing function of Soret number (Sr). One can say from figure 7 that increasing values of Soret number reduces the temperature distribution but increases the concentration distribution.

Figures 8–9 disclose the impact of radiation parameter (R) on velocity, temperature and concentration fields. From these figures, we found that velocity and temperature profiles increase with an increase in R. This may happen due to the fact that increase in radiation parameter releases heat energy in the flow. From figure 9, we notice that radiation parameter depreciates the concentration profiles. It is important to mention that temperature profiles are more effected by R while compared with concentration profiles. Figs. 10–11 exhibit the impact of unsteadiness parameter (A) on the velocity, temperature and concentration profiles respectively. It is clear from these figures that an increase in unsteadiness parameter slowdowns the fluid motion but suppress the temperature and concentration profiles. This agrees with the results obtained by Ishak et al. [2]. From Fig. 11, it can be also noted that A shows same amount of variation on temperature and concentration distribution.

From table 1, it is interesting to note that Soret and Dufour numbers have the tendency to enhance the friction factor. A rise in the values of Soret number or unsteadiness parameter enhances the heat transfer rate. Meanwhile, increasing values of either Dufour number or radiation parameter decreases the rate of heat transfer but increase the mass transfer rate significantly.

4 Concluding remarks

This paper deals with the study of thermo diffusion and diffusion thermo effects on Casson fluid flow over an unsteady stretching surface in presence of thermal radiation and magnetic field. The influence of various governing parameters has been examined with the help of graphs and tables. The conclusions are summarized below.

  • Casson parameter and unsteadiness parameter have tendency to depreciate the velocity distribution.

  • Temperature and concentration profiles have been significantly affected by Dufour and Soret numbers respectively.

  • A raise in Soret number or unsteadiness parameter increases the heat transfer rate.

  • Dufour number significantly suppresses the rate of heat transfer.

  • Sherwood number increases with an increase in the values of Dufour number or radiation parameter.

References

[1] Ibrahim F.S., Elaiw A.M., Bakr A.A., et al., Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction, Comm. Nonlinear Sci. Num. Sim., 2008, 13, 1056-1066.10.1016/j.cnsns.2006.09.007Suche in Google Scholar

[2] Ishak A., Nazar R., Pop I., et al., Boundary layer flow and heat transfer over an unsteady stretching vertical surface, Meccanica, 2009, 44, 369-375.10.1007/s11012-008-9176-9Suche in Google Scholar

[3] Bhargava R., Sharma R., Beg O.A., et al., Oscillatory chemically-reacting MHD free convection heat and mass transfer in a porous medium with soret and dufour effects: Finite element modeling, Int. J. Appl. Math. Mech., 2009, 5, 15-37.Suche in Google Scholar

[4] Hayat T., Qasim M., Abbas, Z., et al., Radiation and mass transfer effects on the magneto hydrodynamic unsteady flow induced by a stretching sheet, Z. Naturforsch., 2010, 65, 231-239.10.1515/zna-2010-0312Suche in Google Scholar

[5] Vempati S.R., Laxmi-Narayana-Gari A.B., Soret and dufour effects on unsteady MHD flow past an infinite vertical porous plate with thermal radiation, Appl. Math. Mech., 2010, 31, 1481-1496.10.1007/s10483-010-1378-9Suche in Google Scholar

[6] Chamkha A.J., Aly A.M., Heat and mass transfer in stagnation-point flow of a polar fluid towards a stretching surface in porous media in the presence of soret, dufour and chemical reaction effects, Chem. Eng. Comm., 2010, 198, 214-234.10.1080/00986445.2010.500161Suche in Google Scholar

[7] Pal D., Mondal H., Effects of Soret Dufour , chemical reaction and thermal radiation on MHD non-darcy unsteady mixed convective heat and mass transfer over a stretching sheet, comm. Nonlinear Sci. Num. Sim., 2011, 16, 1942-1958.10.1016/j.cnsns.2010.08.033Suche in Google Scholar

[8] Hayat T., Mustafa M., Obaidat S., et al., Soret and dufour effects on the stagnation-point flow of micropolar fluid towards a stretching sheet, J. Fluids Eng., 2011, 133.10.1115/1.4003505Suche in Google Scholar

[9] Mustafa M., Hayat T., Pop I., Aziz A., et al., Unsteady boundary layer flow of a casson fluid due to an impulsively started moving flat plate, Heat Trans. Asian Res., 2011, 40, 563-576.10.1002/htj.20358Suche in Google Scholar

[10] Sandeep N., Reddy A.V.B., Sugunamma V., et al., Effect of radiation and chemical reaction on transient MHD free convective flow over a vertical plate through porous media, Chem. Proc. Eng. Res., 2012, 2, 1-9.Suche in Google Scholar

[11] Hayat T., Shehzad S.A., Alsaedi A., Soret and dufour effects on magneto hydrodynamic (MHD) flow of Casson fluid, Appl. Math. Mech., 2012, 33, 1301-1312.10.1007/s10483-012-1623-6Suche in Google Scholar

[12] Sharma B.K., Yadav K., Mishra N.K., Chaudhary R.C., et al., Soret and dufour effects on unsteady MHD mixed convection flow past a radiative vertical porous plate embedded in a porous medium with chemical reaction, Appl. Math., 2012, 3, 717-723.10.4236/am.2012.37105Suche in Google Scholar

[13] Zheng L.C., Jin X., Zhang X.X., Zhang J.H., et al., Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with soret and dufour effects, Acta Mech. Sinica, 2013, 29, 667-675.10.1007/s10409-013-0066-6Suche in Google Scholar

[14] Mukhopadhyay, S., Effects of thermal radiation on casson fluid flow and heat transfer over an unsteady stretching surface subjected to suction/blowing, Chin. Phys., 2013, 22.10.1088/1674-1056/22/11/114702Suche in Google Scholar

[15] Bhattacharya K., MHD stagnation-point flow of casson fluid and heat transfer over a stretching sheet with thermal radiation, J. Therm. 2013, 2013.10.1155/2013/169674Suche in Google Scholar

[16] Alsaadi F.E., Shehzad S.A., Hayat T., Monaquel S.J., et al., Soret and dufour effects on the unsteady mixed convection flow over a stretching surface, J. Mech., 2013, 29, 623-632.10.1017/jmech.2013.44Suche in Google Scholar

[17] Abbasi F.M., Hayat T., Alsaedi A., Ahmed B., et al., Soret and dufour effects on peristaltic transport of MHD fluid with variable viscosity, Appl. Math. Info. Sci., 2014, 8, 211-219.10.12785/amis/080126Suche in Google Scholar

[18] Reddy J.V.R., Sugunamma V., Sandeep N., Krishna P.M., et al., Thermal diffusion and chemical reaction effects on unsteady MHD dusty viscous flow, Adv. Phys, Theor. Appl., 2015, 38, 7-21.10.1166/asem.2015.1765Suche in Google Scholar

[19] Sugunamma V., Reddy J.V.R., Raju C.S.K., Babu M.J., Sandeep N., et al., Effects of radiation and magnetic field on the flow and heat transfer of a nanofluid in a rotating frame, Ind. Eng. Lett., 2014, 4, 9-20.Suche in Google Scholar

[20] Pramanik S., Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation, Ain Shams Eng. J., 2014, 5, 205-212.10.1016/j.asej.2013.05.003Suche in Google Scholar

[21] Khalid A., Khan I., Khan I., Shafie S., et al., Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium, Eng. Res., 2015, 18, 309-317.10.1016/j.jestch.2014.12.006Suche in Google Scholar

[22] Krishna P.M., Vidyasagar G., Sandeep N., Sugunamma V., et al., Soret and dufour effects on MHD free convective flow over a permeable stretching surface with chemical reaction and heat source, Int. J. Sci. Eng. Res., 2015, 6, 143-147.Suche in Google Scholar

[23] Malik M.Y., Khan I., Hussain A., Salahuddin T., et al., Mixed convection flow of MHD Eyring-Powell nanofluid over a stretching sheet: A numerical study, AIP Adv.,2015, 5, Article Id: 117118.10.1063/1.4935639Suche in Google Scholar

[24] Sulochana C., Sandeep N., Sugunamma V., Kumar B.R., et al., Aligned magnetic field and cross-diffusion effects of a nanofluid over an exponentially stretching surface in porous medium, Appl. Nanosci. 2015, 6, 737-746.10.1007/s13204-015-0475-xSuche in Google Scholar

[25] Raju C.S.K., Babu M.J., Sandeep N., Sugunamma V., Reddy J.V.R., et al., Radiation and soret effects of MHD nanofluid flow over a moving vertical plate in porous medium, Chem. Proc. Eng. Res., 2015, 30, 9-23Suche in Google Scholar

[26] Mythili D., Sivaraj R., Rashidi M.M, Yang Z., et al., Casson fluid flow over a vertical cone with non-uniform heat source/sink and high order chemical reaction, J. Naval Arch. Mar. Eng., 2015, 12, 125-136.10.3329/jname.v12i2.25269Suche in Google Scholar

[27] Narayana P.V.S., Efects of variable permeability and radiation absorption on magneto hydrodynamic (MHD) mixed convective flow in a vertical wavy channel with travelling thermal waves, Prop. Pow. Res., 2015, 4, 150-160.10.1016/j.jppr.2015.07.002Suche in Google Scholar

[28] C.S.K. Raju, N. Sandeep, Heat and mass transfer in MHD non-Newtonian bio-convection flow over a rotating cone/plate with cross-diffusion, J. Mol. Liq., 2016, 215, 115-126.10.1016/j.molliq.2015.12.058Suche in Google Scholar

[29] C.S.K. Raju, N. Sandeep, M.J. Babu, et al., Effects of non uniform heat source/sink and chemical reaction on unsteady MHD nanofluid flow over a permeable stretching surface, Adv. Sci. Eng. Med.,2016, 8, 165-174.10.1166/asem.2016.1845Suche in Google Scholar

Received: 2016-4-11
Accepted: 2017-2-28
Published Online: 2017-4-2

© K. Pushpalatha et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Artikel in diesem Heft

  1. Regular Articles
  2. The Differential Pressure Signal De-noised by Domain Transform Combined with Wavelet Threshold
  3. Regular Articles
  4. Robot-operated quality control station based on the UTT method
  5. Regular Articles
  6. Regression Models and Fuzzy Logic Prediction of TBM Penetration Rate
  7. Regular Articles
  8. Numerical study of chemically reacting unsteady Casson fluid flow past a stretching surface with cross diffusion and thermal radiation
  9. Regular Articles
  10. Experimental comparison between R409A and R437A performance in a heat pump unit
  11. Regular Articles
  12. Rapid prediction of damage on a struck ship accounting for side impact scenario models
  13. Regular Articles
  14. Implementation of Non-Destructive Evaluation and Process Monitoring in DLP-based Additive Manufacturing
  15. Regular Articles
  16. Air purification in industrial plants producing automotive rubber components in terms of energy efficiency
  17. Regular Articles
  18. On cyclic yield strength in definition of limits for characterisation of fatigue and creep behaviour
  19. Regular Articles
  20. Development of an operation strategy for hydrogen production using solar PV energy based on fluid dynamic aspects
  21. Regular Articles
  22. An exponential-related function for decision-making in engineering and management
  23. Regular Articles
  24. Usability Prediction & Ranking of SDLC Models Using Fuzzy Hierarchical Usability Model
  25. Regular Articles
  26. Exact Soliton and Kink Solutions for New (3+1)-Dimensional Nonlinear Modified Equations of Wave Propagation
  27. Regular Articles
  28. Entropy generation analysis and effects of slip conditions on micropolar fluid flow due to a rotating disk
  29. Regular Articles
  30. Application of the mode-shape expansion based on model order reduction methods to a composite structure
  31. Regular Articles
  32. A Combinatory Index based Optimal Reallocation of Generators in the presence of SVC using Krill Herd Algorithm
  33. Regular Articles
  34. Quality assessment of compost prepared with municipal solid waste
  35. Regular Articles
  36. Influence of polymer fibers on rheological properties of cement mortars
  37. Regular Articles
  38. Degradation of flood embankments – Results of observation of the destruction mechanism and comparison with a numerical model
  39. Regular Articles
  40. Mechanical Design of Innovative Electromagnetic Linear Actuators for Marine Applications
  41. Regular Articles
  42. Influence of addition of calcium sulfate dihydrate on drying of autoclaved aerated concrete
  43. Regular Articles
  44. Analysis of Microstrip Line Fed Patch Antenna for Wireless Communications
  45. Regular Articles
  46. PEMFC for aeronautic applications: A review on the durability aspects
  47. Regular Articles
  48. Laser marking as environment technology
  49. Regular Articles
  50. Influence of grain size distribution on dynamic shear modulus of sands
  51. Regular Articles
  52. Field evaluation of reflective insulation in south east Asia
  53. Regular Articles
  54. Effects of different production technologies on mechanical and metallurgical properties of precious metal denture alloys
  55. Regular Articles
  56. Mathematical description of tooth flank surface of globoidal worm gear with straight axial tooth profile
  57. Regular Articles
  58. Earth-based construction material field tests characterization in the Alto Douro Wine Region
  59. Regular Articles
  60. Experimental and Mathematical Modeling for Prediction of Tool Wear on the Machining of Aluminium 6061 Alloy by High Speed Steel Tools
  61. Special Issue on Current Topics, Trends and Applications in Logistics
  62. 10.1515/eng-2017-0001
  63. Special Issue on Current Topics, Trends and Applications in Logistics
  64. The Methodology of Selecting the Transport Mode for Companies on the Slovak Transport Market
  65. Special Issue on Current Topics, Trends and Applications in Logistics
  66. Determinants of Distribution Logistics in the Construction Industry
  67. Special Issue on Current Topics, Trends and Applications in Logistics
  68. Management of Customer Service in Terms of Logistics Information Systems
  69. Special Issue on Current Topics, Trends and Applications in Logistics
  70. The Use of Simulation Models in Solving the Problems of Merging two Plants of the Company
  71. Special Issue on Current Topics, Trends and Applications in Logistics
  72. Applying the Heuristic to the Risk Assessment within the Automotive Industry Supply Chain
  73. Special Issue on Current Topics, Trends and Applications in Logistics
  74. Modeling the Supply Process Using the Application of Selected Methods of Operational Analysis
  75. Special Issue on Current Topics, Trends and Applications in Logistics
  76. Possibilities of Using Transport Terminals in South Bohemian Region
  77. Special Issue on Current Topics, Trends and Applications in Logistics
  78. Comparison of the Temperature Conditions in the Transport of Perishable Foodstuff
  79. Special Issue on Current Topics, Trends and Applications in Logistics
  80. E-commerce and its Impact on Logistics Requirements
  81. Topical Issue Modern Manufacturing Technologies
  82. Wear-dependent specific coefficients in a mechanistic model for turning of nickel-based superalloy with ceramic tools
  83. Topical Issue Modern Manufacturing Technologies
  84. Effects of cutting parameters on machinability characteristics of Ni-based superalloys: a review
  85. Topical Issue Desktop Grids for High Performance Computing
  86. Task Scheduling in Desktop Grids: Open Problems
  87. Topical Issue Desktop Grids for High Performance Computing
  88. A Volunteer Computing Project for Solving Geoacoustic Inversion Problems
  89. Topical Issue Desktop Grids for High Performance Computing
  90. Improving “tail” computations in a BOINC-based Desktop Grid
  91. Topical Issue Desktop Grids for High Performance Computing
  92. LHC@Home: a BOINC-based volunteer computing infrastructure for physics studies at CERN
  93. Topical Issue Desktop Grids for High Performance Computing
  94. Comparison of Decisions Quality of Heuristic Methods with Limited Depth-First Search Techniques in the Graph Shortest Path Problem
  95. Topical Issue Desktop Grids for High Performance Computing
  96. Using Volunteer Computing to Study Some Features of Diagonal Latin Squares
  97. Topical Issue on Mathematical Modelling in Applied Sciences, II
  98. A polynomial algorithm for packing unit squares in a hypograph of a piecewise linear function
  99. Topical Issue on Mathematical Modelling in Applied Sciences, II
  100. Numerical Validation of Chemical Compositional Model for Wettability Alteration Processes
  101. Topical Issue on Mathematical Modelling in Applied Sciences, II
  102. Innovative intelligent technology of distance learning for visually impaired people
  103. Topical Issue on Mathematical Modelling in Applied Sciences, II
  104. Implementation and verification of global optimization benchmark problems
  105. Topical Issue on Mathematical Modelling in Applied Sciences, II
  106. On a program manifold’s stability of one contour automatic control systems
  107. Topical Issue on Mathematical Modelling in Applied Sciences, II
  108. Multi-agent grid system Agent-GRID with dynamic load balancing of cluster nodes
https://doi.org/10.1515/eng-2017-0013
Schlagwörter für diesen Artikel
thermal radiation; MHD; unsteady; chemical reaction; cross diffusion effects; stretching surface
Creative Commons
BY-NC-ND 3.0

Artikel in diesem Heft

  1. Regular Articles
  2. The Differential Pressure Signal De-noised by Domain Transform Combined with Wavelet Threshold
  3. Regular Articles
  4. Robot-operated quality control station based on the UTT method
  5. Regular Articles
  6. Regression Models and Fuzzy Logic Prediction of TBM Penetration Rate
  7. Regular Articles
  8. Numerical study of chemically reacting unsteady Casson fluid flow past a stretching surface with cross diffusion and thermal radiation
  9. Regular Articles
  10. Experimental comparison between R409A and R437A performance in a heat pump unit
  11. Regular Articles
  12. Rapid prediction of damage on a struck ship accounting for side impact scenario models
  13. Regular Articles
  14. Implementation of Non-Destructive Evaluation and Process Monitoring in DLP-based Additive Manufacturing
  15. Regular Articles
  16. Air purification in industrial plants producing automotive rubber components in terms of energy efficiency
  17. Regular Articles
  18. On cyclic yield strength in definition of limits for characterisation of fatigue and creep behaviour
  19. Regular Articles
  20. Development of an operation strategy for hydrogen production using solar PV energy based on fluid dynamic aspects
  21. Regular Articles
  22. An exponential-related function for decision-making in engineering and management
  23. Regular Articles
  24. Usability Prediction & Ranking of SDLC Models Using Fuzzy Hierarchical Usability Model
  25. Regular Articles
  26. Exact Soliton and Kink Solutions for New (3+1)-Dimensional Nonlinear Modified Equations of Wave Propagation
  27. Regular Articles
  28. Entropy generation analysis and effects of slip conditions on micropolar fluid flow due to a rotating disk
  29. Regular Articles
  30. Application of the mode-shape expansion based on model order reduction methods to a composite structure
  31. Regular Articles
  32. A Combinatory Index based Optimal Reallocation of Generators in the presence of SVC using Krill Herd Algorithm
  33. Regular Articles
  34. Quality assessment of compost prepared with municipal solid waste
  35. Regular Articles
  36. Influence of polymer fibers on rheological properties of cement mortars
  37. Regular Articles
  38. Degradation of flood embankments – Results of observation of the destruction mechanism and comparison with a numerical model
  39. Regular Articles
  40. Mechanical Design of Innovative Electromagnetic Linear Actuators for Marine Applications
  41. Regular Articles
  42. Influence of addition of calcium sulfate dihydrate on drying of autoclaved aerated concrete
  43. Regular Articles
  44. Analysis of Microstrip Line Fed Patch Antenna for Wireless Communications
  45. Regular Articles
  46. PEMFC for aeronautic applications: A review on the durability aspects
  47. Regular Articles
  48. Laser marking as environment technology
  49. Regular Articles
  50. Influence of grain size distribution on dynamic shear modulus of sands
  51. Regular Articles
  52. Field evaluation of reflective insulation in south east Asia
  53. Regular Articles
  54. Effects of different production technologies on mechanical and metallurgical properties of precious metal denture alloys
  55. Regular Articles
  56. Mathematical description of tooth flank surface of globoidal worm gear with straight axial tooth profile
  57. Regular Articles
  58. Earth-based construction material field tests characterization in the Alto Douro Wine Region
  59. Regular Articles
  60. Experimental and Mathematical Modeling for Prediction of Tool Wear on the Machining of Aluminium 6061 Alloy by High Speed Steel Tools
  61. Special Issue on Current Topics, Trends and Applications in Logistics
  62. 10.1515/eng-2017-0001
  63. Special Issue on Current Topics, Trends and Applications in Logistics
  64. The Methodology of Selecting the Transport Mode for Companies on the Slovak Transport Market
  65. Special Issue on Current Topics, Trends and Applications in Logistics
  66. Determinants of Distribution Logistics in the Construction Industry
  67. Special Issue on Current Topics, Trends and Applications in Logistics
  68. Management of Customer Service in Terms of Logistics Information Systems
  69. Special Issue on Current Topics, Trends and Applications in Logistics
  70. The Use of Simulation Models in Solving the Problems of Merging two Plants of the Company
  71. Special Issue on Current Topics, Trends and Applications in Logistics
  72. Applying the Heuristic to the Risk Assessment within the Automotive Industry Supply Chain
  73. Special Issue on Current Topics, Trends and Applications in Logistics
  74. Modeling the Supply Process Using the Application of Selected Methods of Operational Analysis
  75. Special Issue on Current Topics, Trends and Applications in Logistics
  76. Possibilities of Using Transport Terminals in South Bohemian Region
  77. Special Issue on Current Topics, Trends and Applications in Logistics
  78. Comparison of the Temperature Conditions in the Transport of Perishable Foodstuff
  79. Special Issue on Current Topics, Trends and Applications in Logistics
  80. E-commerce and its Impact on Logistics Requirements
  81. Topical Issue Modern Manufacturing Technologies
  82. Wear-dependent specific coefficients in a mechanistic model for turning of nickel-based superalloy with ceramic tools
  83. Topical Issue Modern Manufacturing Technologies
  84. Effects of cutting parameters on machinability characteristics of Ni-based superalloys: a review
  85. Topical Issue Desktop Grids for High Performance Computing
  86. Task Scheduling in Desktop Grids: Open Problems
  87. Topical Issue Desktop Grids for High Performance Computing
  88. A Volunteer Computing Project for Solving Geoacoustic Inversion Problems
  89. Topical Issue Desktop Grids for High Performance Computing
  90. Improving “tail” computations in a BOINC-based Desktop Grid
  91. Topical Issue Desktop Grids for High Performance Computing
  92. LHC@Home: a BOINC-based volunteer computing infrastructure for physics studies at CERN
  93. Topical Issue Desktop Grids for High Performance Computing
  94. Comparison of Decisions Quality of Heuristic Methods with Limited Depth-First Search Techniques in the Graph Shortest Path Problem
  95. Topical Issue Desktop Grids for High Performance Computing
  96. Using Volunteer Computing to Study Some Features of Diagonal Latin Squares
  97. Topical Issue on Mathematical Modelling in Applied Sciences, II
  98. A polynomial algorithm for packing unit squares in a hypograph of a piecewise linear function
  99. Topical Issue on Mathematical Modelling in Applied Sciences, II
  100. Numerical Validation of Chemical Compositional Model for Wettability Alteration Processes
  101. Topical Issue on Mathematical Modelling in Applied Sciences, II
  102. Innovative intelligent technology of distance learning for visually impaired people
  103. Topical Issue on Mathematical Modelling in Applied Sciences, II
  104. Implementation and verification of global optimization benchmark problems
  105. Topical Issue on Mathematical Modelling in Applied Sciences, II
  106. On a program manifold’s stability of one contour automatic control systems
  107. Topical Issue on Mathematical Modelling in Applied Sciences, II
  108. Multi-agent grid system Agent-GRID with dynamic load balancing of cluster nodes
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 19.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/eng-2017-0013/html
Button zum nach oben scrollen