### Combined Effects of Chemical Reaction and Wall Slip on MHD Flow in a Vertical Wavy Porous Space with Traveling Thermal Waves

#### Abstract

This paper investigates the magnetohydrodynamic (MHD) mixed convective heat and mass transfer flow in a vertical wavy porous space in the presence of a heat source with the combined effects of chemical reaction and wall slip condition. The dimensionless governing equations are perturbed into: mean (zeroth-order) part and a perturbed part, using amplitude as a small parameter. The perturbed quantities are obtained by perturbation series expansion for small wavelength in which terms of exponential order arise. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, magnetic field, porous medium, heat source/sink parameter and wall slip condition. Further, the results of the skin friction and rate of heat and mass transfer at the wall are presented for various values of parameters entering into the problem and discussed with the help of graphs.

#### Keywords

#### Full Text:

PDF#### References

W Aung. Mixed Convection in Internal Flow. In: S Kakac, RK Shah, W Aung (eds.). Hand Book of Single Phase Convective Heat Transfer. Chapter 15, Wiley, New York, 1987.

WM Rohsenow, JP Hartnett and YI Cho. Handbook of Heat Transfer. McGraw-Hill, New York, 1998.

K Vajravelu. Combined free and forced convection in hydromagnetic flows in vertical wavy channels, with traveling thermal waves. Int. J. Eng. Sci. 1989; 27, 289-300.

A Barletta. Laminar mixed convection with viscous dissipation in a vertical channel. Int. J. Heat Mass Tran. 1998; 41, 3873-85.

AJ Chamkha. Flow of two-immiscible fluids in porous and non-porous channels. J. Fluids Eng. ASME 2000; 22, 117-24.

JC Umavathi and MS Malashetty. Magnetohydrodynamic mixed convection in a vertical. Int. J. Nonlinear. Mech. 2005; 40, 91-101.

M Guria and RN Jana. Hydrodynamic flows through vertical wavy channel with traveling thermal waves embedded in porous medium. Int. J. Appl. Mech. Eng. 2006; 3, 609-21.

NT Eldabe, MF El-Sayed, AY Ghaly and HM Sayed. Mixed convective heat and mass transfer in a non-Newtonian fluid at a peristaltic surface with temperature-dependent viscosity. Arch. Appl. Mech. 2008; 78, 599-624.

S Srinivas and R Muthuraj. Effects of thermal radiation and space porosity on MHD mixed convection flow in a vertical channel using homotopy analysis method. Comm. Nonlinear. Sci. Numer. Simulat. 2010; 15, 2098-108.

JP Kumar, JC Umavathi, AJ Chamkha and I Pop. Fully developed free convective flow of micropolar and viscous fluids in a vertical channel. Appl. Math. Model. 2010; 34, 1175-86.

EM Sparrow and SH Lin. Laminar heat transfer in tubes under slip-flow conditions. ASME J. Heat Tran. 1962; 84, 363-9.

RM Inman. Heat transfer for laminar slip flow of a rarefied gas in a parallel plate channel or a circular tube with uniform wall temperature. NASA TN, D-2213, 1964.

J Barrat and L Bocquet. Large slip effect at a nonwetting fluid-solid interface. Phys. Rev. Lett. 1999; 82, 4671-4.

R Pit, H Hervet and L Leger. Direct experimental evidence of slip in hexadecane: solid interfaces. Phy. Rev. Lett. 2000; 85, 980-3.

C Derek, DC Tretheway and CD Meinhart. Apparent fluid slip at hydrophibic micro channel walls. Phys. Fluids 2002; 14, L9-L12.

R Taneja and NC Jain. MHD flow with slip effects and temperature dependent heat source in a viscous incompressible fluid confined between a long vertical wavy wall and parallel flat wall. Def. Sci. J. 2004; 54, 21-9.

J Hron, CL Roux, J Malik and KR Rajagopal. Flows of incompressible fluids subject to Navierâ€™s slip on the boundary. Comput. Math. Appl. 2008; 56, 2128-43.

N Ali, Q Hussain, T Hayat and S Asghar. Slip effects on the peristaltic transport of fluid with variable viscosity. Phys. Lett. A 2008; 372, 1477-89.

A Ebaid. Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel. Phys. Lett. A 2008; 372, 4493-9.

S Srinivas, R Gayathri and M Kothandapani. The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport. Comput. Phys. Commun. 2009; 180, 2115-22.

S Srinivas and R Muthuraj. MHD flow with slip effects and temperature dependent heat source in a vertical wavy porous space. Chem. Eng. Comm. 2010; 197, 1387-403.

UN Das, RK Deka and VM Soundalgekar. Effect of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction. Forschung im Ingenieurwesen 1994; 60, 284-7.

R Muthucumarswamy and P Ganesan. Diffusion and first-order chemical reaction on impulsively chemical reaction on impulsively started infinite vertical plate with variable temperature. Int. J. Therm. Sci. 2002; 41, 475-9.

KV Prasad, S Abel and PS Datti. Diffusion of chemically reactive species of a non- Newtonian fluid immersed in a porous medium over a stretching sheet. Int. J. Nonlinear. Mech. 2003; 38, 651-7.

FT Akyildiz, H Bellout and K Vajravelu. Diffusion of chemically reactive species in a porous medium over a stretching sheet. J. Math. Anal. Appl. 2006; 320, 322-9.

PM Patil and PS Kulkarni. Effects of chemical reaction on free convective flow of a polar fluid through a porous medium in the presence of internal heat generation. Int. J. Thermal. Sci. 2008; 47, 1043-54.

T Hayat, Z Abbas and M Sajid. Heat and mass transfer analysis on the flow of a second grade in the presence of chemical reaction. Phys. Lett. A 2008; 372, 2400-8.

RA Mohamed and SM Abo-Dahab. Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation. Int. J. Thermal. Sci. 2009; 48, 1800-13.

D Pal and B Talukdar. Perturbation analysis of unsteady magneto hydro dynamic con- vective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction. Comm. Nonlinear. Sci. Numer. Simulat. 2010; 15, 1813-30.

J Zueco and S Ahmed. Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source. Appl. Math. Mech. Eng. Ed. 2010; 31, 1217-30.

SJ Liao. On the homotopy Analysis Method for non linear problems. Appl. Math. Comput. 2004; 147, 499-513.

S Abbasbandy. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys. Lett. A 2006; 360, 109-13.

J Zhu, L Zheng and X Zhang. Analytical solution to stagnation-point flow and heat transfer over a stretching sheet based on homotopy analysis. Appl. Math. Mech. 2009; 30, 463-74.

WX Ma and JH Lee. A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation. Chaos, Solitons & Fractals 2009; 42, 1356-63.

WX Ma and E Fan. Linear superposition principle applying to Hirota bilinear equations. Comput. Math. Appl. 2011; 61, 950-9.

WX Ma, Y Zhang, Y Tang and J Tu. Hirota bilinear equations with linear subspaces of solutions. Appl. Math. Comput. 2012; 218, 7174-83.

AK Shukla, TR Ramamohan and S Srinivas. Homotopy analysis method with a non-homogeneous term in the auxiliary linear operator. Comm. Nonlinear. Sci. Numer. Simulat. 2012; 17, 3776-87.

### Refbacks

- There are currently no refbacks.

**Online ISSN: 2228-835X****http://wjst.wu.ac.th **

**Last updated:**13 February 2019