## THERMAL SCIENCE

International Scientific Journal

### DOUBLY STRATIFIED EFFECTS IN A FREE CONVECTIVE FLOW OVER A VERTICAL PLATE WITH HEAT AND MASS TRANSFER

**ABSTRACT**

An analysis is performed to study the effects of thermal and mass stratification in a transient free convective flow of a viscous, incompressible fluid past an isothermal vertical plate. The governing boundary layer equations are solved numerically using an implicit finite difference scheme of Crank-Nicolson type. The doubly stratified effects on the velocity, temperature and concentration are shown graphically. It is observed that an increase in thermal stratification parameter decreases the velocity, temperature profiles and increases the concentration profiles. As well, increase in mass stratification parameter decreases the velocity, concentration profiles and increases the temperature profiles. Also, the influence of the thermal and mass stratification parameter on local as well as average skin-friction, the rate of heat and mass transfer are discussed and presented graphically. The results are compared with particular solutions available in the literature. The present results are found to be in good agreement with the existing particular solution of the problem.

**KEYWORDS**

PAPER SUBMITTED: 2011-10-06

PAPER REVISED: 2012-08-15

PAPER ACCEPTED: 2012-10-26

**THERMAL SCIENCE** YEAR

**2014**, VOLUME

**18**, ISSUE

**2**, PAGES [365 - 376]

- Siegel, R., Transient free convection from a vertical flat plate, Trans. ASME, 80(1958), pp. 347-359.
- Hellums, J. D., Churchill, S. W., Transient and steady state, free and natural convection, numerical solutions, Part I, The isothermal vertical plate, A.I.CH.E. Jl., 8(1962), pp. 690-692.
- Callahan, G. D., Marner, W. J., Transient free convection with mass transfer on an isothermal vertical flat plate, Int. J. Heat Mass Transfer, 19(1976), pp. 165-174.
- Gebhart, B., Pera, L., The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion, Int. J. Heat Mass Transfer, 14(1971), pp. 2025-2050
- Soundalgekar, V. M., P. Ganesan, Finite difference analysis of transient free convection with mass transfer on an isothermal vertical flat plate, International Journal of Engineering Science, 19 (1981), pp. 757-770.
- Ogulu, A. and Makinde, O. D.'Unsteady hydromagnetic free convection flow of a dissipative and radiating fluid past a vertical plate with constant heat flux, Chemical Engineering Communications, 196(2009), pp. 454 - 462.
- Shyam Sunder TAK., Rajeev MATHUR., Rohit Kumar GEHLOT., and Aiyub KHAN., MHD free convection-radiation interaction along a vertical surface embedded in Darcian porous medium in presence of Soret and Dufour's effects, Thermal science, 14(2010), pp. 137-145
- Makinde, O. D., On MHD mixed convection with Soret and Dufour effects past a vertical plate embedded in a porous medium. Latin American Applied Research, 41(2011), pp. 63-68.
- Makinde, O. D., Olanrewaju, P.O., Unsteady mixed convection with Soret and Dufour effects past a porous plate moving through a binary mixture of chemically reacting fluid, Chemical Engineering Communications, 198 (2011), pp. 920-938
- Makinde, O. D., Similarity solution for natural convection from a moving vertical plate with internal heat generation and a convective boundary condition, Thermal science, 15(2011), Suppl. 1, pp. S137-S143
- Satishkumar, N.V, Patel, A.G, Maheswari, N.K, Vijayan, P.K. and Saha, D., Thermal stratification studies related to the passive decay heat removal system of advanced heavy water reactor, Bhabha atomic research centre, www.iaea.org/OurWork/ST/NE/NENP/NPTDS/Downloads/SRCM_NCP_2005_AUG/sess3_phen1_vijayan.pdf
- Chen, C. C., Eichhorn, R., Natural convection from a vertical surface to a thermally stratified fluid, ASME Journal of Heat Transfer, 98(1976), pp. 446-451
- Srinivasan, J., Angirasa, D., Numerical study of double-diffusive free convection from a vertical surface, Int. J. Heat Mass Transfer, 31(1988), pp. 2033-2038
- Angirasa, D., Srinivasan, J., Natural convection flows due to the combined buoyancy of heat and mass diffusion in a thermally stratified medium, ASME Journal of Heat Transfer, 111(1989), pp. 657-663
- Saha, S. C., Hossain, M. A., Natural convection flow with combined buoyancy effects due to thermal and mass diffusion in thermally stratified media, Non-linear Analysis: Modelling and Control, 9(2004), pp. 89-102
- Geetha, P., Moorthy, M. B. K., Variable Viscosity, Chemical reaction and thermal stratification effects on mixed convection heat and mass transfer along a semi-infinite vertical plate, American Journal of Applied Sciences, 8(2011), pp. 628-634
- Noor Halini Baharim., Razali Ismail., Mohamad Hanif omar., Effects of thermal stratification on the concentration of iron and manganese in a tropical water supply reservoir, Sains Malaysiana, 40(2011), pp. 821-825.
- Rathish kumar, B. V., Shalini Gupta, Combined influence of mass and thermal stratification on double-diffusion non-darcian natural convection from a wavy vertical wall to porous media, Journal of heat transfer, 127(2005), pp. 637-647
- Herrmann Schlichting, Boundary Layer Theory. John Wiley and Sons, New York, 1969
- Carnahan, B., Luther, HA., Wilkes, JO., Applied Numerical Methods. John Wiley and Sons, New York, 1969