Viscous and Ohmic heating effects in doubly stratified free convective flow over vertical plate with radiation and chemical reaction

doi:10.1007/s10483-013-1659-8

Abstract

Abstract:

An analysis is carried out to study the combined effects of viscous and Ohmic heating in the transient, free convective flow of a viscous, incompressible, and doubly stratified fluid past an isothermal vertical plate with radiation and chemical reactions. The governing boundary layer equations are solved numerically by an implicit finite difference scheme of the Crank-Nicolson type. The influence of different parameters on the velocity, the temperature, the concentration, the skin friction, the Nusselt number, and the Sherwood number is discussed with graphical illustrations. It is observed that an increase in either the thermal stratification or the mass stratification parameter decreases the velocity. An increase in the thermal stratification increases the concentration and decreases the temperature while an opposite effect is observed for an increase in the mass stratification. An augmentation in viscous and Ohmic heating increases the velocity and temperature while decreases the concentration. The results are found to be in good agreement with the existing solutions in literature.

Key words: mass stratification, viscous dissipation, pansystems, prediction, blow-up, singularity, break off, chemical reaction, Ohmic dissipation, radiation, thermal stratification

P. GANESAN;R. K. SUGANTHI;P. LOGANATHAN. Viscous and Ohmic heating effects in doubly stratified free convective flow over vertical plate with radiation and chemical reaction. Applied Mathematics and Mechanics (English Edition), 2013, 34(2): 139-152.

TrendMD

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-013-1659-8

https://www.amm.shu.edu.cn/EN/Y2013/V34/I2/139

[1] Siegel, R. Transient free convection from a vertical flat plate. ASME Journal of Heat Transfer, 80, 347–359 (1958)

[2] Hellums, J. D. and Churchill, S. W. Transient and steady state, free and natural convection, numerical solutions, part I, the isothermal vertical plate. American Institute of Chemical Engireers Journal, 8, 690–692 (1962)

[3] Callahan, G. D. and Marner, W. J. Transient free convection with mass transfer on an isothermal vertical flat plate. International Journal of Heat and Mass Transfer, 19, 165–174 (1976)

[4] Gebhart, B. and Pera, L. The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion. International Journal of Heat and Mass Transfer, 14, 2025–2050 (1971)

[5] Soundalgekar, V. M. and Ganesan, P. Finite difference analysis of transient free convection with mass transfer on an isothermal vertical flat plate. International Journal of Engineering Science, 19, 757–770 (1981)

[6] Barvinschi, P. Numerical simulation of Ohmic heating in idealized thin-layer electrodeposition cells. Journal of Optoelectronics and Advanced Materials, 8, 271–279 (2006)

[7] Gebhart, B. Effects of viscous dissipation in natural convection. Journal of Fluid Mechanics, 14, 225–232 (1962)

[8] Soundalgekar, V. M., Lahurikar, R. M., and Pohanerkar, S. G. Transient free convection flow of an incompressible viscous dissipative fluid. Heat and Mass Transfer, 32, 301–305 (1997)

[9] Tacken, R. A. and Janssen, L. J. J. Applications of magnetoelectrolysis. Journal of Applied Electrochemistry, 25, 1–5 (1995)

[10] Takami, I., Hisayoshi, M., and Yasuhiro, F. Water electrolysis under a magnetic field. Journal of the Electrochemical Society, 154, 112–115 (2007)

[11] Palani, G. and Srikanth, U. MHD flow past a semi-infinite vertical plate with mass transfer. Nonlinear Analysis: Modelling and Control, 14, 345–356 (2009)

[12] 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, 454–462 (2009)

[13] Dulal, P. and Babulal, T. Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating. Communications in Nonlinear Science and Numeric Simulation, 15, 2878–2893 (2010)

[14] Chen, C. H. Combined effects of Joule heating and viscous dissipation on magnetohydrodynamic flow past a permeable, stretching surface with free convection and radiative heat transfer. Journal of Heat Transfer, 132, 064503 (2010)

[15] Zueco, J. and Ahmed, S. 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. -Engl. Ed., 31(10), 1217–1230 (2010) DOI 10.1007/s10483-010-1355-6
[16] Bikash, S. Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transferof a second grade fluid past a radially stretching sheet. Appl. Math. Mech. -Engl. Ed., 31(12), 159–173 (2010) DOI 10.1007/s10483-010-0204-7

[17] Rao, J. A. and Shivaiah, S. Chemical reaction effects on unsteady MHD flow past semi-infinite vertical porous plate with viscous dissipation. Appl. Math. Mech. -Engl. Ed., 32(8), 1065–1078 2011) DOI 10.1007/s10483-011-1481-6

[18] Chen, C. C. and Eichhorn, R. Natural convection from a vertical surface to a thermally stratified fluid. ASME Journal of Heat Transfer, 98, 446–451 (1976)

[19] Srinivasan, J. and Angirasa, D. Numerical study of double-diffusive free convection from a vertical surface. International Journal of Heat and Mass Transfer, 31, 2033–2038 (1988)

[20] Angirasa, D. and 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, 657–663 (1989)

[21] Saha, S. C. and 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, 89–102 (2004)

[22] Takhar, H. S., Chamkha, A. J., and Nath, G. Natural convection flow from a continuously moving vertical surface immersed in a thermally stratified medium. Heat and Mass transfer, 38, 17–24 (2001)

[23] Muhaimin, I., Kandasamy, R., and Khamis, A. Numerical investigation of variable viscosities and thermal stratification effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of a chemical reaction. Appl. Math. Mech. -Engl. Ed., 30(11), 1353–1364 (2009) DOI 10.1007/s10483-009-1102-6

[24] Rathish Kumar, B. V. and Shalini, G. 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, 637–647 (2005)

[25] Sparrow, E. M. and Cess, R. D. Radiation Heat Transfer, Hemisphere Publishing Corporation, Washington, D. C. (1978)

[26] Herrmann Schlichting. Boundary Layer Theory, John Wiley and Sons, New York (1969)

[27] Carnahan, B., Luther, H. A., and Wilkes, J. O. Applied Numerical Methods, John Wiley and Sons, New York (1969)

Viscous and Ohmic heating effects in doubly stratified free convective flow over vertical plate with radiation and chemical reaction

PDF

Knowledge

Cited

Abstract

Cite this article

share this article

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Weidi XIA, Hongxing LI, Guotao ZHA, Fulin GUO, Chongrui LIU, Fuyin MA. Lightweight integrated sound absorbing-insulating metamaterials with low thickness [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(2): 215-234.
[2]	U. L. MANIKANTA, K. J. GOWTHAM, B. J. GIREESHA, P. VENKATESH. Similarity transformation-based modeling of the thermally-radiative tetra-hybrid Casson nanofluid flow over a nonlinear stretching sheet using the Clique polynomial collocation method [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(1): 185-202.
[3]	S. U. KHAN, M. GARAYEV, ADNAN, K. RAMESH, M. EL MELIGY, D. ABDUVALIEVA, M. I. KHAN. Applications of variable thermal features for the bioconvective flow of Jeffrey nanofluids due to stretching surface with masssuction effects: Cattaneo-Christov model [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 391-402.
[4]	C. G. PAVITHRA, B. J. GIREESHA, S. SUSHMA, K. J. GOWTHAM. Analysis of convective-radiative heat transfer in dovetail longitudinal fins with shape-dependent hybrid nanofluids: a study using the Hermite wavelet method [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 357-372.
[5]	Nanxi DING, Hengzhen FENG, H. Z. LOU, Shenghua FU, Chenglong LI, Zihao ZHANG, Wenlong MA, Zhengqian ZHANG. Prediction of velocity and pressure of gas-liquid flow using spectrum-based physics-informed neural networks [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 341-356.
[6]	B. S. SANJU, R. NAVEEN KUMAR, R. S. VARUN KUMAR, A. ABDULRAHMAN. Physics-informed neural network approach to analyze the onset of oscillatory and stationary convections in chemically triggered Navier-Stokes-Voigt fluid layer heated and salted from below [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(11): 2199-2220.
[7]	M. NAVEED, M. IMRAN, T. ASGHAR, Z. ABBAS. Transport mechanism in chemically reactive hybrid nanofluidflow containing gyrotactic micro-organisms overa curved oscillatory surface [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(1): 177-192.
[8]	Zhenliang HU, Xueyang ZHANG, Xianfang LI. Bending strength degradation of a cantilever plate with surface energy due to partial debonding at the clamped boundary [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(9): 1573-1594.
[9]	M. NEMATI, M. SEFID, A. KARIMIPOUR, A. J. CHAMKHA. Lattice Boltzmann method formulation for simulation of thermal radiation effects on non-Newtonian Al₂O₃ free convection in entropy determination [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(6): 1085-1106.
[10]	P. S. REDDY, P. SREEDEVI. Enhanced entropy generation and heat transfer characteristics of magnetic nano-encapsulated phase change materials in latent heat thermal energy storage systems [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(6): 1051-1070.
[11]	C. G. PAVITHRA, B. J. GIREESHA, M. L. KEERTHI. Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fln exposed to magnetic fleld in the presence of a shape-dependent trihybrid nanofluid [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(1): 197-216.
[12]	Yansong WANG, Baolin WANG, Youjiang CUI, Kaifa WANG. Anti-plane pull-out of a rigid line inclusion from an elastic medium [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 809-822.
[13]	Wei CHEN, Guozhen WANG, Yiqun LI, Lin WANG, Zhouping YIN. The quaternion beam model for hard-magnetic flexible cantilevers [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 787-808.
[14]	Jian CHEN, Yawei WANG, Xianfang LI. Antiplane shear crack in a prestressed elastic medium based on the couple stress theory [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(4): 583-602.
[15]	Zinan ZHAO, Nian LI, Yilin QU, Weiqiu CHEN. Novel mode-coupling vibrations of AlN thin film bulk acoustic resonator operating with thickness-extensional mode [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2187-2206.