Transient Mixed Convection Boundary Layer Flow of an Incompressible Fluid Past a Wedge in Presence of Magnetic Field
Applied and Computational Mathematics
Volume 8, Issue 1, February 2019, Pages: 9-20
Received: Feb. 1, 2019;
Accepted: Mar. 11, 2019;
Published: Mar. 25, 2019
Views 71 Downloads 40
Shayma Joya Saha, Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
Litan Kumar Saha, Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
In this paper, an analysis is performed to explorethe transient, laminar two-dimensional, mixed convection boundary layer flow of a viscous and incompressible fluid past a vertical wedge taking into account the effect of magnetic field. With appropriate transformations the boundary layer equations are reduced to a local nonsimilarity equations and the solutions are obtained employing three distinct methods, namely, (i) perturbation method for small time; (ii) asymptotic solution method for large time; (iii) straight forward finite difference method for any time. The agreement between the solutions obtained from prescribed methods is found to be excellent. In this study the evaluation of skin-friction coefficient and the local Nusselt number with the effects of different governing parameters such as different time, τ, the exponent, m (= 0.4, 0.5, 1.0), mixed convection parameter, λ (= 0.0, 0.2, 0.4) and magnetic field parameter, M (=0.0, 1.0) for fluids having Prandtl number, Pr= 0.72, 1.0 and 7.0have been discussed. It is observed that both the local skin friction and local Nusseltnumber decreases due to an increase in the value of M. It is also found that an increase in the value of Prandtl number, Pr, leads to a decrease in the value of local skin friction coefficient and the value of local Nusselt number coefficient increases with the increasing values of Prandtl number.
Shayma Joya Saha,
Litan Kumar Saha,
Transient Mixed Convection Boundary Layer Flow of an Incompressible Fluid Past a Wedge in Presence of Magnetic Field, Applied and Computational Mathematics.
Vol. 8, No. 1,
2019, pp. 9-20.
L. G. Leal, Laminar Flow and Convective Transport Phenomena: Scaling Principles and Asymptotic Analysis, Butterworth Heinemann, Boston, (1992).
K. Gersten, H. Herwig, V. Stramungsmechanik, Braunschweig, Wiesbaden (1992).
H. Schlichting, K. Gersten, Grenzschicht-Theorie, Springer-Verlag, Berlin, (1997).
V. M. Falkner and S. W. Skan, Some Approximate Solutions of the Boundary-Layer Equations, Philosophical Magazine, 12 (1930) 865-896.
D. R. Hartree, On an equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer. In Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 33(1937) 223-239.
J. C. Y. Koh and J. P. Hartnett, Skin friction and heat transfer for incompressible laminar flow over porous wedges with suction and variable wall temperature, International Journal of Heat and Mass Transfer 2 (1961) 185-198.
N. G. Kafoussias and N. D. Nanousis, Magnetohydrodynamic laminar boundary-layer flow over a wedge with suction or injection, Canadian Journal of Physics 75.10 (1997) 733-745.
M. Kumariand Rama Subba Reddy Gorla, Combined convection along a non-isothermal wedge in a porous medium, Heat and Mass Transfer 32.5 (1997) 393-398.
M. A. Hossain, MdSazzadMunir, and David Andrew S. Rees, Flow of viscous incompressible fluid with temperature dependent viscosity and thermal conductivity past a permeable wedge with uniform surface heat flux, International journal of thermal sciences 39.6 (2000) 635-644.
Mahesh Kumari, Harmindar S. Takhar, and GirishwarNath, Mixed convection flow over a vertical wedge embedded in a highly porous medium, Heat and Mass Transfer 37.2 (2001) 139-146.
N. Riley, Unsteady viscous flows. Science Progress 74 (1990) 361-377.
D. R. Telionis, Unsteady viscous flows, Springer-Verlag, New York, 1997.
David K. Ludlow, Peter A. Clarkson, and Andrew P. Bassom, New similarity solutions of the unsteady incompressible boundary-layer equations, Quarterly Journal of Mechanics and Applied Mathematics 53.2 (2000) 175-206.
Stuart H Smith, The impulsive motion of a wedge in a viscous fluid, ZeitschriftfürAngewandteMathematik und Physik (ZAMP) 18.4 (1967) 508-522.
Kenichi Nanbu, Unsteady Falkner-Skan flow, ZeitschriftfürangewandteMathematik und Physik ZAMP 22.6 (1971) 1167-1172.
M. A. Hossain, Bhowmick S, Gorla RS. Unsteady mixed-convection boundary layer flow along a symmetric wedge with variable surface temperature. International journal of engineering science44(10) (2006) 607-620.
M. G. Hall, The boundary layer over an impulsively started flat plate, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 310(1969) 401-414.
Simon D. Harris, Derek B. Ingham, and Ioan Pop, Unsteady heat transfer in impulsive Falkner–Skan flows: constant wall temperature case, European Journal of Mechanics-B/Fluids 21.4 (2002) 447-468.
H. B. Keller and T. Cebeci, Accurate Numerical Methods for Boundary Layer Flows, I. Two-Dimensional Laminar Flows, Lecture Notes in Physics, Proceedings of 2nd International Conference on Numerical Methods in Fluid Dynamics, Springer-Verlag, Berlin. (1971).
E. M. Sparrow and R. D. Cess, The effect of a magnetic field on free convection heat transfer, International Journal of Heat and Mass Transfer 3.4 (1961) 267-274.
K. R. Singh and T. G. Cowling, Thermal convection in magnetohydrodynamic bounadary layers, J. Mech. Appl. Math. 16(1963) 1-5.
GrahamWilks, Magnetohydrodynamic free convection about a semi-infinite vertical plate in a strong cross field, Zeitschriftfür angewandte Mathematik and Physik, ZAMP 27.5 (1976) 621-631.
M. H. Cobble, Free convection with mass transfer under the influence of a magnetic field, Nonlinear Analysis: Theory, Methods & Applications 3.1 (1979) 135-143.
M. A. Hossain, K. C. A. Alam, and D. A. S. Rees, MHD forced and free convection boundary layer flow along a vertical porous plate, Applied Mechanics and Engineering 2.1 (1997) 33-51.
P. Ganesanand G. Palani, Finite difference analysis of unsteady natural convection MHD flow past an inclined plate with variable surface heat and mass flux, International journal of heat and mass transfer 47.19 (2004) 4449-4457.
G. Palani and Kwang-Yong Kim, The effects of MHD on free-convection flow past a semi-infinite isothermal inclined plate, Journal of Engineering Physics and Thermophysics 81.4 (2008) 724-731.
S. M. Mahfooz, M. A. Hossain, and Rama Subba Reddy Gorla, Radiation effects on transient magnetohydrodynamic natural convection flow with heat generation, International Journal of Thermal Sciences 58 (2012) 79-91.
L. K. Saha, M. A. Hossain, and Rama Subba Reddy Gorla, Effect of Hall current on the MHD laminar natural convection flow from a vertical permeable flat plate with uniform surface temperature, International journal of thermal sciences 46.8 (2007) 790-801.
SP Anjali Devi and R. Kandasamy, Thermal stratification effects on laminar boundary-layer flow over a wedge with suction or injection, Mechanics Research Communications 28.3 (2001) 349-354.
H. Schlichting, K. Gersten, E. Krause and H. Oertel, Boundary-layer theory, New York(1960).
Nepal C. Roy and M. Anwar Hossain, Unsteady Magnetohydrodynamic Mixed Convection Flow of Micropolar Fluid Past a Permeable Sphere, Journal of Thermophysics and Heat Transfer (2017).
Kai-Long Hsiao, MHD mixed convection for viscoelastic fluid past a porous wedge, International Journal of Non-Linear Mechanics 46.1 (2011) 1-8.
S. Siddiqaand M. A. Hossain, Mixed convection boundary layer flow over a vertical flat plate with radiative heat transfer, (2012).
John C. Butcher, Implicit Runge-Kutta processes, Mathematics of Computation, 18.85 (1964) 50-64.
Philip R. Nachtsheim and Paul Swigert, Statisfaction of asymptotic boundary conditions in numerical solution of systems of nonlinear equations of boundary-layer type, NASA TND-3004(1965).