Flow and Heat Transfer on a Moving Flat Plate in a Parallel Stream with Constant Surface Heat Flux: A Stability Analysis
Numerical solutions for the moving flat plat in a parallel stream with constant heat flux have been studied. The governing equations which are continuity, momentum and energy are convert to an ordinary differential equation using a non-similar transformation. By using shooting method with Maple implementation, the results of the equations can be solved numerically. Numerical results indicate that the velocity ratio parameter λ < 0, the non-unique solutions do exist. Then, the analysis of stability is carried out into two non-unique solutions to determine which is more stable between both of the solution by bvp4c solver in Matlab. From the result of stability analysis, the eigenvalues for the upper branch is positive while the lower branch is negative. Therefore, the first solution is stable than second solution.
- Jaluria Y. Transport from continuously moving material undergoing thermal processing. Annual Review of Heat Transfer. 1992; 4(4):187–245
- Blasius H. Grenzschichten in flüssigkeitenmitkleinerReibung. Z. Math Physics. 1908; 56:1–37.
- Sakiadis BC. Boundary layer behaviour on continuous solid surface: I. Boundary-layer equations for two dimensional and axisymmetric flow. AIChE Journal. 1961 Mar 1; 7(1):26–8.
- Sakiadis BC. Boundary-layer behaviour on continuous solid surface: II. The boundary layer on a continuous flat surface. AIChE Journal. 1961 Jun 1; 7(2):221–5.
- Sakiadis BC. Boundary-layer behaviour on continuous solid surface: III. The boundary layer on a continuous cylindrical surface. AIChE Journal. 1961 Sep 1; 7(3):467–72.
- Tsou FK, Sparrow EM, Goldstein RJ. Flow and heat transfer in the boundary layer on a continuous moving surface. International Journal of Heat and Mass Transfer. 1967 Feb 28; 10:219–35.
- Bianchi MV, Viskanta R. Momentum and heat transfer on a continuous flat surface moving in a parallel counterflow free stream. Wärme-Und Stoffübertragung. 1993 Dec 1; 29(2):89–94.
- Watanabe T, Pop I, Gota F. MHD stability of boundary layer flow over a moving flat plate. Tech Mech 1995; 15(325):32.
- Hassanien IA. Flow and heat transfer on a continuous flat surface moving in a parallel free stream of power-law fluid. Applied mathematical modeling. 1996 Oct 31; 20(10):779–84.
- Ishak A, Nazar R, Pop I. Flow and heat transfer characteristics on a moving flat plate in parallel stream with constant surface heat flux, Heat and Mass Transfer. 2009 Mar 1; 45(5):563–7.
- Mureithi EW, Mwaonanji JJ, Makinde OD. On the boundary layer flow over a moving surface in a fluid with temperature-dependent viscosity. Open Journal of Fluid Dynamics. 2013; 3:135–40.
- Merkin JH. On dual solutions occurring in mixed convection in a porous medium. Journal of Engineering Mathematics. 1986 Jun 1; 20(2):171–9.
- Afzal N, Badaruddin A, Elgarvi AA. Momentum and transport on a continuous flat surface moving in a parallel stream. International Journal of Heat and Mass Transfer. 1993 Sep 30; 36(13):3399–403.
- Afzal N. Momentum transfer on power law stretching plate with free stream pressure gradient. International Journal of Engineering Science. 2003 Jul 31; 41(11):1197–207.
- Weidman PD, Kubitschek DG, Davis AM. The effect of transpiration on self-similar boundary layer flow over moving surfaces. International Journal of Engineering Science. 2006 Jul 31; 44(11):730–7.
- Postelnicu A, Pop I. Falkner–Skan boundary layer flow of a power-law fluid past astretching wedge. Applied Mathematics and Computation. 2011 Jan 1; 217(9):4359–68.
- Roşca AV, Pop I. Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip. International Journal of Heat and Mass Transfer. 2013 May 31; 60:355–64.
- Ishak A. Flow and heat transfer over a shrinking sheet: A stability analysis. International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering. 2014 Apr 1; 8:872–6.
- Sharma R, Ishak A, Pop I. Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet. Computers and Fluids. 2014 Oct 10; 102:94–8.
- Mahapatra TR, Nandy SK, Gupta AS. Dual solution of MHD stagnation-point flow towards a stretching surface. Engineering. 2014 May 4; 2(04):299–305.
- Mahapatra TR, Nandy SK. Stability analysis of dual solutions in stagnation-point flow and heat transfer over a power-law shrinking surface. International Journal of Nonlinear Science. 2011; 12(1):86–94.
- Harris SD, Ingham DB, Pop I. Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport Porous Media. 2009 Mar 1; 77(2):267–85.
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.