Forced convection problem of laminar quasi-incompressible boundary layer for the stagnation slip flow at a relatively low Mach number, considering the simultaneous effects of viscous dissipation and pressure work, has been investigated. The system of coupled partial differential equations was first transformed into a system of coupled ordinary differential equations through suitable transformations, which was then solved using Runge–Kutta–Fehlberg fourth-fifth order method. The solution obtained here is much better suited to formulating and solving the variable-property of chemically reacting flows that occur in practice, by taking into account the slip boundary conditions at the gas–wall interface. The effects of the Eckert number and the slip parameter on the heat transfer characteristics are presented graphically and discussed. The numerical results show that the pressure work, viscous dissipation play significant role on the heat transfer and could not be neglected under any circumstance for rarefied gas flows.
- Park J. H., Sudarshan T. S. (Eds.). Chemical vapor deposition (Vol. 2). ASM international (2001).
- Acikalin T., Garimella S. V. Analysis and prediction of the thermal performance of piezoelectrically actuated fans. Heat transfer engineering. 30 (6), 487–498 (2009).
- Ju Y., Maruta K. Microscale combustion: technology development and fundamental research. Progress in energy and combustion science. 37 (6), 669–715 (2011).
- Hua J., Wu M., Kumar K. Numerical simulation of the combustion of hydrogen–air mixture in micro-scaled chambers. Part I: Fundamental study. Chemical engineering science. 60 (13), 3497–3506 (2005).
- Buffi M., Cappelletti A., Rizzo A. M., Martellia F., Chiaramonti D. Combustion of fast pyrolysis bio-oil and blends in a micro gas turbine. Biomass and Bioenergy. 115, 174–185 (2018).
- Lin T. C., Schaaf S. A. Effect of Slip on Flow Near a Stagnation Point and in a Boundary Layer. NACA 1951; TN: 2568.
- Kogan M. N. Rarefied Gas Dynamics. Plenum, New York (1969).
- Wang C. Y. Stagnation Flows with Slip: Exact Solutions of the Navier–Stokes Equations. Zeitschrift für Angewandte Mathematik und Physik. 54 (1), 184–189 (2003).
- Wang C. Y. Stagnation Slip Flow and Heat Transfer on a Moving Plate. Chemical Engineering Science. 61 (23), 7668–7672 (2006).
- Wang C. Y. Similarity stagnation point solutions of the Navier–Stokes equations - Review and extension. Eur. J. Mech. B/Fluids. 27 (6), 678–683 (2008).
- Cao K., Baker J. Slip Effects on Mixed Convective Flow and Heat Transfer From a Vertical Plate. International Journal of Heat and Mass Transfer. 52 (15–16), 3829–3841 (2009).
- Sparrow E. M., Quack H., Boerner C. J. Local non similarity boundary layer solutions. American Institute of Aeronautics and Astronautics Journal. 8 (11), 1936–1942 (1970).
- Sparrow E. M., Yu H. S. Local non similarity thermal boundary layer solutions. ASME Journal of Heat Transfer. 93 (4), 328–334 (1971).
- Martin M. J., Boyd I. D. Stagnation-point heat transfer near the continuum limit. AIAA Journal. 47 (1), 283–285 (2009).
- Essaghir E., Oubarra A., Lahjomri J. Non-similar solutions of the boundary layers equations with favorable and adverse pressure gradients, isothermal wall and slip boundary conditions: Application to Falkner–Skan gaseous flow. European Journal of Mechanics-B/Fluids. 77, 281–298 (2019).
- Essaghir E., Haddout Y., Oubarra A., Lahjomri J. Non-similar solution of the forced convection of laminar gaseous slip flow over a flat plate with viscous dissipation: linear stability analysis for local similar solution. Meccanica. 51 (1), 99–115 (2016).
- Batchelor G. K. An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (2000).
- Karniadakis G., Beskok A., Aluru N. Microflows and Nanoflows: Fundamentals and Simulation. Springer, New York (2005).