Micro/nano thermal boundary layer equations with slip creep jump boundary conditions

Abstract

At the micro-and nanoscale, the standard continuity boundary conditions at fluid-solid interfaces of classical transport phenomena do not apply and must be replaced by boundary conditions that allow discontinuities. In this study, the classical thermal laminar boundary layer equations are studied using Lie symmetries with the no-slip boundary condition for tangential velocity and continuous temperature boundary conditions replaced by non-linear slip-creep-jump boundary conditions. These boundary conditions contain an arbitrary index parameter, denoted by n > 0, which appears in the coefficients of the coupled ordinary differential equations to be solved. As an independent check on the numerical procedure, the case of a boundary layer formed in a convergent channel with a sink, which corresponds to n = 1/2, is solved analytically for various values of the Prandtl number and zero Brinkham number. Other values of n for n > 1/2 which correspond to the thermal boundary layer formed in the flow past a wedge are solved numerically for various values of the Prandtl and Brinkham number and constant coefficients appearing in the non-linear slip-creep-jump boundary conditions. It is found that for 1/2 < n < 2, solutions may be found for all values of the constant coefficients, while for n 2 the constant coefficient for the creep term must be set to zero.

Heat transfer of graphene foams and carbon nanotube forests under forced convection

“…The boundary layers are created due to the friction of air with the CNTs and the airflow and heat transfer in these layers (i.e. the fluid and thermal boundary layers, respectively) are lower [32]. Boundary layers around nanoscale structures have similar or larger dimensions than the nanostructure [33], i.e.…”

Entropy Generation Analysis of Open Parallel Microchannels Embedded Within a Permeable Continuous Moving Surface: Application to Magnetohydrodynamics (MHD)

“…where f w , Pr, Ec, and M show the suction/injection parameter, the Prandtl number, the Eckert number and the magnetic parameter respectively: (15) where f w < 0 for mass injection and f w > 0 in the presence of the suction along the surface. Based on the previous work [24], f wp and K p are introduced as suction/injection and slip coefficient, respectively, based on P nx , which are fully independent from x and n:…”

“…In this process, suction is exerted in order to remove reactants, whereas injection is applied to add reactants in the process [2]. Therefore, many researchers have studied the boundary layer problems in the presence of "slip" [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Recently, Yazdi et al [24] have investigated MHD liquid flow over nonlinear permeable stretching surface in the presence of the slip boundary condition and high-order chemical reactions.…”

Hydrodynamic and Thermal Slip Effect on Double-Diffusive Free Convective Boundary Layer Flow of a Nanofluid Past a Flat Vertical Plate in the Moving Free Stream

“…For gaseous flow the slip condition of the velocity and the jump condition of the temperature are and , and are the tangential momentum coefficient, the temperature accommodation Coefficients (Maxwell [19]). Some relevant papers on slip flows are Khare et al [20], Petravic and Harrowella [21], Kim et al [22], Martin and Boyd [23], Fang and Lee [24], Mathews and Hill [25], Kuznetsov and Nield [26].…”