An analogy between vortical and thermal fields subject to the large pressure gradient

Local thermal disturbances generated by a small confined mechanical forcing on the curved surface are under consideration within the framework of the interacting boundary layer in the limit of large Reynolds number. The variations of the self-induced pressure and temperature are found to be explicitly related, and an analytic solution of a linear perturbation analysis is presented. The heat flux associated with the self-induced pressure may attain values comparable with the heat flux existing in the oncoming boundary layer. The analogy between the normal-to-wall vorticity and spanwise derivative of temperature is rigorously derived to supersede locally the well-known analogy by Reynolds. Heavily increased thermal loads can cause severe damage to the engine in operation.     

Thin-layer version of the moment equations in the boundary layer problem

The two-dimensional problem of a hypersonic kinetic boundary layer developing on a thin body in the case of a monatomic gas is considered. The model of the flow arises from the kinetic theory of gases and, within its accuracy, i.e., in the approximation of a hypersonic boundary layer, takes into account the strong nonequilibrium of the flow with respect to translational degrees of freedom. A method for representing the solution of the problem in terms of the solution of a similar classical (Navier-Stokes) hypersonic boundary layer problem is described. For the kinetic version of the problem, it is shown that the shear stress and the specific heat flux on the body surface are equal to their counterparts in the Navier-Stokes boundary layer.     

Natural convection flow from a horizontal circular cylinder with uniform heat flux in presence of heat generation

Natural convection boundary layer laminar flow from a horizontal circular cylinder with uniform heat flux in presence of heat generation has been investigated. The governing boundary layer equations are transformed into a non-dimensional form and the resulting non-linear systems of partial differential equations, which are solved numerically by two distinct methods namely: (i) implicit finite difference method together with the Keller-box scheme and (ii) perturbation solution technique. The results of the surface shear stress in terms of local skin-friction and the rate of heat transfer in terms of local Nusselt number, velocity distribution, velocity vectors, temperature distribution as well as streamlines, isotherms and isolines of pressure are shown by graphically for a selection of parameter set consisting of heat generation parameter.     

Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: A Lie group analysis

In this paper, heat and mass transfer analysis for boundary layer stagnation-point flow over a stretching sheet in a porous medium saturated by a nanofluid with internal heat generation/absorption and suction/blowing is investigated. The governing partial differential equation and auxiliary conditions are converted to ordinary differential equations with the corresponding auxiliary conditions via Lie group analysis. The boundary layer temperature, concentration and nanoparticle volume fraction profiles are then determined numerically. The influences of various relevant parameters, namely, thermophoresis parameter Nt, Brownian motion parameter Nb, Lewis number Le, suction/injection parameter S, permeability parameter k₁, source/sink parameter λ and Prandtl parameter Pr on temperature and concentration as well as wall heat flux and wall mass flux are discussed. Comparison with published results is presented.     

Effects of thermal radiation on the boundary layer flow of a Jeffrey fluid over an exponentially stretching surface

In the present investigation we have analyzed the boundary layer flow of a Jeffrey fluid over an exponentially stretching surface. The effects of thermal radiation are carried out for two cases of heat transfer analysis known as (1) Prescribed exponential order surface temperature (PEST) and (2) Prescribed exponential order heat flux (PEHF). The highly nonlinear coupled partial differential equations of Jeffrey fluid flow along with the energy equation are simplified by using similarity transformation techniques based on boundary layer assumptions. The reduced similarity equations are then solved analytically by the homotopy analysis method (HAM). The convergence of the HAM series solution is obtained by plotting (^h/_2p)\hbar-curves for velocity and temperature. The effects of physical parameters on the velocity and temperature profiles are examined by plotting graphs.     

The heat transfer problem in the wall region of a turbulent boundary layer

The problem of heat transfer in the wall region of a turbulent boundary layer has been investigated. The resonant triad in the theory of hydrodynamic stability was used to obtain the velocity field induced by the coherent structures in the wall region of the turbulent boundary layer, while the small scale turbulence was represented by a simple model. By such a new approach of modeling, the 3-D temperature field is calculated, the mean temperature profile in the wall region and the Nusselt number characterizing the heat flux, which was found to be in good agreement with the experimental observations are obtained. The instantaneous temperature field had streaky structures, thus offering a mechanism for their generation found in numerical simulations. Project supported by the National Natural Science Foundation of China (Grant No. 19132011).     

Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition

In this paper the boundary layer flow over a flat plat with slip flow and constant heat flux surface condition is studied. Because the plate surface temperature varies along the x direction, the momentum and energy equations are coupled due to the presence of the temperature gradient along the plate surface. This coupling, which is due to the presence of the thermal jump term in Maxwell slip condition, renders the momentum and energy equations non-similar. As a preliminary study, this paper ignores this coupling due to thermal jump condition so that the self-similar nature of the equations is preserved. Even this fundamental problem for the case of a constant heat flux boundary condition has remained unexplored in the literature. It was therefore chosen for study in this paper. For the hydrodynamic boundary layer, velocity and shear stress distributions are presented for a range of values of the parameter characterizing the slip flow. This slip parameter is a function of the local Reynolds number, the local Knudsen number, and the tangential momentum accommodation coefficient representing the fraction of the molecules reflected diffusively at the surface. As the slip parameter increases, the slip velocity increases and the wall shear stress decreases. These results confirm the conclusions reached in other recent studies. The energy equation is solved to determine the temperature distribution in the thermal boundary layer for a range of values for both the slip parameter as well as the fluid Prandtl number. The increase in Prandtl number and/or the slip parameter reduces the dimensionless surface temperature. The actual surface temperature at any location of x is a function of the local Knudsen number, the local Reynolds number, the momentum accommodation coefficient, Prandtl number, other flow properties, and the applied heat flux.     

Modeling of thermal response and ablation in laminated glass fiber reinforced polymer matrix composites due to lightning strike

Thermal response and ablation of laminated glass fiber reinforced polymer matrix composites subjected to lightning strike are studied. The associated nonlinear time-dependent heat transfer model includes specific features of lightning arcs observed in physical measurements such as lightning channel radius expansion, non-uniform lightning current density, and associated heat flux. Moving spatially and temporally non-uniform lightning-current-induced heat flux boundary and moving boundary due to material phase transition caused by rapid surface ablation are also included. To predict moving phase boundary in the laminated anisotropic composites, an element deletion method is developed and embedded into finite element analysis (FEA), which is performed using ABAQUS. The Umeshmotion + ALE method based on the user subroutine Umeshmotion and arbitrary Lagrangian–Eulerian (ALE) adaptive mesh technique is also used, when applicable (i.e., moving phase boundary is confined within a top layer of the composite laminate). Heat transfer analysis is performed for a non-conductive laminated glass fiber reinforced polymer matrix composite panel representing the SNL 100-00 wind turbine tip. Thermal response of the panel subjected to pulsed and continuing lightning currents at three different lightning protection levels, LPL I, LPL II, and LPL III, is studied. Temperature-dependent anisotropic thermal properties of the composite panel are included in the analysis. The FEA results include temperature distributions and ablation zone profiles. The results show the Umeshmotion + ALE method is sufficient for the pulsed lightning current at all three LPL levels since the moving phase boundary, i.e. the ablation front, is found to be confined within the top layer of the laminate. For the continuing lightning currents at all three LPL levels, the Umeshmotion + ALE method is not applicable since the moving phase boundary comes to rest at depths exceeding the thickness of the top layer of the composite laminate.     

MHD three-dimensional flow of viscoelastic fluid over an exponentially stretching surface with variable thermal conductivity

This study models the magnetohydrodynamic (MHD) three-dimensional boundary layer flow of viscoelastic fluid. The flow is due to the exponentially stretching surface. The heat transfer analysis is performed through prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The thermal conductivity is taken temperature dependent. Series solutions of velocities and temperatures are constructed. Graphical results for PST and PHF cases are plotted and analyzed. Numerical values of skin-friction coefficients and Nusselt numbers are presented and discussed.     

Natural convection boundary layer flow of fluid with temperature-dependent viscosity from a horizontal elliptical cylinder with constant surface heat flux

This study deals with the temperature-dependent viscosity effects on the natural convection boundary layer on a horizontal elliptical cylinder with constant surface heat flux. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the heat transfer characteristics are presented as functions of eccentric angle for various values of viscosity variation parameters, Prandtl numbers and aspect ratios. Results show that an increase in the viscosity variation parameter tends to accelerate the fluid flow near the surface and increase the maximum velocity, thus decreasing the velocity boundary layer thickness. As the viscosity variation parameter is increased, the surface temperature tends to decrease, thus increasing the local Nusselt number. Moreover, the local Nusselt number of the elliptical cylinder increases as the Prandtl number of the fluid is increased.     

Continuous dependence on the heat source and non-linear stability for convection with internal heat generation

It is shown that the solution to the boundary-initial value problem for a heat-conducting viscous fluid depends continuously on changes in the heat supply function, for the improperly posed backward in time problem. A non-linear convection threshold is also determined for the problem of a layer of fluid heated internally (non-uniformly), with zero neat flux on the lower boundary and constant-temperature upper surface.     

Oscillatory convection and the Cattaneo law of heat conduction

The problem of thermal convection is investigated for a layer of fluid when the heat flux law of Cattaneo is adopted. The boundary conditions are those appropriate to two fixed surfaces. It is shown that for small Cattaneo number the critical Rayleigh number initially increases from its classical value of 1707.765 until a critical value of the Cattaneo number is reached. For Cattaneo numbers greater than this critical value a notable Hopf bifurcation is observed with convection occurring at lower Rayleigh numbers and by oscillatory rather than stationary convection. The aspect ratio of the convection cells likewise changes.     

Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux

In this paper, a powerful analytical method, called homotopy analysis method (HAM) is used to obtain the analytical solution for a nonlinear ordinary deferential equation that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. Nonlinear ODE which is obtained by similarity solution has been solved through homotopy analysis method (HAM). The main objective is to propose alternative methods of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The obtained analytical solution in comparison with the numerical ones represents a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region.     

The Reynolds analogy for the mixed convection over a vertical surface with prescribed heat flux

The steady mixed convection boundary layer flow over a vertical surface with prescribed heat flux is revisited in this Note. The subset of solutions which can be obtained with the aid of the Reynolds analogy is discussed in a close relationship with the dual solutions reported by Merkin and Mahmood [1] for impermeable, and more recently by Ishak et al. [2], for permeable surfaces.     

Heat and mass transfer in MHD non-Darcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with non-uniform heat source and thermal radiation

A mathematical analysis has been carried out to study magnetohydrodynamic boundary layer flow, heat and mass transfer characteristic on steady two-dimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field. Momentum boundary layer equation takes into account of transverse magnetic field whereas energy equation takes into account of Ohmic dissipation due to transverse magnetic field, thermal radiation and non-uniform source effects. An analysis has been performed for heating process namely the prescribed wall heat flux (PHF case). The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations which are then linearized by quasi-linearization method and solved very efficiently by finite-difference method. Favorable comparisons with previously published work on various special cases of the problem are obtained. The effects of various physical parameters on velocity, temperature, concentration distributions are presented graphically and in tabular form.     

Analysis of fluid flow and heat transfer over an unsteady stretching surface

This article considers two situations involving unsteady laminar boundary layer flow due to a stretching surface in a quiescent viscous incompressible fluid. In one configuration, the surface is impermeable with prescribed heat flux, in the other, the surface is permeable with prescribed temperature. The boundary value problems governing a similarity reduction for each of these situations are investigated and the existence of a solution is proved for all relevant values of physical parameters. The uniqueness of the solution is also proved for some (but not all) values of the parameters. Finally, a priori bounds are obtained for the skin friction coefficient and local Nusselt number.     

The Reynolds analogy for the mixed convection over a vertical surface with prescribed heat flux

The steady mixed convection boundary layer flow over a vertical surface with prescribed heat flux is revisited in this Note. The subset of solutions which can be obtained with the aid of the Reynolds analogy is discussed in a close relationship with the dual solutions reported by Merkin and Mahmood [1] for impermeable, and more recently by Ishak et al. [2], for permeable surfaces.      

Unsteady flow and heat transfer of a second grade fluid over a stretching sheet

The problem of unsteady boundary layer flow of a second grade over a stretching sheet is investigated in this paper. The governing equations of motion are reduced into a partial differential equation with two independent variables by using similarity transformations. The heat transfer analysis has been also carried out for two heating processes namely the prescribed surface temperature (PST case) and prescribed surface heat flux (PHF case). The series solutions of the problem are developed by employing homotopy analysis method (HAM). Convergence of the obtained series solutions are analyzed. It is noted that the present solutions of a second grade are valid for all dimensionless times. Finally, the results are obtained and discussed through graphs for various parameters of interest.     

多层介质的发汗冷却自适应控制

针对一维固定边界复合介质发汗冷却系统的自适应控制问题 ;给出了一个根据实际观测 .基于对气动加热面边界热流密度的估算 ,由热平衡方程及热阻滞函数的特征确定控制输入的自校正控制方法 .理论和数据试验显示 ,对时变的热流及未知的热阻滞函数 ,此方法可以取得很好的控制效果 .     

比热容非常值对高超声速平板边界层稳定性的影响

在高超声速条件下,边界层中气体的温度可能很高,以致气体的比热容不再是常数而与温度有关．这时边界层中的流动稳定性如何是值得研究的问题．采用线性稳定性理论,考虑比热容与温度有关时高超声速可压缩平板边界层的稳定性,并与假定比热容为常值的情况作比较,发现对第一模态和第二模态波的中性曲线、最大增长率都有影响．因此,在高超声速情况下,比热容随温度变化是研究边界层稳定性时必须考虑的一个因素．