Forced convection of gaseous slip-flow in porous micro-channels under Local Thermal Non-Equilibrium conditions

Steady laminar forced convection gaseous slip-flow through parallel-plates micro-channel filled with porous medium under Local Thermal Non-Equilibrium (LTNE) condition is studied numerically. We consider incompressible Newtonian gas flow, which is hydrodynamically fully developed while thermally is developing. The Darcy–Brinkman–Forchheimer model embedded in the Navier–Stokes equations is used to model the flow within the porous domain. The present study reports the effect of several operating parameters on velocity slip and temperature jump at the wall. Mainly, the current study demonstrates the effects of: Knudsen number (Kn), Darcy number (Da), Forchheimer number (Γ), Peclet number (Pe), Biot number (Bi), and effective thermal conductivity ratio (K _R) on velocity slip and temperature jump at the wall. Results are given in terms of skin friction (C _f Re ^*) and Nusselt number (Nu). It is found that the skin friction: (1) increases as Darcy number increases; (2) decreases as Forchheimer number or Knudsen number increases. Heat transfer is found to (1) decreases as the Knudsen number, Forchheimer number, or K _R increases; (2) increases as the Peclet number, Darcy number, or Biot number increases.     

Diffusion bonding in multi-layers systems

 A mathematical model is presented to simulate the diffusion bonding in multi-layers systems. The model is solved analytically using Green's function method. The time required by the bonding material to attain its maximum solvability in the other two layers is estimated. Received on 4 January 2000     

The hyperbolic heat conduction equation in an anisotropic material

In this work, the phase-lag concept in the wave theory of heat conduction is extended to describe the thermal behavior of anisotropic material. This is achieved by assuming that there are phase-lags of different magnitudes between each component of the heat flux vector and the summation of temperature gradients in all directions of the orthogonal coordinate system. Also, expressions are provided to specify the locations of the principal coordinate axes, the principal thermal conductivities and the principal thermal relaxation times. Received on 26 March 1999     

Unsteady non-darcian fluid flow in parallel-plates channels partially filled with porous materials

Using Green's function method, analytical solutions are obtained for the problem of transient fluid flow in parallel-plate channels partially filled with porous materials. The unsteadiness in the fluid flow is caused either by a sudden change in the imposed pressure gradient or (and) by a sudden change in the velocity of the channel boundaries. The Brinkman-extended Darcy model is used to model the flow inside the porous domain. Received on 9 April 1997     

Examination of the Thermal Equilibrium Assumption in Transient Natural Convection Flow in Porous Channel

The local thermal equilibrium assumption in the transient natural convection channel flow is investigated numerically. The Darcy–Brinkman–Forchheimer model is used to model the flow inside the porous domain. The effect of different parameters on the validity of the local thermal equilibrium assumption is examined. It is found that the volumetric Nusselt number has the most significant effect on the local thermal equilibrium assumption.     

Validation of Thermal Equilibrium Assumption in Transient Forced Convection Flow in Porous Channel

The validity of the local thermal equilibrium assumption in the transient forced convection channel flow is investigated analytically. Closed form expressions are presented for the temperatures of the fluid and solid domains and for the criterion which insures the validity of the local thermal equilibrium assumption. It is found that four dimensionless parameters control the local thermal equilibrium assumption. These parameters are the porosity , the volumetric Biot number Bi, the dimensionless channel length _max and the solid to fluid total thermal capacity ratio C _R. The qualitative and quantitative aspects of the effects of these four parameters on the channel thermal equilibrium relaxation time are investigated.     

Entropy generation during fluid flow in a channel under the effect of transverse magnetic field

Entropy generation due to fluid flow and heat transfer inside a horizontal channel made of two parallel plates under the effect of transverse magnetic field is numerically investigated. The flow is assumed to be steady, laminar, hydro-dynamically and thermally fully developed of electrically conducting fluid. Both horizontal walls are maintained at constant temperatures higher than that of the fluid. The governing equations in Cartesian coordinate are solved by an implicit finite difference technique. After the flow field and the temperature distributions are obtained, the entropy generation profiles are computed and presented graphically. The factors, which were found to affect the problem under consideration are the magnetic parameter, Eckert number, Prandtl number, and the temperature parameter (θ_∞). It was found that, entropy generation increased as all parameters involved in the present problem increased.     

Transient thermal behavior of a cylindrical brake system

A mathematical model is presented to describe the thermal behavior of a brake system which consists of shoe and drum. The model is solved analytically using Green's function method for any type of the stopping braking action. In terms of the obtained solutions, the transient temperature distribution of the brake is described. The thermal behavior is investigated for three specified braking actions which are the impulse, unit step and trigonometric stopping actions. Received on 14 April 1999     

Validation of the thermal equilibrium assumption in the transient conjugated forced convection channel flow

 The validity of the local thermal equilibrium assumption in the transient conjugated forced convection channel flow is investigated analytically. Closed form expressions are presented for the temperatures of the fluid and solid domains and for the criterion which insure the validity of the local thermal equilibrium assumption. It is found that three dimensionless parameters control the local thermal equilibrium assumption. These parameters are the Biot number Bi, the dimensionless channel length ξ_max and the solid to fluid total thermal capacity ratio C _R. The qualitative and quantitative aspects of the effects of these three parameters on the channel thermalization time are investigated. Received on 9 August 2000