This paper presents an analytical and numerical study on the heat transfer characteristics of forced convection across a microchannel heat sink. Two analytical approaches are used: the porous medium model and the fin approach. In the porous medium approach, the modified Darcy equation for the fluid and the two-equation model for heat transfer between the solid and fluid phases are employed. Firstly, the effects of channel aspect ratio (χs) and effective thermal conductivity ratio ( ) on the overall Nusselt number of the heat sink are studied in detail. The predictions from the two approaches both show that the overall Nusselt number (Nu) increases as χs is increased and decreases with increasing . However, the results also reveal that there exists significant difference between the two proaches for both the temperature distributions and overall Nusselt numbers, and the discrepancy becomes larger as either as or is increased. It is suggested that this discrepancy can be attributed to the indispensable assumption of uniform fluid temperature in the direction normal to the coolant flow invoked in the fin approach. The effect of porosity (e) on the thermal performance of the microchannel is subsequently examined. It is found that whereas the porous medium model predicts the existence of an optimal porosity for the microchannel heat sink, the fin approach predicts that the heat transfer capability of the heat sink increases monotonically with the porosity. The effect of turbulent heat transfer within the microchannel is next studied, and it is found that turbulent heat transfer results in a decreased optimal porosity in comparison with that for the laminar flow. A new concept of microchannel cooling in combination with microheat pipes is proposed, and the enhancement in heat transfer due to the heat pipes is estimated. Finally, two-dimensional numerical calculations are conducted for both constant heat flux and constant wall temperature conditions to check the accuracy of analytical solutions and to examine the effect of different boundary conditions on the overall heat transfer.

The propagation of a pre-existing edge crack across a finite plate subjected to cold shock has been studied. The plate, initially at uniform temperature, is exposed to a cold shock on one surface whilst three dierent types of heat transfer boundary condition are separately considered for the opposing face: cold shock, thermal insulation and fixed temperature. For all three boundary conditions, the plate experiences tensile stress near the cold-shocked surface and compressive stressing near the mid-plane. Consequently, a Mode I edge crack extending into the compressive region may grow in one of three different modes: continued extension in plane strain, channelling and spalling. The thermal shock conditions governing each failure mode are quantified, with a focus on crack channelling and spalling. The dislocation method is employed to calculate the energy release rates for plane strain cracking and steady-state channelling. For steady-state spalling, the energy release rate is obtained by an energy analysis of elastic beams far ahead and far behind the crack tip. Analytical solutions are also obtained in the short crack limit in which the problem is reduced to an edge crack extending in a half space; and the parameter range over which the short crack solution is valid for a finite plate is determined. Failure maps for the various cracking patterns are constructed in terms of the critical temperature jump and Biot number, and merit indices are identified for materials selection against failure by thermal shock.

The influence of each of the six different types of morphological imperfection-waviness, non-uniform cell wall thickness, cell-size variations, fractured cell walls, cell-wall misalignments, and missing cells-on the yielding of 2D cellular solids has been studied systematically for biaxial loading. Emphasis is placed on quantifying the knock-down effect of these defects on the hydrostatic yield strength and upon understanding the associated deformation mechanisms. The simulations in the present study indicate that the high hydrostatic strength, characteristic of ideal honeycombs, is reduced to a level comparable with the deviatoric strength by several types of defect. The common source of this large knock-down is a switch in deformation mode from cell wall stretching to cell wall bending under hydrostatic loading. Fractured cell edges produce the largest knock-down effect on the yield strength of 2D foams, followed in order by missing cells, wavy cell edges, cell edge misalignments, г Voronoi cells,θ Voronoi cells, and non-uniform wall thickness. A simple elliptical yield function with two adjustable material parameters successfully ®ts the numerically predicted yield surfaces for the imperfect 2D foams, and shows potential as a phenomenological constitutive law to guide the design of structural components made from metallic foams.

Sandwich panels with two-dimensional metal cores can be used to carry structural load as well as dissipate heat through solid conduction and forced convection. This work attempts to uncover the nature of heat transfer in these lightweight systems, with emphasis on the eects of varying cell morphologies and cell arrangements. The types of cell shape and cell arrangement considered include regular hexagon, square with connectivity 4 or 3, and triangle with connectivity 6 or 4. Two analytical models are developed: corrugated wall and eective medium. The former models the cellular structure in detail whilst, the latter models the fluid saturated porous structure using volume averaging techniques. The overall heat transfer coeffcient and pressure drop are obtained as functions of relative density, cell shape, cell arrangement, fluid properties, and overall dimensions of the heat sink. A two-stage optimization is subsequently carried out to identify cell morphologies that optimize the structural and heat transfer performance at speci

A minimum-weight flexural actuator is designed. The actuator comprises a triangular corrugated core with shape memory alloy (SMA) faces. It is clamped at one end and free at the other. For design and optimization, the temperature history of the face sheets upon heating and subsequent cooling is 7rst obtained as a function of the cooling e8ciency (Biot number) and the operational frequency deduced. Based upon this response, a phenomenological model is employed to represent the martensite evolution. Thereafter, the end de'ection is calculated as a function of temperature. The minimum weight is calculated subject to the provisos that: (i) the end de'ection attains a speci7ed value; (ii) the power consumed is less than the upper limit of the supply; and failure is averted by (iii) face=core yielding and (iv) face=core buckling; (v) the operational frequency of the panel achieves a speci7ed limit.