Al.M. Morega

Optimal Arrays of Pin Fins and Plate Fins in Laminar Forced Convection

We report the optimal geometry of an array of fins that minimizes the thermal resistance between the substrate and the flow forced through the fins. The flow regime is laminar. Two fin types are considered: round pin fins, and staggered parallel-plate fins. The optimization of each array proceeds in two steps: The optimal fin thickness is selected in the first step, and the optimal thickness of the fluid channel is selected in the second. The pin-fin array is modeled as a Darcy-flow porous medium. The flow past each plate fin is in the boundary layer regime. The optimal design of each array is described in terms of dimensionless groups

Optimal Spacing Between Pin Fins With Impinging Flow

This is an experimental, numerical, and theoretical study of the heat transfer on a pin-finned plate exposed to an impinging air stream. The pin fins are aligned with the air approach velocity. The base plate and the fin cross section are square. It is demonstrated experimentally that the thermal conductance between the plate and the air stream can be maximized by selecting the fin-to-fin spacing S. Next, a simplified numerical model is used to generate a large number of optimal spacing and maximum heat transfer data for various configurations, which differ with respect to fin length (H), fin thickness (D), base plate size (L), fluid type (Pr), and air velocity (Re L ). Finally, the behavior of the optimal spacing data is explained and correlated theoretically based on the intersection of asymptotes method. The recommended correlations for optimal spacing, S opt /L≃0.81 Pr -0.25 Re L -0.32 , and maximum thermal conductance, (q/ΔT) max /k a H ≃ 1.57 Pr 0.45 Re L 0.69 (L/D) 0.31 , cover the range D/L = 0.06 - 0.14, H/L = 0.28-0.56, Pr = 0.72-7, Re D = 10-700, and Re L = 90-6000.

Heatline visualization of forced convection laminar boundary layers

Abstract This paper reports in closed form the similarity heatfunctions H for laminar boundary layer flow on a flat wall. Plots of the constant -H lines (‘heatlines’) show that the path of convection from a hot free stream to a cold wall is unlike the path of convection from a hot wall to a cold fluid. The true path of convection in laminar boundary layer flow is visualized in charts drawn for both heat transfer modes (cold wall, hot wall), several Prandtl numbers (0.02, 0.72, 7) and isothermal walls and constant-flux walls. The paper stresses the heat transfer features that are brought into view for the first time by the heatline patterns. As a supplementary contribution, the paper reports the exact similarity solution for the wall with uniform flux in the Pr → 0 limit, and proposes a closed-form local Nusselt number correlation that covers the entire Pr range.

Heatline visualization of forced convection in porous media

Abstract The patterns of heatlines reported in this paper illustrate for the first time the true path of convective heat transfer through a saturated porous medium. Heatline patterns are reported for the following fundamental configurations: the boundary layer near an isothermal wall, the boundary layer near a wall with uniform heat flux, and the two-dimensional porous layer confined by two parallel plates. Emphasis is placed on the convection features that are being visualized for the first time by the heatline method, i.e., not by traditional methods such as the use of isotherms. It is shown that the heatlines of a flow in which the wall serves as heat sink are unlike the heatlines of the same flow with a wall that serves as heat source. The seepage flow with slip at the boundary is visualized by heatlines that leave a hot wall at an angle. The wall heat-flux distribution is visualized by the density of the heatlines that intersect the wall. The heatline pattern in fully developed flow of a pure fluid through a parallel-plate channel is also reported in order to emphasize that the pure-fluid pattern is not exactly the same as the pattern in the corresponding two-dimensional space filled with seepage flow through a porous medium.

Free stream cooling of a stack of parallel plates

Abstract This paper addresses the fundamental heat transfer augmentation question of how to arrange a stack of parallel plates (e.g. fins of heat sink, printed circuit boards) in a free stream such that the thermal resistance between the stack and the stream is minimum. It is shown that the best way of positioning the plates relative to one another is by spacing them equidistantly. When the overall dimensions of the stack are specified, there is an optimal number of plates for minimum thermal resistance. The optimal number and minimum resistance are anticipated theoretically and correlated into compact formulas that agree with numerical and experimental results in the ReL range 102-104. Finally, it is shown that a stack with more plates than the optimal number can be modeled more expediently as a porous block immersed in a free stream.

Optimal spacing of parallel boards with discrete heat sources cooled by laminar forced convection

This paper shows numerically how to select the optimal spacing between boards mounted in a stack of specified volume, so that the overall thermal conductance between the stack and the forced coolant is maximum. Several configurations are considered: boards with uniform flux, flush-mounted discrete sources, and protruding heat sources. The flow is laminar and the pressure difference across the stack is fixed (Δp). It is shown that for all the board geometries and thermal boundary conditions studied, the optimal board-to-board spacing is correlated by (Dopt/l ∼ 2.7(Δpl2 / μα)−¼where l is the effective longitudinal (flow) distance occupied by the discrete sources and the unhealed patches contained between them, and μ and α are the viscosity and thermal diffusivity of the fluid. If U∞is the free-stream velocity upstream of the stack, the optimal spacing is given by (Dopt/l) ∼ 3.2pr−¼(U∞l / v)−½.

Cooling of stacks of plates shielded by porous screens

Abstract This paper addresses the question of how to cool a stack of parallel, heat-generating boards when the flow is impeded by electromagnetic screens placed upstream and downstream of the stack. Four separate designs are considered: (1) forced convection cooling of a stack with board-to-board spacing selected to minimize the stack-coolant thermal resistance; (2) forced convection cooling of stack with fixed board-to-board spacing; (3) natural convection cooling of a vertical stack with spacing selected to minimize the overall thermal resistance; and (4) natural convection cooling of a vertical stack with fixed spacing. The optimal spacings in designs (1) and (3) are determined by intersecting the known asymptotic solutions for stacks with small spacings and stacks with large spacings. The results of parts (1) and (2) are extended to applications where the stack is cooled by immersion in a free stream. We show that the effect of the screen is controlled by a single dimensionless group, which is identified for each class of designs; namely, forced versus natural convection, and high- versus low-screen Reynolds number. Engineering results are reported for the design of screens made of wire meshes, or perforated plate with square (sharp) edges.

Optimization of pulsating heaters in forced convection

Abstract This is a theoretical, numerical and experimental study that shows how to optimize the performance of on and off pulsating heaters in forced convection. Scale analysis shows that there exists an optimal heat pulse interval or frequency that maximizes the overall thermal conductance between the heater and the free stream U∝. Numerical results for a flat plate heater and experimental results for a cylinder in cross-flow validate the theory. Numerically it is shown that the optimal pulsating regime can be identified accurately by using a complete simulation of the flow and temperature field around the heater. Boundary layer simplified numerical methods fail to simulate the short-times (high frequency) range of the process. The maximized overall conductance of a pulsating heater does not exceed the conductance associated with a steady (continuous) heater. The experimental and numerical results are nondimensionalized and correlated by using the scales recommended by theory. When the ‘on’ and ‘of’ intervals are comparable, the optimal heat pulse interval is approximately 0.1 L U ∝ , where L is the scale of the swept length of the heater shape. This conclusion also applies to a pulsating heater embedded in a porous medium with uniform flow.

The cooling of a heat-generating board inside a parallel-plate channel

This paper addresses the fundamental question of how to position a heat-generating board inside a parallel-plate channel, where it is cooled by forced convection. It is shown that when the board substrate is a relatively good thermal conductor, the best board position is near one of the channel walls, and the worst position is in the middle of the channel. The best and worst positions switch places when the board substrate is a relatively poor conductor. The optimal spacing between a heat-generating surface (uniform temperature, or uniform heat flux) and the insulated wall that completes a parallel-plate channel is reported. Finally, it is shown under what conditions it is advantageous to divide a heat-generating board into two or more equidistant boards inside the same channel, when the total rate of heat generation of all the boards and the channel spacing are fixed.

Melting around a shaft rotating in a phase-change material

Abstract In this paper we describe the thin-film melting of a block of solid phase-change material (the bearing) around a rotating cylinder (the shaft). We determine the relation between the force applied on the shaft and the speed with which the shaft migrates into the bearing, the relation between the applied force and the torque, and the angle between the applied force and the direction of migration into the bearing. The method is based on contact melting theory, which combines the Reynolds thin-film lubrication theory with an analysis of phase-change heat transfer in the melt. The paper addresses three limiting regimes of the contact melting phenomenon: (1) the long bearing with melting due to frictional heating in the melt layer; (2) the short bearing with melting due to frictional heating in the melt layer, and (3) the short bearing with melting due to a temperature difference imposed between the hot cylinder and the cold phase-change material.