Ren Anderson

Heat transfer through single and double vertical walls in natural convection: Theory and experiment

The heat transfer through vertical partitions surrounded by thermally-stratified fluids is studied theoretically and experimentally. The theory is based on the Oseen linearization method. The analytical results show the effect of thermal stratification on the partition temperature, fluid flow and heat flux. The relationship between overall heat transfer (Nusselt number) and the degrees of thermal stratification on both sides of the partition is determined. The experimental part of the study confirms the heat transfer features predicted analytically. In particular, it is shown that the theoretical Nusselt number calculation is in good agreement with experimental measurements. It is shown also that the net heat transfer between the two ends of a rectangular enclosure is proportional to (1 + n)−0.61, where n is the number of vertical partitions inserted in the middle of the enclosure.

Heat transfer across a vertical impermeable partition imbedded in porous medium

Abstract This article examines the buoyancy induced circulation occurring on both sides of a vertical impermeable partition separating two semi-infinite porous reservoirs maintained at different temperatures. The circulation is found to consist of two counterflowing boundary layers which interact thermally across the partition, transferring heat from the hot side to the cold side. The net heat transfer rate is calculated and the effect of the thickness and conductivity of the partition on the heat transfer rate is determined. It is demonstrated that the insertion of a vertical impermeable partition in the middle of a vertical porous layer reduces significantly the net heat transfer rate through the layer.

Natural Convection on Both Sides of a Vertical Wall Separating Fluids at Different Temperatures

This paper describes an analytical study of laminar natural convection on both sides of a vertical conducting wall of finite height separating two semi-infinite fluid reservoirs of different temperatures. The countercurrent boundary layer flow formed on the two sides is illustrated via representative streamlines, temperature and heat flux distributions. The net heat transfer between reservoirs is reported for the general case in which the wall thermal resistance is not negligible relative to the overall reservoir-to-reservoir thermal resistance.

Natural Convection at the Interface Between a Vertical Porous Layer and an Open Space

This paper examines the interaction by natural convection between a fluid-saturated porous medium and a fluid reservoir separated by a vertical impermeable partition. The two fluid systems are maintained at different temperatures. The analysis is simplified by assuming Pr > > 1 in the fluid reservoir. It is shown analytically that the flow and temperature fields in the boundary layer regime consist of two fluid layers in counterflow. The interface temperature is shown to increase monotonically with altitude. The important dimensionless group which governs the fluid mechanics is B = (kRaK 1/2 ) / (k′ Ra1/4 ), where k, k′ , RaK and Ra are, respectively, the porous medium conductivity, reservoir fluid conductivity, Darcy-modified Rayleigh number based on partition height, and the reservoir Rayleigh number based on partition height. The effect of parameter, B, on the flow, temperature, and heat transfer is documented in the range 0 < B < ∞.

Efficiency of transient contaminant removal from a slot ventilated enclosure

Abstract This paper reports the results of a fundamental study of the transient removal of a contaminant from a two-dimensional enclosure with one inlet and one outlet. The evolution of the flow and concentration fields are simulated numerically using Jones and Launders low Reynolds number k-e model. The Reynolds number is varied over the range 5–5000, where Re is based on the jet inlet width. The effectiveness of this forced convection mass transfer process is documented quantitatively in terms of a ventilation efficiency and a critical concentration decay time. The relationship between these quantitative performance parameters, the Reynolds number and the ventilation jet orientation, is reported. It is shown that significant gains in ventilation efficiency (or a shortening of the critical concentration decay time) can be made by properly orienting and positioning the inlet and outlet ports relative to each other and to the enclosure. The numerical ventilation efficiency results are summarized by a compact analytical expression based on a theoretical two-zone model of the enclosure flow.

Removal of contaminant generated by a discrete source in a slot ventilated enclosure

Abstract This paper reports the results of a numerical study of the time-dependent removal of contaminant from a two-dimensional enclosure with one inlet and one outlet. The contaminant is generated beginning with the time t = 0 by a concentrated source located inside the enclosure. The contaminant is removed by the through flow established between the inlet and outlet ports. The flows studied cover the laminar and turbulent regimes represented by 30 ⩽ Re ⩽ 3000, where Re is the Reynolds number based on the inlet width and mean velocity. The effectiveness of the contaminant removal scheme is documented in terms of the removal efficiency η r , the volume-averaged concentration of contaminant C , and the critical (clean up) time t c . The effects of Re , ventilation jet orientation and source location are reported. It is shown that the movement and distribution of contaminant is complex and depends strongly on the source location. It is also shown how the relative positioning of the ports and the source location influence the contaminant removal process. The optimal inlet/outlet configuration associated with each position of the concentrated source of contaminant is reported. Slower ventilation schemes can lead to lower contaminant levels when a short contaminant removal time is not a major requirement.

Method for Determining Optimal Residential Energy Efficiency Retrofit Packages

Businesses, government agencies, consumers, policy makers, and utilities currently have limited access to occupant-, building-, and location-specific recommendations for optimal energy retrofit packages, as defined by estimated costs and energy savings. This report describes an analysis method for determining optimal residential energy efficiency retrofit packages and, as an illustrative example, applies the analysis method to a 1960s-era home in eight U.S. cities covering a range of International Energy Conservation Code (IECC) climate regions. The method uses an optimization scheme that considers average energy use (determined from building energy simulations) and equivalent annual cost to recommend optimal retrofit packages specific to the building, occupants, and location. Energy savings and incremental costs are calculated relative to a minimum upgrade reference scenario, which accounts for efficiency upgrades that would occur in the absence of a retrofit because of equipment wear-out and replacement with current minimum standards.

Tree-shaped fluid flow and heat storage in a conducting solid

This paper documents the time-dependent thermal interaction between a fluid stream configured as a plane tree of varying complexity embedded in a conducting solid with finite volume and insulated boundaries. The time scales of the convection-conduction phenomenon are identified. Two-dimensional and three-dimensional configurations are simulated numerically. The number of length scales of the tree architecture varies from one to four. The results show that the heat transfer density increases, and the time of approach to equilibrium decreases as the complexity of the tree designs increases. These results are then formulated in the classical notation of energy storage by sensible heating, which shows that the effective number of heat transfer units increases as the complexity of the tree design increases. The complexity of heat transfer designs in many applications is constrained by first cost and operating cost considerations. This work provides a fundamental basis for objective evaluation of cost and performance tradeoffs in thermal design of energy systems with complexity as an unconstrained parameter that can be actively varied over a broad range to determine the optimum system design.

High Rayleigh number natural convection in partially divided air and water filled enclosures

Abstract This paper describes an experimental study aimed at determining the effect of internal partitions on the natural convection heat transfer across an enclosure. Experiments are conducted using a representative cubic geometry differentially heated from the side with an internal partial vertical partition. Two test cells with different working fluids are used, an air (Pr∼-0.7) and a water (Pr∼-0.6) cell. Nusselt-Rayleigh-aperture width correlation curves are developed for both the air and the water data using a resistance model. For a constant Rayleigh number, as the aperture width is decreased, the flow field undergoes a transition from a boundary layer regime to a blocked flow bulk density driven regime.

Serpentine thermal coupling between a stream and a conducting body

Here we document the effect of flow configuration on the heat transfer performance of a serpentine shaped stream embedded in a conducting solid. Several configurations with fixed volume of fluid are considered: U-shaped with varying spacing between the parallel portions of the U, serpentine shapes with three elbows, and conducting soil with several parallelepipedal shapes. We show that the spacing must be greater than a critical value in order for the heat transfer density of the stream-solid configuration to be the highest that it can be. Spacings larger than this critical value do not yield improvements in heat transfer density. We also show that even though the heat transfer is time dependent, the stream-solid configuration has an effective number of heat transfer units Ntu that is nearly constant in time. The larger Ntu values correspond to the configurations with greater heat transfer density.