Geometric optimization of a convective T-shaped cavity on the basis of constructal theory

The aim of this paper is to optimize, by means of Bejan’s theory, the geometry of a T-shaped cavity that intrudes into a solid conducting wall. One direction in which the optimization of intrusion geometry can be pursued is that of increasing the complexity of the growing structures. When the heat generated by the volume is removed through one port, and when the smallest volume element size is fixed, the optimization of geometry generates a tree-shaped flow structure. The simplest tree-shaped structure is a ‘first construct’, or an optimized assembly of elemental volumes. The simplest first construct is the T-shaped tree here treated. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The structure has four degrees of freedom: L₀/L₁ (ratio between the lengths of the stem and bifurcated branches), H₁/L₁ (ratio between the thickness and length of the bifurcated branches), H₀/L₀ (ratio between the thickness and length of the stem) and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (?). The purpose of the numerical investigation is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The simulations were performed for the following values of the cavity volume fractions (after having fixed H/L = 1): ? = 0.05, 0.1, 0.2 and 0.3. The first optimization, referred to the degree of freedom L₀/L₁, highlighted one “intermediate” optimal shape, i.e., the best geometry was not obtained for the extremes values of L₀/L₁. As for the degree of freedom H₁/L₁, the optimal geometries were obtained for lowest ratio of H₁/L₁. Finally, when compared to the C-shaped cavity, i.e. the basic configuration, the T-shaped cavity performs approximately 45% better under the same thermal and geometric conditions.     

Geometric optimization of shapes on the basis of Bejan''s Constructal theory

This paper documents the optimization of architecture in accordance with Bejan's Constructal theory. For illustration, we consider the optimization of a cavity that intrudes into a solid conducting wall, having internal heat generation and adiabatic conditions on the outer surfaces. The cavity is rectangular, with fixed volume and variable aspect ratio, and the solid is trapezoidal. The objective is to minimize the global thermal resistance between the volume of the entire system (cavity and solid) and the surroundings. The performance improves as the cavity becomes slender. The geometry is optimal when the cavity penetrates the conducting wall completely.     

Numerical investigation of a PCM-based heat sink with internal fins: Constant heat flux

Melting of a phase change material (PCM) is studied in a heat sink with vertical internal fins and a horizontal base to which a constant heat flux is applied. The phase change material is stored between the fins. A detailed parametric investigation explores various fin height and thickness, PCM layer thickness, and applied heat flux. Transient numerical simulations are performed using the Fluent 6 software. The results show how the transient phase change process depends on the heat flux from the base, heat capacity of the PCM, and fin dimensions. Dimensional analysis of the results is performed, and the generalized results are presented in terms of the melt fractions and Nusselt numbers vs. the Fourier, Stefan and Rayleigh numbers.     

Numerical investigation of a PCM-based heat sink with internal fins

The present study explores numerically the process of melting of a phase-change material (PCM) in a heat storage unit with internal fins open to air at its top. Heat is transferred to the unit through its horizontal base, to which vertical fins made of aluminum are attached. The phase-change material is stored between the fins. Its properties used in the simulations, including the melting temperature of 23-25 °C, latent and sensible specific heat, thermal conductivity and density in solid and liquid states, are based on a commercially available paraffin wax.A detailed parametric investigation is performed for melting in a relatively small system, 5-10 mm high, where the fin thickness varies from 0.15 mm to 1.2 mm, and the thickness of the PCM layers between the fins varies from 0.5 mm to 4 mm. The ratio of the PCM layer to fin thickness is held constant. The temperature of the base varies from 6 °C to 24 °C above the mean melting temperature of the PCM.Transient three- and two-dimensional simulations are performed using the Fluent 6.0 software, yielding temperature evolution in the fins and the PCM. The computational results show how the transient phase-change process, expressed in terms of the volume melt fraction of the PCM, depends on the thermal and geometrical parameters of the system, which relate to the temperature difference between the base and the mean melting temperature, and to the thickness and height of the fins.In search for generalization, dimensional analysis of the results is performed and presented as the Nusselt numbers and melt fractions vs. the Fourier and Stefan numbers and fin parameters. In some cases, the effect of Rayleigh number is significant and demonstrated.     

Correlations and optimization of a heat exchanger with offset-strip fins

The thermo-flow characteristics of a heat exchanger with offset-strip fins are numerically investigated for various fin geometries and working fluids. Previous correlations underestimate f values in the laminar and turbulent regimes and overestimate j values in the laminar regime, as the blockage ratio increase. Therefore, new correlations, which apply to offset-strip fins with blockage ratios of greater than 20%, are presented. Even though the working fluid was changed, the f values did not vary. However, the j values differed according to the working fluid. New j correlations were suggested as functions of the Prandtl number. Design variables of the offset-strip fins in a fuel cooler were optimized by using the correlations and the design of experiment. As a result, the JF factor of the optimized offset-strip fin was enhanced by 24% compared with that of the reference offset-strip fin.     

Experimental and numerical investigation of low melting point metal based PCM heat sink with internal fins

In this paper, low melting point metal (LMPM), eutectic alloy Bi_31.6In_48.8Sn_19.6 (E-BiInSn), was adopted as phase change material for potential thermal management applications. First, E-BiInSn was prepared and its main thermophysical properties were characterized. Then, transient thermal performances of E-BiInSn based heat sinks with internal crossed fins were tested, in comparison with that of organic PCM (octadecanol) which has close melting point. Three types of heat sink structures which have different number of internal fins were studied. Three heating conditions were applied, namely 80 W (2.2 W/cm²), 200 W (5.6 W/cm²) and 320 W (8.9 W/cm²). For all of the cases, E-BiInSn exhibited much superior thermal performance than that of octadecanol. Furthermore, cyclic test of the E-BiInSn heat sink was carried out, which showed good repeatability and stability, and without supercooling. Finally, a simplified 3D conjugate numerical model was developed to simulate the melting process of LMPM heat sink, which showed good agreement with the experimental results. This simplified model would be much useful in practical thermal design and optimization of LMPM heat sink, for that it would significantly save the computational time consumption.     

Natural convection heat transfer from a hollow horizontal cylinder with external longitudinal fins: A numerical approach

Abstract

The continuity, momentum, and the energy equations have been solved in 3D to predict the thermal plume and flow field around an isothermal horizontal longitudinally finned hollow cylinder in air. Effect of Rayleigh number (Ra), L/D, H/D, and s/D on heat transfer from the finned cylinder have been investigated where the input parameters are varied in a wide range of 10⁴ ≤ Ra ≤10⁷, 0.5?≤?L/D?≤?5, 0.0833?≤?H/D?≤?2, and 0.0785?≤?s/D?≤?0.785. Average surface Nusselt number (Nu) increases with increase in Ra and decreases with increase in cylinder length and fin number for all H/D. Nu for a finned solid cylinder is found to be marginally higher than that of the hollow cylinder except at low H/D of 0.0833 and high Ra of 10⁷ when s/D is less than 0.2617 for all L/D. Fin effectiveness is found to be increased with addition of taller fins for both the solid and hollow cylinder with longitudinal fins. Efficiency of the finned cylinder decreases with increase in fin height and Ra for all L/D and s/D. A general correlation of Nu as a function of all the pertinent input parameters (Ra, L/D, H/D, and s/D) has been proposed separately for the hollow isothermal cylinder having longitudinal fins, which can be used for industrial and academic purposes.     

Scroll heat sink: A novel heat sink with the moving fins inserted between the cooling fins

In this paper, a new type of a fan-integrated heat sink named a scroll heat sink is proposed and demonstrated. The most striking feature of the scroll heat sink is that heat dissipation and fluid pumping occurs simultaneously in the whole cooling space without requiring any additional space for a fan module. In the scroll heat sink, the moving fins, which rotate with two eccentric shafts, are inserted between the fixed (cooling) fins. By a relative motion between the moving fins and the cooling fins, a coolant is drawn into the space between them, takes heat away from the cooling fins, and the heated coolant is discharged out of the heat sink. In the present study, an experimental investigation is performed in order to demonstrate the concept of the scroll heat sink. Average coolant velocities and thermal resistances of the scroll heat sink are measured for various rotating speeds of the moving fins from 200 rpm to 500 rpm. Experimental results show that measured flow rates of the coolant are almost linearly proportional to the rotating speed of the moving fins. A theoretical model is also developed to estimate the required pumping power and the thermal resistance, and validated using experimental results. The theoretical model shows that optimized scroll heat sinks have lower thermal resistances than optimized plate-fin heat sinks under the fixed pumping power condition.     

Experimental investigation of thermal resistance of a heat sink with hexagonal fins

In the present work, the effects of the heights, widths of the hexagonal fins, streamwise and spanwise distances between fins and flow velocity on thermal resistance and pressure drop characteristics were investigated using Taguchi experimental design method. Also the temperature distribution within the selected pin fins was determined. Thermal resistance and dimensionless pressure drop were considered as performance statistics. L₁₈(2¹*3⁷) orthogonal array was selected as an experimental plan for the five parameters mentioned above. While the optimum parameters were determined, due to the goals (above aims) more than one being, the trade-off among goals was considered. First of all, each goal was optimized, separately. Then, all the goals were optimized together, considering the priority of the goals, and the optimum results were found to be fin width of 14 mm, fin height of 150 mm, spanwise distance between fins of 20 mm, streamwise distance between fins of 10 mm and flow velocity of 4 m/s.     

A model on the basis of analytics for computing maximum heat transfer in porous fins

This study presents an analytical work on the performance and optimum design analysis of porous fin of various profiles operating in convection environment. Straight fins of four different profiles, namely, rectangular, convex parabolic and two exponential types are considered for the present investigation. An analytical technique based on the Adomian decomposition method is proposed for the solution methodology as the governing energy equations of porous fins for all the profiles are non-linear. A comparative study has been carried out among the results obtained from the porous and solid fins, and an appreciable difference has been noticed for a range of design conditions. Finally, the result shows that the heat transfer rate in an exponential profile with negative power factor is much higher than the rectangular profile but slightly higher than the convex profile. On the other hand, the fin performance is observed to be better for exponential profiles with positive power factor than other three profiles. A significant increase in heat transfer through porous fins occurs for any geometric fin compared to that of solid fins for a low porosity and high flow parameter.     

A numerical investigation of conjugated-natural convection heat transfer enhancement of a nanofluid in an annular tube driven by inner heat generating solid cylinder

Laminar conjugate heat transfer by natural convection and conduction in a vertical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal cylindrical boundary has been studied by a numerical method. It is assumed that the two sealed ends of the tube to be adiabatic. Governing equations are derived based on the conceptual model in the cylindrical coordinate system. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. Results are presented for the flow and temperature distributions and Nusselt numbers on different cross sectional planes and longitudinal sections for Rayleigh number ranging from 10⁵ to 10⁸, solid volume fraction of 0‹φ‹0.05 with copper-water nanofluid as the working medium. Considering that the driven flow in the annular tube is strongly influenced by orientation of tube, study has been carried out for different inclination angles.     

A numerical investigation on the heat and fluid flow of various nanofluids on a stretching sheet

Following the necessity of investigating fluid flow and heat transfer in the stretching sheet problem and effect of nanofluids on them, performance of various nanofluids were investigated in the present study. Three base fluids (deionized water, ethylene glycol, and engine oil) in combination with 18 nanoparticles (metals and their oxides) were investigated. While experimental methods are preferable, a mathematical model was developed and solved by applying differential quadrature method due to lack of such experimental data. With the results obtained in the real dimensions, the error caused by the cancellation of the viscosity effect due to the dimensionless variables was omitted. Effects of magnetic field and volume fraction of nanoparticle on the fluid flow and heat transfer characteristics were investigated. Highest heat transfer rate as well as small amounts of shear stress was obtained for deionized water–Al and deionized water–Mg nanofluids. Increasing volume fraction of nanoparticle was observed to increase both heat transfer and shear stress rates, while presence of a magnetic field caused an increase in shear stress and decrease in heat transfer rate.     

Numerical investigation on the multi-objective optimization of a shell-and-tube heat exchanger with helical baffles

An improved method combining numerical simulation with multi-objective genetic algorithm (MOGA) was applied to study the flow and heat transfer characteristics of shell-and-tube heat exchanger with helical baffles (STHXsHB). It overcomes the dependence on empirical correlations. The helix angle and overlapped degree of helical baffles were chosen as optimization parameters, while the overall heat transfer coefficient K and pressure drop ΔP of STHXsHB were optimized by MOGA. The results showed that both overall heat transfer coefficient K and pressure drop ΔP varied adversely with the helix angles. The pressure drop ΔP was favorably affected by the overlapped degrees. The overall heat transfer coefficient K did not vary significantly with the overlapped degree. Three optimum configurations were obtained by the MOGA to maximize the overall heat transfer coefficient K and minimize the shell-side pressure drop ΔP. Compared with the original heat exchanger, the overall heat transfer coefficient K increased averagely by 28.3%, while the average pressure drop reduced averagely by 19.37%.     

Experimental investigation of heat transfer during melting around a horizontal tube with and without axial fins

Melting phenomena around horizontal tubes with and without axial fins were investigated experimentally. While melting around a horizontal tube results in the well known deformation of the solid-liquid interface, a different heat transfer behavior is to be found by mounting nearly isothermal axial copper fins or nearly adiabatic axial PVC fins. Moreover melting patterns and heat transfer rates are influenced by the geometric fin arrangement. Mean heat transfer rates are correlated, depending on the different investigated convection schemes. Special attention was drawn to the fluid flow behavior at the interface, where Görtler vortices could be detected.     

A numerical study on the performance of PEMFC with wedge-shaped fins in the cathode channel

The gas flow field design has a significant influence on the overall performance of a proton exchange membrane fuel cell (PEMFC). A single-channel PEMFC with wedge-shaped fins in the cathode channel was proposed, and the effects of fin parameters such as volume (0.5 mm³, 1.0 mm³, and 1.5 mm³), number (3, 5, and 9), and porosity of the gas diffusion layer (GDL) (0.2, 0.4, 0.6, and 0.8) on the performance of PEMFC were numerically examined based on the growth rate of power density (GRPD) and polarization curve. It was shown that wedge-shaped fins could effectively improve the PEMFC performance. With an increase in fin volume, the distributions of oxygen mass fraction in the outlet area of the cathode channel were lower, the drainage effect of the PEMFC improved, and GRPD also increased accordingly. Similar results were obtained as the number of fins increased. The GDL porosity had a greater effect than the wedge-shaped fins on the improvement in PEMFC performance, but the influence of GDL porosity weakened and the GRPD of porosity decreased as the porosity increased. This study provides an effective guideline for the optimization of the cathode channel in a PEMFC.     

Frost behavior on a fin considering the heat conduction of heat exchanger fins

A mathematical model is proposed for predicting frost behavior on a heat exchanger fin under frosting conditions, taking into account fin heat conduction. The change in the three-dimensional airside airflow caused by frost growth is reflected in this model. The numerical estimates of frost thickness are consistent with experimental data, with an error of less than 10%. Due to fin heat conduction, frost thickness decreases exponentially toward the fin tip, while considerable frost growth occurs near the fin base. When a constant fin surface temperature is assumed, the predicted frost thickness was larger by more than 200% at maximum, and the heat flux by more than 10% on average, compared to results obtained with fin heat conduction taken into account. Therefore, fin heat conduction could be an essential factor in accurately predicting frost behavior. To improve prediction accuracy under the assumption of constant fin surface temperature, the equivalent temperature (for predicting frost behavior) is defined to be the temperature at which the heat transfer rate neglecting fin heat conduction is the same as the heat transfer rate with fin heat conduction taken into consideration. Finally, a correlation for predicting the equivalent temperature is suggested.     

Parametric study on the performance of a heat exchanger with corrugated louvered fins

The Taguchi method is a well-known parametric study tool in engineering quality and experimental design. This study analyzes five experimental factors (flow depth, ratio of fin pitch and fin thickness, tube pitch, number of louvers and angle of louver) affecting the heat transfer and pressure drop of a heat exchanger with corrugated louvered fins using the Taguchi method. Fifteen samples are selected from experimental database and the heat transfer and flow friction characteristics are analyzed. The results show that flow depth, ratio of fin pitch and fin thickness and the number of the louvers are the main factors that influence significantly the thermal hydraulic performance of the heat exchanger with corrugated louvered fins. Therefore, these three factors are considered as the main factors for an optimum design of a heat exchanger.     

A numerical and experimental investigation of flow maldistribution in a micro-channel heat sink

A study of flow mal-distribution in U-type micro-channel configuration is presented. Numerical simulations indicate that flow deceleration and associated pressure recovery in the inlet header lead to flow separation and recirculation which cause oscillations in channel-wise mass flow distribution. Increase in flow resistance by decrease in channel depth, width or number of channels or increase in channel length, results in a more uniform distribution. Mal-distribution increases at high flow rate or low viscosity due to the dominance of inertial phenomena. Experiments performed on a 25-channel setup illustrate that small manufacturing variations in channel dimensions introduce random fluctuations in flow distribution.     

Comprehensive numerical investigations on the thermal performance of heat recirculating micro combustor with pin fins for micro-thermal voltaic system applications

Aiming at improving the relatively low energy output and energy conversion efficiency of the micro-thermal voltaic (MTPV) system, an innovative heat recirculating micro combustor with pin fins is designed. The effects of pin fins arrangement, hydrogen/air equivalent ratio on the energy output and performance of CHMC, HMCP and HMCI are compared and investigated. The result shows that when the V_in is 6 m/s and Φ is 1.0, the emitter power of CHMC is 72.76W, and that of HCMP and HCMI micro combustor are 75.99W and 76.35W. and the emitter efficiency of CHMC, HCMP and HCMI is 41.93%, 43.26% and 44.01%. HMCI has better energy output capability compared with CHMC and HMCP. Even though, HMCI brings a higher pressure drop, it is within the acceptable range. When the V_in is 6 m/s, the pressure drop from the pin fins only accounts for 26.4% of the total pressure drop for HMCI. Through the study of equivalent ratio, it is found that HMCI has good adaptability in different equivalent ratio range. This work provides new ideas for the development of MTPV system in the future.