# Computational Investigation Of Convective Heat Transfer Biology Essay

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Use of dimples on the surface can significantly intensify the heat transfer enhancement. Some typical examples for use of dimples for heat transfer enhancement are turbine blade cooling, tube heat exchangers in chemical and textile industries, car radiators etc. Further concept for reduction in thermal resistance and consequent enhancement in heat transfer is to increase the depth of the dimples. Introducing the dimples on the surface not only increase the surface area available for heat transfer but also reduces the hydrodynamic resistance for the fluid flow over the surface, resulting in less pressure drop. The vortices formed inside the dimples results in thinning and to disturb the thermal boundary layer formed over the surface during coolant flow and serve ultimately to bring about enhancement of heat transfer between the fluid and its neighboring surface at the price of less increase in pressure. Moon et. al. [1] studied the channel height effect on heat transfer over the dimpled surfaces. Heat transfer coefficient and friction factors were computationally investigated in rectangular channels, which had dimples on one wall. The heat transfer coefficients were *Corresponding author. Tel- +91 02112 254424 calculated for relative channel heights (H/D ratio of 0.37, 0.74, 1.11 and 1.49) in a Reynolds number range from 12,000 to 60,000.The heat transfer enhancement was reported mostly outside of the dimples. The heat transfer enhancement was lowest on the upstream dimpled wall and highest in the vicinity of the downstream rim (edge) of the dimple. The heat transfer coefficient distribution exhibited a similar pattern throughout the studied H/D range (0.37<H/D<1.49).

Kuethe[2] was the first one to suggest using surface dimples for heat transfer enhancement. Surface dimples are expected to promote turbulent mixing in the flow and enhance the heat transfer, as they behave as a vortex generator.

Syred et.al. [3] studied the effect of surface curvature on heat transfer and hydrodynamics within a single hemispherical dimple. Heat transfer behavior in a ''curved'' dimple is identical to that in a ''flat'' dimple. Mahmood et.al. [4] investigated the effect of dimples on local heat transfer and flow structure over a dimpled channel. Experimental results obtained on and above a dimpled test surface placed on one wall of a channel were given for Reynolds number varying from 1250 to 61500. These include flow visualizations, streamwise velocity and local Nusselt numbers. The H/D ratio was kept constant as 0.5. They reported that the flow visualizations show vortical fluid and vortex pairs shed from the dimples, including a large upwash region and packets of fluid emanating from the central regions of each dimple, as well as vortex pairs and vortical fluid that form near dimple diagonals. These vortex structures augment local Nusselt numbers near the downstream rims of each dimple, both slightly within each depression, and especially on the flat surface just downstream of each dimple. The results also showed that as the ratio of inlet to wall temperature decreases, the coolest part of the test surface which corresponds to the highest value of baseline Nusselt number ratio (Nu/Nuoo) intensifies and extends farther away from the downstream rims of the dimples. Mahmood and Ligrani [5] analyzed experimentally the influence of dimple aspect ratio, temperature ratio, Reynolds number and flow structures in a dimpled channel at Reynolds number varying from 600 to 11,000 and H/D ratio varying as 0.20, 0.25, 0.5 and 1.00. The results showed that the vortex pairs which were periodically shed from the dimples become stronger as channel height decreases with respect to the imprint diameter. Oliveira et.al.[6] studied the Nusselt number behavior on deep dimpled surface . Experimental results were presented for a dimpled test surface placed on one wall of a channel. Reynolds number was varied from 12,000 to 70,000 whereas Î´/D ratio was kept as 1.0. These results were compared to measurements from other investigations with different Î´/D ratios to provide information on the influences of dimple depth. These results include local Nusselt numbers and globally averaged Nusselt numbers. Results showed that at all Reynolds number considered, local Nusselt number augmentations increases as the Î´/D ratio increases from 0.2 to 0.3(and all other experimental and geometric parameters were held constant). Burgess and Ligrani [7] showed the experimental results for the dimple depth to dimple print diameter (Î´/D) ratios varying as 0.1, 0.2, and 0.3 to provide information on the influences of dimple depth. They reported that at all Reynolds numbers considered, Nusselt number augmentations increases as dimple depth increases Beves et.al.[8] studied the flow structure within a two-dimensional spherical cavity on a flat surface, numerically and experimentally. They observed that the recirculation zone formed inside the cavity slightly reciprocate around itself.

## Vortex Heat Transfer Enhancement Technique

The vortex formed inside the dimple causes the scrubbing action of flowing fluid inside the dimple as shown in Fig.1. Vortex Heat Transfer Enhancement (commonly known as VHTE) is the Enhancement of heat transfer by a system of 3-Dimensional surface cavities (dimples) having specific geometry, dimensions and mutual orientation .Each dimple acts as a "vortex generator" which provides an intensive and stable heat and mass transfer between the dimpled surface and gaseous heating/cooling media.

Fig.1: VHTE Mechanism

Each dimple acts as a "Vortex Generator" which provides an intensive and stable heat and mass transfer between the dimpled surface and gaseous heating/ cooling media. Taking advantages of VHTE, as a) Higher heat transfer coefficient b) Negligible pressure drop c) Potential pro fouling rate reduction d) Simplicity in design and fabrication e) Compactness and/or lower cost. This method is potentially used in heat transfer enhancement in convective passages for industrial boilers, process heaters and furnaces and heat exchangers variety for other industries like automotive (radiators, oil coolers etc.),heat treating (recuperates etc.), power electronics(convective coolers etc.), aerospace ,military, food processors etc.

## Heat Transfer and Flow Structure on and Above a Dimpled Surface

Flow visualizations[3] show vortical fluid and vortex pairs shed from the dimples. These include a large upwash region and packets of fluid emanating from the central regions of each dimple, as well as vortex pairs and vortical fluid, which form near dimple diagonals.

Fig.2: Sketch of three-dimensional flow structure

These help to augment surface heat transfer levels as they periodically impact the test surface and periodically produce an influx of bulk fluid. This occurs as the vortices and vortical fluid act to ''pump'' fluid to and away from the surface over different length scales, which helps to augment transport of different sized packets of fluid with different temperatures to and away from the surface. The periodic nature of the shedding of vortical fluid from the dimples also aids the heat transfer augmentation process.

The effects of the vortex structures are particularly pronounced near the downstream rims of each dimple as shown in fig.2 , both slightly within each depression, and on the flat surface just downstream of each dimple. The resulting high local Nusselt number region on the flat surface is spread over a region that is approximately parallel to the downstream edge of each dimple, and along two strips of flat surface located near the span wise edges of downstream-diagonal, adjoining dimples as shown in fig.2. Such augmentations are spread over larger surface areas and become more pronounced as the ratio of inlet stagnation temperature to local surface temperature decreases. This is due to the actions of different-sized vortex pairs and secondary flows in effectively advecting cool fluid from the central parts of the channel to regions close to the hotter dimpled surface. Downwash regions from the vortex pair emanating from the central part of each dimple, from the vortex pairs generated along dimple diagonals, and from rotating secondary flows spread over the entire channel cross section all make contributions to this process.

## Computational Procedure

The flow structure within a three dimensional cavity on a flat plate has been studied using STAR-CD code. The width of air passage over the dimple is taken as 38 mm. These initial conditions are necessary for numerical stability. At inlet the temperature of the coolant gas (air) is 305 K while the velocity of the air is 2.5 m/s and 1.01 bar pressure given to the geometry as inflow parameter. The fluid domain is assumed to be isothermal. The geometry of hemispherical cavity under consideration was developed in star design modeling as show in Fig.3.

Fig. 3: Three-dimensional cavity with mesh formation on surface

In the solver setting we have to mention the number of iteration and residual. Due to that we get the solution at appropriate time and convergence.

Number of iteration 200

Maximum residual tolerance 0.001

In the present work we have studied heat transfer enhancement by working with dimpled test surfaces with varying dimple densities. Dimple Î´/D ratio varied as 0.4and 0.5 with inline and staggered arrangement among the dimples. Test section was the main body of the whole computational setup where the heat exchange from hot test surface to cold fluid take place by forced convection. The test section consists of a wooden box (dimensions 400x38.1x38.1mm3) in which plain test plate and dimpled test plates, of varying dimple densities and dimple arrangements were enclosed.

Fig. 4: Schematic of Test Section

Only top dimpled surface of the test plate was exposed to the air stream from which the convective heat transfer to the air stream takes place. The remaining four non-dimpled sides of the test plates were also insulated. Fig.4 shows the schematic of test section with dimpled plate (inline arrangements among the dimples). Fig.5 shows the schematic of the computational set up which gives the clear idea of the air flow bench prepared to conduct the forced convection heat transfer tests.

## Test Plates

Total seven aluminum test plates were taken for analysis. The size of the test plates chosen were as 400 mm in length, 38.1 mm in width and 12 mm thickness. The thickness of the plates was chosen as 12 mm to give the channel thickness to dimple print diameter ratio as 1.2. Hence in each plate dimple print diameter was kept as 10 mm where as the dimple depth was kept as 4 mm to obtain Î´/D ratio as 0.4 and it was increased later to 5 mm to increase Î´/D ratio to 0.5. Computation analysis was done for both the cases of Î´/D ratios. Three test plates were analyzed with 59, 62 and 35 number of dimples on the top surface with staggered arrangement among the dimples. Fig. 6 shows the schematic of dimpled plate to show the inline arrangement of dimples on the surface. Three test plates were conducted with 60, 63 and 36 number of dimples on its top surface with inline arrangements among the dimples. The test plate used were Plain test surface with no dimple, dimpled surfaces with 59, 62 and 35 numbers of dimples and staggered / inline arrangement among the dimples having Î´/D ratio as 0.4 / 0.5. The heat input was varied from 60 Watts to 140 Watts.

## Computational Results

Figure 7 shows the velocity within the single dimple where Î´/D ratio is taken as 0.5 (i.e. hemispherical cavity) for simplicity, while Fig.8 shows pressure variation along the flow over a single hemispherical dimple distribution. Fig.9 shows the turbulence profile within the hemispherical dimple.

Fig. 7: Velocity vector profile within dimple

Fig. 8: Pressure vector profile within dimple

Fig. 9 clearly shows the vortex shedding formed within the cavity. It is observed that the centre of recirculation exists (at approximately 0.5Î´) below the surface within which the cavity sits and towards the upstream face of the cavity.

Fig. 9: Turbulence profile within dimple

The simulation was carried out for forced convection heat transfer over the dimpled surfaces for various combinations of varying parameters.

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Î´/D=0.5, Staggered Dimple Arrangement

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## Nusselt Number

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## Reynolds Number

Fig. 10: Variation of Nusselt Number with Reynolds Number at 60 Watts, Staggered Dimple Arrangement and Î´/D=0.5

The varying parameters were dimple density on plates (varied as 59,62,35,60,63,36 number of dimples on the test surface) with varying dimple arrangements (inline and staggered arrangements), Reynolds number (varied from 200000 to 360000), and Î´/D ratio (varied as 0.4 and 0.5). The sample computational results obtained are presented in graphical forms as shown in Fig. 10 to 13

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## Reynolds Number

## Nusselt Number

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Î´/D=0.5 Inline Arrangement

Fig. 11: Variation of Nusselt Number with Reynolds Number at 80 Watts, Inline Dimple Arrangement and Î´/D=0.5

Fig. 10 to 13 represents the variation of Nusselt number with Reynolds number. Figure 10 shows the results for the plain surface and the dimpled surfaces with Î´/D ratio equals to 0.5. The Reynolds number varies from 200000 to 360000 and heat input 60 Watts. The number of dimples on surfaces varies as 59, 62 and 35 with staggered arrangements among them.

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Fig. 12: Variation of Nusselt Number with Reynolds Number at 120 Watts, Staggered Dimple Arrangement and Î´/D=0.4

As the Reynolds number increases the Nusselt number value increases for all the test surfaces considered. The similar graphs are obtained for other parametric combinations as mentioned earlier. It is observed from the graphs that the maximum value of Nusselt number obtained increases with increase in heat input and Reynolds numbers for each test surface. The Nusselt number values also goes on increasing with increasing the dimple density of test surfaces. Again the values of Nusselt numbers obtained for Î´/D equals to 0.5 are greater than that for Î´/D equals to 0.4 when all other parameters are kept constant.

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Nu60

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## Nusselt Number

Fig. 13: Variation of Nusselt Number with Reynolds Number at 140 Watts, Inline Dimple Arrangement and Î´/D=0.4

## Summery and Conclusion

In the present work aluminum plates of dimensions 400x38.1x12 mm3 was considered as test surfaces. Variation of Nusselt numbers with Reynolds numbers are investigated, with various parameters combinations. Effect of dimple density, dimple depth and dimple arrangement on heat transfer in terms of Nusselt number enhancement is also reported. The main conclusions are summarized as:

Heat transfer rate from the test surface increases with increase in mass flow rate of flowing fluid and heat input.

The use of dimples on the surface results in heat transfer augmentation in forced convection heat transfer with lesser pressure drop . The value of maximum Nusselt number obtained for staggered arrangement of dimples is greater than that for inline arrangement, keeping all other parameters constant. At all Reynolds number considered Nusselt number augmentation increases as the dimple density of test plates increases (all other computational and geometric parameters are kept constant).This is because the more number of dimples produce:(i) increase in the strength and intensity of vortices and associated secondary flows ejected from the dimples (ii) increases in the magnitudes of three-dimensional turbulence production and turbulence transport. But the percent increase in Nusselt number enhancement per unit percent increase in area decreases beyond a particular value of dimple density. More number of dimples beyond a particular value is believed to trap fluid which then acts as a partially insulating pocket to decrease the rate of Nusselt number enhancement with increase in further dimple density. It also results in decrease in rate of Nusselt number enhancement after a certain value of dimple density of plate (here 35 numbers of dimples for staggered arrangement and 60 numbers of dimples for inline arrangement). Thus it can be concluded that the optimum value of dimple density lies in between 35 and 59 numbers of dimples for staggered arrangement and in between 36 and 60 for inline arrangement of dimples on the considered surface area. At all Reynolds number considered Nusselt number augmentation increases with increase in dimple depth. But the rate of increase in Nusselt number per unit increase in surface area are low after increasing the dimple depth beyond a certain value. This is attributed to larger region of stronger re-circulating flow developed due to dipper dimple. The strong recirculating flows produced believe to trap the fluid which again acts as partially insulating zones results in lowering the rate of increase of Nusselt number enhancement.

## Nomenclature

H - Height of test plate, m

h - Convection heat transfer coefficient, W/m2/K

K - Thermal conductivity of gas, W/m/K

l - Characteristics length of plate, mm

m - Mass flow rate, kg/s

Nu - Nusselt number

Nuoo - Nusselt number obtained for plain plate

Nu35 - Nusselt number obtained dimpled plate with 35 numbers of dimples

Nu36 - Nusselt number obtained dimpled plate with 36 numbers of dimples

Nu59 - Nusselt number obtained dimpled plate with 59 numbers of dimples

Nu60 - Nusselt number obtained dimpled plate with 60 number of dimples

Nu62 - Nusselt number obtained dimpled plate with 62 numbers of dimples

Nu63 - Nusselt number obtained dimpled plate with 63 numbers of dimples

Nu/Nuo - Baseline Nusselt number ratio