3. Results and discussion

where <sup>q</sup>″ and Tw(x) and Tb(x) act as the supplied heat flux and wall and local

Boundary Layer Flows - Theory, Applications and Numerical Methods

<sup>f</sup> <sup>¼</sup> <sup>2</sup> <sup>Δ</sup>P d

The comparison between the enhancement in thermal performance and a penalty in the pressure drop is assessed by introducing the performance evaluation criteria (PEC) of corrugated channels with different roughness dimensions. The

> PEC <sup>¼</sup> Nu=Nus f =fs

where fs and Nus are the friction factor and the Nusselt number of smooth

The performance of corrugated channels is estimated according to different

Re <sup>¼</sup> <sup>ρ</sup> um dh μ

where μ, ρ, dh, and um are dynamic viscosity, density, hydrodynamic diameter,

The ANSYS Fluent CFD package-based control volume method is adopted to discretize the governing equations and simulate thermal flow behavior of corrugated channels. The SIMPLE algorithm is utilized for solving the flow field. The diffusion terms and other resulting terms are discretized by employing the firstorder upwind scheme. The residuals lower than 10�<sup>6</sup> is chosen to achieve the convergence criterion for all variables. A fine grid discretization close to the wall is adopted. Also, the meshing system of 23,964 grids is sufficient for solution accuracy. On the other hand, the numerical code that is validated through a reasonable agreement is shown (Figure 2a) between the Nusselt number of the present work and the same number which is obtained from the well-known Gnielinski correlation [18]. Furthermore, good agreement is indicated for the friction factor (Figure 2b)

(a) Numerical Nu of the present work and that obtained from Gnielinski's correlation [17] and (b) Numerical

values of the Reynolds number which is introduced as

between the present work and the work of San and Huang [5].

<sup>L</sup> <sup>ρ</sup> um<sup>2</sup> (9)

<sup>1</sup>=<sup>3</sup> (10)

(11)

bulk temperatures, respectively. The friction factor is defined as

PEC can be calculated as

channel, respectively.

and mean fluid velocity.

Figure 2.

164

f and that of San and Huang [5].

The flow-thermal features of turbulent flow in corrugated channels are evaluated numerically. The enhanced heat transfer and an accompanied pressure loss are assessed for corrugated channels under the influences of rib arrangement, rib configuration, rib roughness parameters, and rib shapes. The dimensionless parameters Nu, f, and PEC through a wide range of Re are presented to assess the performance of corrugated channels.

#### 3.1 The effect of rib arrangements

Corrugated channels exist in three layouts depending on rib arrangements, IOCC, ICC, and OCC, as described in Figure 1a. The variations of Nu and f with the Re number of all rectangular rib arrangements of corrugated channels and smooth one are presented in Figure 3a and b, respectively. The rate of heat that is transferred in corrugated channels is higher than that of the smooth channel. The heat transfer varies insignificantly with the rib distribution at the low Re. The rib distribution experiences a pronounced influence on the Nusselt number when Re increases. The ICC shows a maximum ability to exchange the heat, while the OCC has a lower thermal performance. On the other hand, there is an additional pressure loss associated with corrugated channels compared with smooth ones as exhibited in Figure 3b. The friction factor decreases slightly with the Re. Also, the OCC has a

Figure 3.

(a) Different rib arrangements of corrugated channels and the influence of rib configuration on Nu, f, and PEC as described in (b), (c), and (d), respectively, for the different values of Re.

minimum friction factor, while the ICC owns a maximum pressure loss. Moreover, the performance evaluation criterion (PEC) varies inversely with the Re as exhibited in Figure 3c. The increase in pressure loss exceeds the enhancement in the heat transfer for all corrugated channel layouts. Also, OCC has higher PEC than both IOCC and ICC channels. This is due to the increase in f of OCC is lower than that of ICC and IOCC. Even though, both ICC and IOCC have higher Nu than IOCC. rate between the core flow and recirculating flow. Thus, the heat exchange between the heating wall and the flow is enhanced. On the other hand, f is higher for corrugated channels than the smooth one as revealed in Figure 4c. In one side, the results revealed that the heat is transferred more effectively in the corrugated channel than the smooth one due to the additional surface area, suppressing the boundary layer thickness associated with corrugated channels. On the other side, the corrugation results in a substantial flow recirculation and separation and an extra surface area, and thus it creates higher pressure drop. The corrugated channel C1 registers the highest Nu, while the minimum Nu is achieved for corrugated channel B1. Conversely, the results exhibit that the minimum pressure drop is registered for B1 configuration channel among other corrugated channels. Moreover, the influence of rib configuration of corrugated channels on the PEC is presented in Figure 4d. The results reveal that there is a monotonic decrease of PEC with the Re. The optimum performance is accomplished at the lower Re. As Re increases the conflict between the augmentation in thermal performance and degradation in pressure drop is initiated. The higher values of PEC are obtained for C3 and B1 corrugated channels, whereas D1 and D2

Thermal-Hydrodynamic Characteristics of Turbulent Flow in Corrugated Channels

configurations have the minimum values of PEC.

DOI: http://dx.doi.org/10.5772/intechopen.84736

Nu, f, and PEC for different (a) rib heights, (b) rib pitches, and (c) rib widths.

Figure 5.

167
