# Chaotic advection induced heat transfer enhancement in a chevron-type plate heat exchanger

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## Abstract

The present work examines the role of chaotic mixing as a means of heat transfer enhancement in plate heat exchangers. In order to demonstrate the chaotic behavior, sensitivity to initial conditions and horseshoe maps are visualized. The Nusselt number and the friction factor were computed in the range of reynolds number, 1 < *Re* < 10. The Nusselt number increases considerably in chaotic models whereas the friction factor increases only marginally.

## Keywords

Heat Transfer Heat Exchanger Nusselt Number Lyapunov Exponent Chevron## List of symbols

- A
_{p} Projected length (m)

- A
_{s} Cross section of PHE (m

^{2})- b
Distance between chevron plates (m)

- Bx
Sugar to water mass ratio in the mixture

- C
_{p} Specific heat capacity (Jkg

^{−1}K^{−1})- D
_{H} Hydraulic diameter (m)

- d
_{0} Distance of two article at time t = 0 (m)

- \( \overline{{{\text{d}}_{\text{n}} }} \)
Mean distance of M tracers (m)

- f
Fanning friction factor

- h
Heat transfer coefficient (Jm

^{−2}K^{−1}s^{−1})- k
Fluid Thermal conductivity (Jm

^{−1}K^{−1}s^{−1})- kk
Global iteration number

- L
Effective of chevron plate length (m)

- LT
Total length of chevron plate (m)

- M
_{v} Volumetric flow rate (kg/s)

- Nu
Nusselt number

- p
_{c} Wave length of chevron plate corrugation (m)

- q
Constant heat flux (W/m

^{2})*Re*Reynolds number

- t
Time (s)

- T
Temperature (K)

- T
_{b} Bulk fluid temperature (K)

- \( {\text{T}}_{\text{w}} \)
Mean wall temperature in PHE channel cross section (K)

- u
x component of fluid velocity (m/s)

- \( \overline{\text{u}} \)
Mean velocity in PHE channel (m/s)

- V
Velocity vector of fluid element (m/s)

- v
y component of fluid velocity (m/s)

- w
z component of fluid velocity (m/s)

- W
Chevron plate width (m)

- WT
Total width of chevron plate (m)

- x
x position (m)

- x
_{0} Initial

*x*position (m)- y
y position (m)

- y
_{0} Initial y position (m)

- z
z position (m)

- z
_{0} Initial z position (m)

## Greek symbols

- β
Chevron plate angle (º)

- γ
Channel aspect ratio

- ∆
*P* Pressure loss (Pa)

- Δt
Time step (s)

- λ
Lagrangian Lyapunov exponent

- λ
_{n} Localized Lyapunov exponent

- \( \overline{{{{\uplambda}}_{\text{n}} }} \)
Finite time Lyapunov exponent

- μ
Viscosity of apple juice (Pa.s)

- \( {{\upmu}}_{\text{w}} \)
Viscosity of water (Pa.s)

- \( {{\uprho}} \)
Density of fluid (kg/m

^{3})- \( \phi \)
Area enlargement factor

- \( \psi \)
Degrees of freedom

- \( M_{\psi } \)
Convergence monitor

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