# Numerical simulation of fluid flow and heat transfer characteristics in channel with V corrugated plates

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## Abstract

A detailed numerical study is carried out to investigate fluid flow and heat transfer characteristics in a channel with heated V corrugated upper and lower plates. The parameters studied include the Reynolds number (*Re* = 2,000–5,500), angles of V corrugated plates (*θ* = 20°, 40°, 60°), and constant heat fluxs (*q*″ = 580, 830, 1,090 W/m^{2}). Numerical results have been validated using the experimented data reported by Naphon, and a good agreement has been found. The angles of V corrugated plates (*θ*) and the Reynolds number are demonstrated to significantly affect the fluid flow and the heat transfer rate. Increasing the angles of V corrugated plates can make the heat transfer performance become better. The increasing Reynolds number leads to a more complex fluid flow and heat transfer rate. The numerical calculations with a non-equilibrium wall function have a better accuracy than with a standard wall function for solving high Reynolds numbers or complex flow problems.

## Keywords

Heat Transfer Reynolds Number Nusselt Number Heat Transfer Rate Heat Transfer Characteristic## List of symbols

*A*Area

*A*_{c}The surface area of corrugated plate

*A*_{cross}The cross section area of channel

*C*_{1},*C*_{2},*C*_{μ}Turbulent constant

*C*_{p}Specific heat (J/kg K)

*D*_{h}Hydraulic diameter (m)

*E*Enhancement ratio

*H*The height of the channel

*h*_{c}Mean heat transfer coefficient (W/m

^{2}K)*I*Turbulence intensity

*k*_{f}Thermal conductivity of fluid (W/m K)

*k*_{S}Thermal conductivity of solid (W/m K)

*k*Turbulent kinetic energy (m

^{2}/s^{2})*Nu*Nusselt number (\( Nu = h_c H \bar{\sigma }/2k_f \bar{X} \))

*m*_{a}The air mass flow rate

*n*Normal vector

*P*Pressure (atm)

*P*_{c}Wetted perimeter of the channel (m)

*Pr*Prandtl number

*Q*_{a}Heat transferred to the cooling air form the corrugated plates (W)

*Q*_{heater}Heat flux added to the top and bottom corrugated plates (W)

*q*″Heat flux (W/m

^{2})*Re*Reynolds number (

*Re*=*uD*_{ h }/*υ*)*T*_{a}Mean temperature of air (°C)

*T*_{in}Temperature of inlet (°C)

*T*_{s}Mean temperature of surface (°C)

- \( \bar{u}_{i} ,\;\bar{u}_{j} \)
Velocity component (m/s)

*u*_{in}Mean velocity of inlet (m/s)

- \( \bar{X} \)
The distance of the corrugated plate (m)

*x*_{i},*x*_{j}Coordinate (m)

## Greek symbols

*ρ*Density (kg/m

^{3})*μ*_{l},*μ*_{t}Viscosity of laminar and turbulent flow (N s/m

^{2})*υ*Kinematic viscosity (m

^{2}/s)*ε*Dissipation rate of turbulent energy (m

^{2}/s^{2})*θ*Angle of corregated plate

- \( \bar{\sigma } \)
Distance along the corrugated surface

*σ*_{ε},*σ*_{k},*σ*_{T}*k*–*ε*Turbulence model constant for*ε*,*k*and*T*

## Subscripts

- ave
Average

*s*Surface

- in
Inlet

*w*Wall

*l*Laminar

*t*Turbulent

- out
Outlet

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