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Optimization of Convective Heat Transfer in Microchannels Equipped by Porous Ribs

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Abstract

One methods of cooling electronic components is embedding microchannels in these devices. In these microchannels, the rate of heat transfer can be increased by making changes in their geometry. In this paper, the use of porous ribs on the microchannel wall to increase the heat transfer rate has been studied. For this purpose, the governing equations including continuity, momentum and energy based on Fortchimer–Brinkman–Darcy equations are solved numerically using a control volume method. The velocity field is solved using the SIMPLE method. The periodic boundary condition is applied for the inlet and outlet of the channel and the constant heat flux boundary condition is applied on the walls. The obtained results are compared to the analytical results and a good agreement is observed. Two types of arrangements are considered for the ribs. For both types, the results show an increase in pressure drop and heat transfer rate in the presence of the ribs compared to simple channels. The main purpose of this study is to find the optimum height of ribs for both arrangements. In the first type of arrangement, the ratio of rib height to microchannel height is 0.167 or 0.292 depend on the Reynolds number for the optimal state, and for the second type of arrangement, is 0.167.

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Abbreviations

A :

Non-dimensional height of the porous rib

B :

Non-dimensional width of the porous rib

C F :

Inertia coefficient

Cp :

Heat capacity, kJ kg−1 K−1

Da:

Darcy number

F :

Friction coefficient

H :

Height of the microchannel, m

H :

Heat transfer coefficient W m−2 K−1

K :

Thermal conductivity, W m−1 K−1

k p :

Permeability, m2

k eff :

Effective thermal conductivity, W m−1 K−1

L :

Channel length, m

Nu:

Nusselt number

p, P :

Non-dimensional and dimensional pressure, Pa

Pe:

Peclet number

Pr:

Prandtl number

q″:

Heat flux

Re:

Reynolds number

T :

Non-dimensional temperature

U, V :

Velocity component in x, y directions, m s−1

u, v :

Non-dimensional velocity component in x, y directions

X, Y :

X, y coordinate, m

x, y :

Non-dimensional x, y coordinate

\(\varepsilon\) :

Porosity

\(\theta\) :

Temperature, K

\(\lambda\) :

Periodic length, m

\(\mu\) :

Dynamic viscosity, Pa s

\(\rho\) :

Density, kg m−3

*:

Non-dimensional channel length

B:

Fluid bulk value

dn:

Down wall

F:

Fluid

In:

Inlet

S:

Solid (porous)

up:

Upper wall

W:

Wall

X:

Local Nusselt number

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  1. Department of Mechanical Engineering, Faculty of Engineering, Razi University, P. Box: 6714414971, Kermanshah, Iran

    Javad Rostami

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  1. Javad Rostami
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Rostami, J. Optimization of Convective Heat Transfer in Microchannels Equipped by Porous Ribs. Transp Porous Med 141, 439–468 (2022). https://doi.org/10.1007/s11242-021-01727-7

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