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Heat transfer in circular microchannels during volumetric heating with magnetic field

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Abstract

Convective heat transfer within circular microchannels in a rectangular solid substrate with heat generation due to imposed magnetic field was studied. A detailed parametric study was performed by varying Reynolds number, magnetic field strength, working fluid, and the diameter of the channel. It was found that the heat transfer coefficient decreases downstream along the channel. Nusselt number increased with Reynolds number. The tube diameter, properties of the working fluid, and magnetic field strength affected the temperature distribution and heat transfer rate at the solid-fluid interface.

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Abbreviations

d :

channel diameter, m

D :

dimensionless channel diameter, d/H

g o :

heat generation rate, W/m3

G :

magnetic field strength, T

h :

heat transfer coefficient, W/m2-K

H :

height of the substrate, m

k :

thermal conductivity, W/m-K

L :

channel length, m

n x :

number of intervals in x-direction

n y :

number of intervals in y-direction

n r :

number of intervals in r-direction within the tube

n z :

number of intervals in z-direction

p :

pressure, Pa

r :

distance in radial direction, m

Re:

Reynolds number, Vd/ν

S :

volume of the solid substrate, m3

T :

temperature, °C

V :

Average velocity of fluid in the channel, m/s

W :

half of the tube spacing, m

x :

distance along x-direction, m

y :

distance along y-direction, m

z :

distance along z-direction, m

Z :

dimensionless distance along axial direction, z/L

α:

thermal diffusivity, m2/s

ρ:

density, kg/m3

ν:

kinematic viscosity, m2/s

ϕ:

angular coordinate, radian

θ:

dimensionless temperature, (T−T in)/[(g o ·S)/(k s ·L)]

f :

fluid

in:

inlet

max:

maximum

r :

radial

s :

solid

z :

axial

ϕ:

angular

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Acknowledgments

The authors would like to acknowledge financial support received from NASA under grant number NAG3-2751.

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Authors and Affiliations

  1. University of South Florida, Tampa, FL, 33620, USA

    Muhammad M. Rahman, Abdullatif A. Gari & Shantanu Shevade

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  1. Muhammad M. Rahman
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  2. Abdullatif A. Gari
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  3. Shantanu Shevade
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Correspondence to Muhammad M. Rahman.

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Rahman, M.M., Gari, A.A. & Shevade, S. Heat transfer in circular microchannels during volumetric heating with magnetic field. Heat Mass Transfer 44, 463–472 (2008). https://doi.org/10.1007/s00231-007-0257-4

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