# Heat transfer in circular microchannels during volumetric heating with magnetic field

- 173 Downloads
- 3 Citations

## 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.

## Keywords

Reynolds Number Heat Transfer Coefficient Nusselt Number Interface Temperature Heat Generation Rate## List of symbols

*d*channel diameter, m

*D*dimensionless channel diameter, d/H

*g*_{o}heat generation rate, W/m

^{3}*G*magnetic field strength, T

*h*heat transfer coefficient, W/m

^{2}-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, m

^{3}*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

## Greek symbols

- α
thermal diffusivity, m

^{2}/s- ρ
density, kg/m

^{3}- ν
kinematic viscosity, m

^{2}/s- ϕ
angular coordinate, radian

- θ
dimensionless temperature, (

*T*−*T*_{in})/[(*g*_{ o }·*S*)/(*k*_{ s }·*L*)]

## Subscripts

*f*fluid

- in
inlet

- max
maximum

*r*radial

*s*solid

*z*axial

- ϕ
angular

## Notes

### Acknowledgments

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

## References

- 1.Peng XF, Peterson GP (1996) Convective heat transfer and flow friction for water flow in microchannel structures. Int J Heat Mass Transf 39:2599–2608CrossRefGoogle Scholar
- 2.Papautsky I, Gale B, Mohanty S, Ameel T, Frazier AB (1999) Effects of rectangular microchannel aspect ratio on laminar friction constant. In: Proceedings of SPIE. The International Society of Optical Engineering, Santa Clara, pp 147–158Google Scholar
- 3.Pfund D, Rector D, Shekarriz A, Popescu A, Welty J (2000) Pressure drop measurements in a microchannel. AIChE J 46(8):1496–1507CrossRefGoogle Scholar
- 4.Rahman MM (2000) Measurements of heat transfer in microchannel heat sinks. Int Commun Heat Mass Transf 27(4):495–506CrossRefGoogle Scholar
- 5.Garmat G, Favre-Marinet M, Asendrych D (2005) Conduction and entrance effect on laminar liquid flow and heat transfer in rectangular microchannels. Int J Heat Mass Transf 48:2943–2954Google Scholar
- 6.Lee WY, Wong M, Zohar Y (2001) Flow separation in constriction microchannels. In: IEEE micro electro mechanical systems (MEMS), the 14th IEEE international conference, Interlaken, Switzerland, pp 495–498Google Scholar
- 7.Cao B, Chen GW, Yuan Q (2005) Fully developed laminar flow and heat transfer in smooth trapezoidal microchannel. Int Commun Heat Mass Transf 32:1211–1220CrossRefGoogle Scholar
- 8.Kohl MJ, Abdel-Khalik SI, Jeter SM, Sadowski DL (2005) An experimental investigation of microchannel flow with internal pressure measurements. Int J Heat Mass Transf 48:1518–1533CrossRefGoogle Scholar
- 9.Yu D, Warrington R, Barron R, Ameel T (1995) An experimental and theoretical investigation of fluid flow and heat transfer in microtubes. In: Proceedings ASME/JSME thermal engineering conference 1, pp 523–530Google Scholar
- 10.Adams TM, Abdel-Khalik SI, Jeter SM, Qureshi ZH (1998) An experimental investigation of single-phase forced convection in microchannels. Int Chem Eng 41:851–857Google Scholar
- 11.Gnielinski V (1976) New equations for heat and mass transfer in turbulent pipe and channel flow. Int Chem Eng 16(2):359–368Google Scholar
- 12.Tunc G, Bayazitoglu Y (2002) Heat transfer in rectangular microchannels. Int J Heat Mass Transf 45:765–773zbMATHCrossRefGoogle Scholar
- 13.Nield DA, Kuznetsov AV (2003) Investigation of forced convection in an almost circular microtube with rough walls. Int J Fluid Mech Res 30(1):1–10CrossRefGoogle Scholar
- 14.Lelea D, Nishio S, Takano K (2004) The experimental research on microtube heat transfer and fluid flow of distilled water. Int J Heat Mass Transf 47:2817–2830CrossRefGoogle Scholar
- 15.Owhaib W, Palm B (2004) Experimental investigation of single-phase forced convection heat transfer in circular microchannels. Exp Therm Fluid Sci 28:105–110CrossRefGoogle Scholar
- 16.Celata GP, Cumo M, Zummo G (2004) Thermal-hydraulic characteristics of single-phase flow in capillary pipes. Exp Therm Fluid Sci 28:87–95CrossRefGoogle Scholar
- 17.Koo J, Kleinstreuer C (2004) Viscous dissipation effects in microtubes and microchannels. Int J Heat Mass Transf 47(14–16):3159–3169CrossRefGoogle Scholar
- 18.Giulio C, D’Agaro P (2005) Numerical simulation of roughness effect on microchannel heat transfer and pressure drop in laminar flow. J Phys D Appl Phys 38:1518–1530CrossRefGoogle Scholar
- 19.Grohmann S (2005) Measurements and modeling of single-phase and flow-boiling heat transfer in microtubes. Int J Heat Mass Transf 48 (19–20):4073–4089CrossRefGoogle Scholar
- 20.Broderick SL, Webb BW, Maynes D (2005) Thermally developing electro-osmotic convection in microchannels with finite Debye-layer thickness. Numer Heat Transf Part A 48(10):941–964CrossRefGoogle Scholar
- 21.Chakraborty S (2006) Analytical solutions of Nusselt number for thermally fully developed flow in microtubes under a combined action of electroosmotic forces and imposed pressure gradients. Int J Heat Mass Transf 49(3–4):810–813CrossRefGoogle Scholar
- 22.Hwang YW, Kim MS (2006) The pressure drop in microtubes and correlation development. Int J Heat Mass Transf 49(11–12):1804–1812CrossRefGoogle Scholar
- 23.Rao PSC, Rahman MM, Soliman HM (2006) Numerical simulation of steady state conjugate heat transfer in a circular microtube inside a rectangular substrate. Numer Heat Transf Part A 49(7):635–654CrossRefGoogle Scholar
- 24.Rahman MM, Rosario L (2004) Thermodynamic analysis of magnetic refrigerators. In: Proceedings of the ASME international mechanical engineering congress and exposition, Anaheim, CA, pp 51–55Google Scholar
- 25.White FM (1991) Viscous fluid flow. McGraw-Hill, New YorkGoogle Scholar
- 26.Özisik MN (1993) Heat conduction. Wiley, New YorkGoogle Scholar
- 27.Pechasky VK, Gschneider KA (1999) Magnetocaloric effect and magnetic refrigeration. J Magn Magn Mater 200:44–56CrossRefGoogle Scholar