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Convective heat transfer in a rotating square channel with oblique cross section

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Abstract

A numerical study has been performed to study the fluid flow and convective heat transfer inside a rotating square isothermal channel with the channel cross-section having oblique angles to the rotational axis. The channel is subjected to a radial rotation. Computations are carried out for flows at Re=500, 1000 and 2000 and range from the channel entrance to a flow distance of 300 and 600 times the hydraulic diameter, depending upon the Reynolds number. Results reveal the vortex flow structures, and consequently the heat transfer phenomena, are quite different from that of previous studies with zero oblique angle. The channel with 45 degree oblique angle yields the best overall heat transfer performance.

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Abbreviations

a :

channel height in the y-direction, m

b :

channel width in the z-direction, m

C p :

specific heat, kJ/kg °C

D h :

hydraulic diameter, m

Gr :

Rotational Grashof number, \(\Omega ^2 L_x \beta (T_w - T_o )D_h^3 /v^2 \)

H :

distance from rotational axis to inlet, m

h :

convective heat transfer coefficient, W/m2 °K

h ⋆ :

nondimensional distance from rotational axis to inlet, H/D h

k :

thermal conductivity of fluid, W/m °K

L x :

characteristic length in the x-direction, m

Nu x :

locally-averaged Nusselt number over a wall, hD hk

Nu :

circumferentially-averaged Nusselt number

Nu ∞ :

Nusselt number for fully developed flow in stationary and γ=0° cases

\(\overline {Nu} \) :

average Nusselt number over the computational channel length

P :

pressure, Pa

P ⋆ :

reduced pressure, \(P - \frac{1}{2}\rho \Omega ^2 [X^2 + (Y\cos \gamma + Z\sin \gamma )^2 ],{\text{ }}Pa\),

P c :

characteristic pressure, μ(U o/a)

P :

dimensionless reduced pressure

Pr :

Prandtl number, ν/α

Re :

Reynolds number, U oDh/ν

Ro :

Rossby number, ΩD h/Uo

Ta :

Taylor number, ReRo

T :

temperature, °K

T b :

local bulk mean temperature, °K

T c :

characteristic temperature, (T w-To, °K

T o :

inlet mean temperature, °K

T w :

wall temperature, °K

ΔT :

temperature difference, (T w-To, °K

U, V, W :

velocity components in the x-,y-,z-directions, respectively, m/s

U o :

inlet mean velocity, m/s

V c, Wc :

characteristic transverse velocity components in y-and z-directions, respectively,

u, v, w :

dimensionless velocity components in (x, y, z) directions, respectively

X :

distance in the axial direction measured from flow inlet, m

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Authors and Affiliations

  1. Department of Mechanical Engineering, and Applied Mechanics, The University of Michigan, 48109, Ann Arbor, Michigan, USA

    S. Fann & W. -J. Yang

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  1. S. Fann
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  2. W. -J. Yang
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Communicated by Y. Jaluria, 28 February 1994

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Fann, S., Yang, W.J. Convective heat transfer in a rotating square channel with oblique cross section. Computational Mechanics 14, 513–527 (1994). https://doi.org/10.1007/BF00377603

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