Summary
The problem of heat transfer in a two-dimensional porous channel has been discussed by Terrill [6] for small suction at the walls. In [6] the heat transfer problem of a discontinuous change in wall temperature was solved. In the present paper the solution of Terrill for small suction at the walls is revised and the whole problem is extended to the cases of large suction and large injection at the walls. It is found that, for all values of the Reynolds number R, the limiting Nusselt number Nu ∞ increases with increasing R.
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Abbreviations
- ψ :
-
stream function
- 2h :
-
channel width
- x, y :
-
distances measured parallel and perpendicular to the channel walls respectively
- U :
-
velocity of fluid at x=0
- V :
-
constant velocity of fluid at the wall
- η=y/h :
-
nondimensional distance perpendicular to the channel walls
- f(η):
-
function defined in equation (1)
- ν :
-
coefficient of kinematic viscosity
- R=Vh/ν :
-
suction Reynolds number
- ρ :
-
density of fluid
- C p :
-
specific heat at constant pressure
- K :
-
thermal conductivity
- T :
-
temperature
- x=x 0 :
-
position where temperature of walls changes
- T 0, T 1 :
-
temperature of walls for x<x 0, x>x 0 respectively
- θ = (T − T 1)/T 0 − T 1):
-
nondimensional temperature
- ξ=x/h :
-
nondimensional distance along channel
- R * = Uh/v :
-
channel Reynolds number
- Pr = μC p/K :
-
Prandtl number
- λ n :
-
eigenvalues
- B n(η):
-
eigenfunctions
- B (0)n , (η):
-
eigenfunctions for R=0
- B (i)0 , B (ii)0 ...:
-
change in eigenfunctions when R≠0 and small
- K n :
-
constants given by equation (13)
- h ∣ :
-
heat transfer coefficient
- Nu :
-
Nusselt number
- θ m :
-
mean temperature
- C n :
-
constants given by equation (18)
- \(\varepsilon = \left| {\frac{1}{{R P\gamma }}} \right|\) :
-
perturbation parameter
- B 0i (η):
-
perturbation approximations to B 0(η)
- Q = ∂B 0/∂λ 0 :
-
derivative of eigenfunction with respect to eigenvalue
- z :
-
nondimensional distance perpendicular to the channel walls
- F(z):
-
function defined by (54)
References
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Van der Does de Bye, J. A. W. and J. Schenk, Appl. Sci. Res. A 3 (1952) 308.
Schenk, J. and H. L. Beckers, Appl. Sci. Res. A 4 (1954) 405.
Cess, R. D. and C. C. Schaffer, Appl. Sci. Res. A 8 (1959) 339.
Cess, R. D. and C. C. Schaffer, Appl. Sci. Res. A 9 (1959) 64.
Terrill, R. M., Intern. J. Heat Mass Tr. 8 (1965) 1491.
Hatton, A. P. and J. S. Turton, Intern. J. Heat Mass Tr. 5 (1962) 673.
Terrill, R. M., Aeron. Quart. XV (1964) 299.
Terrill, R. M., Aeron. Quart. XVI (1965) 323.
Berman, A. S., Appl. Phys. 24 (1953) 1232.
Whittaker, E. T. and G. N. Watson, A course of modern analysis, Cambridge University Press 1940.
Rosser, J. B., Theory and application of \(\int\limits_0^Z {{\text{e}} - x^2 {\text{d}}x} {\text{ }}and{\text{ }}\int\limits_0^Z {{\text{e}} - p^2 y^2 } {\text{ d}}y{\text{ }}\int\limits_0^y {{\text{e}} - x^2 {\text{d}}x} \), OSRD 5861 (1945), Office of Scientific Research and Development.
Bateman, H., Higher transcendental functions, Volume II, Bateman Manuscript Project, McGraw-Hill Publ. Co., New York 1953.
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Terrill, R.M., Walker, G. Heat and mass transfer in laminar flow between parallel porous plates. Appl. Sci. Res. 18, 193–220 (1968). https://doi.org/10.1007/BF00382347
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DOI: https://doi.org/10.1007/BF00382347