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Numerical and experimental studies of natural convective heat transfer from vertical and inclined narrow isothermal flat plates

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Abstract

Natural convective heat transfer from an isothermal narrow flat plate embedded in a plane adiabatic surface and inclined at moderate positive and negative angles to the vertical has been numerically and experimentally studied. The solution has the Rayleigh number, the dimensionless plate width, the angle of inclination, and the Prandtl number as parameters. Attention was restricted to a Prandtl number of 0.7. The numerical results have been obtained for Rayleigh numbers between 103 and 107 for dimensionless plate widths of between 0.3 and 1.2 and for angles of inclination between +45° and −45°. In the experimental study, results have been obtained for Rayleigh numbers between 4 × 102 and 105 for dimensionless plate widths of 0.4 and 2.5 and for angles of inclination between +45° and −45° to the vertical. Empirical equations for the heat transfer rate have been derived.

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Abbreviations

A :

Heat transfer area of the heated plate (m2)

g :

Gravitational acceleration (m s−2)

h :

Height of heated plate (m)

h c :

Mean heat transfer coefficient (W m−2 K−1)

I :

Current pass through the heater (A)

V :

Voltage drop across the heater (V)

K :

Thermal resistance of Plexiglass (W m−2 K−1)

k :

Thermal conductivity of fluid (W m−1 K−1)

Nu :

Mean Nusselt number based on h and on (T H  − T F )

Nu 0 :

Mean Nusselt number when edge effects are negligible

Nu y :

Local Nusselt number based on y and on (T H  − T F )

Nu L :

Local Nusselt number based on h and on (T H  − T F )

Nu memp :

Mean Nusselt number given by correlation equation for vertical and for inclined plate facing up and facing down

P :

Dimensionless pressure

p :

Pressure (Pa)

p F :

Pressure in fluid (Pa)

Pr :

Prandtl number

\( \bar{q}^{\prime } \) :

Mean heat transfer rate per unit area (W m−2)

\( q_{x}^{\prime } \) :

Local heat transfer rate per unit area (W m−2)

\( Q_{\text{conv}} \) :

Total rate of heat loss by convection (W)

\( Q_{\text{cond}} \) :

Total rate of heat loss by conduction (W)

\( Q_{\text{rad}} \) :

Total rate of heat loss by radiation (W)

Ra :

Rayleigh number based on h and on (T H  − T F )

Ra y :

Rayleigh number based on y and on (T H  − T F )

T :

Temperature (K)

T F :

Temperature of fluid (K)

T H :

Temperature of plate (K)

\( T_{{w_{\text{avg}} }} \) :

Average temperature of the plate (K)

U X :

Dimensionless velocity component in X direction

u x :

Velocity component in x direction (m s−1)

u r :

Reference velocity (m s−1)

U Y :

Dimensionless velocity component in Y direction

u y :

Velocity component in y direction (m s−1)

U Z :

Dimensionless velocity component in Z direction

u z :

Velocity component in z direction (m s−1)

w :

Width of plate (m)

W :

Dimensionless width of plate, w/h

X :

Dimensionless horizontal coordinate normal to plate

x :

Horizontal coordinate normal to plate (m)

Y :

Dimensionless vertical coordinate

y :

Vertical coordinate (m)

Z :

Dimensionless horizontal coordinate in plane of plate

z :

Horizontal coordinate in plane of plate (m)

α :

Thermal diffusivity (m2 s−1)

β :

Bulk expansion coefficient (K−1)

φ :

Angle of inclination from the vertical (Degrees)

ν :

Kinematic viscosity (m2 s−1)

θ :

Dimensionless temperature

ε :

Emissivity

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Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada and the Public Authority for Applied Education and Training of Kuwait.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Abdulrahim Kalendar & Patrick H. Oosthuizen

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  1. Abdulrahim Kalendar
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Correspondence to Abdulrahim Kalendar.

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Kalendar, A., Oosthuizen, P.H. Numerical and experimental studies of natural convective heat transfer from vertical and inclined narrow isothermal flat plates. Heat Mass Transfer 47, 1181–1195 (2011). https://doi.org/10.1007/s00231-011-0778-8

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