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Transient conjugate heat transfer from a hemispherical plate during free liquid jet impingement on the convex surface

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Abstract

This paper considers the analysis of transient heating of a hemispherical solid plate of finite thickness during impingement of a free liquid jet. A constant heat flux was imposed at the inner surface of the hemispherical plate at t = 0 and heat transfer was monitored for the entire duration of the transient until a steady state condition was reached. Calculations were done for Reynolds number (Re) ranging from 500 to 1,500 and dimensionless plate thicknesses to nozzle diameter ratio (b/d n) from 0.083 to 1.5. Results are presented for local and average Nusselt number using water as the coolant and various solid materials such as silicon, constantan, and copper. It was detected that increasing the Reynolds number decreases the time for the plate to achieve the steady-state condition. Also, a higher Reynolds number increases the Nusselt number. Hemispherical plate materials with higher thermal conductivity maintain lower temperature non-uniformity at the solid–fluid interface. Increasing the plate thickness decreases the maximum temperature in the solid and increases the time to reach the steady-state condition.

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Abbreviations

b :

Plate thickness, ro–ri [m]

d n :

Diameter of the nozzle [m]

Fo:

Fourier number, α f t/d 2n

g :

Acceleration due to gravity [m/s2]

h :

Heat transfer coefficient [W/m2K], qint/(T int−T j)

h av :

Average heat transfer coefficient [W/m2K], defined by equation (16)

H n :

Distance of the nozzle from the point of impingement [m]

k :

Thermal conductivity [W/m K]

Nu:

Nusselt number (h·d n)/k f

Nuav :

Average Nusselt number for the entire surface (h av·d n)/k f

p :

Pressure [Pa]

q :

Heat flux [W/m2]

q av :

Average heat flux [W/m2]

r :

Radial coordinate [m]

r i :

Inner radius of hemisphere [m]

r o :

Outer radius of hemisphere [m]

Re :

Reynolds number (V J·d n)/ν f

s:

Coordinate along the arc length, r o Φ [m]

t :

Time [s]

T :

Temperature [K]

V J :

Jet velocity [m/s]

V r,z :

Velocity component in the r, z-direction [m/s]

z:

Axial coordinate [m]

α :

Thermal diffusivity [m2/s]

δ :

Liquid film thickness [m]

ν :

Kinematic viscosity [m2/s]

Θ:

Dimensionless temperature, 2·kf ·(Tint –Tj)/(qw·dn)

Φ:

Azimuthal coordinate [rad]

ρ :

Density [kg/m3]

atm:

Ambient

av:

Average

f:

Fluid

int:

Solid–fluid interface

j:

Jet or inlet

i:

Initial condition

max:

Maximum

n:

Nozzle

s:

Solid

SS:

Steady state

w:

Inner surface of hemisphere

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of South Florida, Tampa, FL, 33620, USA

    Muhammad M. Rahman & Cesar F. Hernandez

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  1. Muhammad M. Rahman
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  2. Cesar F. Hernandez
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Correspondence to Muhammad M. Rahman.

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Rahman, M.M., Hernandez, C.F. Transient conjugate heat transfer from a hemispherical plate during free liquid jet impingement on the convex surface. Heat Mass Transfer 47, 69–80 (2011). https://doi.org/10.1007/s00231-010-0670-y

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