Abstract
Subject of this paper is the effect of air temperature on the characteristics of a hot wire. Hot wires of four different lengths have been calibrated over a range of air temperatures from 20 °C to 60 °C. Finite wire length corrections that account for the effects of heat conduction at the ends have been applied to obtain the heat transfer characteristics of an infinitely long heated wire. The reduced data show that the dependence of the heat transfer from an infinitely long heated wire on fluid temperature is such that the Nusselt number vs. Reynolds number relationship, when these are evaluated with property values at the “film temperature”, do not collapse to a single curve. The reduced data show that a linear variation of the heat transfer with a temperature difference corresponds more closely to the experimental observations.
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Abbreviations
- d w , l w m:
-
diameter and length of hot wire
- V b Volts:
-
voltage across Wheatstone bridge of anemometer circuit
- V w Volts:
-
voltage across hot wire
- I w Amperes:
-
current through wire
- r o Ohms:
-
resistance of hot wire at fluid temperature 7 (cold resistance)
- R w Ohms:
-
resistance of hot wire under operating conditions
- R a Ohms:
-
resistance in series with hot wire in Wheatstone bridge
- R k Ohms:
-
cable resistance (R k= 0.6 Ohms)
- T w K:
-
operating wire temperature
- Θ w K:
-
temperature difference, \(\Theta _w = (T_w - T_f ) = \overline \Theta\)
- h Wm-2K-1 :
-
convective heat transfer coefficient, Eq. (6)
- Q J W:
-
Joule heating in hot wire
- Q E W:
-
heat conduction from wire ends
- Q C W:
-
overall convective heat transfer from hot wire
- q c (x) Wm−1 :
-
local convective heat transfer from hot wire
- U ms-1 :
-
flow velocity
- T f K:
-
fluid (air) temperature
- T s (x) K:
-
local wire temperature
- T max K:
-
maximum wire temperature (at the middle of the wire x = 0)
- \(\overline \Theta\) K:
-
“mean” wire temperature difference, \(\overline \Theta = T_w - T_f\)
- Θ(x) K:
-
local temperature difference wire to fluid, \(\Theta (x) = T_s (x) - T_f\)
- Θ + :
-
temperature difference referred to Θ ref, \(\Theta ^{\text{ + }} = \Theta /\Theta _{{\text{ref}}}\)
- k t Wm−1 K−1 :
-
thermal conductivity of hot-wire material
- α t K−1 :
-
thermal coefficient of electrical resistance of hot-wire material
- ρ t0 ohm m-1 :
-
electrical resistance per unit length of hot wire at fluid temperature T f
- ρ t ohm m-1 :
-
electrical resistance per unit length of hot wire under operating conditions, ρ t = ρ t 0(1 + α t ρ(x))
- ρ kg m-3 :
-
density
- μ kgm-1s-1 :
-
dynamic viscosity
- k Wm-1 K-1 :
-
thermal conductivity
- c p m2s−2K−1 :
-
specific heat at constant pressure
- Re = (ρ Ud w )/μ :
-
Reynolds number
- Pr = (c p μ)/k :
-
Prandtl number
- f :
-
denotes value at fluid temperature T f , or evaluated with property value at this temperature
- f 0 :
-
denotes value at fluid temperature T f0, or evaluated with property value at this temperature
- s :
-
denotes value at temperature T s (x), or evaluated with property value at this temperature
- m :
-
denotes value at “local film temperature” (T s + T f )/2, or evaluated with property value at this temperature
- w :
-
denotes value at “wire film temperature” (T w +T f )/2, or evaluated with property value at this temperature
- Nu f :
-
local Nusselt number, Nu f = q c (x)/πk f (T) s (x) − T f
- Ñu f :
-
local Nusselt number, Ñu f = q c /πk f0 (T) s − T f 0
- Nu m :
-
local Nusselt number, Nu m = Nu f = q c /πk m (T)s − Tf
- Nu w :
-
“wire” Nusselt number, Nu w = Q c /πl w k w (T) w − T f
- C m -2 :
-
Eq. (7c)
- Θ ref K:
-
reference temperature difference, Eq. (7b)
- A f ,B f ,n :
-
in Nu f = A f + B f (Re f )n
- A w ,B w :
-
in Nu w = A w + B w (Re w )n
- +:
-
denotes quantities normalised with Θ ref
- ∼:
-
(as in Ñu f ) with property values at a fixed temperature T f0
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Dedicated to Prof. Dr.-Ing. M. Fiebig's 60th birthday
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Kostka, M., Ram, V.V. On the effects of fluid temperature on hot wire characteristics. Experiments in Fluids 13, 155–162 (1992). https://doi.org/10.1007/BF00218162
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DOI: https://doi.org/10.1007/BF00218162