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Estimation of boundary heat flux using experimental temperature data in turbulent forced convection flow

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Abstract

Heat flux at the boundary of a duct is estimated using the inverse technique based on conjugate gradient method (CGM) with an adjoint equation. A two-dimensional inverse forced convection hydrodynamically fully developed turbulent flow is considered. The simulations are performed with temperature data measured in the experimental test performed on a wind tunnel. The results show that the present numerical model with CGM is robust and accurate enough to estimate the strength and position of boundary heat flux.

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Abbreviations

b :

Height of duct (m)

c p :

Specific heat capacity of fluid [J/(kg K)]

d :

Direction of descent, defined by Eq. 6

k :

Thermal conductivity [W/(m K)]

J :

Objective function, defined by Eq. 3

l :

Length of duct (m)

nx :

Numbers of control volume in x direction

nx :

Numbers of control volume in y direction

M :

Number of measured data

P :

Heater input power (W)

q :

Heat flux (W/m2)

R :

Resistance (Ω)

Re :

Reynolds number

RTD:

Resistance temperature detectors

T :

Temperature (K)

T in :

Inlet temperature (K)

u :

Velocity in x coordinate (m/s)

V :

Voltage

x, y :

Cartesian coordinate

α :

Thermal diffusivity (k/ρcp) (m2/s)

β :

Search step-size, defined by Eq. 8

δ :

Dirac delta function

ε :

Convergence criteria

ε H :

Eddy thermal diffusivity (m2/s)

γ :

Conjugation coefficient, defined by Eq. 7

λ :

Lagrange multiplier

ρ :

Density of fluid (kg/m3)

σ :

Standard deviation of measurements

σ P , σ V and σ R :

Uncertainties in power, voltage and resistance respectively

ξ :

New space variable converting final value problem to initial value

n :

Iteration number

m :

Measurement location for a single sensor

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Ajit K. Parwani, Prabal Talukdar & P. M. V. Subbarao

Authors
  1. Ajit K. Parwani
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  2. Prabal Talukdar
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  3. P. M. V. Subbarao
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Correspondence to Prabal Talukdar.

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Parwani, A.K., Talukdar, P. & Subbarao, P.M.V. Estimation of boundary heat flux using experimental temperature data in turbulent forced convection flow. Heat Mass Transfer 51, 411–421 (2015). https://doi.org/10.1007/s00231-014-1421-2

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  • DOI: https://doi.org/10.1007/s00231-014-1421-2

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