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Non-uniform heat transfer to fluids flowing in conduits

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Summary

The general theory of the temperature distribution in a fluid flowing in a heated conduit is discussed. Equations are derived for the temperature distribution throughout the fluid stream, and an expression is presented for the Nusselt modulus as a function of downstream position. A definite criterion is proposed for estimation of the thermal entry length. In addition, it is shown that the asymptotic value of the Nusselt modulus depends not only upon the geometry and the hydrodynamics of the system, but also upon the temperature boundary conditions imposed. A simple procedure is given for computation of the heat transfer coefficient when velocity and effective thermometric conductivity distributions are available. Both round pipes and parallel wall conduits are considered.

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Abbreviations

a :

radius of tube or half-height of duct, (cm)

A :

wall area, (cm2)

f :

friction factor

h :

local internal heat transfer coefficient, (cal/s cm2 °C)

h w :

local wall heat transfer coefficient, (cal/s cm2 °C)

k :

thermal conductivity of fluid, (cal/s cm2 °C/cm)

Nu :

Nusselt modulus

(Nu) w :

Nusselt modulus based onh w

Pr :

Prandtl Modulus

q w :

rate of heat transfer through tube wall, (cal/s)

r :

radius variable or distance from centerline of duct, (cm)

Re :

Reynolds modulus

u :

local velocity, (cm/s)

u m :

average velocity, (cm/s)

x :

distance variable in direction of flow (cm)

α :

ratioε c /ε m

γ :

Nusselt modulus for tube wall = (Nu) w

ε c :

effective turbulent thermal diffusivity, (cm2/s)

ε m :

effective turbulent kinematic viscosity, (cm2/s)

x :

thermal diffusivity of fluid, (cm2/s)

ν :

kinematic viscosity of fluid, (cm2/s)

θ :

temperature of fluid, (°C)

θ w :

temperature of wall, (°C)

θ ∞ :

temperature of surroundings, (°C)

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Authors and Affiliations

  1. Stanolind Oil and Gas Company, Tulsa, Oklahoma

    V. J. Berry

Authors
  1. V. J. Berry
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Berry, V.J. Non-uniform heat transfer to fluids flowing in conduits. Appl. sci. Res. 4, 61–75 (1953). https://doi.org/10.1007/BF03184666

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  • DOI: https://doi.org/10.1007/BF03184666

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