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Heat transfer due to stagnation point flow of a non-Newtonian fluid

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Summary

Heat transfer analysis for steady, laminar flow of an incompressible, homogeneous, non-Newtonian fluid of second grade at a stagnation point is presented. A pseudosimilarity solution is used that enables computation of the flow characteristics for any value of the dimensionless normal stress modulus,K, of the fluid. The energy equation is discretized using central differences, and solved using the Thomas algorithm. A powerlaw variation for the wall temperature is assumed. Results provide the effect of non-Newtonian nature of the fluid on the heat transfer characteristics for different values of Prandtl and Eckert numbers, and wall-temperature variation. Results match exactly with those from an earlier perturbation analysis for smallK. For largeK as well as for the effect of viscous dissipation, no results are available heretofore. Amongst other applications, the analysis is relevant to the impingement of a non-Newtonian jet on a flat surface.

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Abbreviations

A 1,A 2 :

first two Rivlin-Ericksen tensors

b :

body force

B :

proportionality constant for wall temperature distribution

c :

specific heat

curl:

the curl operator

div:

the divergence operator

e :

specific internal energy

Ec:

Eckert number

f(η):

proportional to stream function

grad:

the gradient operator

h :

heat transfer coefficient [=heat flux/(θ w −θ ∞)]

k :

thermal conductivity

K :

dimensionless normal stress modulus

L :

characteristic length

L :

velocity gradient

n :

wall temperature distribution index

Nu:

Nusselt number (=hL/k)

p :

thermodynamic pressure

Pr:

Prandtl number

q :

heat flux vector

r :

radiant heating

Re:

Reynolds number

t :

time

T :

Cauchy stress in the fluid

u, v :

velocity components in thex, y directions, respectively

U(x) :

potential flow velocity over the body surface

v :

velocity vector

x, y :

coordinates along and normal to the body

α1, α1 :

normal stress moduli

ϕ:

potential

η:

similarity coordinate

μ:

dynamic viscosity

ϑ:

temperature

ϱ:

density

ω:

vorticity

Δ:

Laplacian

∇:

norm for vectors or trace norm for tensors

t :

partial derivative with respect to time

w :

value at the body surface

∞:

value in the free stream

′:

differentiation with respect to η

-:

dimensionless quantity

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Author notes

  1. V. K. Garg

    Present address: Internal Fluid Mechanics Division, NASA Lewis Research Center, Mail Stop 5-11, 44135, Cleveland, OH, USA

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    Garg, V.K. Heat transfer due to stagnation point flow of a non-Newtonian fluid. Acta Mechanica 104, 159–171 (1994). https://doi.org/10.1007/BF01170062

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