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Flow and Heat Transfer to a Newtonian Fluid Over Non-linear Extrusion Stretching Sheet

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Abstract

The paper presents flow and energy transfer to a Newtonian fluid over non-linear extrusion stretching sheet problem involving a Newtonian fluid and suction (injection). Two different temperature conditions are studied, namely (i) prescribed surface temperature and (ii) prescribed wall heat flux, while considering heat transfer. Similarity transformation is used on the governing equations to arrive at a system of non-linear ordinary differential equations. A new analytical approach is then followed for solving the equation. Analytical expression is obtained for stream function and temperature in terms of the stretching parameters. The result in respect of the stretching sheet problem without the boundary layer approximation is obtained using those obtained with the boundary layer approximation. An asymptotic analysis is presented for large and small Prandtl numbers.

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Abbreviations

\(C_{f}\) :

Skin friction coefficient

\(C_{p}\) :

Specific heat at constant pressure

\(C_{v}\) :

Specific heat at constant volume

F :

Kummer’s function

G :

Non-dimensional temperature (for the PHF case), (\(T - T_{\infty }) / (T_{w} - T_{\infty })\)

k :

Thermal conductivity

\(N_{\mathrm{I}}\) :

Heat source/sink parameter, \(Q^{*}/\alpha \,\rho \,C_p \)

\(p^{*}\) :

Hydrostatic pressure

P :

Hydromagnetic pressure

Pr :

Prandtl number, \(\mu \,C_p /k\)

\(Q^{*}\) :

Heat source (sink) coefficient

\(q_{w}\) :

Heat flux at the wall

T :

Liquid temperature

\(T_{\infty }\) :

Temperature at a large distance from the wall (sheet)

\(T_{w}\) :

Temperature at wall (sheet)

U :

Dimensionless horizontal velocity

u :

Dimensional horizontal velocity component

v:

Dimensional vertical velocity

\(\hbox {v}_{w}\) :

Dimensional suction/injection parameter

V :

Dimensionless vertical velocity

\(V_{w}\) :

Dimensionless suction/injection parameter, \(\hbox {v}_w /\sqrt{\alpha \nu }\)

X :

Dimensionless horizontal coordinate

x :

Horizontal coordinate

Y :

Dimensionless vertical coordinate

y :

Vertical coordinate

\(\alpha \) :

Linear stretching coefficient

\(\beta \) :

Non-linear stretching coefficient

\(\beta _T \) :

Constant power of the surface temperature

\(\delta \) :

Non-linear stretching coefficient

\(\delta ^{*}\) :

Dimensionless non-linear stretching parameter, \(\delta /2\alpha \)

\(\chi \) :

Thermal conductivity

\(\mu \) :

Dynamic viscosity

\(\nu \) :

Kinematic viscosity, \(\mu /\rho \)

\(\psi \) :

Stream function

\(\rho \) :

Density

\(\varTheta \) :

Nondimensional temperature for the PST case, (\(T - T_{\infty })/(T_{w} - T_{\infty })\)

w :

Wall temperature

\(\infty \) :

Ambient temperature condition

*:

Dimensionless quantities

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Authors and Affiliations

  1. Department of Mathematics, Bangalore University, Bangalore, 560 056, India

    P. G. Siddheshwar

  2. Department of Mathematics, Government First Grade College for Women, Hassan, 573 201, India

    U. S. Mahabaleshwar

Authors
  1. P. G. Siddheshwar
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  2. U. S. Mahabaleshwar
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Correspondence to U. S. Mahabaleshwar.

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Siddheshwar, P.G., Mahabaleshwar, U.S. Flow and Heat Transfer to a Newtonian Fluid Over Non-linear Extrusion Stretching Sheet. Int. J. Appl. Comput. Math 4, 35 (2018). https://doi.org/10.1007/s40819-017-0466-6

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