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Magnetohydrodynamic Heat Transfer of Nanofluids Past a Stretching Cylinder with Non-Uniform Heat Source/Sink and Chemical Reaction

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Abstract

In this investigation, we intend to present the magnetohydrodynamic (MHD) heat and mass transfer of nanofluids along a stretching cylinder in the presence of non-uniform heat source/sink and chemical reaction under the prescribed surface heat flux boundary conditions on the cylinder surface. The governing partial differential equations are approximated by a system of non-linear locally similarity ordinary differential equations which are solved numerically using fifth-order Runge–Kutta–Fehlberg (RKF45) integration scheme shooting method. Present results are compared with the previously published results in some limiting cases and the results are found to be in an excellent agreement. Three different kinds of nanoparticles, namely copper (Cu), alumina (\({\hbox {Al}}_2{\hbox {O}}_3\)) and titanium dioxide (\({\hbox {TiO}}_2\)) with water as base fluid are considered here. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as on local skin-friction coefficient, local Nusselt number and Sherwood number have been constructed and illustrated graphically to reveal some interesting physical phenomena. The results of the present paper show that the flow velocity and temperature on the stretching cylinder and also skin-friction coefficient are strongly influenced by the curvature parameter.

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Abbreviations

\(A^*\) :

Space dependent heat source/sink parameter

\(B^*\) :

Temperature dependent heat source/sink parameter

\(C_f\) :

Skin-friction coefficient

\(C_p\) :

Specific heat at constant pressure

\(D_m\) :

Specific diffusitivity

M :

Magnetic field parameter

\(Nu_x\) :

Local Nusselt number

Pr :

Prandtl number

\(q'''\) :

Non-uniform heat source/sink

\(Re_x\) :

Local Reynolds number

Sc :

Schmidt number

T :

Temperature of the fluid

\(T_{\infty }\) :

Free stream temperature

\(T_w\) :

Temperature at the wall

u :

Velocity component in x-direction

\(u_w\) :

Stretching/shrinking sheet velocity

U :

Free stream velocity of the nanofluid

v :

Velocity component in y-direction

x, y :

Direction along and perpendicular to the plate, respectively

\(\alpha _{nf}\) :

Effective thermal diffusivity of the nanofluid

\(\alpha _f\) :

Fluid thermal diffusivity

\(\phi \) :

Solid volume fraction of the nanoparticles

\(\eta \) :

Similarity variable

\(\gamma \) :

Carveture parameter

\(\varGamma \) :

Chemical reaction parameter

\(\mu _{nf}\) :

Effective dynamic viscosity of the nanofluid

\(\mu _f\) :

Dynamic viscosity of the fluid

\(\nu _f\) :

Kinematic viscosity of the fluid

\(\rho _{nf}\) :

Effective density of the nanofluid

\(\theta \) :

Dimensionless temperature of the fluid

\(\theta _w\) :

Wall temperature excess ratio parameter

\({\psi }\) :

Stream function

\(\kappa _{nf}\) :

Effective thermal conductivity of the nanofluid

\(\kappa _f\) :

Thermal conductivity of the fluid

\('\) :

Differentiation with respect to y

nf :

Nanofluid

f :

Fluid

s :

Solid

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Authors and Affiliations

  1. Department of Mathematics, Siksha Bhavana, Visva-Bharati University, Santiniketan, West Bengal, 731 235, India

    Dulal Pal

  2. Siksha Satra, Visva-Bharati University, Sriniketan, West Bengal, 731 236, India

    Gopinath Mandal

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  1. Dulal Pal
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Correspondence to Dulal Pal.

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Pal, D., Mandal, G. Magnetohydrodynamic Heat Transfer of Nanofluids Past a Stretching Cylinder with Non-Uniform Heat Source/Sink and Chemical Reaction. Int. J. Appl. Comput. Math 3, 2889–2908 (2017). https://doi.org/10.1007/s40819-016-0241-0

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