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# On the Radiative Heat Transfer in a Viscoelastic Boundary Layer Flow Over a Stretching Sheet

[+] Author and Article Information
Chava Y P D Phani Rajanish

Department of Mechanical Engineering,
KL University,
Guntur 522502, India
e-mail: phanirajanish@gmail.com

B. Nageswara Rao

Department of Mechanical Engineering,
KL University,
Guntur 522502, India
e-mails: bnrao52@rediffmail.com;
bnrao52@kluniversity.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 21, 2016; final manuscript received July 28, 2016; published online August 30, 2016. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 139(1), 014501 (Aug 30, 2016) (3 pages) Paper No: HT-16-1219; doi: 10.1115/1.4034351 History: Received April 21, 2016; Revised July 28, 2016

## Abstract

Many researchers have studied the radiative heat transfer in a viscoelastic boundary layer flow over a stretching sheet after simplifying the complex nature of the radiative heat flux by expanding the fourth power of temperature $(T4)$ in Taylor series about free-stream temperature $(T∞)$ and neglecting the higher-order terms. Similarity solutions obtained by them are found to be valid only in the asymptotic region. This article suggests a modification in the linearization of $T4$ by introducing wall temperature $(Tw)$ as well as freestream temperature $(T∞)$ to capture the realistic nature of the temperature distribution in the boundary layer flows from locally nonsimilar solutions.

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## References

Bataller, R. C. , 2007, “ Viscoelastic Fluid Flow and Heat Transfer Over a Stretching Sheet Under the Effects of a Non-Uniform Heat Source, Viscous Dissipation, and Thermal Radiation,” Int. J. Heat Mass Transfer, 50(15–16), pp. 3152–3162.
Datti, P. S. , Prasad, K. V. , Abel, M. S. , and Joshi, A. , 2004, “ MHD Viscoelastic Fluid Flow Over a Non-Isothermal Stretching Sheet,” Int. J. Eng. Sci., 42(8–9), pp. 935–946.
Siddheshwar, P. G. , and Mahabaleswar, U. S. , 2005, “ Effects of Radiation and Heat Source on MHD Flow of a Viscoelastic Liquid and Heat Transfer Over a Stretching Sheet,” Int. J. Nonlinear Mech., 40(6), pp. 807–820.
Bataller, R. C. , 2007, “ Effects of Heat Source/Sink, Radiation and Work Done by Deformation on Flow and Heat Transfer of a Viscoelastic Fluid Over a Stretching Sheet,” Comput. Math. Appl., 53(2), pp. 305–316.
Abel, M. S. , Siddeshwar, P. G. , and Nandeppanavar, M. M. , 2007, “ Heat Transfer in a Viscoelastic Boundary Layer Flow Over a Stretching Sheet With Viscous Dissipation and Non-Uniform Heat Source,” Int. J. Heat Mass Transfer, 50(5–6), pp. 960–966.
Abel, M. S. , and Mahesha, N. , 2008, “ Heat Transfer in MHD Viscoelastic Fluid Flow Over a Stretching Sheet With Variable Thermal Conductivity, Non-Uniform Heat Source and Radiation,” Appl. Math. Model, 32(10), pp. 1965–1983.
Sajid, M. , and Hayat, T. , 2008, “ Influence of Thermal Radiation on the Boundary Layer Flow Due to an Exponentially Stretching Sheet,” Int. Comm. Heat Mass Transfer, 35(3), pp. 347–356.
Bidin, B. , and Nazar, R. , 2009, “ Numerical Solution of the Boundary Layer Flow Over an Exponentially Stretching Sheet With Thermal Radiation,” Eur. J. Sci. Res., 33(4), pp. 710–717.
Hayat, T. , Nawaz, M. , Sajid, M. , and Asghar, S. , 2009, “ The Effect of Thermal Radiation on the Flow of a Second Grade Fluid,” Comput. Math. Appl., 58(2), pp. 369–379.
Gaffar, S. A. , Prasad, V . R. , Reddy, E. K. , and Be, O. A. , 2015, “ Thermal Radiation and Heat Generation/Absorption Effects on Viscoelastic Double-Diffusive Convection From an Isothermal Sphere in Porous Media,” Ain Shams Eng. J., 6(3), pp. 1009–1030.
Akinbobola, T. E. , and Okoya, S. S. , 2015, “ The Flow of Second Grade Fluid Over a Stretching Sheet With Variable Thermal Conductivity and Viscosity in the Presence of Heat Source/Sink,” J. Nigerian Math. Soc., 34(3), pp. 331–342.
Patankar, S. V. , 1980, Numerical Heat Transfer & Fluid Flow, Hemisphere Publishing, New York.
Nageswara Rao, B. , 1996, “ Flow of a Fluid of Second Grade Over a Stretching Sheet,” Int. J. Nonlinear Mech., 31(4), pp. 547–550.
Lawrence, P. S. , Sarma, M. S. , and Nageswara Rao, B. , 1997, “ Heat Transfer in a Viscoelastic Boundary Layer Flow Over a Stretching Sheet Revisited,” J. Physics D Appl. Phys., 30(24), pp. 3330–3334.
Sarma, M. S. , and Nageswara Rao, B. , 1998, “ Heat Transfer in a Viscoelastic Fluid Over a Stretching Sheet,” J. Math. Anal. Appl., 222(1), pp. 268–275.
Nataraja, H. R. , Sarma, M. S. , and Nageswara Rao, B. , 1998, “ The Closed-Form Solutions for a Nonsimilar Viscoelastic Boundary Layer Flow and Heat Transfer,” Indian J. Eng. Mater. Sci., 5(10), pp. 339–342.
Pillai, K. M. C. , Sai, K. S. , Shivakumarswamy, N. , Nataraja, H. R. , Tiwari, S. B. , and Nageswara Rao, B. , 2004, “ Heat Transfer in a Viscoelastic Boundary Layer Flow Through a Porous Medium,” Int. J. Comput. Mech., 34(1), pp. 27–37.
Arnold, J. C. , Asir, A. A. , Somasundaram, S. , and Christopher, T. , 2010, “ Heat Transfer in a Viscoelastic Boundary Layer Flow Over a Stretching Sheet,” Int. J. Heat Mass Transfer, 53(5–6), pp. 1112–1118.

## Figures

Fig. 1

Comparison of (T/T∞)4 profiles to examine the validity of the linearization process

Fig. 2

Comparison of the results of (T/T∞)4 to examine the accuracy of the linearization process

Fig. 3

Comparison of the nondimensional temperature (θ) profiles for NR0=1, σ=3, A*=B*=0.2, Ec=0.1, k1=0.1 and (Tw/T∞)=1.5

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