Wavelet Collocation Solution for Convective Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity
Surjan Singh1, Dinesh Kumar2, K. N. Rai3
1Surjan Singh, Research Scholar DST- Centre for Interdisciplinary Mathematical Sciences Banaras Hindu University Varanasi, Utter Pradesh, India.
2Dinesh Kumar, Research Scholar DST- Centre for Interdisciplinary Mathematical Sciences Banaras Hindu University Varanasi, Utter Pradesh, India.
3K. N. Rai, Department of Applied Mathematics IIT BHU, Varanasi, India.
Manuscript received on March 05, 2013. | Revised Manuscript received on April 14, 2013. | Manuscript published on April 30, 2013. | PP: 10-16 | Volume-2, Issue-4, April 2013. | Retrieval Number: D1240042413/2013©BEIESP
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Abstract: In this paper, the temperature distribution in convective radiative continuously moving fin with variable thermal conductivity, which is loosing heat by simultaneous convection radiation to surroundings, is studied. We consider three particular cases, namely thermal conductivity is (I) constant (II) a linear function of temperature and (III) an exponential function of temperature. Wavelet Collocation Method is used to solve this nonlinear heat transfer problem. The exact solution obtained in absence of radiation- conduction fin parameter are compared with Wavelet Collocation solution are same. The fin efficiency is computed in absence of radiation-conduction fin parameter. The whole analysis is presented in dimensionless form and effect of different parameters such as thermal conductivity parameter ‘a’, Peclet number ‘Pe’, convection-conduction parameter ‘Nc ’, radiation-conduction parameter ‘Nr ’, dimensionless convection sink temperature ‘θa ’ and dimensionless radiation sink temperature ‘θs ’ on the fin temperature is discussed in detail.
Keywords: Wavelet, Collocation, Convection, Radiation, heat transfer, fin, Conductivity.