Analysis of Thermal Characteristics of Transient Heat Conduction through Long Fin and Comparison with Exact Fin Theory and Quasi Steady Theory

--The paper work incorporates the analysis of transient heat conduction through long fins and comparison with the theory based on it termed as “exact fin theory” & “quasi steady theory” at different locations of fin at different parameters. Fins are the extended surfaces used for enhancing the dissipation of heat transfer rate and different geometrical fins are used as per requirement its accessibility depends. Fins are extensively used in heat exchanging devices in automobiles radiators, industrial sectors, power plants, newer technology like fuel cells. Earlier, Work under steady state conduction had been carried out extensively. Transient heat conduction analysis for the fins is being considered for simplifying heat transfer queries. Transient Closed form solutions had been derived earlier by various researchers. The exact local and mean temperature distribution had been generated by numerical technique methods. Exact solutions are given for the transient temperature in flux-base fins with the method of Green’s functions (GF) in the form of infinite series for three different tip conditions. Here the time of convergence is improved by replacing the series part from required equations. For long fin case, exact fin solution and a quasisteady solution is presented with numerical as well as graphical solutions. Numerical values are presented and the conditions under which the quasi-steady solution is accurate are determined. Comparison between quasi steady theory & exact fin theory for long fin is made here. Programmed solutions are determined for analysis of quasi steady theory and exact fin theory. The dimensionless temperature distribution is presented for both quasi steady theory and exact fin theory and compared with their results. This work has been done with dimensionless positions of Fin and dimensionless temperatures in different segments for premium solutions. The graphical results are incorporated in the work for the generalized thermal characters of composite fins, mostly emphasizing on Heat Exchanger. The effect on thermal performance for different conditions is analyzed in the work. The results obtained theoretically are found in agreement to the effect of the various parameters. Further conclusions and future scope is also manifested at the end of the work. Keywords--Fin; Green’s functions; Quasi steady theory; Unsteady heat; Heat transfer ; Transient; Transient Conduction; Parameter estimation; Extended Surface; Exact Solution. Nomenclatures English Symbols Ah surface area of fin for convection, [m 2 ] Bi Biot number, [ hi (V/Ah) / K ] GF Green’s function h heat transfer coefficient, [W m -2 K -1 ] k thermal conductivity, [W m -1 K -1 ] k Thermal diffusivity, [m 2 s -1 ] L length of fin, [m] Nn norm [eq. (1.14)], (m) m fin parameter, [m -1 ] M dimensionless fin parameter = mL qo heat flux, [W m -2 ] Q Heat rate ,[W] Q Heat transfer,[W] T temperature, [K] t time, [s] V fin volume, [m 3 ] W transformed temperature, [eq. (1.13)] g Internal heat generation d Diameter, [m] dt Differential time,[s] dT Differential temperature,[K] dX Differential length,[m] dV Differential volume, [m 3 ] x x-coordinate q Heat flux,[W/m 2 ] q Heat flux rate,[W/m 2 /s] T1,T2.T4 Temperatures, [K] Te ,T∞ Temperature of the ambient,[K] Ts Temperature of sourrinding,[K] Greek symbols α thermal diffusivity, [m 2 s -1 ] βn eigen value, [eq. (1.14)] θ dimensionless temperature ξ, X dimensionless x-coordinate τ, dt dimensionless time ρ Density, [kg/m 3 ] ∂ Differential operator ∇ Gradient operator Σ Summation → Vector Form International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae. com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 11, November 2014) 158 < Less Than ≤ Less Than or Equal To ( ) Cycle average quantity ∫ Cyclic integral Superscripts q quasi-steady s steady state