Abstract
Numerical solutions of, unsteady laminar free convection from an incompressible viscous fluid past a vertical cone with uniform surface heat flux is presented in this paper. The dimensionless governing equations of the flow that are unsteady, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicolson type. The velocity and temperature fields have been studied for various parameters Prandtl number and semi vertical angle. The local as well as average skin-friction and Nusselt number are also presented and analyzed graphically. The present results are compared with available results in literature and are found to be in good agreement.
Highlights
Natural convection flows under the influence of gravitational force have been investigated most extensively because they occur frequently in nature as well as in science and engineering applications
In order to prove the accuracy of our numerical results, the present results in steady state at X = 1.0 obtained and considering the modified Grashof number GrL∗ = GrL cos φ, (i.e. the numerical solutions obtained from the equations (9)–(11) are independent of semi vertical angle of the cone φ) are compared with available similarity solutions in literature
The velocity and temperature profiles of the cone for P r = 0.72 are displayed in Fig. 2 and the numerical values of local skin-friction τX, temperature T, for different values of Prandtl number are shown in Table 1 are compared with similarity solutions of Lin [9] in steady state using suitable transformation (i.e. Y = (20/9)1/5η, T = (20/9)1/5(−θ(0)), U = (20/9)3/5f ′(η), τX = (20/9)2/5f ′′(0))
Summary
Natural convection flows under the influence of gravitational force have been investigated most extensively because they occur frequently in nature as well as in science and engineering applications. When a heated surface is in contact with the fluid, the result of temperature difference causes buoyancy force, which induces the natural convection. Heat flux applications are widely using in industries, engineering and science fields. Heat flux sensors can be used in industrial measurement and control systems. Examples of few applications are detection fouling (Boiler Fouling Sensor), monitoring of furnaces (Blast Furnace Monitoring/General Furnace Monitoring) and flare monitoring. Use of heat flux sensors can lead to improvements in efficiency, system safety and modeling
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