Abstract
In order to compute the convective heat transfer coefficient, the present study develops a new technical approach of the constitutive equations of the fluid, based on a realistic physical model of heat transfer for an inclined and an isothermal plate with finite dimensions. Two separate regions with different fluid motions are distinguished. Using suitable transformations of differential equations, the similarity ordinary differential equations were obtained and then solved by an appropriate and simple finite difference method. The analysis of numerical results for some special cases of inclination with visualization photographs is found to be in very good agreement. Numerical results for the dimensionless velocity and temperature profiles are obtained and reported graphically for various values of the parameters entering into the problem. It has observed that Lorenz forces are suitable to control the velocity. Discrepancy between the quasi-analytical formula and the present numerical results are recorded for the Nusselt number and for both the two regions. DOI: http://dx.doi.org/10.5755/j01.mech.23.4.14709
Highlights
X y y2 x inclined (b) and horizontal (c) plate. According to this pattern model, the streamlines are radial, and fluid flows toward a point at the centre of the plate where the boundary layer transforms into a y2 cp where ± signs are for region I and region II, respectively; β is the coefficient of thermal expansion; σ is the electrical conductivity ;ν is the kinematic viscosity; α is the thermal diffusivity and Cp is the specific heat capacity of the fluid, and ρ is the density of the fluid. It must be pointed out, that P is the static pressure difference induced by the buoyancy force (i.e. P = 0 outside the boundary layer)
The set of Eq (14) and Eq (15), with the boundary conditions (12), which are valid for 0°≤ φ
Discrepancy between the quasi-analytical formula and the present numerical results are recorded for the Nusselt number and for both the two regions
Summary
Using the proposed general model as it is shown in (Fig. 3, b), which encompasses all angles inclination, and as discussed previously, we assume that due to the inclination of the plate, the boundary layer behavior permit to obtain two main flow (regions I and II), one frame at each leading edge. The thermo-physical properties of the fluid are assumed to be constant except for the density variation that induces the buoyancy force With this assumption and the application of the Oberbeck-Boussinesq approximation, the governing conservation equations for laminar boundary layer free convection flow can be written as:. X y y2 cp where ± signs are for region I and region II, respectively; β is the coefficient of thermal expansion; σ is the electrical conductivity ;ν is the kinematic viscosity; α is the thermal diffusivity and Cp is the specific heat capacity of the fluid, and ρ is the density of the fluid It must be pointed out, that P is the static pressure difference induced by the buoyancy force (i.e. P = 0 outside the boundary layer). Accurate solutions of the system can be checked with better approximation as prescribed in the two-level method
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