Analytical Study of the Convection Heat Transfer From an Isothermal Wedge Surface to Fluids

Abstract

In this work, we attempt to establish a general analytical approximation of the convection heat transfer from an isothermal wedge surface to fluids for all Prandtl numbers. The flow has been assumed to be laminar and steady state. The governing equations have been written in dimensionless form using a similarity method. A simple ad hoc technique is used to solve analytically the governing equations by proposing a general formula of the velocity profile. This formula verifies the boundary conditions and the equilibrium of the governing equations in the whole spatial region and permits us to obtain analytically the temperature profiles for all Prandtl numbers and for various configurations of the wedge surface. A comparison with the numerical results is given for all spatial regions and in wide Prandtl number values. A new Nusselt number expression is obtained for various configurations of the wedge surface and compared with the numerical results in wide Prandtl number values.

Heat Transfer From a Wedge to Fluids at Any Prandtl Number Using the Asymptotic Model

“…= 1. Figure 3 shows comparison of the asymptotic model with n = 3, and 6 as suggested in the present paper, and by Lin and Lin [24], respectively, with the exact solutions of Evans [8,10], Cheng and Lin [27] correlation, and Bachiri and Bouabdallah [30] correla tion, Eq. (7), for isothermal wedges (ft = 0) and the wide fluids (10 4 < Pr < 104).…”

“…Bachiri and Bouabdallah [30] attempted to establish a general analytical approximation of the convection heat transfer from an isothermal wedge surface to fluids for all Prandtl numbers. They Andersson [25] considered the heat transfer in Falkner-Skan similarity boundary layers.…”

Strouhal Number Effects on Dynamic Boundary Layer Evolution Over a Wedge Surface from Initial Flow to Steady Flow: Analytical Approach

“…Equation (3.3) admits numerical solutions and analytical approaches with a high order of approximation. In our study given in [17], an accurate analytical approach is proposed using a dimensionless velocity profile formula ( )…”

“…The principal result concerned the evolution of the skin friction coefficient in two regime flows from initial to steady solutions. They also [17] studied the steady state momentum and energy equations over an isothermal wedge surface and gave a new expression of the Nusselt number valid for all Prandtl numbers and for different wedge surface positions. So, as a complementary investigation given in [17], we investigate the unsteady dynamic boundary layer over a wedge surface to establish an analytical formulation of the velocity profile as a function of Strouhal numbers over all time values.…”

“…They also [17] studied the steady state momentum and energy equations over an isothermal wedge surface and gave a new expression of the Nusselt number valid for all Prandtl numbers and for different wedge surface positions. So, as a complementary investigation given in [17], we investigate the unsteady dynamic boundary layer over a wedge surface to establish an analytical formulation of the velocity profile as a function of Strouhal numbers over all time values. In addition, in this paper, an analytical expression of the velocity is proposed by superposition method, which must consider the boundary conditions, the solutions of Rayleigh, Blasius and Falkner-Skan, and the equilibrium of the unsteady momentum equation.…”