The Effect of a Nonisothermal Free Stream on Boundary-Layer Heat Transfer

1959 ◽  
Vol 26 (2) ◽  
pp. 161-165
Author(s):  
E. M. Sparrow ◽  
J. L. Gregg
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Exact Solution ◽  
Energy Equation ◽  
Free Stream ◽  
Convection Heat Transfer ◽  
Stream Temperature ◽  
Convection Heat ◽  
Prandtl Numbers ◽  
Laminar Forced Convection

Abstract An analysis is made for laminar forced-convection heat transfer from a flat plate to a nonisothermal free stream. An exact solution of the boundary-layer energy equation is found for the situation of linearly varying free-stream temperature. Numerical calculations are carried out for Prandtl numbers in the range 0.01 ⩽ Pr ⩽ 50. Results are presented for the change in heat transfer due to the variation in free-stream temperature. This effect decreases with increasing Prandtl number.

Approximate Analytical Solution of Forced Convection Heat Transfer From Isothermal Spheres for All Prandtl Numbers

1994 ◽  
Vol 116 (4) ◽  
pp. 838-843 ◽  
Author(s):  
G. Refai Ahmed ◽  
M. M. Yovanovich
Keyword(s):  
Heat Transfer ◽  
Forced Convection ◽  
Energy Equation ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Forced Convection Heat Transfer ◽  
Effective Velocity ◽  
Blending Method ◽  
Heat Transfer Correlations ◽  
Prandtl Numbers

A new, simple and approximate analytical method based on linearization of the energy equation is proposed to develop solutions for forced convection heat transfer from isothermal spheres. Furthermore, heat transfer correlations from spheres are proposed in the range of Reynolds number, 0 ≤ ReD ≤ 2 × 104, and all Prandtl numbers. This technique is performed as follows. The first step is to approximate the energy equation to the form of a transient heat conduction equation that has an existing solution. The second step is to evaluate the effective velocity through scaling analysis in the limit of Pr → ∞ and Pr → 0 and then resubstitute the effective velocity into the solution of the energy equation. Finally, a “blending method” is used to provide a general model for all Prandtl numbers. Comparison of the heat transfer correlations for NuD versus ReD from the present study with the available correlations in the literature reveals very good agreement.

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jinhu Zhao ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fawang Liu ◽  
Xuehui Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Prandtl Number ◽  
Fractional Derivative ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Elastic Effect

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

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

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. Bachiri ◽  
A. Bouabdallah
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Ad Hoc ◽  
Convection Heat Transfer ◽  
Analytical Approximation ◽  
Numerical Results ◽  
Convection Heat ◽  
Governing Equations ◽  
Wedge Surface ◽  
Prandtl Numbers

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.

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