Approximate Analytical Solution of Forced Convection Heat Transfer From Isothermal Spheres for All 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 ≤ Re_D ≤ 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 Nu_D versus Re_D from the present study with the available correlations in the literature reveals very good agreement.