Fins with temperature dependent surface heat flux—II. Multi-boiling heat transfer

Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems

“…In HAM, we have the so-called rule of solution expression, i.e. the solution of (1) must be expressed in the same form as (3). Under the first rule of solution expression and according to the condition y(0) = C, it is straightforward to choose the initial approximation of y(x) as Therefore, the embedding parameter q increases from 0 to 1, /(x; q) varies from the initial guess y 0 (x) to the solution y(x).…”

“…x and the dimensionless variable x is measured from the fin tip, y is the temperature, M is the convective-conductive parameter of the fin and the exponent m depends on the heat transfer mode (cf. [2,3]). three for nucleate boiling and four for radiation [1].…”

A simple design of fins for boiling heat transfer

“…4 depicts the effects of the excavated-hole diameters on the heat transfer rate of the fins. An analytical solution of a solid pin fin [9] is included in this figure for comparison. Similar to previous work [9], a hysteresis region is found, i.e.…”

“…An analytical solution of a solid pin fin [9] is included in this figure for comparison. Similar to previous work [9], a hysteresis region is found, i.e. there are two solutions at a certain range of DT b .…”

“…Good agreements were observed between their results and the experimental data of Haley and Westwater [5]. Lately, employing hypergeometric functions, Liaw and Yeh [9] have presented a solution procedure to obtain the temperature distribution and the heat transfer rate of a fin when various types of boiling occur simultaneously at adjacent locations on its surface. In addition, the results were verified with their own data using copper pin fins subjected to saturated water and isopropyl alcohol.…”