Effects of axial heat conduction in a vertical flat plate on free convection heat transfer

The Rate of Heat Flow through Non-Isothermal Vertical Flat Plate

“…In the vicinity of x = y = 0, the boundary layer approximation breaks down and the calculation based on this approximation cannot yield reliable results as pointed out already by Miyamoto et al (1980). However, we believe that this conclusion is not so crucial since the contribution of the surface area near the leading edge of the convective flow to the total heat rate is proportional to x 0 /H, where x 0 is small compared to H (Pozzi & Lupo, 1988).…”

“…(2), for example, and the expressions for the heat transfer coefficients as determined above. Using the result obtained by Kao et al (1977) and quoted by Miyamoto et al (1980) (eq. …”

“…(1) and (2) describe correctly the total heat flow Q across the wall. Free convection along a vertical flat plate has been studied extensively in the past, however, it has been commonly restricted to one surface of the wall only (Pohlhausen, 1921;Ostrach, 1953;Miyamoto et al, 1980;Pozzi & Lupo, 1988;Vynnycky & Kimura, 1996;Pop & Ingham, 2001). The thermal conditions at the other surface have been prescribed by either constant temperature or constant heat flux.…”

“…Similarity arguments (Landau & Lifshitz, 1987) for free convection suggest that we write the stream function as ψ(x, y) = ψ* (x/H, y/H, G, P), where G = g(T s -T 0R )H 3 / 2 and P = / are the Grashof and Prandtl numbers, respectively, and T s is a temperature characteristic of the surface. In addition, since we anticipate the surface temperatures to be close to uniform, except in the vicinity of x = 0 (Miyamoto et al, 1980;Pozzi & Lupo, 1988;Vynnycky & Kimura, 1996), we further specify the stream function to have the form (y > 0)…”

“…may be, according to Miyamoto et al (1980), for P = 0.7, approximated closely by Equating the right-hand sides of (20a, b) and integrating the resulting equation with respect to x* from 0 to 1, we obtain ( )…”