The heat transfer rate per unit width (normal to the page) from a longitudinal section, x2 x1, can be expressed as q'12 = h12

The heat transfer rate per unit width (normal to the page) from a longitudinal section, x2 – x1, can be expressed as q'12 = h12 (x2 – xl)(Ts – T∞), where h12 is the average coefficient for the section of length (x2 – x1). Consider laminar flow over a flat plate with a uniform temperature Tx. The spatial variation of the local convection coefficient is of the form hx = Cx-1/2, where C is a constant.

(a) Beginning with the convection rate equation in the form dq' = hx _ dx(Ts – T∞), derive an expression for hl2 in terms of C, x1, and x2.

(b) Derive an expression for h12 in terms of x1, x2, and the average coefficients h1 and h2, corresponding to lengths x1 and x2, respectively.

dq q'12 dx X2 L.x