Heat transfer from a cylindrical,heavily finned surface

The transfer of heat from a strongly heated, heavily finned surface is examined. The material of the surface and of the fins has high thermal conductivity (copper), while the heat transfer fluid has comparatively low thermal conductivity (oil). Under these conditions, increase in the number of fins and reduction of the distance between them makes possible a high value of the coefficient of heat transfer from the heated surface to the fluid.Notation R₂ and r₁ radii of cylindrical surface at tip and base of fins, respectively - r, z coordinate axes - angle between planes of adjacent slots - x slot width - b anda coordinates of tip and base of fin - thermal conductivity of fin material - t fin temperature - u mean fluid temperature over slot width - coefficient of heat transfer from fin surface to fluid - c specific heat of fluid - v fluid velocity (since the viscosity is considered constant over the flow, v is also constant) - q density of heat flux through base of fin - specific weight of fluid - ¯t, ¯u Laplace transforms - p Laplace transform parameter, s-auxiliary quantity determined from equation (13) - I, K, J, Y Bessel functions - u⁰ mean fluid temperature over height of slot