CIV. Convective cooling of wires in streams of viscous liquids

Abstract

Study has been made of the cooling of wires immersed in streams of various liquids. Theoretical considerations point to a formula of the type , where H = Heat loss per unit time per unit length of the wire per degree temperature elevation, k = Thermal conductivity of the fluid, c = Specific heat of the fluid per unit volume, ν = Kinematical viscosity of the fluid, v = Velocity of the fluid stream, d = Diameter of the wire. Since (k/cν) is practically constant for gases, the present experiments with liquids were undertaken to reveal its importance. The apparatus consisted of a motor-driven whirling arm which carried the test-wire and forced it continually through the liquid contained in an annular circular trough. Observation was made of the temperature of the wire and of the electric energy necessary to maintain a measured temperature difference between the wire and the general body of the liquid. Wires of three sizes were used, and various liquids whose physical constants were measured. The results show that the above formula is fairly satisfactory, except that a factor must be included to cover certain small residual effects dependent upon d (and possibly upon, θ) and due to some cause, possibly free convection, not fully investigated. It was found that the function F could not be represented by the product of two independent terms in vdc/k and k/cν respectively, but that each influences to some extent the effect of the other. The following form was found to be satisfactory :— where R represents the residual factors referred to. Curves are given showing the forms of the two functions. If they are represented by power terms thus, f(x)=x ^−m, and F(x)=x ⁿ, m and n vary with circumstances but lie within the limits given by 0<mnvelocity of the natural convection current set up by the heated wire.