Convective Heat Transfer of Laminar, Single-phase Flow in Randomly Rough Microtubes

Convective heat transfer of laminar, single-phase flow in rough microtubes is studied. Wall roughness and slope are assumed to possess Gaussian, isotropic distributions. Fractal concepts are used to model the rough microtube. It is shown that due to the existence of wall roughness, both cross-sectional and inside surface areas are increased. A new concept is defined as a figure of merit for assessing thermal performance of rough microtubes. As a result of increasing roughness, an enhancement is observed in the thermal performance of microtubes. The present model can be extended to analyze other geometries such as rectangular and trapezoidal microchannels. Nomenclature Ac = cross-sectional area, m A = surface area, m a = mean radius of rough microtube, m cp = fluid specific heat, kJ/kgK D = microtube diameter, m h = convection heat transfer coefficient, W/mK k = fluid thermal conductivity, W/mK L = sampling length, m mabs = mean absolute surface slope, [−] ṁ = mass flow rate, kg/s Nu = Nusselt number ≡ hD/k qw = wall heat flux, W/m r = local microtube radius, m 1Post-Doctoral Fellow. Mem. ASME. Corresponding author. Email: [email protected]. 2Distinguished Professor Emeritus. Fellow ASME. 3Associate Professor and Director of MHTL. Mem. ASME. T = temperature, K u = fluid velocity, m/s x = fluid flow direction Greek 2 = relative roughness, σ/a η = non-dimensional radial location ≡ r/a ζ = non-dimensional length, x/L θ = surface angle, rad θT = non-dimensional temperature ρ = fluid density, kg/m σ = roughness standard deviation, m σm = slope standard deviation, rad Subscripts 0 = smooth microtube θ = in angular direction m = mean value x = in longitudinal direction