Showing papers on "Nusselt number published in 1977"

Viscous Dissipation in Shear Flows of Molten Polymers

Abstract: Publisher Summary Heat transfer in flowing molten polymers is largely influenced by rheology–– the rheological properties of the polymer and by the flow geometry. The rheology of steady shear flow can treat most of the heat transfer problems completely. This chapter discusses the heat transfer problem, and classifies the heat transfer and viscous dissipation in molten polymers. The heat transfer in shear flow is analyzed and a large emphasis is laid on replacing the commonly used idealized boundary conditions–– constant wall temperature or constant wall heat flux by more general conditions. The heat transfer at the wall is described by an outer temperature difference and the Biot number that is used successfully for describing the boundary conditions for temperature calculations in solids. The Biot number is appropriate for describing the boundary conditions between isothermal and adiabatical, as they occur in real processes. A unifying concept is developed that makes it possible to comprise the most important shear flow cases into a single one that can be solved with one numerical program. The nonviscometric flow in channels and flow with free boundaries is also discussed. An example of heat transfer in unsteady unidirectional shear flow is also provided.

Steady and transient thermal convection in a fluid layer with uniform volumetric energy sources

Abstract: Measurements of the overall heat flux in steady convection have been made in a horizontal layer of dilute aqueous electrolyte. The layer is bounded below by a rigid zero-heat-flux surface and above by a rigid isothermal surface. Joule heating by an alternating current passing horizontally through the layer provides a uniformly distributed volumetric energy source. The Nusselt number at the upper surface is found to be proportional to Ra0[sdot ]227 in the range 1[sdot ]4 ≤ Ra/Rac ≤ 1[sdot ]6 × 109, which covers the laminar, transitional and turbulent flow regimes. Eight discrete transitions in the heat flux are found in this Rayleigh number range. Extrapolation of the heat-transfer correlation to the conduction value of the Nusselt number yields a critical Rayleigh number which is within -6[sdot ]7% of the value given by linearized stability theory. Measurements have been made of the time scales of developing convection after a sudden start of volumetric heating and of decaying convection when volumetric heating is suddenly stopped. In both cases, the steady-state temperature difference across the layer appears to be the controlling physical parameter, with both processes exhibiting the same time scale for a given steady-state temperature difference, or [mid ]ΔRa[mid ]. For step changes in Ra such that [mid ]ΔRa[mid ] > 100Rac, the time scales for both processes can be represented by Fo [vprop ] [mid ]ΔRa[mid ]m, where Fo is the Fourier number of the layer. Temperature profiles of developing convection exhibit a temperature excess in the upper 15–20 % of the layer in the early stages of flow development for Rayleigh numbers corresponding to turbulent convection. This excess disappears when the average core temperature becomes large enough to permit eddy transport and mixing processes near the upper surface. The steady-state limits in the transient experiments yield heat-transfer data in agreement with the results of the steady-state experiments.

Numerical solutions of single-mode convection equations

Abstract: In the Boussinesq approximation, single-mode equations describing thermal convection are constructed by expanding the fluctuating velocity and temperature fields in a complete set of functions (or planforms) of the horizontal coordinates and retaining just one term. Numerical solutions of the single-mode equations are investigated, chief consideration being given to hexagonal planforms. Extensive surveys of steady solutions are presented for various Rayleigh numbers, Prandtl numbers, and horizontal wavenumbers. The dependences on Rayleigh number and Prandtl number at very large Rayleigh number are in satisfactory agreement with the results of asymptotic expansions.

Heat, Mass, and Momentum Transfer

Abstract: Life depends on heat and mass transfer between organisms and their surroundings. Such processes as carbon dioxide exchange between leaves and the atmosphere, oxygen uptake by microorganisms, oxygen and carbon dioxide exchange in the lungs of animals, or convective heat loss from the surfaces of animal coats are fundamental to the existence of living organisms. A thorough understanding of these exchange processes is therefore a necessary part of the study of physical ecology. In this chapter we will first discuss molecular diffusion. It is by this process that heat and mass are transported in still air or water, as they are in parts of the lungs of animals, in soils, and in the substomatal cavities of leaves. Molecular diffusion is also important in convective heat and mass transfer between surfaces and fluids flowing over them since a thin boundary layer is always formed near the surface through which transport is by diffusion. After diffusion processes are discussed, we will then present convective heat and mass transfer theory as it applies to fluids moving over plates, cylinders, and spheres. Finally, we will discuss momentum exchange and the force of moving fluids on objects in them.

Turbulent Heat Transfer Studies in Annulus With Inner Cylinder Rotation

Abstract: Experimental investigations of turbulent heat transfer are made in a large-gap annulus with both rotating and nonrotating inner cylinder. The vertical annular channel has an electrically heated outer wall; the inner wall i thermally and electrically insulated. The axial air flow is allowed to develop before rotation and heating are imparted. The resulting temperature fields are investigated using thermocouple probes located near the channel exit. The wall heat flux, wall axial temperature development, and radial temperature profiles are measured. For each axial Reynolds number, three heat flux rates are used. Excellent correlation is established between rotational and nonrotational Nusselt number. The proper correlation parameter is a physical quantity characterizing the flow helix. This parameter is the inverse of the ratio of axial travel of the flow helix in terms of hydraulic diameter, per half revolution of the spinning wall.

Numerical solution of natural convection flow past a non-isothermal vertical flat plate

Abstract: The problem of natural convection over a semi-infinite flat plate with non-uniform wall temperature is studied by using a numerical method. The local rates of heat transfer as a function of the distance along the plate are tabulated for a range of Prandtl numbers (0.01 to 100) and for a few cases of wall temperature distributions. Such tabulations serve as a reference against which other approximate solutions can be compared in the future.

Heat transfer coefficients for leaves on orchard apple trees

Abstract: The coefficient for heat transfer from apple tree leaves was measured from the energy balance of leaves which were prevented from transpiring by applying ‘Vaseline’ (petroleum jelly). Vaseline had negligible effect on the absorption of short-wave radiation by the leaves. The Nusselt number (Nu) describing heat flux from a leaf in terms of its average temperature was related to Reynolds numbers (Re) in the range 103 to 104 by Nu = 0.46 Re0.54 Pr0.33, where Pr is the Prandtl number. This supports Landsberg and Powell's (1973) wind-tunnel results for transfer from leaves subject to mutual interference.

Heat transfer in laminar entrance region of a flat channel for the temperature boundary condition of the third kind

Abstract: To explore the influence of the developing flow in a flat channel on the laminar forced convection heat transfer, the non-linear momentum and the linear energy equation are solved successively by employing the Galerkin-Kantorowich method of variational calculus. Assuming constant fluid properties, negligible axial diffusion and temperature boundary condition of the third kind, semi analytic solution for velocity and temperature is derived. The local Nusselt numbers are tabulated for various values of Biot and Prandtl number.

fast viscous convection

Abstract: A method is described for the asymptotic study of natural convection problems in the limit of fast flow, when the dimensionless Rayleigh number R tends to infinity. The Boussinesq approximation is used, and attention is confined to a viscous limit, with the Prandtl number taken as infinite; this makes the fluid momentum negligible. The flow is nevertheless so fast that the temperature is disturbed only in thin layers. The heat equation is studied in these layers, and the effect of the buoyancy in the layers on the motion is expressed in terms of the heat flux. The method is applied to steady two-dimensional convection from a heated strip of an infinite horizontal plane, with a no-stress free-surface boundary, and with a non-slip fixed-surface boundary. The respective results for the total dimensionless heat flux are as R → ∝, where the Rayleigh number R is defined in terms of the half-width of the strip, and Г is the gamma function.

Transient Convective Heat Transfer for Laminar Boundary Layer Flow With Effects of Wall Capacitance and Resistance

Abstract: Transient forced convective heat transfer from a laminar boundary layer flow over a flat plate with appreciable thermal capacity and resistance is studied analytically. In the analysis, the flow is assumed to be steady and incompressible and the solid plate is subjected to a uniform step heat input at the lower surface. The integral method is utilized to reduce systems of nonlinear partial differential equations to a single integro-differential equation in terms of interfacial temperature which is then solved with the aid of finite difference technique. Numerical results for the fluid-solid interface temperature, heat transfer coefficient, and temperature distributions within the fluid and solid are presented. Some limiting solutions are found to agree well with the results of the previous theoretical analyses.

Entry region heat transfer in rotating radial tubes.

Abstract: An experimental study of the effect of rotation on the entrance region heat transfer inside straight radially aligned circular tubes is presented. Average coolant passage Nusselt numbers were determined for passage length-to-diameter ratios of 6, 12, and 24 over ranges of radially outward air flows and rotational speeds. Results are presented in terms of the ratio of rotating-to-s tationary heat transfer. Comparisons are made with the rotational heat-transfer enhancement expected for fully developed flow conditions with rotation. The present results, conducted in the absence of entry swirl, show that only a small rotational effect on heat transfer can be expected for relatively short cooling passages.

Heat Transfer in Rotating Cylindrical Cavities

Abstract: Nusselt numbers are measured on the heated disc of a rotating cylindrical cavity, with either an axial throughflow or a radial outflow of coolant, over a range of gap ratios, 0.13 ≤ G ≤ 0.4, flow r...