The Nusselt number for forced convection is a function of Reynolds number, Prandtl number, and surface shape and orientation. Due to the mass movement of a viscous fluid, there are hydraulic (velocity) and thermal. Boundary layer development for flow over a flat plate and different flow regimes.
The relative thickness of the velocity and thermal boundary layers is best described by. To keep the analysis at a manageable level, we assume that the flow is steady and two-. We take the direction of flow along the surface to be x and the normal direction to be.
Conservation of Mass Equation
Noting that the mass flow rate is equal to the product of density, mean velocity, and cross-sectional area perpendicular to the flow, the velocity at . The rate at which the fluid exits the control volume from the right surface can be .
Conservation of Momentum Equations
Note that flow is steady and two-dimensional and thus u is u(x, y), the total differential of u. The normal stress is related to the velocity gradients u/x and v/y, which are much smaller than u/y, to which shear stress is related.
Navier-Stoke Equation
It means that for a given x, the pressure in the boundary layer is equal to the pressure in the free stream. The pressure can be determined from a special analysis of the fluid flow in the free stream (it is. Therefore, for the flow over a flat plate, the pressure remains constant over the entire plate (both inside and outside the boundary layer).
Conservation of Energy Equation
The total energy of a flowing liquid stream per mass unit is e = h + ke + pe, where h is the enthalpy. The Tass flow rate of the fluid entering the control volume from the left is u(dy.1). The rate of energy transfer to the control volume by mass in the x direction is.
The net rate of energy transfer to the control volume is determined in relation to the mass. The energy equation for a steady two-dimensional fluid flow with constant properties and negligible shear stresses is. When viscous shear stresses are not negligible, their effect is taken into account by expressing the energy equation as
This manifests itself as a significant increase in the liquid temperature due to the conversion of the. For the special case of a stationary liquid, u=v=0 and the energy equation is reduced to the stable two-dimensional heat conduction equation.
SOLUTIONS OF CONVECTION EQUATIONS FOR A FLAT PLATE
Once the velocity distribution is available, we can determine the friction coefficient and boundary layer thickness using them. Finding such a variable, assuming it exists, is more of an art than a science and requires a good understanding of it. Noting that the general shape of the velocity profile remains the same across the plate,
Differentiating these relations u and v can be shown to be the derivatives of the velocity components. Using the definitions of f and , the boundary conditions in terms of similarity variables can be expressed as The problem was first solved by Blasius in 1908 using the power series expansion approach and this original solution is known as the Blasius solution.
The Energy Equation
Obtaining an equation for as a function of itself confirms that the temperature profiles are similar, and thus a similarity solution exists. Note that these relations are valid only for laminar flow over an isothermal flat plate. Blasius' solution provides important insights, but its value is largely historical.
NONDIMENSIONALIZED CONVECTION EQUATIONS AND SIMILARITY
FUNCTIONAL FORMS OF FRICTION AND CONVECTION COEFFICIENTS
Note that the Nusselt number corresponds to the dimensionless temperature gradient at the surface. Integration will remove the dependence on x* and the average friction coefficient and Nusselt number can be expressed as.
ANALOGIES BETWEEN MOMENTUM AND HEAT TRANSFER
Therefore, the functions u* and T* must be identical, and so the first derivatives of u* and T* in. The Reynolds analogy is of limited use because of the constraints Pr = 1 and P*/x* = 0 on it, and it is desirable to have an analogy that is applicable over a wide range of Pr. A 2-m x 3-m flat plate is suspended in a room and subjected to air flow parallel to it.
A flat plate is exposed to the air flow and the drag force acting on it is measured.
7-3 Forced convection over a flat plate
The local heat transfer coefficient, hx, is the heat transfer coefficient at the point x measured from the leading edge of the surface. The average convection heat transfer coefficient is the average value from the leading edge to point x.
Nusselt number correlations for parallel flow over a flat plate
Steps to calculate convection heat transfer rate — external flow
Flow across cylinders
Drag Coefficients
Effect of Roughness
Fluid properties are determined at the mean temperature of the fluid film.
Flow Across Tube Banks
In tube banks, the flow characteristics are dominated by the maximum velocity Vmax occurring in the tube bank, rather than the approach velocity. Several correlations, all based on experimental data, have been proposed for the mean Nusselt number for cross flow over tube banks. Note that all properties except Prs must be evaluated at the arithmetic mean temperature of the fluid determined from.
The average Nusselt number relationships in Table 7–2 are for tube strings with 16 rows or more. These ratios can also be used for tube banks with NL, provided they are modified as . When the Nusselt number and thus the average heat transfer coefficient for the whole series of pipes is known, the heat.
The correct temperature difference for internal flow (flow over tube banks is still internal flow through the shell) is the logarithmic mean temperature difference Tln defined as. Here N is the total number of tubes in the bank, NT is the number of tubes in a transverse plane, L is the length of the tubes, and V is the velocity of the fluid just before it enters the tube bank.
Pressure Drop
Friction factor & Correction Factor
In an industrial facility, the air must be preheated before entering the furnace with geothermal water at 120ºC flowing through the tubes of a tube bank located in a duct. Air enters the duct at 20ºC and 1 atm with an average velocity of 4.5 m/s and flows over the pipes in the normal direction. The outer diameter of the tubes is 1.5 cm, and the tubes are arranged accordingly.
Laju perpindahan panas ke udara dan kehilangan tekanan udara harus ditentukan. Investigasi Numerik dan Eksperimental Formasi Horseshoe Vortex pada Annular Fined Tubes, Prosiding, Seminar Nasional Teknik Mesin II, Universitas Andalas, Padang, Desember 2003. Pengamatan Visual Formasi Horseshoe Vortex pada Susunan Gormetrik Annular Fined Tubes, Prosiding, Seminar Nasional Mekanikal Teknik II , Universitas Andalas, Padang, Desember 2003.
Pengaruh Parameter Geometri dan Konfigurasi File Ring Pipa Terhadap Posisi Jarak Permukaan Ujung, Jurnal Sains Spindle Jurusan Teknik Mesin Fakultas Teknik Universitas Tarumanegara, Vol. Simulasi numerik perhitungan tegangan geser dan momen pada flow meter bahan bakar tipe perpindahan positif dengan variasi laju aliran pada sudut putar yang berbeda. Analisis Aliran pada Rotor Turbin Angin Sumbu Horizontal Menggunakan Pendekatan Komputasi, Exergy, Jurnal Teknik Energi POLINES, Vol.
Optimization of Texture of the Multiple Textured Lubricated Contact with Slip, International Conference on Computation in Science and Engineering, Journal of Physics: Conf. Effect of Texture Depth on Hydrodynamic Performance of Lubricated Contact Considering Cavitation, Proceedings of the International Conference on Advances in Mechanical Engineering Research and Application (ICOMERA 2018), Malang, October 2018. Comparison of Thermal-Hydraulic Performance of Embedded Perforated Concave Delta Winglet Vortex Generators on a Heated Plate: An Experimental Study and Flow Visualization, Proceedings of the International Conference on Advances in Mechanical Engineering Research and Application (ICOMERA 2018), Malang, October 2018.
Effect of Rushton Fan Speed on Biogas Production in Continuous Stirred Bioreactor Anaerobic Digestion, Journal of Advanced Research in Biofuels and Bioenergy, Vol. Experimental and Computational Study on Heat Transfer of a 150 KW Air-Cooled Eddy Current Dynamometer, Proc. CFD simulation of the width and angle of the rotor blade on the airflow rate of a 350 kW air-cooled eddy current dynamometer, Proc.
