Flat plates uniform heat flux

Air flows at a velocity of 6 m/s over a wide flat plate that has a length of 2 cm in the flow direction. There is a uniform heat flux of 3 kW/m2 at the surface of the plate. Using the similarity solution results, plot the variation of local temperature along the plate. The air ahead of the plate has a temperature of 10°C. 

Discuss how the analysis of natural convective flow over a vertical flat plate in a saturated porous medium must be modified if there is a uniform heat flux rather than a uniform temperature at the surface. 

Friction Coefficient 400 Heat Transfer Coefficient 401 Flat Plate with Unhealed Starting I engih 403 Uniform Heat Flux 403... 

When a flat plate is subjected to uniform heat flux instead of uniform temperature, Ihc local Nusselt number is given by... 

For forced convection of liquid metals (Pr 1) over a horizontal flat plate subject to a uniform heat flux qm, evaluate the Nusselt number based on a uniform velocity and linear temperature profiles (Eg. 5P-2). 

FIGURE 4.8 Comparison of local heat transfer measurements of Qureshi and Gebhart [222] with Eq. 4.34 for a uniform heat flux, vertical flat plate in water. 

For a vertical cylinder of length L and diameter D, first calculate the Nusselt number Nur and Nu, for a vertical flat plate of height L, using Eq. 4.33 if the cylinder is isothermal and Eq. 4.36 if it has uniform heat flux. These Nusselt numbers are based on the length L of the plate (see Fig. 4.6) and are renamed Nuplale and NufiPlate here. The laminar Nusselt number for the vertical cylinder (defined in Fig. 4.14), Nuf, is then calculated from... 

Consider a steady, laminar boundary layer flow of incompressible, transparent fluid along a flat plate, with a constant applied heat flux qw Btu/(hr ft2) at the wall surface. The properties of the fluid are assumed constant. The main considerations are conduction to the fluid, and radiation from the plate to the environment at Te. Surface of the plate is opaque and gray, and the uniform emissivity is 8. The fluid which is at a temperature of T,, flows at a uniform velocity of Uo. Flow velocities are sufficiently small so that viscous dissipation may be neglected. 

For any prescribed values of Pr and n, 0 It o will have a specific value. It therefore follows that qw will be proportional to (Tw - T )/xo s. Hence, the case where the heat flux at the surface of the plate is uniform corresponds to the case where n - 0.5, i.e., a similarity solution exists for flow over a flat plate with a uniform surface heat flux. 

Air flows over a wide t-m long flat plate which has a uniform surface temperature of 80°C, the temperature of the air ahead of the plate being 20°C. The air velocity is such that the Reynolds number bas J on the length of the plate is 5 x 106. Derive an expression for the local wall heat flux variation along the plate. Use the Reynolds analogy and assume the boundary layer transition occurs at a Reynolds number of 10 ... 

Air at a temperature of 0°C and standard atmospheric pressure flows at a velocity of 50 m/s over a wide flat plate with a total length of 2 m. A uniform surface heat flux is applied over the first 0.7 m of the plate and the rest of the surface of the plate is adiabatic. Assuming that the boundary layer is turbulent from the leading edge, use the numerical solution to derive an expression for the plate temperature at the trailing edge of the plate in terms of the applied heat flux. What heat flux is required to ensure... 

Consider a flat plate of thickness t, initially in an ambient at uniform temperature 1. From this condition, one surface is subjected to uniform flux q". Heat is transferred from the other surface with coefficient h. 

The authors of most experimental studies and analyses have focused their attention on the local values defined in Fig. 4.44. Churchill [55] fitted the local Nu values for assisting flow using Eq. 4.159 with m = 3 and with each average value on the right side of the equation replaced by its local value counterpart. Mucoglu and Chen [201] have solved the inclined flat plate problem for uniform wall temperature and heat flux and have presented local heat transfer results for mixed convection. 

For each steady state heat flux, seven ten eratures were measured for every condition of velocity and water/air mass flow ratio investigated to ensure that a reliable trend could be determined. The radial profiles of tenqierature at 500°C widiout water addition and with 4.75% water/air mass flow ratio are shown in Figure 3. The ten erature profiles are flat or sUghdy increasing toward the edges and have errors of 2.2% and 5.2% for no water addition and 4.75% water/air mass flow ratio respectively. The steady state ten erature was chosen to be that of the center zone of the plate, 2.54 cm in diameter. The three thermocouples used to record the temperatures in this zone exhibited a uniform temperature profile. 

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