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  • Convection

    • Checklist
      Students must
      Check-off items: 90%
    • Nusselt Number from Temperature Profile Page
      ME-2014-S1-46-ht
      The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by \[ \frac {T_w-T}{T_w-T_\infty } = a + b\frac {y}{L}+c\left (\frac {y}{L}\right )^2 \] where \(y\) is measured perpendicular to the plate, \(L\) is the plate length, and \(a\), \(b\) and \(c\) are arbitrary constants. \(T_w\) and \(T_\infty \) are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is \(k\) and the wall heat flux is \(q\), the Nusselt number \(\displaystyle \text {Nu} = \frac {q}{T_w-T_\infty }\frac {L}{k}\) is equal to
      1. \(a\)
      2. \(b\)
      3. \(2c\)
      4. \((b+2c)\)
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    • Heat Flux from Temperature Distribution in Boundary Layer Page
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    • Heat Transfer Coefficient from given Correlation Page
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    • Surface Temperature from Heat Transfer Correlation Page
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    • Heat Transfer Coefficient for Uniform Heat Flux - Laminar Flow in Pipe Page
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    • Heat Transfer Coefficient for Constant Wall Temperature - Laminar Flow Page
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    • Thermally Developed Flow for Constant Wall Heat Flux Page
      ME-2019-S1-32
      The wall of a constant diameter pipe of length 1 m is heated uniformly with flux \(q\) by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and steady all through the pipe. The bulk temperature of the fluid is equal to 0oC at the inlet and 50oC at the exit. The wall temperatures are measured at three locations, P, Q and R, as shown in the figure. The flow thermally develops after some distance from the inlet. The following measurements are made:
      Point P Q R
      Wall Temperature (oC) 50 80 90

      Among the locations P, Q and R, the flow is fully developed at
      1. P, Q and R
      2. P and Q only
      3. Q and R only
      4. R only
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    • Temperature of Surface for Constant Heat Flux Page
      ME-2022-S2-65
      Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk mean temperature of the fluid at the entrance to the pipe is 200oC. The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 W/(m.K) and 2600 J/(kg.K), respectively. The correlation \(\text{Nu} = 0.023\text{Re}^{0.8}\text{Pr}^{0.4}\) is applicable, where the Nusselt number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ______ oC (round off to the nearest integer).
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    • Velocity and Heat Transfer Coefficient from Colburn Analogy Page
      2002-8-ht
      Air flows through a smooth tube, 2.5 cm diameter and 10 m long, at 37\(^\circ \)C. If the pressure drop through the tube is 10000 Pa, estimate:
      1. the air velocity (in m/s) through the tube.
      2. the heat transfer coefficient (in W/m\(^2\).K) using Colburn Analogy [\(j_H = (\text {St})(\text {Pr})^{0.67}\)], where \(\text {St}\) is the Stanton Number and \(\text {Pr}\) is the Prandtl Number.
      Gas constant, \(R\) = 82.06 cm\(^3\).atm/mol.K. Darcy friction factor \( = 0.184/\text {Re}^{0.2}\). Other relevant properties of air under the given conditions: viscosity = \(1.8\times 10^{-5}\) kg/m.s, density = 1.134 kg/m\(^3\), specific heat capacity, \(C_P\) = 1.046 kJ/kg.\(^\circ \)C, thermal conductivity = 0.028 W/m.\(^\circ \)C.
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    • Heat Flux Estimation from Experiments Page
      2016-41-ht
      In an experimental setup, mineral oil is filled in between the narrow gap of two horizontal smooth plates. The setup has arrangements to maintain the plates at desired uniform temperatures. At these temperatures, ONLY the radiative heat flux is negligible. The thermal conductivity of the oil does not vary perceptibly in this temperature range. Consider four experiments at steady state under different experimental conditions, as shown in the figure below. The figure shows plate temperatures and the heat fluxes in the vertical direction.

      What is the steady state heat flux (in W/m2) with the top plate at 70oC and the bottom plate at 40oC? _________ (26 / 39 / 42 / 63)
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    • Relative Thicknesses of Boundary Layers Page
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    • Heat Flux and Temperature for Convective Heat Transfer Page
      ME-2013-50-51
      Water (specific heat, \(C_P=4.18\) kJ/[kg.K]) enters a pipe at a rate of 0.01 kg/s and a temperature of 20oC. The pipe, of diameter 50 mm and length 3 m, is subjected to a wall heat flux \(q_w\) in W/m2:
      1. If \(q_w=2500x\), where \(x\) is in m and in the direction of flow (\(x=0\) at the inlet), the bulk mean temperature of the water leaving the pipe in oC is _____ (42 / 62 / 74 / 104)
      2. If \(q_w=5000\) and the convection heat transfer coefficient at the pipe outlet is 1000 W/(m2.K), the temperature in oC at the inner surface of the pipe at the outlet is _____ (71 / 76 / 79 / 81)
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