## Question:

Free convection in air at atmospheric pressure is found to experience a convection heat-transfer coefficient that varies as h = A(∆T)n, where ∆T is the temperature difference between the surface and the surrounding air, A is a constant, and n is some exponent. You are to devise a way to determine the constant and exponent in this equation by utilizing an experiment in combination with a lumped-capacity analysis. Consider a complex finned structure like that shown in Figure 2-13, where the mass, material of construction, and surface area can be determined. The structure is heated to a uniform initial temperature in an appropriate oven and then allowed to cool while exposed to room air at about 20ºC. The initial temperature may be taken as about 200ºC. The temperature of the structure is measured by a thermocouple device embedded within the structure and is displayed on a readout device. The structure is coated with a black paint so that it radiates as an ideal blackbody exchanging heat with a large enclosure according to Equation (1-12) with ε = 1.0. Recall that the temperatures in this equation must be in degrees Kelvin. Write the finite-difference equation for cooling of the structure, taking account of both convection and radiation loss, and describe how experimental data for cooling of the body may be used to determine the values of the constant A and exponent n.