A computer consists of an array of five printed circuit boards (PCBs), each dissipating P, = 20 W of power. Cooling of the electronic components on a board is pro- vided by the forced flow of air, equally distributed in passages formed by adjoining boards, and the convec- tion coefficient associated with heat transfer from the components to the air is approximately h= 200 W/m².K. Air enters the computer console at a temperature of T= 20°C, and flow is driven by a fan whose power consumption is P₁ = 25 W. Outlet air, T PCB, P 1000 040040 090040 CUJU ttt Inlet air , Ti Fan, Pf (a) If the temperature rise of the airflow, (T. -T), is not to exceed 15°C, what is the minimum allowable volu- metric flow rate of the air? The density and specific heat of the air may be approximated as p = 1.161 kg/m³ and c, = 1007 J/kg. K, respectively. (b) The component that is most susceptible to thermal failure dissipates 1 W/cm² of surface area. To mini- mize the potential for thermal failure, where should the component be installed on a PCB? What is its surface temperature at this location?

A shaft of 0.06-m diameter is heat treated in a gas-fired furnace whose gases is at 1200 K and provide a convection coefficient of 125 W/m² K. If the shaft enters the furnace at 300 K and stays in the furnace. (1) What is the centerline temperature (in K) of the shaft after 900 seconds? (2) What is the value of the dimensionless Fourier number? The shaft material has a density of 7000 kg/m², thermal conductivity of 50 W/m.K, and specific heat capacity 500 J/kg.K. Please show your work and assumptions.

3 An electrical current of 700 A flows through a stainless steel cable having a diameter of 5 mm and an electrical resistance of 6 x 104 /m (i.e., per meter of cable length). The cable is in an environment having a tem- perature of 30°C, and the total coefficient associated with convection and radiation between the cable and the environment is approximately 25 W/m².K. (a) If the cable is bare, what is its surface temperature? (b) If a very thin coating of electrical insulation is applied to the cable, with a contact resistance of 0.02 m² K/W, what are the insulation and cable surface temperatures? (c) There is some concern about the ability of the insula- tion to withstand elevated temperatures. What thick- ness of this insulation (k = 0.5 W/m .K) will yield the lowest value of the maximum insulation temper- ature? What is the value of the maximum tempera- ture when this thickness is used? Note: The 25 W/m²K includes not only convection but also radiation.

A thin metal plate 1 mx 1 m is placed on a rooftop. It receives radiant heat from the sun directly at the rate of 170 W/m². If heat transfer from the plate to the ambient occurs purely by free convection, calculate the steady state temperature of the plate. Assume that there is no heat loss from the bottom of the plate. The ambient temperature is 25°C.