For the plane wall shown, solve the conduction equation, deriving an algebraic expression for the steady temperature, T(x). Then, plot the wall temperature on the (T,x) axes below. What is the slope of T(x) at x = 0 ? The left surface of the wall is insulated, and the right surface is exposed to a fluid. Assume 1-D conduction, uniform internal heat generation, and neglect radiation. L= 20.0 cm T(°C) fluid k= 15 W/m•K T= 20°C h = 100 W/m²-K ġ = 10$ W/m³ x (cm) 0.0 5.0 10.0 15.0 20.0

A metallic sphere of radius R is heated in an oven to a temperature of 600 ° F throughout, and then removed from the oven and allowed to cool in ambient air to T∞ = 75 ° F, by convection and radiation (see attached figure). The thermal conductivity of the ball material is known to vary linearly with temperature. Assuming that the ball is uniformly cooled starting from the entire outer surface, obtain the differential equation that describes the change in temperature in the sphere during cooling. Note: In the image, the translation would be: metallic sphere

Estimate the natural convection heat transfer coefficient of the horizontal pipe. The temperature of the outer surface of the pipe is 120 ° C. The ambient air temperature is 25 ° C. The outer diameter of the pipe is 10 cm. Convection coefficient = Answer W / m² ° C.

Two identical 7.5-cm cubes of copper at 425 and 90°C are brought into contact. Assuming that the blocks exchange heat only with each other and that there is no resistance to heat flow as a result of the contact of the blocks, plot the temperature of each block as a function of time, using the lumped-capacity method of analysis. That is, assume the resistance to heat transfer is the conduction resistance of the two blocks. Assume that all surfaces are insulated except those in contact.