A large heat exchanger transfers a total of 100 MW. Assume the wall separating steam and seawater is 4 mm of steel, conductivity 15 W/m K and that a maximum of 5°C difference between the two fluids is allowed. Find the required minimum area for the heat transfer.

Consider a pan placed on top of electric range to cook. The bottom section of the pan is 0.4 cm thick and has a diameter of 18 cm. The electric heating unit on the range top consumes 800 W of power during cooking, and 80 percent of the heat generated in the heating element is transferred uniformly to the pan. Assuming constant thermal conductivity and steady state operation. The heat transfer can be approximated as being one-dimensional through the bottom surface to the top. Take the direction normal to the bottom surface to be the x-axis. a)Perform an energy balance on a thin element of the pan during a small-time interval △t , and indicate which terms may be neglected or ignored and why? b)Assuming constant thermal conductivity, obtain the differential equation that describes the variation of the temperature in the bottom section of the pan during steady state operation.

The thermal conductivities of human tissues vary greatly. Fat and skin have conductivities of about 0.20 W/m K and 0.020 W/m · K respectively, while other tissues inslde the body have conductivities of about 0.50 W/m · K. Assume that between the core region of the body and the skin surface lies a skin layer of 1.0 mm, fat layer of 0.50 cm, and 3.2 cm of other tissues. (a) Find the R-factor for each of these layers, and the equivalent R-factor for all layers taken together, retaining two digits. Rakin m2. K/W Rat m2 . K/W Rissue m2. K/W m2- K/W (b) Find the rate of energy loss when the core temperature is 37°C and the exterior temperature is 0°C. Assume that both a protective layer of clothing and an insulating layer of unmoving air are absent, and a body area of 2.0 m.