Consider a thin 16-cm-long and 20-cm-wide horizontal plate suspended in air at $20^\circ C.$ The plate is equipped with electric resistance heating elements with a rating of 20 W. Now the heater is turned on and the plate temperature rises. Determine the temperature of the plate when steady operating conditions are reached. The plate has an emissivity of 0.90 and the surrounding surfaces are at $17^\circ C.$ As an initial guess, assume a surface temperature of $50^\circ C.$ Is this a good assumption?

Consider a person who is trying to keep cool on a hot summer day by turning a fan on and exposing his entire body to air flow. The air temperature is $85^\circ F$ and the fan is blowing air at a velocity of 6 ft/s. If the person is doing light work and generating sensible heat at a rate of 300 Btu/h, determine the average temperature of the outer surface (skin or clothing) of the person. The average human body can be treated as a 1-ft-diam-eter cylinder with an exposed surface area of $18 ft^2.$ Disregard any heat transfer by radiation. What would your answer be if the air velocity were doubled? Evaluate the air properties at $100^\circ F.$

Consider a thin 16-cm-long and 20-cm-wide horizontal plate suspended in air at $20^{\circ} \mathrm{C}.$ The plate is equipped with electric resistance heating elements with a rating of 20 W. Now the heater is turned on and the plate temperature rises. Determine the temperature of the plate when steady operating conditions are reached. The plate has an emissivity of 0.90 and the surrounding surfaces are at $17^{\circ} \mathrm{C} .$ As an initial guess, assume a surface temperature of $50^{\circ} \mathrm{C}.$ Is this a good assumption?

Inside a condenser, there is a bank of seven copper tubes with cooling water flowing in them. Steam condenses at a rate of 0.6 kg/s on the outer surfaces of the tubes that are at a constant temperature of $68^\circ C.$ Each copper tube is 5-m long and has an inner diameter of 25 mm. Cooling water enters each tube at $5^\circ C$ and exits at $60^\circ C.$ Determine the average heat transfer coefficient of the cooling water flowing inside each tube and the cooling water mean velocity needed to achieve the indicated heat transfer rate in the condenser.

An aluminum soda can of 150 mm in length and 60 mm in diameter is placed horizontally inside a refrigerator compartment that maintains a temperature of $4^{\circ} \mathrm{C}.$ If the surface temperature of the can is $36^{\circ} \mathrm{C},$ estimate heat transfer rate from the can. Neglect the heat transfer from the ends of the can.

Two water reservoirs $A$ and $B$ are connected to each other through a $40$-m-long, $2$-cm-diameter cast iron pipe with a sharp-edged entrance. The pipe also involves a swing check valve and a fully open gate valve. The water level in both reservoirs is the same, but reservoir $A$ is pressurized by compressed air while reservoir $B$ is open to the atmosphere at $95\ \mathrm{kPa}$. If the initial flow rate through the pipe is $1.5 \mathrm{~L} / \mathrm{s}$, find the absolute air pressure on top of reservoir $A$. Take the water temperature to be $10^{\circ} \mathrm{C}$.

Consider steady one-dimensional heat transfer through a multilayer medium. If the rate of heat transfer $\dot{Q}$ is known, explain how you would determine the temperature drop aeross each layer.

A $50-\mathrm{cm} \times 50-\mathrm{cm}$ circuit board that contains $121$ square chips on one side is to be cooled by combined natural convection and radiation by mounting it on a vertical surface in a room at $25^{\circ} \mathrm{C}$. Each chip dissipates $0.18 \mathrm{~W}$ of power, and the emissivity of the chip surfaces is $0.7$. Assuming the heat transfer from the back side of the circuit board to be negligible, and the temperature of the surrounding surfaces to be the same as the air temperature of the room, Find the surface temperature of the chips.

Is the following system

$$\left[\begin{array}{c}{\dot{x}_{1}} \\ {\dot{x}_{2}} \\ {\dot{x}_{3}}\end{array}\right]=\left[\begin{array}{rrr}{0} & {1} & {0} \\ {0} & {0} & {1} \\ {-6} & {-11} & {-6}\end{array}\right]\left[\begin{array}{l}{x_{1}} \\ {x_{2}} \\ {x_{3}}\end{array}\right]+\left[\begin{array}{l}{0} \\ {0} \\ {1}\end{array}\right] uy=\left[\begin{array}{lll}{20} & {9} & {1}\end{array}\right]\left[\begin{array}{l}{x_{1}} \\ {x_{2}} \\ {x_{3}}\end{array}\right]$$

completely state controllable and completely observable?

Consider a 1.2-m-high and 2-m-wide glass window whose thickness is 6 mm and thermal conductivity is $k = 0.78 W/m \cdot K.$ Determine the steady rate of heat transfer through this glass window and the temperature of its inner surface for a day during which the room is maintained at $24^\circ C$ while the temperature of the outdoors is $−5^\circ C.$ Take the convection heat transfer coefficients on the inner and outer surfaces of the window to be $h_1= 10 W/m^2 \cdot K$ and $h_2 = 25 W/m^2 \cdot K,$ and disregard any heat transfer by radiation.

A SAE grade 5, UNF bolt carries a static tensile load of 2000 lb with a safety factor of 5 based on proof strength. The bolt is used with a nut made of steel of SAE grade 1 specifications.

(a) What size of bolt is required?

(b) What is the least number of threads that must be engaged for the thread shear strength to be equal to the bolt tensile strength?

Consider a third order linear and homogeneous differential equation. How many arbitrary constants will its general Solution involve?

Consider a 2-ft × 2-ft thin square plate in a room at $75^\circ F.$ One side of the plate is maintained at a temperature of $130^\circ F,$ while the other side is insulated. Determine the rate of heat transfer from the plate by natural convection if the plate is (a) vertical; (b) horizontal with hot surface facing up; and (c) horizontal with hot surface facing down.

A 10-cm-diameter and 10-m-long cylinder with a surface temperature of $10^\circ C$ is placed horizontally in air at $40^\circ C.$ Calculate the steady rate of heat transfer for the cases of (a) free-stream air velocity of 10 m/s due to normal winds and (b) no winds and thus a free stream velocity of zero.