An aluminum pan whose thermal conductivity is $237 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$ has a flat bottom with diameter 15 cm and thickness 0.4 cm. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of 1400 W. If the inner surface of the bottom of the pan is at $105^\circ C,$ determine the temperature of the outer surface of the bottom of the pan.

An aluminum pan whose thermal conductivity is $237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$ has a flat bottom with diameter $15 \mathrm{~cm}$ and thickness $0.4 \mathrm{~cm}$. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of $800 \mathrm{~W}$. If the inner surface of the bottom of the pan is at $105^{\circ} \mathrm{C}$, find the temperature of the outer surface of the bottom of the pan.

An aluminum pan whose thermal conductivity is $237 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ has a flat bottom whose diameter is $20 \mathrm{~cm}$ and thickness $0.4 \mathrm{~cm}$. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of $500 \mathrm{~W}$. If the inner surface of the bottom of the pan is $105^{\circ} \mathrm{C}$, Find the temperature of the outer surface of the bottom of the pan.

The inner and outer surfaces of a 4-m × 7-m brick wall of thickness 30 cm and thermal conductivity $0.69 W/m \cdot K$ are maintained at temperatures of $26^\circ C$ and $8^\circ C,$ respectively. Determine the rate of heat transfer through the wall, in W.

Consider an aluminum pan used to cook stew on top of an electric range. The bottom section of the pan is L = 0.25 cm thick and has a diameter of D = 18 cm. The electric heating unit on the range top consumes 900W of power during cooking, and 90 percent of the heat generated in the heating element is transferred to the pan. During steady operation, the temperature of the inner surface of the pan is measured to be $108^\circ C.$ Assuming temperature- dependent thermal conductivity and one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary conditions) of this heat conduction problem during steady operation. Do not solve.

A wood slab with a thickness of 0.05 m is subjected to a heat flux of $40 W/m^2$. The left and right surface temperatures of the wood slab are kept at constant temperatures of $40^\circ C$ and $20^\circ C,$ respectively. What is the thermal conductivity of the wood slab?

Consider a long pipe of inner radius $r_1,$ outer radius $r_2,$ and thermal conductivity k. The outer surface of the pipe is subjected to convection to a medium at $T_{\infty}$ with a heat transfer coefficient of h, but the direction of heat transfer is not known. Express the convection boundary condition on the outer surface of the pipe.

A spherical metal ball of radius ro is heated in an oven to a temperature of $T_1$ throughput and is then taken out of the oven and dropped into a large body of water at $T_{\infty}$ where it is cooled by convection with an average convection heat transfer coefficient of h. Assuming constant thermal conductivity and transient one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary and initial conditions) of this heat conduction problem. Do not solve.

The inner and outer surfaces of a 0.5-cm thick $2-m \times 2-m$ window glass in winter are $10^{\circ} \mathrm{C} \text { and } 3^{\circ} \mathrm{C},$ respectively. If the thermal conductivity of the glass is $0.78 \mathrm{W} / \mathrm{m} \cdot \mathrm{K},$ determine the amount of heat loss through the glass over a period of 5 h. What would your answer be if the glass were 1 cm thick?

The inner and outer surfaces of a 0.5-cm thick $2-m \times 2-m$ window glass in winter are $10^\circ C$ and $3^\circ C,$ respectively. If the thermal conductivity of the glass is $0.78 W/m \cdot K,$ determine the amount of heat loss through the glass over a period of 5 h. What would your answer be if the glass were 1 cm thick?

Consider the East wall of a house that has a thickness of L. The outer surface of the wall exchanges heat by both convection and radiation. The interior of the house is maintained at $T_{\infty_{1}},$ while the ambient air temperature outside remains at $T_{\infty 2}$. The sky, the ground, and the surfaces of the surrounding structures at this location can be modeled as a surface at an effective temperature of $T_{sky}$ for radiation exchange on the outer surface. The radiation exchange between the inner surface of the wall and the surfaces of the walls, floor, and ceiling it faces is negligible. The convection heat transfer coefficients on the inner and outer surfaces of the wall are $h_1s$ and $h_2,$ respectively. The thermal conductivity of the wall material is k and the emissivity of the outer surface is $\varepsilon_{2}.$ Assuming the heat transfer through the wall to be steady and one-dimensional, express the mathematical formulation (the differential equation and the boundary and initial conditions) of this heat conduction problem. Do not solve.

The inner and outer surfaces of a $0.5-\mathrm{cm}$ thick $2-\mathrm{m} \times$ $2-\mathrm{m}$ window glass in winter are $10^{\circ} \mathrm{C}$ and $3^{\circ} \mathrm{C}$, respectively. If the thermal conductivity of the glass is $0.78 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$, Find the amount of heat loss through the glass over a period of $5 \mathrm{~h}$. What would your answer be if the glass were $1 \mathrm{~cm}$ thick?

Consider two walls of a house that are identical except that one is made of 10-cm-thick wood, while the other is made of 25-cm-thick brick. Through which wall will the house lose more heat in winter?

A wood slab with a thickness of 0.05m is subjected to a heat flux of 40 W/$m^2$. The left and right surface temperatures of the wood slab are kept at constant temperatures of 40 degree C and 20 degree C, respectively. What is the thermal conductivity of the wood slab?