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Consider two plates, A and B, that are each initially isothermal and each of thickness
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Chapter 3 Solutions
Introduction to Heat Transfer
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- A rectangular nylon [E = 8 GPa; v = 0.35; d = 29 x 10-6/°C] plate has a circular hole in its center. At an initial temperature of T; = 19°C, the plate width is b = 360 mm, the plate height is h = 190 mm, the diameter of the central hole is d = 55 mm, and the thickness of the plate is t = 21 mm. At a final temperature of T=45°C, determine (a) the diameter d of the central hole. (b) the thickness t of the plate. Answers: (a) df = i (b) t= i b Save for Later d eTextbook and Media mm mm Attempts: 0 of 5 used Submit Answerarrow_forwardJust want to understand this review examplearrow_forwardA solid nylon [E = 8 GPa; v = 0.35; a = 29x106/°C] rod is initially unconstrained. The initial length of the rod is L = 600 mm and its diameter is d = 24 mm. If the temperature of the unconstrained rod is increase by 33°C above the initial temperature, determine (a) the change in the rod's length. (b) the change in the rod's diameter. Answers: (a) AL = i (b) Δd = i eTextbook and Media Save for Later mm mm Attempts: 0 of 5 used Submit Answerarrow_forward
- A steel rod with a cross-sectional area of 199 mm2 is stretched between two fixed points. The tensile load at 29°C is 7,100 N. At what temperature will the stress be zero? ? Assume α = 11.7 × 10-6 m/(m·°C) and E = 203 GPa. Answer must be in degree Celsius.arrow_forwardA thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 50 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1). Put u4(2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.arrow_forwardA 3.25 – meter steel column was placed between two concrete blocks at 20. 6°C. Calculate the gap needed if the temperature rises to 125°F. The coefficient of linear expansion of steel is 11. 88 x 10-6°C-1. The coefficient of linear expansion of steel is 10. 72 x 10-6°C-1arrow_forward
- An aluminum pipe has a length of 75 m at a temperature of 18°C. An adjacent steel pipe at the same temperature is 5 mm longer than the aluminum pipe. At what temperature (°C) will the aluminum pipe be 15 mm longer than the steel pipe? (Assume that the coefficients of thermal expansion of aluminum and steel are αa = 23 x 10^–6/°C and αs = 12 x 10^–6/°C, respectively.)arrow_forwardA square steel bar of side length w = 0.21 m has a thermal conductivity of k = 15.6 J/(s⋅m⋅°C) and is L = 2.7 m long. One end is placed near a blowtorch so that the temperature is T1 = 95° C while the other end rests on a block of ice so that the temperature is a constant T2. a. input an expression for the heat transferred to the cold end of the bar as a function of time using A=w^2 as the cross-sectional area of the bar. b. how much energy in joules was conducted in 1 hour, assuming t2=0*C c. input an expression for the mass of the water melted in one hour using Q1 from above and Lf in the latent heat of fusion. mw=arrow_forwardIn the diagram below, metal 1 is made of gold and metal 2 is aluminum. Both bars have the same length and area of cross-section but their thermal conductivities are different. The temperature Th is maintained at a constant 88.0°C at the end A while the temperature T, at the end B is maintained at 19.0°C. A. T metal 1 metal 2 T (a) What is the temperature T; at the junction of the two bars? The thermal conductivity of gold is 318 J/(s · m · °C) and that for aluminum is 220 J/(s• m · °C). °C (b) If metals 1 and 2 are now interchanged, but the values of Th and T, are the same as in part (a), what will be the temperature of the junction? °Carrow_forward
- Bar A has a cross-sectional area of 0.04 m2, modulus of elasticity E = 70 GPa, and coefficient of thermal expansion α = 14E‐6 C-1. Bar B has a cross sectional area of 0.01 m2, modulus of elasticity E = 120 GPa, and coefficient of thermal expansion α = 16E‐6 C-1. There is a gap b = 0.4 mm between the ends of the bars. What minimum increase in the temperature of the bars above their initial temperature T is necessary to cause them to come into contact?arrow_forwardRead the question carefully and give me all a, b & c solutions. Note: kindly answer all otherwise leave it. A circular nylon [E = 8 GPa; ν = 0.35; α = 22 ×10-6/°C] disk with a circular hole in its center is shown. At an initial temperature of Ti = 15°C, the outer diameter of the disk is D = 200 mm, the diameter of the central hole is d = 55 mm, and the thickness of the disk is t = 22 mm. At a final temperature of Tf = 51°C, determine:(a) the change in diameter Δd of the central hole (assume an increase Δd as positive, otherwise as negative).(b) the change in thickness Δt of the disk (assume an increase Δt as positive, otherwise as negative).(c) the normal strain in the circumferential direction around the outside of the diskarrow_forwardinclude diagram.arrow_forward
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