List of top Engineering Sciences Questions asked in GATE Mechanical Engineering

A very large metal plate of thickness d and thermal conductivity k is cooled by a stream of air at temperature \(T_\infty = 300\) K with a heat transfer coefficient h, as shown in the figure. The centerline temperature of the plate is \(T_P\). In which of the following case(s) can the lumped parameter model be used to study the heat transfer in the metal plate? 

Consider a laterally insulated rod of length L and constant thermal conductivity. Assuming one-dimensional heat conduction in the rod, which of the following steady-state temperature profile(s) can occur without internal heat generation? 

 

Consider a mixture of two ideal gases, X and Y, with molar masses \(M_X\) = 10 kg/kmol and \(M_Y\) = 20 kg/kmol, respectively, in a container. The total pressure in the container is 100 kPa, the total volume of the container is 10 m³, and the temperature of the contents of the container is 300 K. If the mass of gas-X in the container is 2 kg, then the mass of gas-Y in the container is ............... kg. (Rounded off to one decimal place)
Assume that the universal gas constant is 8314 J kmol⁻¹K⁻¹.
Which one of the following statements is FALSE?
Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and the cross-sectional area of the cylinder is \(A\). The fluid inside the cylinder is air (considered as a perfect gas), with \(\gamma\) being the ratio of the specific heat at constant pressure to the specific heat at constant volume for air. The piston is initially located at a position \(L_1\). The initial pressure of the air inside the cylinder is \(P_1 \gg P_0\), where \(P_0\) is the atmospheric pressure. The stop \(S_1\) is instantaneously removed and the piston moves to the position \(L_2\), where the equilibrium pressure of air inside the cylinder is \(P_2 \gg P_0\). What is the work done by the piston on the atmosphere during this process?
A cylindrical rod of length \(h\) and diameter \(d\) is placed inside a cubic enclosure of side length \(L\). \(S\) denotes the inner surface of the cube. The view-factor \(F_{S-S}\) is
Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being \(T_{1, in} = 300\) K and \(T_{2, in} = 350\) K. The heat capacity rates of the two fluids are \(C_1 = 1000\) W/K and \(C_2 = 400\) W/K, and the effectiveness of the heat exchanger is 0.5. The actual heat transfer rate is ............... kW. (Answer in integer)
Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and velocity profiles. The Nusselt number for this flow depends on
A heat engine extracts heat (\(Q_H\)) from a thermal reservoir at a temperature of 1000 K and rejects heat (\(Q_L\)) to a thermal reservoir at a temperature of 100 K, while producing work (\(W\)). Which one of the combinations of [\(Q_H\), \(Q_L\) and \(W\)] given is allowed?