On the stability of non-isothermal flow in channels

Summary We study here stability of non-isothermal flow between two closely spaced, heat conducting, infinite parallel flat plates of lengthl and distanceh apart. Fluid enters uniformly alongx = 0 at temperatureT ₁ >T _w the plate temperature. The flow non-uniformity is assumed to occur due to coupling between the energy equation, which describes the heat transfer mechanism between fluid and channel walls, and the flow equation which includes the temperature dependence of viscosity.The model for the flow assumes that similarity profiles exist for velocity and temperature in the flow direction. The stability of the unidirectional flow by a linearized first order perturbation analysis of the proposed model is examined.Notation b rheological parameter of the fluid defined by eq. 4] - B dimensionless viscosity-temperature parameter defined by eq. 11] - C rheological parameter defined by eq. 4] - h distance between the two parallel plates, ft. - H a thermal transfer coefficient (l/h) - l length of the plates, ft. - p pressure - P inlet pressure - G _z Graetz number defined by eq. 11] - t time, h - T mean temperature as defined by eq. 2] - T ₁ inlet temperature - u velocity vector withu _x ,u _y ,u _z as component velocities - v mean velocity vector as defined by eq. 1] - V mean steady state axial velocity - x, y, z Cartesian coordinate system - w refers to wall condition - thermal diffusivity, ft²/h - A effective thermal diffusivity tensor - dimensionlessx coordinate - wave number iny direction - dimensionless wave number iny direction - µ ₀ viscosity of fluid - density of fluid - dimensionless velocity inx direction - growth rate of disturbances - dimensionless growth rate - proportionality constant for heat generation in eq. 5] With 4 figures