Analysis of mixed convection in water boundary layer flows over a moving vertical plate with variable viscosity and Prandtl number

2019 ◽  
Vol 29 (2) ◽  
pp. 602-616 ◽  
Author(s):  
Abhishek Kumar Singh ◽  
A.K. Singh ◽  
S. Roy
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Skin Friction ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Boundary Layer Flows ◽  
Partial Differential ◽  
Content Type ◽  
Reference Velocity

Purpose The purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The non-linear partial differential equation governing the flow and thermal fields are presented in non-dimensional form by using appropriate transformation. The quasi-linearization technique in combination with implicit finite difference scheme has been adopted to solve the nonlinear-coupled partial differential equation. The numerical results are displayed graphically to illustrate the influence of various non-dimensional physical parameters on velocity and temperature. Further, the numerical results for local skin-friction coefficient and local Nusselt number are also reported. The present findings are compared with previously reported results, and these comparisons are found to be in excellent agreement. Design/methodology/approach The nonlinear partial differential equations governing the flow and thermal fields have been solved numerically using the implicit finite difference scheme in combination with the quasi-linearization technique. The numerical results are presented in terms of skin friction and heat transfer rate which are useful in determining the surface heat requirements for stabilizing the laminar boundary layer flow over a moving plate in water. Findings The effect of the ratio of free-stream velocity to the composite reference velocity is significant on the velocity profile. Near the wall region, as ratio of free stream velocity to composite reference velocity increases form 0.1 to 0.5, the velocity overshoot gets enhanced from 3 per cent to 41 per cent. The influence of buoyancy parameter and ration of free stream velocity to composite reference velocity on temperature profile is comparatively less than on velocity profiles. The increase in the skin friction coefficient is dependent on the increase in the value of ratio of free stream velocity to composite reference velocity if the buoyancy parameter λ is fixed and vice versa and increases in ΔT results in a decrease in N and Pr. Originality/value The present investigation is to deal with the solution of steady laminar water boundary layer flows over a moving plate with temperature-dependent viscosity and Prandtl number applicable for water using practical data. The fluid considered here is water, as it is one of the most common working fluids found in engineering applications.

Skin Friction and Heat Transfer for Laminar Boundary-Layer Flow With Variable Properties and Variable Free-Stream Velocity

1953 ◽  
Vol 20 (3) ◽  
pp. 415-421
Author(s):  
S. Levy ◽  
R. A. Seban
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Layer Flow

Abstract Numerical solutions of the momentum and energy equations are presented for particular types of laminar boundary-layer flow analogous to the Hartree “wedge flows.” Variation of the viscosity and of the thermal conductivity is considered under the circumstances of no dissipation, favorable pressure gradient, and the product of conductivity and density a constant. The solution is based on approximate representations of the velocity and temperature profiles in the boundary layer and these are of such character that the labor of calculation is minimized and the accuracy of the results preserved. The differential equations are reduced to two algebraic equations which rapidly yield the skin friction and the heat transfer in terms of the wall to free-stream temperature ratio for the desired value of Prandtl number. Numerical results are given for a range of wedge flows with gases of Prandtl number 0.70 and 1.0. These results reveal that when the free-stream velocity is variable the temperature difference between the wall and the free stream exerts a substantial effect on the velocity distribution in the boundary layer and on the skin-friction coefficient. Alternatively, the heat-transfer coefficient is not affected radically. A calculation method is presented for the determination of the heat transfer and skin friction for a flow with an arbitrary variation of velocity over an isothermal surface. This method utilizes the results of the present analysis for the variable property wedge flows.

scholarly journals Surface temperature and free-stream velocity oscillation effects on mixed convention slip flow from surface of a horizontal circular cylinder

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 13-23
Author(s):  
Zia Ullah ◽  
Muammad Ashraf ◽  
Saqib Zia ◽  
Ishtiaq Ali
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Surface Temperature ◽  
Skin Friction ◽  
Slip Velocity ◽  
Free Stream ◽  
Slip Flow ◽  
Stream Velocity ◽  
Velocity Oscillation

The present phenomena address the slip velocity effects on mixed convection flow of electrically conducting fluid with surface temperature and free stream velocity oscillation over a non-conducting horizontal cylinder. To remove the difficulties in illustrating the coupled PDE, the primitive variable formulation for finite dif?ference technique is proposed to transform dimensionless equations into primitive form. The numerical simulations of coupled non-dimensional equations are exam?ined in terms of fluid slip velocity, temperature, and magnetic velocity which are used to calculate the oscillating components of skin friction, heat transfer, and cur?rent density for various emerging parameters magnetic force parameter, ?, mixed convection parameter, ?, magnetic Prandtl number, ?, Prandtl number, and slip factor, SL. It is observed that the effect of slip flow on the non-conducting cylinder is reduced the fluid motion. A minimum oscillating behavior is noted in skin friction at each position but maximum amplitude of oscillation in heat transfer is observed at each position ? = ?/4 and 2?/3. It is further noticed that a fluid velocity increas?es sharply with the impact of slip factor on the fluid-flow mechanism. Moreover, due to frictional forces with lower magnitude between viscous layers, the rise in Prandtl number leads to decrease in skin fiction and heat transfer which is physi?cally in good agreement.

scholarly journals Prediction of Heat Transfer From Laminar Boundary Layers, With Emphasis on Large Free-Stream Velocity Gradients and Highly Cooled Walls

1966 ◽  
Vol 88 (3) ◽  
pp. 249-256 ◽  
Author(s):  
L. H. Back ◽  
A. B. Witte
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Gradient ◽  
Free Stream ◽  
Variable Density ◽  
Similarity Solutions ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Gradient Parameter

Laminar boundary-layer heat transfer and shear-stress predictions from existing similarity solutions are extended in an approximate way to perfect gas flows with a large free-stream velocity gradient parameter β and variable density-viscosity product ρμ across the boundary layer resulting from a highly cooled wall. The dimensionless enthalpy gradient at the wall gw′, to which the heat flux is related, is found not to vary appreciably with β. Thus the application of similarity solutions on a local basis to predict heat transfer from accelerated flows to an arbitrary surface may be a reasonable approximation involving a minimum amount of calculation time. Unlike gw′, the dimensionless velocity gradient at the wall fw″, to which the shear stress is related, is strongly dependent on β.

Effects of Partial Slip on Chemically Reactive Solute Distribution in MHD Boundary Layer Stagnation Point Flow Past a Stretching Permeable Sheet

2015 ◽  
Vol 13 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Swati Mukhopadhyay
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Stream Velocity ◽  
Slip Parameter ◽  
Mhd Boundary Layer

Abstract This paper presents the magnetohydrodynamic (MHD) boundary layer stagnation point flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet in presence of partial slip. With the help of similarity transformations, the partial differential equations corresponding to momentum and the concentration equations are transformed into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity and the stretching velocity. Velocity decreases with the increasing magnetic parameter when the free-stream velocity is less than the stretching velocity but the opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. With increasing velocity slip parameter, velocity increases when the free-stream velocity is greater than the stretching velocity. But the concentration decreases in this case. Concentration decreases with increasing mass slip parameter.

Sign in / Sign up

Export Citation Format

Share Document