Prove the boundness and monotonicity wrt parameter of solutions to this PDE

Question

the problem is: (11) Let $Q=(0, l) \times(0, \infty)$ and $u_h=u_h(x, t)$ be a solution of $$ \begin{aligned} u_t-u_{x x} & =0 \quad \text { in } Q, \\ u(x, 0) & =0 \quad \text { in }(0, l), \\ \left.u\right|_{x=l}=0, & \\ \left.\left(\partial_x u+h\left(u_0-u\right)\right)\right|_{x=0}=0, & \end{aligned} $$ for positive constants $u_0$ and $h$. Prove (a) $0 \leq u \leq u_0$ in $(0, l) \times(0, \infty)$; (b) $u_h$ is monotone increasing for $h$.
I have tried a few ways, the first thing is the maximum principle, but I don't how to deal with the robin boundary condition at $x=0$, I want to construct $v=u-u_{0}$ to construct a zero neumann condition at $x=0$, but I'm still stuck, and I can't find alternative to hopf's lemma to deal with the neumann condition, could you please help me?thank you